On Digital Radio ReceiverPerformance in Electromagnetic

Disturbance Environments

Peter Stenumgaard

RADIO COMMUNICATION SYSTEMS LABORATORY

On Digital Radio ReceiverPerformance in Electromagnetic

Disturbance Environments

Peter Stenumgaard

December 2000

TRITA - S3 - RST – 0007ISSN 1400-9137

ISRN KTH/RST/R--00/07--SE

RADIO COMMUNICATION SYSTEMS LABORATORYDEPARTMENT OF SIGNALS, SENSORS AND SYSTEMS

To

Astrid

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AbstractADIATED emission from electronic equipment, co-located to adigital radio receiver, can severely affect receiving performance. It

is therefore of great importance that this undesired emission be consid-ered in the early design phase of a system containing radio equipment.For this purpose, methods to estimate the performance degradation ondigital radio receivers in such environment must be available.

Radiated emission is regulated by means of international standards inwhich special measurement methods, including a measurement detector,are specified. Furthermore, present emission standards are developedwith respect to analog radio receivers, which is why an immediate con-nection to digital radio receivers does not exist. The work of developingmeasurement procedures considering a digital radio receiver has startedboth in CISPR and ITU. This work is, however, still i n its beginning,and it will probably take a long time before new standards including anew measurement detector, can be presented and approved. This thesispresents a method of handeling present emission standards as well as asuggestion for which measurement detector could be used in futurestandards. A necessary basis for this work is proper models of the actualdisturbance sources that affect communication performance. Therefore,a theoretical model of the dominant radiated disturbance signals fromco-located personal computers has been developed. The model has beenjustified by measurements.

In a milit ary application, the communication system could also be sub-jected to hostile jamming. In this case, the abilit y to withstand jammingis degraded by the undesired disturbance, as the latter degrades the sig-nal protection devices (e.g. error correcting codes) in the communica-tion system. A tactical consequence of this is that the jammer can obtainthe same result at a larger distance. A suggestion is given for how theperformance degradation could be interpreted to parameters that are use-ful for tactical considerations.

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Acknowledgments

EFORE I started working on this thesis, I had heard that research isnot a one-man job. Now that statement has become a part of my

own experience. A number of people have inspired and supported meduring this work. First of all , I would like to thank my adviser, ProfessorJens Zander. Without his scientific guidance, enthusiastic encourage-ment and professional coaching, this thesis would never been written.Jens has truly been the professional coach I wish every PhD studentwould have. I have really experienced that the most important choice fora PhD student is the choice of advisor.

All of my colleagues at the Department of Communication Systems atthe Swedish Defence Research Agency provide a positive and support-ing environment to work in and are acknowledged for that. I would liketo thank Lars Ahlin, the former head of the Department, for giving methe opportunity and encouragement to perform this work. Furthermore,Christian Jönsson, the present head of this Department, is sincerely ac-knowledged for his invaluable support during the final phase of thiswork. My former project manager, Björn Johansson, and close col-league, Kia Wiklundh, are also greatly acknowledged. Finally I wish tothank our Administrative Assistant Suzanne Rehn for her warm and pa-tient attitude toward us, sometimes absent-minded scientists.

The vision that resulted in the problem investigated in this thesis wascarried by Thomas Theiler. Thomas is acknowledged for his never-ending enthusiasm that finally influenced me to start working with thisproblem. At that time, Thomas was with the Swedish Defence MaterielsAdministration (FMV), which is acknowledged for financing part of thework. Thomas successor was Göran Undén, who is acknowledged forcontinuing the support for the work initialized by Thomas. Chef Engi-neer Ralph Persson, at FMV, is acknowledged for invaluable commentsand especially for his abilit y of focusing on the reality behind the theo-retical models. Dr. Jan Welinder at the Swedish National Testing andResearch Institute (SP) is acknowledged both for cooperation duringsome of the measurements, and for helpful discussions. Dr. Mats Bäck-ström at the Swedish Defence Research Agency is also acknowledged

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for his helpful comments during the planning of the final work in thethesis.

PhD studies is a project that involves the whole family. In my case, Ihave had the privilege of having an understanding wife; Helena. Helenais my most important co-worker and has given me necessary encour-agement and support during different phases of this period. Further-more, my two wonderful children, Sara and Jacob, have provided mewith refreshing relaxation from my research. My parents, who have al-ways been my faithful supporters, “prepared” the basis for this work along time ago and have supported me in every moment.

During my work towards this thesis, I have received invaluable advicefrom people that probably do not realize how valuable their advice hasbeen. I therefore especially wish to thank the following three people forsuch advice. I have also summarized their advice with my own words.

Dr. Eva Englund, Ericsson Radio Systems;

- The key issue in PhD studies is to work hard for a confident relationbetween the advisor and the PhD student.

Dr. Bengt Lundborg, the Swedish Defence Research Agency;

- One diffi cult part in research is to learn how to work slowly.

Dr. Bengt-O Bengtsson, the University Hospital of Linköping;

- Do not only prepare your defence, but also your “a ttack”.

Linköping, a rainy evening in November 2000,

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Contents

1 INTRODUCTION....................................................................................11

1.1 DIGITAL RADIO SYSTEMS IN ELECTROMAGNETIC DISTURBANCE

ENVIRONMENTS......................................................................................111.2 PROBLEM OVERVIEW AND THE INTENDED STRATEGY FOR SOLVING

THE PROBLEM .........................................................................................161.2.1 The system design problem .............................................................161.2.3 Performance measure selection .....................................................181.2.4 Problem to solve ..............................................................................191.2.5 Disturbance sources considered.....................................................211.2.6 Design strategy ................................................................................22

1.3 PUBLICATIONS.........................................................................................231.4 THESIS OUTLINE ......................................................................................251.5 CONTRIBUTIONS......................................................................................26

2 EMI DETECTORS..................................................................................29

2.1 GENERAL................................................................................................. 292.2 THE QUASI-PEAK DETECTOR....................................................................312.3 THE PEAK DETECTOR...............................................................................322.4 THE DEVELOPMENT TOWARD NEW DETECTORS .......................................352.5 SUMMARY OF DETECTOR CHARACTERISTICS ...........................................35

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3 DISTURBANCE SOURCE MODEL.....................................................37

3.1 INTRODUCTION........................................................................................373.2 MODELS IN THE LITERATURE................................................................... 383.3 DISTURBANCE SOURCE MODEL ................................................................403.4 RESULTS FROM MEASUREMENTS .............................................................443.5 MODULATED NARROW BAND EMISSION...................................................513.6 CONCLUSION...........................................................................................52

4 METHODS FOR ESTIMATING BEP..................................................53

4.1 APPROACH ..............................................................................................534.2 METHOD FOR BROAD BAND DISTURBANCE ..............................................574.3 METHOD FOR NARROW BAND CW DISTURBANCE....................................60

5 ANALYSIS FOR MSK SYSTEMS........................................................61

5.1 THE CHOICE OF MSK ..............................................................................615.2 THE MSK MODULATION SCHEME............................................................625.3 ESTIMATION OF BEP FOR MSK IN A MIXTURE OF GAUSSIAN AND CW DISTURBANCE..........................................................................................645.4 RESULTS.................................................................................................. 65

5.4.1 Comparison of BEP for the ideal receiver with measured BEP on a real system .....................................................................655.4.2 Results..............................................................................................70

5.5 SENSITIVITY ANALYSIS...........................................................................73

6 EMI DETECTORS FOR FUTURE EMISSION STANDARDS........75

6.1 INTRODUCTION........................................................................................756.2 REVIEW OF WEIGHTING DETECTORS FUNDAMENTALS..............................776.3 ANALYSIS................................................................................................796.4 RESULTS.................................................................................................. 81

6.4.1 The quasi-peak detector and digital radio receivers .....................816.4.2 Results for the RMS detector..........................................................836.4.3 Comparison with results from CISPR work. ................................. 88

6.5 THE RELATION BETWEEN BEP AND RMS VALUE FOR BPSK ..................906.6 CONCLUSION...........................................................................................97

7 ANALYSIS FOR THE JAMM ING CASE............................................99

7.1 INTRODUCTION........................................................................................997.2 JAMMERS...............................................................................................1007.3 IMPACT OF DISTURBANCE ON THE DUEL BETWEEN JAMMER AND

COMMUNICATION SYSTEM......................................................................1017.3.1 The narrow-band method in the CW tone jamming situation....1017.3.2 The narrow-band method and Gaussian approximated jamming signal ..............................................................................103

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7.4 RESULTS FOR THE JAMMING CASE .........................................................104

8 PERFORMANCE MEASURES FOR TACTICALCONSIDERATIONS..................................................................................107

8.1 BACKGROUND .......................................................................................1078.2 THE IMPACT ON OPERATING RANGE AS A MEASURE OF PERFORMANCE

DEGRADATION.......................................................................................1088.3 THE ”JAMMING LOSS” AS A MEASURE OF AN INCREASED VULNERABILITY

TO A HOSTILE JAMMER ..........................................................................1108.3.1 Definition of jamming loss ...........................................................1108.3.2 Example of jamming loss for a system using error correcting code ................................................................................................112

9 DISCUSSION .........................................................................................121

APPENDIX A ..............................................................................................127

APPENDIX B ..............................................................................................131

APPENDIX C ..............................................................................................135

APPENDIX D ..............................................................................................137

APPENDIX E ..............................................................................................143

REFERENCES............................................................................................147

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1 Introduction

1.1 Digital radio systems in electromagneticdisturbance environments

ECHNOLOGICAL advances in the electronics industry are ex-tremely rapid, resulting in far-reaching consequences for practically

every single individual and activity in society. These developments arelargely based on the demands and possibiliti es of civili an society. Thisis a situation that will also, to a large extent, guide milit ary developmentand the feasibilit y of designing command and control systems within thearmed forces in years to come. From a historical point of view, milit arytechnology has always retained a pole position in the application of newtechnology. In the current situation, the technical developments on thecivili an market have caught up on the milit ary technology in a numberof f ields. Together with reduced defence budgets, this situation opens upcompletely new possibiliti es for the armed forces to use civili an elec-tronics in milit ary applications. This so-called dual use technology willbe a reality in the future, leading to an increased amount of different ci-vili an electronics, such as information technology equipment (ITE), inthe vicinity of milit ary radio systems. In milit ary applications, the use ofITE in the vicinity of communication systems is rapidly increasing. Thisis due to the increased need of quick and accurate information for com-mand and control in a battlefield characterized by fast changes. After theend of the cold war, a shift in milit ary philosophy has occurred. Milit ary

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Figure 1.1: The use of ITE in the vicinity of communication systems israpidly increasing due to the increased need of quick and accurateinformation for command and control.

planners now realize that the era of prolonged wars is long gone. In-creasingly, milit ary forces are relying on superior technology and lesson manpower to detect and combat hostile threats [1]. One key issue isDominant Battlespace Awareness (DBA), which in simple words meanshaving the best knowledge of what is going on in the battlefield andhaving the abilit y to take advantage of this knowledge. The future bat-tlefield will require several new services to support the battle command.The abilit y to visualize the battlefield by accessing broadcast data is oneexample of requirements considered in the development of future com-mand and control systems, see figure 1.1. This requires the abilit y tomanage sensors eff iciently, so that sensor data can be collected, proc-essed and fused before displaying these to the commanders. The goal isto create a common picture of the battlefield so that a rapid and effectiveconcentration of combat power can be provided. The only way to reach

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this goal is by means of wireless technologies with high requirements oncapacity, availabilit y and mobilit y. This vision is often described interms of digitizing the battlefield as an increased share of overall de-fence spending will be paid on systems for control, command, commu-nications, computers and intelli gent sensors. From a communicationperformance point of view, these different electronics will contribute tothe electromagnetic interference (EMI) environment at the radio re-ceiver. In general, the electromagnetic environment surrounding a digi-tal radio receiver consists of different kinds of disturbance sources. Thetotal disturbance is a mixture of natural disturbance, such as atmos-pheric disturbance, and man-made disturbance. One way of categorizingman-made disturbance sources is the division into intentional and unin-tentional, see figure 1.2. Intentional sources include other transmittingequipment which typically works with some kind of modulated signalsand whose disturbance typically consists of harmonics and intermodula-tion products. As intentional sources consist of co-located transmitters,hostile jammers are not included in this category. Unintentional sources

Sources “Victim”intentional transmitter

unintentional transmitter

Figure 1.2: The definition of disturbance sources and the “victim”.

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are other electronic systems that are not intended to produce any radi-ated electromagnetic energy. As radiated emission from electronicequipment, co-located to a digital radio receiver, can affect receivingperformance, it is of great importance that this undesired emission beconsidered in the early design phase of a system containing radioequipment. For this purpose, methods of estimating the performancedegradation on digital radio receivers in such an environment must beavailable. From a milit ary point of view, such methods are necessaryboth for design purposes and for analyzing the tactical consequences ofinherent interference. One tactical consequence is that undesired EMIwill decrease the operating range of the radio communication link [2]. Ina milit ary application, the communication system could also be sub-jected to hostile jamming. In this case, the abilit y to withstand jammingis degraded by the undesired disturbance, as the latter degrades the sig-nal protection devices (e.g. error correcting codes) in the communica-tion system. A tactical consequence of this is that the jammer can obtainthe same result at a larger distance than if no inherent EMI was present[3].

In this thesis, a method of performing these kinds of performance analy-ses is proposed. The basic assumption is that the radiated disturbance isknown as a result of a standard emission measurement, see section 1.2.2.One diff iculty with this assumption is that present radiated emissionstandards have been developed to protect analog communication serv-ices. A suggestion for how to handle present standards and a contribu-tion to the work of developing standards suitable for digital communi-cation services are made. Most published system design methods con-sidering the impact of radiated disturbance on digital radio systems haveso far been focused on the impact from other transmitting systems in thevicinity of the radio receiver. The most extensive work concerning com-plex systems, such as aircraft and ships, has been carried out under thesponsorship of the Department of Defense (DoD) in the United States.The work was initially performed by the DoD Electromagnetic Com-patibilit y Analysis Center (ECAC). During the 1970s, an automatedprocedure for topside communications RF system design was developedfor the Naval Command Control and Ocean Surveill ance Center(NOSC) [4] [5]. The first published algorithm to be used in EMC designtools was the Co-Site Analysis Model (COSAM) [6]. COSAM was thebasic design tool on which several further developments were based.COSAM handled disturbance from intentional transmitters on analog“victim”s, see figure 1.2. Since then, the co-location problem between

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intentional transmitters and receivers has been well i nvestigated [7] -[14]. In the late 1970s, a more general EMC design tool called the Intra-system Electromagnetic Compatibilit y Program (IEMCAP) [15] wasdeveloped. In this design tool, it was possible to consider disturbancefrom electronics that are not intentional transmitters. The “victim” wasanalog communication systems, and the basic disturbance criterion wasto compare the disturbance power with a certain power threshold levelin the receiver of the “victim” . The analog “victim” was treated in pub-lications as late as in the middle of the 1990s [16] [17] [52]. At the sametime, the digital radio receiver as a “victim” began to be treated in pub-lished EMC system design tools [17]. Even if much theoretical work hasbeen carried out on disturbance on digital receivers since the 1960s,methods suitable for engineering purposes did not start to show up untilthe 1990s. This work was a further development of the system designalgorithms developed during the 1970s and 1980s.

In [17], the problem of estimating the bit error probabilit y (BEP) for adigital radio receiver, for a known disturbance signal is treated. This isdone by determining the probabilit y density function of the disturbancesignal and then calculating the BEP. How to determine the BEP for adigital radio receiver subjected to a known disturbance signal has beenwell known for a long time, but during the 1990s methods suitable forothers than scientists started to be published. However, no research hasbeen published on how to estimate the BEP for a disturbance waveform, only specified as the result of a standard emission measurement.Previous work relies on the basic assumption that the system designerhas detailed knowledge about the different disturbance levels and waveforms present in the actual system. In this thesis, the case when no suchinformation is available is treated. This case corresponds to the early de-sign phase of a complex milit ary system, when not all hardware hasbeen developed. Up to only a few years ago, the financial situation forthe milit ary forces allowed the designer always to place the strongestemission requirements on all electronics in a milit ary system. Thus, sev-eral potential disturbance problems, caused by unintentional disturbancesources, were solved by the wallet. Today, the financial situation doesnot allow this solution, which is why a method for quantification of theimpact from radiated emission on digital radio receivers is needed.

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1.2 Problem overview and the intended strategyfor solving the problem

1.2.1 The system design problem

In the early design phase of electronic systems, different electromag-netic compatibilit y (EMC) requirements are chosen for all subsystemsand equipment. The purpose of applying these requirements is to mini-mize the risk of disturbance problems in the system. These requirementsare normally divided into two groups; emission and immunity require-ments. In this thesis, emission requirements are treated. Emission re-quirements control the maximum permitted levels of electromagneticdisturbance produced, while immunity requirements control how muchelectromagnetic disturbance the systems must be able to withstand with-out performance degradation.

From the designer’s point of view, it is of vital importance that all re-quirements be thoroughly chosen so that an accurate trade-off is madebetween economics and the risk of running into disturbance problems.Furthermore, when all requirements have been chosen, and production isin progress, it is normally very diff icult to change EMC requirementswithout considerably increasing the cost. Many standardized EMC re-quirements have been developed during recent decades, including bothcivili an and milit ary standard EMC requirements. In general, the mil i-tary standards have higher requirements than the civili an, which is whymilit ary-specified electronics require more expensive measures to fulfillsuch requirements. From a milit ary point of view, the interest in civili anradiated emission limits has increased as a result of the dual use situa-tion. As the choice of radiated emission requirements is of major con-cern in system design, disturbance levels that equal such limits are usedfor the evaluation of the results in this thesis. This implies a worst caseanalysis with respect to the emission level.

1.2.2 Emission standards

The background to emission standards is to be found in the 1920s, whenbroadcasting services started to reach a larger part of the society. Quiteearly it became obvious that radiated disturbance had to be limited inorder to create good conditions for the reception of these new services.

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However, imposing limitations on electrical equipment and householdappliances could cause trading problems if different countries applieddifferent requirements. This problem was soon realized on national lev-els, which led to the foundation of the International Special Committeeon Radio Disturbance (CISPR). The International ElectrotechnicalCommission (IEC) and the International Telecommunication Union(ITU) were cofounders. The first goal was to reach an agreement onmeasurement procedures. This work was carried out during the 1930s.After that the work of developing standard emission limits could start[18], [19]. The first standard produced was at a national level when theBS613 (British Standard) concerning components for radio disturbancesuppression devices was published in England. In 1937, the BS727 con-cerning characteristics of an apparatus for measuring of radio distur-bance was published. This standard had a major impact on the stan-dardization work within CISPR. Today, a large variety of radiated emis-sion standards exists. Standards for intentional transmitters differ fromstandards applicable to unintentional transmitters. Depending on thefrequency region of interest, maximum limits on magnetic or electricfield are usually specified. In general, magnetic field is specified at thelower frequency regions while electric field is specified in the higherfrequency bands. The frequency limit between magnetic and electric

EUT

80 - 90 cm

1 mAntenna

Ground plane

Ground plane

120 cm

Figure 1.3: Simplified figure of the measurement setup during a stan-dard radiated emission measurement according to the MIL-STD-461D.

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field specification depends on the specific standard. In the commonlyused milit ary standard, MIL-STD-461D [38], electric field is specifiedat frequencies above 10 kHz, whereas the civili an European EN55022,required for electronics sold in the European Union, specifies the elec-tric field at frequencies above 30 MHz. Every standard has special re-quirements on the measurement setup and measurement procedure. Infigure 1.3, a simpli fied description of the test setup for the emission testRE102, in MIL-STD-461D, is shown. The equipment under test (EUT)is placed on a ground plane. Cables for powering and monitoring areconnected according to special requirements. During the test the EUT ispowered up and set into normal operation modes while the radiated in-terference is measured with the antenna. The antenna is connected to ameasurement device supplying a special measurement detector. Themeasurement device often consists of a spectrum analyzer, which workswith a superheterodyne receiver.

1.2.3 Performance measure selection

In order to make a performance analysis, a performance measure mustbe selected. In this thesis, the bit error probabilit y (BEP) of the digitalradio system is used. The reason is that the BEP is a common measureof the quality of the information received in the radio, and is also used insystem specifications. Other related measures such as block error rateand message error rate can also be specified depending on the specificsystem properties. However, the bit error probabilit y is often the basicsystem performance measure, to which other measures can be related.Another type of performance measures is, what could be called thehardware dependent measures. This means performance degradationscaused by hardware limitations, due to the fact that in reality ideal com-ponents do not exist. An example is reciprocal mixing which is due todisturbance caused by mixing the receiver’s local oscill ator noise withan interfering signal in the receiver front end pass band [20]. Anotherkind of performance degradation is desensitization, arising when astrong disturbance signal causes an apparent decrease in receiver sensi-tivity [21]. As methods of analyzing these kinds of hardware-dependenteffects are available, they will not be treated in this thesis. Conse-quently, choosing BEP as the performance measure of interest, it mustbe assumed that the hardware-related degradations can either be ana-lyzed with known methods or be neglected. If the BEP caused by a cer-tain emission level can be estimated, this value can be compared with

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certain acceptable limits, depending on the kind of information trans-ferred on the radio channel. Examples of typical li mits for the BEP canbe 10 3− for speech and 10 5− for data transfer. If a disturbance problemoccurs, there are generally two basic principles for solving the problem.The first is just to increase the physical distance between the disturbancesource and radio receiver. The second is to decrease the emission levelby means of an electromagnetic shielding device. As this is just a practi-cal question, assuming that the BEP can be estimated, the variation inseparation distance will be used to evaluate the results. In some cases,the disturbance problem could be handled on a higher system level bythe use of forward error correcting codes. However, allowing inherentdisturbance from co-located electronics to be handled in that way ishazardous, as the error correcting code is always implemented to takecare of other problems such as hostile jammers or changes in the radiochannel. If the error correcting code can handle the disturbance from co-located equipment, the user will not recognize that a disturbance prob-lem is present until the problem, for which the error correcting code isintended to handle shows up. Thus, in this thesis we will not count onthe possibiliti es of handeling disturbance from co-located equipment bythe use of error correcting codes.

1.2.4 Problem to solve

The assumptions above lead to the conclusion that the issue of interest ishow to translate an emission level to BEP for a digital radio receiver at agiven distance r from the disturbance source (see figure 1.4 and 1.5).Up to now, no method for this specific purpose has been published. Pre-sent radiated standard emission limits are in most cases specified asmaximum allowed electric (or magnetic) field strength as a function offrequency and at a certain distance r from the disturbance source, seeFigure 1.4 and 1.5. Furthermore, the standards are specified for a speciallaboratory test setup with a particular measurement detector (EMI de-tector). In this thesis the emission level expressed as the output from astandard emission measurement will be used as input to the analysis.Current emission standards have been developed with respect to analogradio receivers, which is why an immediate connection to digital radioreceivers does not exist. Current measurement procedures and detectorsare based on the work carried out in the standardization organizations

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Distance

BEP at a certain frequency

Frequency

Electric field strength

Estimationmethod

Figure 1.4: The estimation problem.

during 1930 - 1939 [19]. The work of developing measurement proce-dures considering a digital radio receiver as “v ictim” has started both inCISPR [22] and ITU-R [23]. This work is, however, only in beginning,

Frequency

Estimation of Pb

DISPLAY

LO

RF

IFEMI detector

Electric fieldstrength

Pb

r

Desired signal

γI

Figure 1.5: Problem overview, where Iγ and bP are defined in section 1.2.6.

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and it will probably take a long time before new standards including anew EMI detector can be presented. Furthermore, as long as analogsystems exist, present standards will be used, which means that theknowledge of how to handle present standards for a digital “v ictim” willbe needed not only today, but probably for at least one or two decades.Another practical problem is that even when new standards are avail-able, manufacturers comply with the old standards cannot be expected toautomatically verify ”off- the-shelf” equipment against new standards.Thus, the knowledge of how to handle the relation between present EMIdetectors and digital radio receivers will be of great importance for sys-tem designers for at least the next one or two decades. However, in thisthesis an EMI detector for future emission standards is proposed andevaluated. We show that the existing RMS-detector exhibits propertiesthat make it a promising candidate for future emission standards wherethe impact on digital communication receivers is considered.

1.2.5 Disturbance sources considered

Among several diff iculties with the problem analyzed in this thesis, onebasic diff iculty is that the wave form of disturbance signal, which po-tentially could reach the emission limit, is unknown in an early designphase [24]. This complicates the situation since the performance of adigital radio receiver is affected by the wave form, not only the ampli-tude, of the disturbance signal. The EMI detector used gives differentresponses for different wave forms of disturbance signals. Conse-quently, a model that describes the dominating wave form characteris-tics of the disturbance source is needed. Thus, given the disturbanceelectric field strength at the radio receiver, the disturbance source modelis used to describe the wave form characteristics so that the performanceof the radio receiver can be estimated, see figure 1.6. As undesired radi-ated emission can vary a lot in signal wave forms and levels, dependingon the type of equipment, some assumptions have to be made to be ableto create a basic disturbance source model for our analyses. Here, thefocus will be

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Disturbancesourcemodel

Performanceestimation

method

Performance Pb

Disturbance level(electric field strength)

Figure 1.6: Connection between disturbance level and performance.

on information technology equipment supplying internal clocks and avideo display as disturbance sources, because ITE is one common typeof equipment that is co-located to milit ary radio systems. No usefuldisturbance source models concerning ITE have been published. In thisthesis, personal computers have been chosen as representatives of typi-cal ITE. A disturbance source model for personal computers is proposedand evaluated by measurements.

1.2.6 Design strategy

Throughout this thesis, the basic assumption is that the method is in-tended for use in an early design phase of a system when no detailed in-formation about the time domain properties of the interfering signals isavailable. For system design applications, such a method should befairly simple to use and, at the same time, deliver useful results. Thisrequires a trade-off between the degree of method complexity and theaccuracy obtained in the results. The strategy for solving this problem isto perform the estimation of BEP in two steps. The first step is to esti-mate the signal to disturbance ratio Iγ , see figure 1.5, at the input to theradio receiver. Secondly, the estimated value Iγ is used to estimate theBEP as a function of the separation distance r. Thus, the estimated BEPcan be written as

( ( ))P f rb = γ I . (1.1)

Furthermore, in a milit ary application, the increase in BEP must be in-terpreted to a measure that can be used for tactical considerations. If theradio system is not subjected to hostile jamming, a useful measure ishow the operating range of a radio system is affected by the disturbance

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it produces itself. If the radio system is subjected to hostile jamming, itis important to know how the inherent disturbance will contribute to thejammer’s effort to damage the communication link. This case is referredto as the jamming case. A measure of this kind of performance degrada-tion will be suggested and discussed in this thesis. The frequency regionof main interest, for the specific examples analyzed, will be the lowerpart of the VHF band, where current combat radio systems typicallywork. However, the method proposed can be used in other frequencybands as long as the basic assumptions are not violated.

1.3 Publications

The work on this thesis has resulted in a number of publications. Themost important publications are listed below. Publication no. 4 is a jointpaper with Kia C. Wiklundh. Kia has contributed with the basic theo-retical analyses concerning the performance of differential MSK sub-jected to CW disturbance.

Publication no. 1:Peter F. Stenumgaard, ”A Simple Method to Estimate the Impact of Dif-ferent Emission Standards on Digital Radio Receiver Performance, ”IEEE Transactions on Electromagnetic Compatibilit y, no. 4, November1997.

Main content: The problem definition and the basic ideas of how tosolve the problem. Results for the case when the disturbance is ofAWGN type are presented. This is the first published paper proposing asolution of the problem of how to relate present emission standards tothe impact on digital radio receiver performance.

Publication no. 2:Peter Stenumgaard, ” Impact of Intersystem Disturbance on the Duelbetween Jammer and Communication System, ”FOA-report: FOA-R—98-00794-504--SE, May 1998.

Main content: The basic ideas of how to analyze the impact of uninten-tional disturbance in a jamming situation. A suggestion of how to relatethe increased BEP to parameters useful for tactical considerations isgiven. Results from a system example are presented.

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Publication no. 3:Peter F. Stenumgaard, ”Digital Radio System Range Reduction Due toRadiated Electromagnetic Disturbance, ” Proceedings of EMC’98 RomaInternational Symposium on Electromagnetic Compatibilit y, pp. 843-846.

Main content: Shows the impact of unintentional disturbance on the op-erating range of a radio system.

Publication no. 4:Peter F. Stenumgaard, Kia C. Wiklundh, ”An Improved Method to Es-timate the Impact on Digital Radio Receiver Performance of RadiatedElectromagnetic Disturbances, ” IEEE Transactions on Electromag-netic Compatibilit y vol. 42, no. 2, pp. 233-239, May 2000.

Main content: An extension of the results in publication 1 to cover thecase where the disturbance source is information technology equipment.A model for the radiated disturbance of ITE is proposed.

Publication no. 5:Peter F. Stenumgaard, “Using the RMS Detector for Weighting of Dis-turbance According to its Effect on Digital Communication Services”Proceedings of EMC Europe 2000 Brügge, Belgium, pp. 377-380 11-15September 2000.

Main content: The possibilit y of using the RMS detector in future radi-ated emission standards is proposed.

Publication no. 6:Peter F. Stenumgaard, “Using the RMS Detector for Weighting of Dis-turbances According to its Effect on Digital Communication Services”To be published in the IEEE Transactions on Electromagnetic Compati-bilit y, November 2000.

Main content: The possibilit y of using the RMS detector in future radi-ated emission standards is investigated in more detail , and results frommeasurements are presented. The conclusion is that the RMS detector isa promising candidate for future emission standards.

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Publication no. 7:Peter F. Stenumgaard, “Disturbance Model for Information TechnologyEquipment” To be published at the EMC 2001 Zurich, InternationalSymposium on Electromagnetic Compatibilit y, February 2001.

Main content: The suggested disturbance model for personal computersis presented and evaluated by extensive measurements.

1.4 Thesis outline

In the thesis, a method of estimating the impact of inherent electromag-netic disturbance on digital radio receivers is developed. To do this, amodel of the dominating disturbance wave forms of the inherent distur-bance is necessary. Therefore, a model for the dominant radiated distur-bance wave forms from personal computers is proposed and evaluatedby measurements. In addition, a measurement detector for future radi-ated emission standards, where the disturbance effect of digital commu-nication services is considered, is proposed and evaluated. Furthermore,methods of evaluating the performance degradation in tactical terms arepresented and applied to some chosen system examples. More specifi-cally, in chapter 2, standard detectors for electromagnetic disturbancemeasurements are analyzed to create some basic knowledge required totranslate a detector output to useful signal parameters of the disturbancemeasured during a standard measurement. In chapter 3, a model of theinherent disturbance is determined for personal computers. This modelis intended to represent the basic behavior of radiated electromagneticdisturbance from that equipment. In chapter 4, the method of how totranslate a disturbance level, measured by a standard procedure, to thebit error probabilit y of a digital radio receiver exposed to this distur-bance is developed. In chapter 5, the suggested method is evaluated forthe modulation scheme minimum shift keying (MSK). It is shown thatthe suggested estimation method gives results close enough to the realvalues to be useful in practical design work. In chapter 6, it is shownthat the RMS detector is a promising candidate for use in future radiatedemission standards where the disturbance effect on digital communica-tion services is considered. In chapter 7, the estimation method is inves-tigated for the multi -tone jamming case. Here the combined effect ofinherent disturbance and the jamming disturbance is considered. It is

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shown that the basic idea of the estimation method can be used for per-formance analyses of the more complex jamming case where severaldisturbance wave forms are involved. In chapter 8, the estimated BEP isrelated to evaluation parameters that are useful for tactical considera-tions in milit ary applications. The suggested evaluation parameters areapplied to system examples to show the usefulness of such parametersand to provide some immediate results that are applicable to existingsystems. Finally, in chapter 9, the conclusions are drawn and the resultsare discussed. Suggestions for future topics are given.

1.5 Contr ibutions

The original contributions in the thesis are the following, see figure 1.7;

1) A method for the estimation of performance degradation for a digitalradio receiver in the presence of inherent disturbance, from co-located ITE equipment, is proposed. This method is intended for usein system applications when radiated emission standards are to bechosen in the early design phase of a larger system. The method pro-vides fairly simple calculations suitable for engineers to use, for in-stance when the impact from different radiated emission standards isto be compared. This method is new in that it makes it possible torelate radiated emission levels, developed for analog radio receiversto the performance degradation of digital radio receivers.

2) The lack of previously published useful mathematical models of thedisturbance from ITE requires that a proposed model be used in thisthesis. Therefore a model is suggested, which, for the purpose of theanalyses, describes the important basic behavior of this disturbance.The disturbance source model is based on results from the literatureand verified with additional measurement results.

3) The development of future emission standards to comply with digitalcommunication receivers requires a change of measurement detector.In the thesis, the RMS detector has been investigated as a possiblechoice. This investigation includes the calculation of the BEP fordisturbance pulses with shorter pulse duration than the symbol time.Up to now, the RMS detector has not been used in standardized EMImeasurements, except for out-of-band emission of radio transmitters.

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The conclusion of our investigation is that the RMS detector is a pro- mising candidate for use in future emission standards.

4) Depending on the tactical situation for a milit ary digital radio system,different performance evaluation measures are proposed. The pur-pose of these measures is to translate the estimated BEP to parame-ters of use for a milit ary off icer. The result when these measures areapplied to a specific situation with typical system parameters is pre-sented.

Figure 1.7: Overview of the contributions in the thesis.

LO

RF

IFEMI detector

Frequency

Estimationmethod

Electric fieldstrength

Pb

DISPLAY

rJ

r ! " # $ " %

& ' ( ) * + , - . * ) * / 0 * 1 - 2 3 ) * / 0

Pb

Tacticalconsequences

Interference

source model

EMI detector forfuture standards

1

43

2

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2 Standard EMI detectors

N this chapter, standard detectors for electromagnetic disturbancemeasurements are analyzed. This is done to create the basic knowl-

edge required to translate a detector output to useful signal parametersof the disturbance measured in a standard measurement.

2.1 General

Typical standard EMI measurement equipment is based on a superhet-erodyne receiver, e.g. a spectrum analyzer, see figure 2.1. The outputfrom the antenna is fed into a radio frequency (RF) ampli fier and is thenmixed with the signal from the local oscill ator (LO). The output fromthe intermediate frequency (IF) filter is then fed into the detector. Emis-sion measurements are sometimes automated to reduce the measurementtime. Often, a computer is used to monitor the measurement receiverand to present the measurement result. A common method is to scan thefrequency region of interest in discrete frequency steps. At each fre-quency, a certain dwell ti me is required to make a correct measurement.The step size and dwell time are generally specified in some way. For

I

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DISPLAY

LO

RF

IF

Peak/Quasi Peak detector

Electric fieldstrength

Frequency

Emission limit

Radiated emission

Measuring equipment

Figure 2.1: EMI measurement receiver of superheterodyne type.

instance, in MIL-STD-461D [38], the step size must be one half incre-ment of the measurement bandwidth or less. The requirements of thesemeasurement parameters result in a maximum sweep time [Hz/s] whichdetermines the total measurement time for scanning a certain frequencyregion.

Two basic types of detectors are used in standard measurements. Thecivili an Euronorm (EN) standard, required for all commercial equipmentsold in the European Union, as well as the American Federal Communi-cations Commission (FCC) regulations, uses the quasi-peak detector.The commonly used milit ary standard, MIL-STD-461D [38], uses thepeak detector. A problem with the peak and quasi-peak detectors is thatnone of them gives a response related to the impact on a digital radioreceiver. This is natural since both detectors were developed when onlyanalog systems existed. Thus, in order to relate the output of such de-tectors to the impact on a digital radio receiver, the characteristics ofthese detectors must be known and be possible to use in the develop-ment of our method. In this thesis, the characteristics of these detectorswill be according to the CISPR 16-1 standard [32] (which is based on[23]) [24]. The basic characteristics required for our analyses will bepresented in the following sections.

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2.2 The quasi-peak detector

Figure 2.2 shows the fundamental quasi-peak circuit which was origi-nally developed to give a response that is proportional to the disturbingeffect on human beings. This was done by the application of psycho-physics (psycho-acoustics for sound radio and psycho optics for TV)[18]. In particular it was necessary to weight impulsive noise from, e.g.electric motors and spark-ignited engines. As the disturbance effect on ahuman being is higher at high pulse repetition frequencies than at lowpulse repetition frequencies, the detector response had to take this intoaccount. The result was a detector that for repeated pulsed disturbancegives a response which increases with the pulse repetition frequency ofthe disturbance. This behavior exists up to a certain limit in pulse repe-tition frequency (typically 10-20 kHz) beyond which a constant re-sponse is obtained. A practical drawback with this detector is its longresponse time, which leads to long measurement time if larger frequencybands are to be measured. For instance, if a measuring bandwidth of 120kHz is used, it takes almost five and a half hours to measure the fre-quency band 30 MHz - 1 GHz [35]. The quasi-peak detector is generallyvery diff icult to analyze theoretically except for a few input wave forms.Thus, different simulation techniques have been used to analyze the re-sponse to other input signal wave forms. Earlier theoretical work deter-mines the time-averaged detector output, >< QPV . These analyses are

based on the assumption that the output of the detector is always close toits time average value. This assumption has been shown to be valid formost practical cases [36]. The meter connected to the output of the

VQP

+

-

R1

RDC

VIF=X(t)

+

-

Meter

Figure 2.2: Fundamental ideal quasi-peak circuit.

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quasi-peak detector has a special requirement of time constant. Thistime constant of the meter movement has the effect of smoothing theoutput. In general, the output >< QPV for a general input signal X t()

with probabilit y density function )(xf X (amplitude distribution) can bedetermined through the integral equation [36] as

dxxfVxR

RV X

V)()(

QPQP

C

DQP ∫ ><−>=<

∞

><, (2.1)

where RD is the discharge resistance and RC is the total charge resis-tance of the quasi-peak circuit. The total charge resistance is the sum ofR1 and the resistance of the diode. This can be numerically solved forzero-mean Gaussian noise input with a standard deviation of σ X , whichgives [34]

< >≈ = =V X t XQP X rmsE185 185 1852. . () .σ . (2.2)

Thus, the ratio between the quasi-peak value and the RMS value for azero-mean Gaussian noise input is approximately 1.85. This is an inter-esting property of the detector, since it is possible to relate the distur-bance power, expressed as a function of the quasi-peak value, to the av-erage disturbance power. This property will be used later in this thesis.

2.3 The peak detector

The peak detector follows the signal IFV at the output of the IF envelopeand holds the peak value until discharge is forced. Thus, this detectordelivers the maximum value of the envelope of the output from the IFstage within a given observation time. The indication is independent ofthe pulse repetition frequency. One advantage of this detector is its shortreaction time, which makes it suitable for pre-scanning disturbancemeasurements before the quasi-peak detector is applied to criti cal emis-sions. This is due to the fact that the peak value is always larger than orequal to the quasi-peak value. The peak detector has a disadvantage inmeasuring noise processes as there is no exact connection between thepeak value and the statistical parameters of such a process. This is a wellknown problem for which a rule of thumb, for practical purposes, is

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10−3

10−2

10−1

100

101

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x

P(x

)

Figure 2.3: )(xP , where x is inversely proportional to the pulse repe-

tition frequency, pDdB

C fRWRx 6Mπ= . WM

6dB is the 6 dB bandwidth of

the IF-filter and pf is the pulse repetition frequency.

101

102

103

104

105

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

Pulse repetition frequency [Hz]

Val

ue r

elat

ive

peak

[dB

]

quasi peakrms

Figure 2.4: Quasi-peak and RMS detector response relative peakfor repetitive pulses for CISPR 16-1 frequency bands C and D (30– 1000 MHz).

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Input wave form tothe RF stage

Peak Quasi-Peak RMS

Sine wave IRMS IRMS IRMS

Periodic pulse(no overlap in thefilters)

2I f W( )Mimp 2I f W P x( ) ( )

Mimp

2I f W f( )Mimp

p

Gaussian amplitudedistribution (0, σn )

∝ WMrn 185. WM

rnnσ WM

rnnσ

Table. 2.1: Basic characteristics of the EMI detectors. IRMS is the RMS

value of the disturbance i(t), )(E 2 tiRMSI = . I(f) is the Fourier

transform of the disturbance signal at the frequency where the meas-urement is done. WM

imp is the impulse bandwidth of the measurement

equipment. WMrn is the noise bandwidth of the measurement equip-

ment. P x( ) is the ratio between quasi-peak and peak value [34].

presented in [37]. This rule of thumb suggests the use of the relationbetween peak and RMS value for a 99.99 % confidence interval for azero-mean Gaussian distribution. This gives the approximate ratio be-tween the peak- and RMS values as 4. The characteristics of the peakand quasi-peak detectors are compared to an RMS (root mean square)detector in figure 2.3 and 2.4 [32] for repetiti ve pulses. The RMS de-

tector delivers E n t2() , where n(t) is the level of the signal at the de-

tector input. All detectors are normally calibrated in terms of the RMSvalue of a sine wave. This is common for most real measurement re-ceivers and will be used throughout this thesis. In figure 2.3, the ratio

)(xP between the quasi-peak and peak detector for repetiti ve pulses isshown. The argument x is inversely proportional to the pulse repetitionfrequency. There is no exact analytical expression for )(xP in [32] and[34], where only a graphic description of )(xP is presented. Therefore,an approximation of that curve is shown in figure 2.3. In figure 2.4, thequasi-peak and RMS values relative to the peak value are shown [32].For pulse repetition frequencies greater than 20-30 kHz, the quasi-peakvalue is approximately the same as the peak value. Table 2.1 [32] showsa comparison between the quasi-peak, peak and RMS detectors.

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2.4 The development toward new detectors

The work of developing measurement procedures considering a digitalradio receiver as “v ictim” has started both in CISPR [22] and ITU-R[23]. The approach adopted in [18] is to create a new type of weighteddetector, representing the disturbance effect on digital radio receivers.Thus, the same strategy that lies behind the quasi-peak detector isadopted. This work is only in its initial stages, and more diff icult prob-lems than in the development of the quasi-peak detector can be ex-pected. The basic reason for this assumption is that the quasi-peak de-tector was developed to react to disturbance more or less as a humanbeing. In the case of digital radio receivers, there are lots of different”ears” and ”eyes” to consider due to the large variety of modulation andcoding schemes. However, if this strategy is to succeed, the time untilnew emission standards are adopted will be long, approximately one ortwo decades, which is why the knowledge of how to relate present EMIdetectors will be relevant both in the near and distant future. In chapter6, an alternative approach to the work within CISPR/ITU is evaluated.Here, we investigate an already existing EMI detector (the RMS detec-tor) as a candidate for future emission standards. The conclusion inchapter 6 is that the RMS detector is a promising candidate for futureemission standards where the impact on digital communication receiversis considered.

2.5 Summary of standard detector characteristics

Important conclusions from this chapter and for further use in this thesisare:

• The detector output when measuring on a sine wave is equal to theRMS value of that sine wave. This applies both to the peak detectorand the quasi-peak detector.

• The output from the quasi-peak detector when measuring on a noiseprocess, with a zero-mean Gaussian amplitude distribution, is ap-proximately 1.85 times the standard deviation of that distribution.

• The output from the peak detector when measuring a noise process,with a zero-mean Gaussian amplitude distribution, cannot be exactly

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related to the RMS value. A commonly used rule of thumb, statingthat the RMS value can be approximately estimated as the peak valuedivided by 4, will t herefore be used in this case.

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3 Disturbance source model

N this chapter, a model of the dominating disturbance wave forms forpersonal computers is proposed and evaluated by measurements. As

the response for both EMI detectors as well as digital communicationreceivers to disturbance is severely dependent on the disturbance waveform characteristics, this model forms a necessary basis for the furtherwork in the thesis.

3.1 Introduction

As stated in chapter 1, man-made disturbance sources surrounding acommunication system can vary a lot in the time domain properties ofthe disturbance signal wave forms. With the rapid technological ad-vances in electronics, new types of disturbance sources are continuouslycreated which contribute to the total disturbance environment. Beforethe second world war, roughly speaking, ignition disturbance from cars,disturbance from electric motors and corona disturbance from powerlines were the man-made sources of major concern. Today, man-madenoise consists of significantly more disturbance sources, to which in-formation technology equipment is one important contributor. In mil i-tary applications, the use of ITE in the vicinity of communication sys-tems is rapidly increasing. This is due to the increased need of quick and

I

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accurate information for command and control in a battlefield charac-terized by rapid changes. As the focus in this thesis will be on distur-bance from ITE, a model that gives a proper description of this distur-bance must be used. No useful model of the disturbance from ITE hasbeen published in the literature. Existing models are mostly concernedwith man-made noise with a shot nature, e.g. impulse noise. These mod-els assume disturbance pulses with stochastic amplitude, duration andarrival time. We will see that the disturbance from ITE does not exhibitthese properties, which is why a special model for this disturbance issuggested.

In this chapter, results from the literature are used to determine the maincharacteristics of radiated emission from ITE. These main characteris-tics are summarized in a suggested model for the disturbance from ITE.As the number of publications in the literature is few, further work onthe basis for such a model is motivated. Therefore additional work wasdone to create a larger experimental basis to verify the model. Personalcomputers are chosen to represent ITE. This is justified by the fact thatpersonal computers are the typical equipment which is co-located tomil itary radio systems.

3.2 Models in the li terature

Much radiated emission measurements are daily produced globally,therefore there is widespread knowledge of what this kind of distur-bance looks like in rough terms. Surprisingly, however, no detailed dis-turbance models have been published that describe the disturbance fromITE in useful mathematical terms. In our case, useful mathematicalterms means usefulness for scientific purposes. Middleton [25] [26] car-ried out extensive work in formulating general mathematical models forman-made noise. The goal was to create useful models that are based ona general physical mechanism and with parameters that can be meas-ured. The main focus was on noise with a shot nature, e.g. impulsenoise. A consequence of connecting the models to general physicalmechanisms is that the focus is placed on non-Gaussian amplitude dis-tributions. Earlier models were mostly concerned with natural noise,such as atmospheric noise, and although they were characterized bymathematical simplicity they were severely limited in usefulness [25].The problem with Middleton’s models is that they are mathematically

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diff icult, and even though they are based on famili ar physical situations,the connection to the physical scenario is not always apparent [27]. Thisis probably the reason why these models have not been adopted as stan-dard tools in describing man-made noise. Furthermore, Middleton’smodels have been shown to be limited in describing many physicalsituations [27], which is another contributory factor to why these modelsare not widely used. The main focus of modeling man-made noise hasbeen on urban environments [56] where the noise is a mixture of distur-bance from cars, power lines, heavy current switchers, arc welders,household equipment, etc. This noise typically has a shot nature and istherefore modeled with some kind of impulse model. These modelstypically contain three random variables: pulse amplitude A (or enve-lope), pulse duration time T and pulse arrival time τ [58]. The resultantdisturbance process i(t) is then typically modeled as a function of time tso that

)()(1

nTn

n tyAtin

τ−= ∑∞

=, (3.1)

where )( nT tyn

τ− is the signal (voltage) wave form appearing at the in-

put to the receiving filter, and with a disturbance pulse of length nT andlevel nA . With this notation, i(t) is the total disturbance signal at the in-put to the receiving filter. In the case of pulses with high amplitude andshort duration, the function )( nT ty

nτ− will be replaced by the Dirac

delta function. It can also be convenient to model the output of a linearreceiving filter to the disturbance pulses [57]. Thus, several alternativesof modeling impulse noise processes are possible, but these three basicparameters are always considered randomly distributed. Typically, thepulse arrival and duration are assumed to be modeled as well -knowndistributions whereas attention is focused on how to model the ampli-tude distribution [56]. Thus, the issue of characterizing man-made noisetheoretically has gained some interest during the past 30 years. On theother hand, comparatively few measurements on this topic have beenpublished. One contributing factor may be that these kinds of measure-ments are technically very diff icult to perform and require expensiveand specifically designed measurement systems. One diff iculty is tomeasure the amplitude of the signal that entered the measurement re-ceiver. This is due to that standard measurement equipment measure theenvelope of the output from the IF-stage. Knowledge of the amplitude

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requires specialized measurement receivers. Thus, standard measure-ment equipment cannot be used without certain modifications for otherthan envelope measurements. Furthermore, deep knowledge within sev-eral areas such as signal processing, detection theory, and antenna the-ory is required to obtain useful measurement results. Concerning ITE,the situation is the opposite considering the relation between theoreticaland measured results. No theoretical models have been published, al-though some publications with measurement results are available. Theseearlier publications concerning measured disturbance from ITE havebeen studied, and the conclusions are summarized as follows. In general,the characteristics of the disturbance from ITE supplying internal high-speed clocks and a video display unit (monitor) can be divided into twobasic parts: one narrow band and one broad band. The narrow band con-sists of harmonics from periodic signals, see for instance [28][29][30].The broad band is caused by non-periodic or random signals [31][29].Furthermore, the narrow band disturbance is typically of much higherlevels than the broad band.

The conclusion to be drawn from these results is that the impulse noisemodels are not convenient to describe the disturbance from ITE. Themain reason is that the impulse models assume stochastic behavior ofthe pulse amplitude, duration and arrival time. The dominant distur-bance contribution from ITE is apparently from periodic signals withfixed amplitude, duration and repetition frequency. Furthermore, thedisturbance in urban environments is generally a mixture of a largeamount of different disturbance sources where no detailed knowledgeabout each source is available. For that environment, the impulse mod-els seem to be the natural approach. In this thesis, however, we are con-cerned with the co-location situation where the disturbance sources arelocated close to the radio system and can be assumed to consist of acertain type of dominant disturbance sources (ITE). Thus a new modelmust be determined for the purpose of our analyses. Such a model issuggested in the next section.

3.3 Disturbance source model

The findings from the literature were used to suggest a model of the ra-diated disturbance from personal computers. The suggested mathemati-

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cal description of the amplitude )(I ti for the dominant disturbance fromour disturbance source is

i t n t i t n t c ekj fkt

kI p() () () () ( )= + = + +

= −∞

∞

∑ 2π ϕ , (3.2)

where )(tn denotes the broad band random noise, here assumed to beGaussian amplitude distributed, and the sum is the Fourier series of theperiodic disturbance )(p ti . The disturbance signal )(I ti is the signal

(voltage) appearing at the output of the receiving antenna of either theradio or the EMI measurement receiver. The phase ϕ is assumed to beuniformly distributed between 0 and 2π . The coeff icients kc are definedas

cT

i t e dtkj fkt

T

T= −

−∫1 2

2

2

pp

p

p()

/

/ π . (3.3)

The Fourier coeff icients, if )(p ti consists of rectangular pulses, are

TfTf

Ac k

kk π

πsin

p

p= (3.4)

where f k Tk = / p , Tp is the period time of the pulse train and Ap is

the pulse amplitude, see figure 3.1. In the frequency domain, )(p ti con-

sists of discrete sine wave components separated with distance 1 / Tp .

T t

Tp

Ap

ip(t)

Figure 3.1: Periodic pulsed signal.

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1/T1/Tp

|ck|

frequency0

Figure 3.2: A simplified figure of the main lobe of the frequency spec-trum of )(p ti

For ITE, Tp is assumed to be the time period of some fundamental bus

(oscill ator) frequency in the system. In typical ITE, a bus frequency ismultiplied to obtain the frequency of the central processing unit (CPU).This is a simple model to describe the property of one broad band andone narrow band part in the disturbance. Furthermore, the narrow bandpart is assumed to be generated from a periodic signal. In the next sec-tion, the validity of this model will be examined by comparison withmeasured results. The final part of this section is used to investigate theconsequences of using this model for the performance analyses in thethesis. The first main lobe of )(p ti is schematically shown in figure 3.2.

As long as the pulse repetition frequency is greater than the bandwidthof the radio receiver, at most one spectral component will enter the re-ceiver. The conclusion is that under these circumstances, the expressionfor the BEP derived for a pure sine wave can be used. The frequencydistance between adjacent spectral components in the Fourier series ofthe periodic disturbance is assumed to be larger than the bandwidth ofthe radio receiver. Typical pulse repetition frequencies today could varyfrom approximately 30 kHz, from the horizontal scanning of the moni-tor, to several hundred MHz from internal clocks. As the frequency re-gion where this narrow band disturbance dominates depends on thepulse repetition frequencies used, there is an upper limit in frequencywhere this assumption is valid. The clock frequencies in current ITE areapproaching 1 GHz, thus this assumption should be valid in the VHF

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region and the lower part of the UHF region. However, as the develop-ment towards faster processors is rapid, this assumption will soon bevalid for the complete UHF band.

The use of the terms ”broad band” and ”narrow band” can be somewhatconfusing at times as these terms are always related to a certain band-width of a receiver. A commonly used definition of broad band distur-bance is that the total power within a bandwidth will i ncrease if thebandwidth is increased. For narrow band noise, the total received powerremains constant if the bandwidth is increased. In our case, the harmon-ics in the Fourier series are denoted narrow band as we have assumed abandwidth smaller than the pulse repetition frequency. For larger band-widths, however, this disturbance component should be denoted broadband as the total disturbance power within the bandwidth would in-crease with the bandwidth. The Gaussian noise is assumed to have anapproximately constant power spectral density within the bandwidth ofthe receiver. Thus this disturbance can be treated as additive whiteGaussian noise (AWGN).

Under the assumption that the power levels from the narrow band dis-turbance are much larger than from the broad band, the analysis can bedivided into two cases, one concerning disturbance from AWGN andone concerning disturbance from sinusoidal disturbance. Furthermorethe thermal noise level, in the radio receiver also assumed to be AWGN,will also be considered. The conclusion of the disturbance model used isthat the performance analysis for a digital radio receiver will concernhow this radio receiver is affected by either pure AWGN or a combina-tion of AWGN and a sine wave assumed to have a uniformly distrib-uted random phase.

As the number of useful publications in the literature is few and the de-velopment within the area of ITE is rapid, further work on the basis forsuch a model is motivated. Therefore additional work was done to createa larger experimental basis behind the choice of disturbance sourcemodel. In this thesis, results from standard emission measurements arethe input from which our analysis method should estimate the final BEP.Standard emission measurements are preferable even in the evaluationof the suggested disturbance model. Another reason is that the rapid de-velopment within the ITE area will require further measurements in thefuture. For comparison purposes it is convenient that standard measure-ment procedures be used as long as the results obtained are suff icient to

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evaluate the model. The following assumptions for the suggested distur-bance model need to be further investigated by the measurements:

1) The assumption of one narrow band and one broad band part of which the narrow band is of much higher levels, i.e. the dominant part.

2) If the narrow band part arises from periodic signals, this will result innarrow peaks with frequency distance in the order of typical oscill a-tor or bus frequencies. Furthermore, the level of these peaks shouldbe independent of measurement bandwidth and detector.

The measurement work is presented in the next section.

3.4 Results from measurements

The results from standard measurements of approximately 20 personalcomputers were examined to create a collection of emission spectrumproperties that could be considered as typical of personal computers.The measurements on these systems were made during the period of1996–1999. In addition, new measurements on four personal computerswere performed during 1999. Both the survey of the results from stan-dard emission measurements of the 20 PCs as well as the new measure-ments were done as a cooperation with the Swedish National Testingand Research Institute (SP). SP is a professional institute involved inresearch and measurements of electromagnetic disturbance, performingstandard emission measurements on different kinds of electronic equip-ment. The measurements are generally performed in a shielded room in8 directions, by means of a rotating test table, and two polarizations(vertical and horizontal). The measurement distance is 3 m. The resultsfrom this work are presented in [55]. Here, the important results andconclusions from [55] are presented. The overall conclusions are sum-marized in seven paragraphs. Furthermore, important results are visual-ized in the following tables and diagrams. The diagrams show emissionmeasurement results from the new measurements of the four PCs. Theoverall conclusions from [55] are summarized below. In addition toconclusions of general class, conclusions based on the classification“ typically” are given. The reason for using the latter class is that emis-sion spectrums are diff icult to evaluate in strictly mathematical terms. In

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our case, where the system design problem is in focus, the word “typi-cally” should be interpreted as “often enough to be considered generalin the engineering application”. Of course this implies some kind of en-gineering judgement in drawing some of the conclusions. However, theimportant conclusions concerning dominating disturbance wave forms,which is the main purpose of this investigation, are general. The overallconclusions are:

1) In general, a radiated emission spectrum contains a mixture of narrowband and broad band emissions. The narrow band originates from highspeed clocks while the broad band originates from the power supply,monitor and data streams. The narrow band emission is present in allmeasured PCs and is concentrated at frequencies which are multiples ofcertain standard frequencies, such as 33 MHz.

2) The narrow band emission appears as single peaks with levels farabove the floor of random noise and broad band emission. The level ofthe narrow band peaks typically increases with the frequency.

3) In general, the level of the narrow band peaks is independent ofmeasurement detector, which shows that the peaks can be seen as thespectral components from the Fourier series of repetiti ve signals. Thebandwidth of the narrow band peaks is less than 10 Hz.

4) In general, the narrow band peaks are unmodulated. In a few cases,peaks appearing to be amplitude modulated were found.

5) The narrow band emission appears at frequencies which are multiplesof some standard frequency e.g. 33, 50 or 100 MHz. The clock signal inthe central processing unit (CPU) is generally created by multiplying alower frequency (bus frequency). For instance, 333 MHz for Pentium IIis created as 66x5 and 450 MHz for Pentium III as 100x4.5.

6) The broad band emission typically appears as “hill s” with a width ofapproximately 1/3 of the center frequency. “Hill s” centered around 30MHz typically originates from the power supply, whereas “hill s” cen-tered around 100 MHz typically originates from the monitor.

7) Special measurements with an electric field probe, which can be usedfor measurements at small distances, were made in an attempt to identifythe dominant contributors to the disturbance. The conclusion was that

_____________________________________________________________________________________46

the main disturbance sources are the monitor, mother board and circuitboards supplying bus functions. The built -in units, e.g. CD-ROM playerand floppy disc station, and the power supply make minor contributions.

As modern radio systems always use some kind of spread spectrumtechnique, the number of narrow band peaks per frequency unit is of in-terest. For instance, for a frequency hopping system the exact locationof the disturbance peaks per frequency unit is of interest of the distur-bance peaks is not of most interest as it is the averaged bit error prob-abilit y over the frequencies that determines the performance. The per-formance is determined by the number of disturbance peaks within thefrequency range, as long as the levels of the peaks are large enough tocause a large BEP, which means a BEP > 10 % (approximately). Theaverage number of narrow band peaks/MHz was determined for both the20 and the 4 personal computers. The result is summarized in table 3.1.At 100 MHz, almost all of the 20 personal computers have a narrowband peak, the level of which is distributed according to table 3.2. Thelevel of the 100 MHz peak is higher than the peaks in the 20 MHz bandjust below 100 MHz. For the broad band emission, the average levelsand standard deviation were determined for certain spot frequencies, seetable 3.3. The maximum measurement uncertainty for the electric fieldlevels is estimated to be ± 4 dB, which complies with the requirementsin CISPR 16 [34] for these kinds of measurements.

Frequency bandLowest fre-

quency [MHz]

Peaks/MHz4 PC

Peaks/MHz20 PC

Peaks/MHzModel with bus

Frequency 33 MHz30 0.05 0.07 0.140 0.00 0.05 050 0.03 0.04 060 0.08 0.05 0.180 0.10 0.07 0.05100 0.08 0.05 0.03200 0.03 0.03 0.03300 0.03 0.02 0.03400 0.04 0.02 0.03500 0.03 0.03 0.03600 0.02 0.03 0.03800 0.02 0.03 0.03

Table 3.1: Average number of narrow band peaks per MHz.

_____________________________________________________________________________________47

Field strength at 3 m[dBµV/m]

Number of peakswithin the interval 80– 99 MHz

Number of peaksclose to 100 MHz

< 20 12 221 - 25 46 326 - 30 16 831 - 35 3 6> 35 0 0

Table 3.2: Number of broad band emission peaks within different fre-quency intervals for the 20 PCs.

The predicted number of peaks for our suggested model with a bus fre-quency of 33 MHz is also shown in table 3.1. The conclusion is thateven if our suggested model gives a very simpli fied description of thedisturbance source, the number of dominating peaks per frequency in-terval does not differ dramatically from the measurements.

The agreement for frequencies above 100 MHz is considered goodenough to justify the notion that our suggested model seems to catch thedominating disturbance component from ITE well . In figure 3.3 –3.5,measured results from the four personal computers are presented.

The diagrams are maximum envelopes over vertical and horizontal po-larization of the measured electric field strength, at a distance of 3 mfrom the equipment under test. The results are also the maximum enve-lopes of measurements from 8 directions and antenna height variations.

The measurements in the diagrams were performed with the peak de-tector. As shown in these figures, the typical lobes , figure 3.2, from theFourier series cannot be seen. This is because the levels of the peaks de-pend on the physical geometry of the device and the test facilit y

Frequency[MHz]

Average level at 3 m[dBµV/m]

Standard deviation[dBµV/m]

30 22 550 17 5100 18 5200 20 5

Table 3.3: Average levels of broad band emission at certain spot fre-quencies.

_____________________________________________________________________________________48

0 200 400 600 800 100010

15

20

25

30

35

40

Frequency [MHz]

Ele

ctric

fiel

d st

reng

th [d

BµV

/m]

Figure 3.3: Measured emission from a Compaq 166 MHz at a dis-tance of 3 meters.

This gives resonances at certain frequencies, which is why the lobesfrom the Fourier series expansion should not be expected to be seen. Ina practical design case, the levels of the peaks should be assumed toequal the actual emission limit for the frequency region of interest.

Finally a maximum emission spectrum were determined both for narrowband and broad band emissions, figure 3.7. These worst case levels areuseful in design considerations when the requirement of robust commu-nication is especially high. As shown in figure 3.7 , the envelope of thenarrow band emissions is in the vicinity of the EN55022 Class B limit.The envelope of the broad band emissions exceeds the narrow band atfrequencies near 30 MHz. These broad band emissions typically origi-nates from the power supply.

_____________________________________________________________________________________49

100 200 300 400 500 600 700 800 900 100010

15

20

25

30

35

40

45

50

Ele

ctric

fiel

d st

reng

th [d

BµV

/m]

Frequency [MHz]

Figure 3.4: Measured emission from a Dell 200 MHz at a distance of 3meters.

100 200 300 400 500 600 700 800 900 100010

15

20

25

30

35

40

45

50

Frequency [MHz]

Ele

ctric

fiel

d st

reng

th [d

BµV

/m]

Figure 3.5: Measured emission from a Fujitsu 333 MHz at a distanceof 3 meters.

_____________________________________________________________________________________50

100 200 300 400 500 600 700 800 900 100010

15

20

25

30

35

40

45

50

Ele

ctric

fiel

d st

reng

th [d

BµV

/m]

Frequency [MHz]

Figure 3.6: Measured emission from a Compaq laptop 350 MHz at adistance of 3 meters.

102

103

0

10

20

30

40

50

60

Frequency [MHz]

Ele

ctric

fiel

d st

reng

th [d

BµV

/m]

Max broad band (3 m) Max narrow band (3 m)Class B (3 m)

Figure 3.7: Maximum envelopes of the emission levels from the 20PCs.

_____________________________________________________________________________________51

3.5 Modulated narr ow band emission

A recent publication [61] discusses the possibilit y of modulated narrow-band emission from digital circuits using clock signals. The backgroundis that if a digital circuit board is subjected to radiated emission fromanother disturbance source, cross modulation between the incidentemission and the clock signals can occur. This will result in a re-emission spectrum that could appear as modulated narrow band signals.The re-emission spectrum will be strongly correlated with the emissionspectrum of the circuit and will contain more narrow band componentsthan the pure emission spectrum from the circuit. With this backgroundit is reasonable to assume that cross modulation could appear, for in-stance, between radiated emission from the monitor and the circuitboards in the computer. This may explain why a few narrow band com-ponents from the measurements showed signs of modulated behavior.However, as this behavior could be seen only in a negligible fraction ofthe cases, the proposed disturbance model is not violated.

As it is of economic interest to pass the radiated emission tests withoutextensive hardware modifications, methods of modifying the signals inelectronic circuits have been proposed. As the purpose of these modifi-cations is only to increase the likelihood of passing the emission test, thefocus is on signal modifications which give a lower measured result forthe bandwidths used in emission standards. One example is to usespread spectrum techniques for the clock signals. In [62] both frequencyhopping (FH) and direct sequence (DS) are proposed for this purpose.As the measurement bandwidth is narrow (120 kHz in CISPR 16-1 for30 MHz-1 GHz) any spread spectrum technique will of course lower themeasured result. The consequence in system design is that extra marginsto the standard emission limits have to be used if such signal modifica-tions are used in the disturbance systems. However, there are other con-sequences of using these techniques simply to pass the radiated emissiontest. One obvious drawback is that disturbance “victim”s with band-widths much greater than the bandwidth in the emission test will suffermore severe performance degradation than predicted for non-modifiedsignals. This can lead to other unpredictable disturbance problems formore complex systems where several electronic units are co-located.

_____________________________________________________________________________________52

3.6 Conclusion

Disturbance models in the literature are mostly concerned with man-made noise with a shot nature, e.g. impulse noise. These models assumedisturbance pulses with stochastic amplitude, duration and arrival time.We have shown that the disturbance from ITE does not exhibit theseproperties, which is why a special model for this disturbance is sug-gested. Our model assumes that the dominant disturbance wave formsarise from periodic signals in the computer hardware. Our model hasbeen investigated by measurements. The conclusion is that the sug-gested model is justified for the further work in the thesis.

_____________________________________________________________________________________53

4 Methods for estimating BEP

URRENT radiated emission standards have been developed withanalog receivers as the disturbance “victim” . In this chapter, a

method for estimating the BEP, when the disturbance is expressed interms of current radiated emission standards, is proposed.

4.1 Approach

As has been shown in the previous sections of this thesis, the problem ofestimating the BEP by use of information provided by an emission stan-dard is complex, involving several diff iculties which have to be handled.Examples of such diff iculties are [24]:

• Differences in detectors used in EMI measurements and those used indigital radio receivers.

• Differences between bandwidths used in EMI measurements andthose used in radio receivers.

• Extrapolation of measured results to other distances.• Near field conditions during some emission measurements.• Only electric field component measured (Thus, no information about

the wave impedance).

C

_____________________________________________________________________________________54

• Differences between the measurement environment of emissionmeasurements and the operation environment of the real system.

• Lack of information about what kind of disturbance signal has giventhe emission measurement results.

Considering these diff iculties, a method that relates an emission level tothe impact on a digital radio receiver could seem almost impossible todevelop. However, by using certain assumptions and having a more orless rough method for engineering purposes in focus, a simple but usefulmethod will be suggested. In a measurement result from a standard radi-ated emission measurement, the detector output from the EMI measure-ment receiver is the only information available. From chapter 2, we canconclude that this result does not really say anything about what kind ofinterfering signal was present at the antenna input of the measurementreceiver. This fact is, of course, also true if the disturbance level is onlyknown as a maximum allowed limit from a standard emission require-ment. The latter case applies to the early design phase of a system whenno hardware is available to perform measurements on, but emission re-quirements are to be chosen. The first step in solving this problem is tolimit the disturbance source to information technology equipment (ITE).This is justified by the fact that ITE is a common type of electronicequipment that is co-located to radio receivers and that ITE is typicalcivili an equipment suitable for dual use considerations. The second stepis to determine a model of the radiated disturbance from this type ofelectronic equipment. With some basic knowledge of the EMI detectorsused, a method of relating the disturbance level to the impact on a co-located digital radio receiver will be developed in this chapter. As wasconcluded in chapter 3, the assumed characteristics of the disturbancesource require two methods for BEP estimation; one for the broad bandGaussian noise and one for the mixture of Gaussian noise and narrowband CW disturbance. The first one is used if the radio receiver band islocated between adjacent spectral components in the disturbance spec-trum. In this case the total disturbance is the sum of two AWGN proc-esses; the disturbance and the thermal noise level in the receiver. Theother one covers the case when one spectral component falls into the re-ceiver band and is added to the thermal noise in the receiver.

To be able to calculate BEP, the disturbance level at the input of the ra-dio receiver must be known. With this information available, it is possi-ble to estimate BEP versus signal to noise ratio (SNR) γ and the separa-

_____________________________________________________________________________________55

tion distance between the unintentional source and the radio antenna.Thus, the methodology for performing these estimations consists of twomajor steps:

1) Translate the emission requirement to the disturbance power levelthat appears at the radio receiver input. The estimated disturbancepower is converted to the estimated signal to disturbance ratio (SIR)4γ I .

2) By using 4γ I , the estimated BEP bP is derived for a fixed γ and a

certain separation distance r .

Here, the physical distance between the disturbance source and the an-tenna is assumed to be large enough so that far field antenna theory canbe used to obtain

4γ I . For the broad band Gaussian disturbance, standard

equations can be used to estimate BEP. For the narrow band CW distur-bance, the strategy is to use an approximation by treating the distur-bance as if it had a Gaussian distributed amplitude so that standardequations for the BEP for additive white Gaussian noise can be usedeven for this case, see figure 4.1. Even if the Gaussian distribution inthat case has no physical relevance, it will be shown that the calculatedBEP will be close enough to the true value. This latter method will re-quire a modification of the method for broad band disturbance. The ad-vantage of using the Gaussian approximation is obviously its simplicity,as the Gaussian distributed disturbance gives fairly simple calculations.Furthermore, the performance of digital modulation schemes is well i n-vestigated for the AWGN channel. This, together with the fact that theGaussian approximation, in several practical cases, is considered to givea worst case, or not too far from a worst case, of the BEP [39][40], isthe main reason why the Gaussian approximation is an interesting ap-proach for system design applications. Another interesting property ofGaussian noise is that the capacity of an additive memoryless channel isminimized, among all power-constrained noise distributions, by inde-pendent and identically distributed (iid) Gaussian noise [41]. Anotherimportant basic assumption used here is that reliable values of the elec-tric field strength are available, either as an emission measurement or asan emission limit that will be verified through reliable measurements.This means that possible problems caused by the emission measurementprocedure itself will not be taken into account as this is regarded as aspecial problem belonging to the process of developing useful standard

_____________________________________________________________________________________56

Emission levelexpressed as quasi-peak or peak value

Estimation ofreceived averagepower

Estimation ofBEP by the useof the Gaussianapproximation

BEP

Figure 4.1: The steps taken in order to estimate the BEP.

emission measurement procedures. In this thesis we focus on the prob-lem of estimating what BEP a co-located digital radio receiver will havefrom an electric field strength of a disturbance source. For instance, theproblem of developing useful emission standards is how to determinethe value of the electric field strength at an arbitrary distance from thedisturbance source when only a measurement at a certain distance ismade. As the electric field strength for a specific standard is specifiedfor a fixed distance from the disturbance source, an assumption of howfast the electric field is attenuated with respect to r must be made. Thisattenuation depends on the physical geometry of the disturbance situa-tion. The problem of how to transform radiated emission limits to otherdistances is diff icult and has, for instance, been treated in [68] and [69].In the system examples analyzed, an 21 r decay of the electric fieldstrength will be used. This assumption can be justified for values of rnot beyond line off sight. For values of r not beyond line of sight, a sim-ple two-beam model can be used to model the wave propagation be-tween disturbance source and radio receiver, see figure 4.2. It can beshown [72] that the received power RP in the receiving antenna can becalculated as

2

212RT

R )2

sin(

≈

r

hh

r

APP

λπ

π, (4.1)

where RA is the effective antenna cross section of the receiving antenna.

If 21hhr >>λ , then xx ≈sin , which gives a 41 r decay of the received

power (thus, a 21 r decay for the electric field strength). For 21hhr <<λ ,the free space attenuation can be used. For practical purposes, the limitbetween these two rules of thumb could be

h h

r1 2 4λ

≈ . (4.2)

_____________________________________________________________________________________57

h1 h2

PT

PR

direct wave

reflected wave

r

Figure 4.2: Geometry for a two-beam plane earth model of the wavepropagation.

The assumptions used are summarized as follows:

• The wave propagation characteristics between disturbance source and“v ictim” can be well modeled by the use of far field antenna theory.

• The disturbance source is assumed to be of ITE type with a dominantdisturbance wave form that can be described with the model sug-gested in chapter 3.

• The conditions during a standard emission measurement can suff i-ciently well be related to the real environment of the radio system.This means that, for instance, the wave propagation characteristics ofboth the measurement environment and the real environment must beknown to a certain extent.

4.2 Method for broad band disturbance

Assuming that the disturbance source is electrically small , far field an-tenna theory can be used. The received disturbance power, IS , at the ra-dio receiver input can then be estimated as [53]

)(4

2RR

0

2

I rEpqGZ

Sπλ= , (4.3)

where

_____________________________________________________________________________________58

λ wavelength [m] of the disturbance signal;GR antenna gain of the radio antenna in the direction to the inter- ference source; p polarization matching factor 0 < p ≤ 1; q matching factor between radio antenna impedance and load impedance, 0<q ≤ 1;E rR( ) electrical field strength [V/m] (measured or specified) of the radiated disturbance at the radio antenna;Z0 wave impedance for free space (= 377 Ω ); r separation distance between the undesired disturbance source and the radio receiver.

The bit error probabilit y in the presence of additive white Gaussiannoise (AWGN) can be calculated relatively easily for different modula-tion techniques, see [42], for instance. In general, the BEP is a functionof the signal to noise ratio γ so that

P Pb bAWGN AWGN= ( )γ , (4.4)

where γ is 0/ NEb . Here, bE is energy per bit and 0N is the single-sidedpower spectral density [W/Hz] of the internal noise level in the receiver.If the internal noise consists of thermal noise only, it will be equal to kT,where k is Boltzmanns constant (=138 10 23. × − J/K) and T is the tem-perature in Kelvin. If we approximate the disturbance from the co-located equipment as Gaussian noise within the radio receiver band, thetotal disturbance in the receiver is the sum of this disturbance and theinternal thermal noise. As the total disturbance is the sum of two inde-pendent zero-mean Gaussian distributions, equation (4.4) can be used byreplacing γ with

γγ

γγγ+

=+

=′I

I

0I NN

Eb , (4.5)

where Iγ is defined as I/ NEb . IN is the corresponding disturbancepower spectral density which is

M

avI

I W

SN = , (4.6)

where WM is the resolution bandwidth used in the standard emission

measurement and avIS is the average disturbance power. The average

_____________________________________________________________________________________59

power is used since by definition ∫=M

)(IavI

W

dffNS [42], where f is the

frequency. In general, the average disturbance power can be written as

)ˆ( ICavI SFS = , (4.7)

where FC is a conversion function which depends on the EMI detectorused for the emission measurements and the dominating disturbancewave form. As the average power is proportional to the square of theRMS-value of the disturbance voltage, the relationship between detectoroutput and RMS-value is needed. From chapter 2, it is known that forthe quasi-peak detector

2

IIC

85.1

ˆ)ˆ(

SSF ≈ , (4.8)

and for the peak detector the rule of thumb, commonly used, gives

2I

IC4

ˆ)ˆ(

SSF ≈ . (4.9)

IS is given by equation (4.1), with )(R rE expressed as the output of theEMI detector. Combining these equations, a closed form of the esti-mated BEP is obtained as

P P PE

WF

ZpqG E r N

Pr

r

b b bb

b

AWGN AWGN AWGN

M

C R R

AWGN IAWGN

IAWGN

= ′ =

+

î

=+

( )

( )

5( )5

( ).

γλπ

γ γγ γ

1

4

2

0

20

(4.10)

Equation (4.10) is thus the basic equation to estimate the BEP by ap-proximating broad band disturbance as AWGN. Thus, from the knowl-edge of the electric field strength of the disturbance, the signal to distur-bance ratio can be estimated. This, together with the signal to noise ratio

_____________________________________________________________________________________60

in the radio receiver, gives an estimated value of the total BEP for thesystem.

4.3 Method for narr ow band CW disturbance

If equation (4.10) is used for a specific emission limit, and the distur-bance source produces narrow band (NB) disturbance, such as spectralcomponents from the Fourier series of a periodic signal, the BEP ob-tained will be seriously underestimated if MW is greater than the band-width RW of the radio receiver [24]. Furthermore, if )(xFC for Gaussiannoise is used in this case, the RMS value of the sine wave will also beunderestimated as the output from the EMI detector is already calibratedto the RMS value and thus does not have to be corrected. Therefore, aspecial narrow band analysis must be performed [43], where

P P PE

W ZpqG E r N

Pr

r

b b bb

b

CW CW CW

RR R

CW ICW

ICW

= ′ =+

=+

( )

( )

6( )6

( ).

γλπ

γ γγ γ

1

4

2

0

20 (4.11)

Thus, for narrow band disturbance it is important to perform the Gaus-sian approximation of the disturbance signal with respect to the band-width of the radio receiver. Furthermore, the fact that standard meas-urement equipment is calibrated in terms of the RMS value of a sinewave must be considered in order not to underestimate the total distur-bance power. The advantage in this case is that the EMI detector outputwill give the correct RMS value and thus the correct disturbance power.Thus, no error contribution from the conversion to RMS value will existfor the narrow band disturbance. In the next chapter equation (4.11) isinvestigated for minimum shift keying (MSK). The difference betweenthis approximation and the exact value of BEP is determined for certaincases with typical system parameters.

_____________________________________________________________________________________61

5 Analysis for MSK systems

N this chapter, the proposed estimation method presented in chapter 4is investigated for the case where no hostile jamming is present. The

disturbance model used assumes that the dominant disturbance waveforms are the narrow band spectral components from the Fourier expan-sion of the periodic disturbance. Thus, in a real situation when maxi-mum radiated emission limits are to be chosen, the narrow band distur-bance will be crucial. Consequently, the consequence of using the nar-row-band method is investigated in this chapter as well as in the jam-ming case later in this thesis.

5.1 The choice of MSK

MSK and closely related variations of this continuous phase modulation(CPM) scheme have aroused considerable interest during the past one ortwo decades. Furthermore, CPM is used in several practical systems, es-pecially in milit ary applications [48]. Examples are in the SwedishArmy (Ra 180), the Swedish Airforce (Ra 90) and the NATO Airforce(JTIDS). Moreover, the difference, in terms of sensitivity to interfer-ence, from other modulation schemes is considered small enough for theintended application of the method. Similar conclusions from the resultsfor MSK have been found in the literature for non coherent BFSK andDPSK. The above properties of MSK make it to a suitable choice for theanalyses in this thesis.

I

_____________________________________________________________________________________62

5.2 The MSK modulation scheme

Minimum shift keying (MSK) is a special form of continuous phasemodulation (CPM). CPM methods have at least two attractive propertiesfor use in digital communications:

• CPM methods require less bandwidth than many other modulationschemes such as amplitude and frequency shift keying;

• The signal has, in general, constant amplitude, which is favorable ifthere are non-linearities in ampli fiers and repeaters.

A drawback with CPM schemes is that the memory introduced in thedata bit stream leads to increased complexity in the receiver, as a se-quence detector is required. MSK, however, has the practical advantagethat a linear detector gives optimum demodulation properties. Differen-tial MSK has been carefully analyzed by Svensson et al, see for instance[44]. The carrier signal of CPM can generally be expressed as

[ ]s t aE

Tf t t ab

b

(, ) cos (, )= +2

2π φc , (5.1)

where Eb is the energy per data bit [Ws] and cf denotes the carrier fre-quency [Hz]. The information is carried in the time varying phase func-tion

φ π(, ) ( )t a a hq t kTk bk

n

= −= −∞∑2 , (5.2)

where

a ak= the sequence of information bits into the modulator, 1±=ka , with equal probabilit y;Tb bit duration time [s];h modulation index;q t kTb( )− normalized wave-forming shape, see equation (5.4);t time.

MSK is a CPM scheme with h=1/2, thus we can rewrite (5.2) as

_____________________________________________________________________________________63

)(2

),(1

b

n

knk nTtqaaat −+= ∑

−

−∞=ππφ . (5.3)

Here, q(t) is

q t

t

t

T t T

t T

b b

b

() =

<

≤ ≤

≥

î

0 0

2 0

1

2

. (5.4)

Thus, the phase of the carrier changes ± π 2 during each bit interval

bT . In Figure 5.1, a parallel differential MSK receiver is shown. Thereceived signal is denoted r(t). Here, the impulse response of the filter is

a t T

t

Tt T

b bb()

cos= ≤

î

2

20

π

otherwise. (5.5)

The decision logic is quite straightforward as it each 2nTb decides

whether the phase is 0 or π, while each (2n+1)Tb it decides whether thephase is + π 2 or − π 2. Making these decisions, the detector can de-cide every bit interval whether the total phase has changed with + π 2

or − π 2 corresponding to data bits ak of +1 or -1. If the radio channelis subjected to disturbance, a bit error will arise if one of two successivephase decisions is incorrect. If the probabilit y of making a phase error isdenotedPph , the corresponding bit error probabilit y is 2 1P Pph ph( )− [44].

If the disturbance consists of additive white Gaussian noise (AWGN)only, with a two-sided power spectral density of N0 2, the phase errorprobabilit y will be the same as the BEP for binary shift keying (BPSK).That is

=

0ph erfc

2

1

N

EP b , (5.6)

where erfc(x) is the complementary error function.

_____________________________________________________________________________________64

5.3 Estimation of BEP for MSK in a mixture ofGaussian and CW disturbance

The disturbance situation is described in figure 5.1. The BEP PbCW for

MSK subjected to a mixture of CW and additive white Gaussian noise(AWGN) is derived for an ideal parallel MSK receiver in Appendix A.This BEP is referred to as the calculated BEP and will be compared tothe measured and the estimated BEP later in this thesis. The estimatedBEP will always be obtained by the method developed in chapter 4. Inthis section, the most important results concerning the calculated BEPare presented. The BEP is generally obtained as

P P PbCW

ph ph= −2 1( ), (5.7)

where phP is the probabilit y of making an error in the phase decision in

one of the branches in the receiver. Here, the disturbance signal )(I ti is

[ ]IIcII )(2cos2

)( ϕπα +∆+= tffT

Eti b , (5.8)

cos2πfct

-sin2πfct

a(t)

a(t)

2nTb

(2n+1)Tb

Decisionlogic

r(t) 7α+

iI(t)

n0(t)

Figure 5.1: Parallel MSK receiver and the present disturbance situa-tion.

_____________________________________________________________________________________65

where α I is a scaling factor related to the MSK-signal amplitude, ∆f I isa frequency shift from the carrier frequency and ϕ I is an arbitrary phaseshift, which is assumed to be a stochastic variable uniformly distributedover [0, 2π]. Tb is the bit duration time. In this disturbance situation theaverage phase error probabilit y is, see Appendix A,

,))4(1(

2coscos41erfc

4

1

),(erfc

2

1

I2I

III2

00

0

IIIph

ϕππ

πϕαπ

ϕλ

πd

Tf

Tf

N

E

N

fEEP

b

bb

b

∆−

∆+=

î

∆+=

∫ (5.9)

where λ I is the inherent disturbance contribution to the decision vari-able in one of the branches (Appendix A). The BEP is averaged over Iϕas the actual Iϕ is not known in a real situation.

5.4 Results

5.4.1 Compar ison of BEP for the ideal receiver with measured

BEP on a real system

The calculated BEP is for an idealized model of a parallel MSK re-ceiver. An important question is how such an idealized model corre-sponds to the BEP obtained in a real system. To investigate how thesecalculated results relate to the BEP obtained when subjecting a realdigital radio system to radiated disturbance, some measurements wereperformed. The main purpose of these measurements was to see whetherthe theoretical analysis performed on an ideal MSK receiver is relevantwith respect to all practical considerations taken into account during thedesign of a real system. As the results are intended to be applicable tothe design of real systems, it is important to check the validity of theideal receiver model. A further purpose is to see how the calculated re-sults relate to those measured when using standard EMC measurementequipment. An MSK digital radio system was subjected to CW andpulsed sine wave disturbance. The extension to pulsed sine wave distur-bance was done to see whether the difference between calculated and

_____________________________________________________________________________________66

measured BEP depends on whether the CW disturbance is pulsed intime or not. Let ρ be the fraction of time where a pulsed sine wavedisturbance is present. This gives 10 ≤≤ ρ . If we assume that the inter-fering signal is either disturbing a whole bit interval bT or not, the biterror probabilit y will be

AWGNCW )1(only AWGN error bit )1(

AWGN + ceinterferen error bit ~

bb

CWb

PPP

PP

ρρρ

ρ

−+=−+

=. (5.10)

The pulsed disturbance was generated with duty cycle ρ = 0.1 and0.875. The BEP was measured as a function of estimated signal to dis-turbance ratio SIR for certain estimated signal to noise ratios (SNRs).The measurement setup is schematically shown in figure 5.2. More de-tailed information is found in [70]. The spectrum analyzer was used tomeasure the signals as they appeared to the radio receiver. This wasdone by connecting the radio antenna directly to the spectrum analyzer.To make accurate measurements of BEP, it is very important that themeasurement time be long enough to register as many bit errors that themeasured BEP is reliable. This implies practical li mitations when verylow values of BEP are to be measured, as it is very diff icult to have astable background noise level when the measurement time is increased.

In the measurements performed, the BEP was measured on line until astabili zed value was obtained. This could require a measurement time upto approximately ten minutes. If the background noise suddenly changedduring this measurement period, the measurement was stopped and re-started until an approved measurement was achieved. SNR was esti-mated by solving equation (5.7) when thermal and background noiseonly were present. This estimated SNR is denoted 8γ in the graphs. SIRwas estimated with the measurement equipment and is denoted I

~γ in thegraphs. The pulsed disturbance was generated with duty cycle ρ = 0.1and 0.875. These values were chosen to get one large and one small dutycycle. The time the disturbance pulse is present is much greater than thebit duration bT . The carrier frequency 45 MHz was chosen to get an ac-ceptably low background disturbance level.

Due to practical diff iculties, the phase between the disturbance and ra-dio signal could not be measured in a reliable way. The differences be-

_____________________________________________________________________________________67

tween measured and calculated results could, at least to a certain extent,be caused by the unknown phase as the calculated BEP is averaged overthe phase interval [0, 2π]. Another contribution could be a slight differ-ence between the carrier frequency and disturbance signal, see equation(5.8). The latter difference will give a lower [73] measured BEP whichis seen especially in figure 5.3. A third contribution to the differences is,of course, the difference between the idealized MSK receiver and thereal implemented hardware system. The time averaged Iγ should beused if comparisons of the three disturbance situations are required.Here, Iγ is defined as

2

I2I

2

I1

)(

)(

ραργ ==

tiE

tsE, (5.11)

and γ γI, dB I= 10 10log ( ). (5.12)

The signals )(ts and )(I ti are the received MSK signal and the distur-bance signal, respectively. The results are presented in Figure 5.3 - 5.5.

A few hundred meters

RaShieldedmonitorfacility BEP BEP

Interferencesignal

MSK45 MHz≈ 16 kbit/s

Ra = Radio with MSK modulationBEP = equipment for BEPmeasurement

Ra

Cable to spectrum analyzerfor the measurement of thesignal levels into the radioreceiver.

Figure 5.2: Measurement setup.

_____________________________________________________________________________________68

−5 0 5 10 15 20 25 30 35 4010

−5

10−4

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10−2

10−1

100

Bit

erro

r pr

obab

ility

CalculatedMeasured

Iγ [dB]

Figure 5.3: Calculated and measured PbCW for γ ≈ 9.5 dB.

−20 −15 −10 −5 0 5 10 15 2010

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10−2

10−1

Bit

erro

r pr

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CalculatedMeasured

Iγ [dB]

Figure 5.4: Calculated and measured ~Pb

CW , for ρ = 0.1 and γ ≈ 8.7dB.

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5 10 15 2010

−4

10−3

10−2

10−1

Bit

erro

r pr

obab

ility

CalculatedMeasured

9γ I [dB]

Figure 5.5: Calculated and measured ~Pb

CW for ρ = 0.875 andγ ≈ 8.7 dB.

The difference between measured and calculated BEP is much less thana factor of ten, except for medium values of γ for CW

bP . These differ-ences between calculated and measured BEP are regarded as acceptabletaking into account the major difference between the idealized model forthe calculations and all the practical consequences of an implementationin a real system. The measurement uncertainty for Iγ is estimated at ap-

proximately ± 2 dB (maximum error), as Iγ is the result of a relativemeasurement in the measurement receiver. The uncertainty in the meas-urement receiver is approximately ±1 dB for each reading. The BEP wasmeasured on line until a stabili zed value was obtained. For the lowestvalues of the BEP, this procedure gives an estimated measurement un-certainty of approximately 510− . The conclusion is that for practicalpurposes, such as system design, the differences in the results are re-garded as low enough to justify a theoretical approach for the evaluationof the method in the next section.

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5.4.2 Results

As the narrow band disturbance is typically of higher disturbance powerthan the broad band we assume that if an emission limit is reached, it isreached by a sine wave from the Fourier expansion of the periodic dis-turbance. The narrow-band method will t hus be of major concern. Infigures 5.6-5.8, the estimated BEP for narrow band disturbance (eq.4.11) is compared to the calculated solution (eq. 5.1 and 5.2) for theideal MSK receiver for CW disturbance for a disturbance level thatequals three standard emission limits. These standard emission limits areEN55022, classes A and B, which are required for all civili an ITE soldin the European Union. Class A applies to industrial equipment, andClass B has to be fulfill ed for equipment intended for use in off ice andresidential environments. The third emission limit is RE102 from MIL-STD-461D. This is a common requirement used for milit ary applica-tions. The requirements for these standard limits are shown in AppendixC. BEP is plotted versus separation distance between the undesired dis-turbance source and the radio receiver. The results are for a digital radioreceiver working with uncoded MSK, an isotropic antenna with gain 0dB, a thermal noise level of -120 dBm at 25 kHz bandwidth and work-ing with a fixed frequency at 60 MHz ( p and q in equation (4.3) are as-sumed to be 1). This gives a noise figure of 10 for the receiver. The fre-quency 60 MHz is chosen as it is located in the middle of the currentfrequency band (30 - 88 MHz) for milit ary combat radios. Evaluating ata single frequency is not a limitation since the variation in separationdistance gives a suff icient variation in signal to disturbance ratio (SIR)

Iγ . The signal to noise ratio (SNR) γ is varied so that different relationsbetween γ and Iγ are obtained. In this example, a γ of 6, 9 and 12 dBhas been used. The two-beam wave propagation model has been used.Both the disturbance source as well as the receiving antenna of the radioare located about 1 meter over what could be regarded as ‘good ground’( 210−=σ S/m, 15r =ε ), thus a 1 2/ r decay is used for the electricfield at these distances [45]. At SNR = 12 dB, the estimated BEP ishigher than the calculated BEP, except for very low and very high val-ues of SIR. However, at those SIRs the BEP is already high or very low,therefore, in practical applications, the estimated BEP could be regardedas a worst case BEP over a broad range of SIRs. This is not true forlower values of SNR, but in a practical situation, SNRs of 6 and 9 dBshould not in general be of great interest since the BEP is already high

_____________________________________________________________________________________71

without any other disturbance than the internal thermal noise. Similarresults are found in [40] for non-coherent binary frequency shift keying(BFSK) and differential phase shift keying (DPSK). As can be seen, thedifference between the estimated and calculated solutions increases withSNR. However, for larger values of SNR, the BEP is too low to causedisturbance problems, thus this dependence of SNR can be neglected.The overall conclusion is that the estimation method suggested gives anestimated BEP close to the calculated BEP. For practical purposes thisestimated BEP can be considered as a worst case. This conclusion is notlimited to MSK only, but also to non-coherent BFSK and DPSK. It isimportant to note that the averaged BEP is considered. In addition, sev-eral important practical conclusions can be drawn from these results.Firstly, the results show large differences in performance degradationbetween levels that equal milit ary and civili an radiated emission limits.Levels that equal civili an limits start to affect the radio receiver at sepa-ration distances in the order of one hundred meters, while levels thatequal milit ary limits will not cause any problems until the separationdistances become smaller than approximately ten meters. This complieswith the well -known experience that a milit ary emission requirement

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Separation distance [m]

RE102 Class B

Class A

CalculatedEstimated

Figure 5.6: Calculated BEP ( PbCW ) and estimated ( :Pb

CW ). Co-locationwith equipment that equals EN 55022, Class A and Class B limit andRE102. CW disturbance. Ideal MSK receiver, 60 MHz, SNR = 6 dB.

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RE102

Class B Class A

CalculatedEstimated

Figure 5.7: Same as figure 5.6 for SNR = 9 dB.

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RE102 Class B

Class A

CalculatedEstimated

Figure 5.8: Same as figure 5.6 for SNR = 12 dB.

_____________________________________________________________________________________73

can only be fulfill ed if disturbance reduction measures are consideredthrough the whole design process, from the circuit board level to the sur-rounding box and cabling. Secondly, another practical consequence isthat some kind of shielding device will be needed if civili an electronicshave to be co-located to digital radio systems. This will i ncrease the costof the total system, which means that the expected savings from usingcivili an instead of milit ary electronics could be heavily reduced or, insome cases, negligible. Of course, the separation distance can be in-creased in order to reduce the impact, but large separation distances arenot always possible in real situations.

5.5 Sensitivity Analysis

A consequence of defining emission limits in terms of a certain band-width and detector is that the differences in disturbance wave forms arenot taken into account as two wave forms with large differences in termsof impact on a digital radio receiver can be approved during an emissiontest. A broad band disturbance, such as AWGN, is treated in the sameway as a narrow band CW signal. This will have consequences for theBEP obtained by these disturbance wave forms. In figure 5.9, the BEPobtained by AWGN and CW, both equaling the Class B limit at 60MHz, is compared. The narrow-band method is used for the CW distur-bance. As shown, the AWGN disturbance will cause a lower BEP thanthe CW. This is due to the fact that the detector output for AWGN isproportional to the square root of the measurement bandwidth. The out-put for the CW disturbance is, however, independent of bandwidth. Inthis case the CISPR measurement bandwidth is 120 kHz, and the re-ceiver bandwidth in the radio is 25 kHz. Thus, the disturbance powerinto the radio receiver in this case will be approximately 25/120 of theCW power. This is a consequence of the definition of the measurementprocedure itself and has to be handled if no information is availableabout what will be the dominant disturbance wave form. For instance, inan electronic unit, whose dominant disturbance wave form cannot bedetermined in an early design phase, one broad band and one narrowband analysis have to be made to obtain knowledge about what couldhappen for these ”extremes” according to disturbance wave forms. Suchanalysis will give results similar to figure 5.9, which can be used for

_____________________________________________________________________________________74

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Bit

erro

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Separation distance [m]

CWAWGN

Figure 5.9: Comparison of CW and AWGN at Class B limit.

design considerations and choice of emission limits. For instance, if thisanalysis shows that narrow band disturbance could cause severe distur-bance problems, the equipment manufacturer could be required to ana-lyze the design at an early stage to see if such disturbance is li kely tooccur in the final hardware. Furthermore, the CW case is applicable tothe case of repetiti ve pulses with pulse repetition frequency greater thanthe bandwidth of the radio receiver.

The conclusion is that if no knowledge of the dominating disturbancewave form exists in the early design phase, the narrow band and broadband methods will serve as useful methods for determining probableworst case limits of the BEP.

_____________________________________________________________________________________75

6 EMI detectors for future emissionstandards

HE RMS detector is proposed and evaluated as a candidate for usein future radiated emission standards. It is shown that the output

from the RMS detector can be related to the corresponding BEP on adigital communication receiver as disturbance “victim” . The results arecompared to the work performed within CISPR/ITU where another ap-proach is used.

6.1 Introduction

As concluded in chapter 2, present emission standards are developedconsidering analog communication services. These standards still usethe quasi-peak detector, which simulates the human perception of elec-tromagnetic (EM) disturbances on analog radio receivers [18][19].However, this detector is not adequate to simulate the effect of EM dis-turbances on digital radio receivers, see section 6.4. Another practicaldisadvantage of the quasi-peak detector is its relatively long responsetime, which makes emission measurements time-consuming. This latterproperty is the reason why emission measurements are often “pre-scanned” with a peak detector to identify frequency regions of interestfor quasi-peak measurements. A method of estimating the impact ondigital communication systems if the disturbance has been measuredwith a quasi-peak detector has been presented in this thesis. This methodcan be used until new emission standards concerning digital communi-

T

_____________________________________________________________________________________76

cation systems have been developed. The work of developing measure-ment procedures considering a digital radio receiver as a disturbance“v ictim” has started both in CISPR [22] and ITU-R [23]. This work issummarized by Stecher [18][63][71]. This is a very complex problemsince there is a large variety of modulation and coding schemes to con-sider as the area of digital communication services undergoes a rapiddevelopment. However, a solution to this problem is necessary in orderto protect these services against radiated electromagnetic disturbance.One approach is to create a new weighted detector, representing thedisturbance effect on digital radio receivers [18][63]. Here, the samestrategy that lies behind the quasi-peak detector is used. An alternativeapproach, presented in this chapter, is based on using an already existingdetector, namely the RMS detector. The analysis relies on the same fun-damental assumptions used by CISPR and in [18][63]:

• The bit error probabilit y (BEP) is the performance parameter of in-terest for the digital communication system.

• The disturbance of interest is a repetiti ve wave form.• Disturbance pulses having a width < 20-30 µs are considered.

In [18][63][71], examples of results from the CISPR/ITU work of f ind-ing a proper weighting curve are presented. The results are based on thepeak level of the disturbance. The result is that the tolerated disturbancelevel for repetiti ve pulses for a certain BEP varies strongly with thepulse width of that disturbance, see figure 6.11 and 6.12. In contrast, ourresults show that the tolerated RMS value corresponding to a certainBEP for a digital communication receiver subjected to repetiti ve pulseddisturbance is, in practice independent of the pulse width of that distur-bance. This is due to the fact that the RMS value automatically takesinto account the effect of a changed pulse width in such a way that evenif the RMS value changes with the pulse width, the RMS value relatedto a certain BEP will remain constant if the pulse width is changed.Furthermore, the weighting curves in [18][63][71] exhibit a strong de-pendence on the pulse repetition frequency of the disturbance. In ourapproach, this variation is much weaker and can easily be modeled. Anapproximate relation between the RMS value and the correspondingBEP is suggested. This relation can be used to maximize the disturbancelevel so that an approximately constant BEP is obtained for all pulserepetition frequencies of interest. The chapter is organized as follows. Areview of weighting detector fundamentals is made in chapter 6.2. In

_____________________________________________________________________________________77

section 6.3, the analysis model for our investigation is presented. Fur-thermore, a general relation between the tolerated RMS value of thedisturbance signal for a constant BEP is suggested. This approximatedrelation is based on the results of the extensive analysis on the modula-tion scheme binary phase shift keying (BPSK) in chapter 6.4. Conse-quently, a weighting curve that provides a constant BEP over the distur-bance pulse repetition frequencies of interest can be determined. Inchapter 6.4 it is shown why the quasi-peak detector is not a properweighting detector for digital communication services. Moreover, theapproximated relation from section 6.3, between the tolerated RMSlevel and the BEP, is compared to calculated and measured results onother modulation schemes than BPSK. The calculated results are for thedigital modulation schemes minimum shift keying (MSK), binary phaseshift keying (BPSK) and quadrature amplitude modulation with level 64(64-QAM). The measured results are for a real MSK communicationsystem. The tight agreement between the approximated relation in sec-tion 6.3 and the results from section 6.4 confirms that the approximatedrelation between the tolerated RMS level and the BEP is not only validfor BPSK but also for other digital modulation schemes. In section 6.5,it is shown that the tolerated RMS value related to a certain BEP doesnot change with the pulse width of the disturbance. This is because theRMS value changes with the pulse width so that the RMS value corre-sponding to a certain BEP will remain constant for different pulsewidths. Furthermore, the detailed analysis behind the approximated re-lation in section 6.3 is presented. Finally, the conclusions are summa-rized in section 6.6. The overall conclusion is that the RMS detector is apromising candidate for future emission standards.

6.2 Review of weighting detectors fundamentals

The quasi-peak (QP) detector was originally developed to give a re-sponse that is proportional to the perceived disturbing effect on humanbeings. This was done by the application of psychophysics (psychoacoustics for sound radio and psycho optics for TV) [18]. In particular itwas necessary to weight impulsive noise from e.g. electric motors andspark-ignited engines. As the disturbance effect perceived by a humanbeing is higher at high pulse repetition frequencies than at low pulserepetition frequencies, the detector response had to take this into ac-count. The result was a detector that for repeated pulsed disturbance

_____________________________________________________________________________________78

gives a response that increases with the pulse repetition frequency of thedisturbance. This behavior exists up to a certain limit in pulse repetitionfrequency (typically 10-20 kHz) beyond which a constant response isobtained. In figure 6.1, the weighting curve [34] of the CISPR QP de-tector is shown for the frequency bands C and D (30 – 1000 MHz). Thiscurve should be interpreted as follows; for instance, a certain distur-bance level at the input of the measurement receiver, see figure 6.1, witha pulse repetition frequency of 1 kHz gives the same disturbance effectas a 9 dB higher level at a pulse repetition frequency of 100 Hz. Thework of developing measurement procedures considering a digital radioreceiver as “v ictim” has started both in CISPR [22] and ITU-R [23]. Theapproach [18] is to create a new weighted detector, representing thedisturbance effect on digital radio receivers. The first issue is to find theproper weighting curve from which a new detector can be developed.One way of determining weighting curves for digital radio receivers isto perform measurements and simulations of the impact from the distur-bance signal on various modulation schemes and then try to summarizethe results to create a general weighting curve. Once the weightingcurve is determined, a detector with these properties can be developed.The measurement setup for such an investigation [18] is shown in figure6.2.

101

102

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104

105

−30

−25

−20

−15

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−5

0

Pulse repetition frequency [Hz]

Qua

si p

eak

rela

tive

peak

out

put [

dB]

Figure 6.1: Weighting curve for the CISPR quasi-peak detector forbands C and D.

_____________________________________________________________________________________79

+

Radio signalgenerator

Disturbancesource withrepetitive pulses

Radio receiver

BERFigure 6.2: Test setup for the determination of the disturbance signallevel for a certain bit error rate (BER).

The first measurement is done to determine the disturbance source out-put level to obtain a constant bit error rate (BER) for all pulse repetitionfrequencies of interest. The next step is to create a measuring receiverwhich weights these disturbance levels in such a way that if the regis-tered disturbance source output levels from figure 6.2 is generated, theoutput from the measuring device will remain constant. This weightingproperty of the measuring device is denoted weighting curve. Differentdigital communication systems will not, of course, respond in the sameway to different types of disturbance signals. Therefore, a compromise[18] will have to be found for the most important digital communicationsystems.

An alternative approach is to investigate existing detectors to see if anyof these could be a candidate. In the following sections, the results fromsuch an investigation are presented for the RMS detector.

6.3 Analysis

The model for the analysis is summarized in figures 6.3 and 6.4. Thedisturbance signal )(d ti consists of repetiti ve square waves with pulserepetition frequency pf , pulse width WT and amplitude level dA . This is

the same disturbance signal wave form used in [18]. The disturbancesignal is modulated on a sine wave so that its frequency spectrum ismoved to the carrier frequency of the digital modulation schemes. Thissine-wave modulation has been done in the measurements in[18][63][71]. We also use that technique here so that our result can becompared with those in [18][63][71].

_____________________________________________________________________________________80

t

1/fp TW

Ad

id(t)

Equal to the carrier frequencyof the digital communicationsystem

Figure 6.3: The disturbance signal model.

The RMS detector delivers )(E 2 ti , where E denotes the expectedvalue and i(t) is the output from the IF-stage of the spectrum analyzer(or some other superheterodyne EMI measurement receiver). Up to now,the RMS detector has not been used in EMI measurements (except forout-of-band emission of radio transmitters) even if the 2nd edition (1972)of CISPR 1 [59] says that experience has shown that an RMS voltmetermight give a more accurate assessment of the disturbance effect onanalog radio than the QP detector does. In section 6.5, we show that theRMS value of the disturbance as a function of pf for certain BEP values

RF

LO IFRMS

DETECTOR

)(E 2 ti

i(t)id(t)

Figure 6.4: The EMI receiver model.

_____________________________________________________________________________________81

RMS value for aconstant BEP [dB]

log fp≈RS

Slope: ≈7.5 dB/frequency decade

≈ 2p0 RS

RSFigure 6.5: The principal weighting curve for constant BEP = p0.

can be approximated by the following relation

î

≥

<<+≈

SpS

dBRMS

SpS0S

p10

S

dBRMS

pdB

RMS

,)1

(

,2log5.7)1

()(

RfR

V

RfRpR

f

RV

fV , (6.1)

where 0p is the chosen value of the constant BEP and RS is the symbolrate of the communication system. Equation (6.1) is graphically shownin figure 6.5. As equation (6.1) is based on the results for BPSK, thisequation is compared with calculated and measured results for othermodulation schemes in section 6.4. The property of main interest is thelinear behavior with a slope of 7.5 dB/frequency decade as this propertyis tractable for modeling purposes. We will show that this linear behav-ior does not correspond to BPSK only, but also to other modulationschemes.

6.4 Results

6.4.1 The quasi-peak detector and digital radio receivers

In figure 6.6, the BEP obtained for a disturbance level which is limitedby the use of the QP detector is shown for the digital modulation scheme

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101

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10−5

10−4

10−3

10−2

Pulse repetition frequency [Hz]

Bit

erro

r pr

obab

ility

Figure 6.6: The BEP obtained for a disturbance level determined bythe weighting function of the quasi-peak detector. The desired BEP isfor the modulation scheme BPSK.

BPSK with a symbol rate of 100 kbit/s. This result is based on the sys-tem parameters according to table 6.1, and a disturbance-pulse width of1 µs. In this figure, the quasi-peak value corresponding to the toleratedBEP is determined for pulse repetition frequencies higher than the bitrate. Then the BEP obtained for lower pulse repetition frequencies hasbeen determined for the same registered quasi-peak value for the lowerpulse repetition frequencies. The desired BEP is 410− , a level which isexceeded at the lowest pulse repetition frequencies because the quasi-peak detector, at lower pulse repetition frequencies, will allow too highdisturbance levels if the quasi-peak value is kept constant. The differ-ence in BEP is approximately a factor 10 from the desired value at thelower frequencies, when the quasi-peak detector is used. This might beacceptable from an engineering point of view, but the problem is that theBEP increases if the quasi-peak detector is used for lower pulse repeti-tion frequencies. If the BEP had always been lower than the desiredvalue, the quasi-peak detector might have been possible to use since thiswould have given a “built i n” margin to the desired BEP.

_____________________________________________________________________________________83

6.4.2 Results for the RMS detector .

In this section, the validity of equation (6.1) is investigated by deter-mining the tolerated RMS value both by calculation and measurementsfor other modulation schemes than BPSK. The important issue is to seeif the approximated slope of 7.5 dB/frequency decade is useful even forother modulation schemes than BPSK. The analysis was performed forthree digital radio systems with parameters according to table 6.1. Theabsolute values of the system parameters are not criti cal for the analy-ses. The important issue is to cover a variation of the relation betweenthe pulse repetition frequency pf and the symbol rate SR . No error cor-

recting codes have been used for the modulation schemes. There areseveral reasons why uncoded modulation has been used. Firstly, errorcorrecting codes are always designed to handle other disturbance prob-lems than disturbance from co-located equipment. Such problems couldinclude varying quality of the radio channel or, in milit ary applications,jamming. The error correcting code is therefore designed to handle cer-tain combinations of disturbance parameters corresponding to the ex-pected most diff icult disturbance problem. Therefore, taking error cor-recting code capacity into account in our case is hazardous because it isunclear how the result should be interpreted as it is not obvious how thedegradation of the error correcting code should be measured for ourdisturbance signal. Furthermore, if the BER is measured after error cor-rection, we will not know how much of the code capacity has been usedfor co-located disturbance. This means that even if the BER is at an ac-ceptable level, the system performance has been degraded in an uncon-trolled manner. The only way to get a reliable answer as to the true im-pact on system performance is to determine the BER before error cor-rection. Thus, the uncoded system gives results that are easier to

Parameter System 1 System 2 _ __ System 3

Modulation scheme: MSK BPSK 64-QAMSymbol rate SR : 18 kbit/s 12.5 kbit/s 12.5 ksymbols/s

System bandwidth: ≈25 kHz (0.7⋅2 SR ) ≈25 kHz (2 SR ) ≈25 kHz (2 SR )Noise figure: 10 dB 10 dB 10dBErr or correction: uncoded uncoded uncoded

Table 6.1: System parameters for the examples analyzed.

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interpret in a performance analysis. The results are presented in figures6.7 and 6.8. The tolerated RMS value of the disturbance level for BEPvalues of 310− , 410− and 510− was calculated for different pulse repeti-tion frequencies of repetiti ve rectangular pulses. The calculation of BEPfor BPSK, MSK and 64-QAM subjected to repetiti ve pulses with pulserepetition frequencies lower than the symbol rate is complex. Thus onlythe final results are presented here. For BPSK, the necessary calcula-tions can be found in section 6.5, from which equation (6.14) is used forthe analysis in this section. For MSK and 64-QAM, the technique issimilar but more complex. However, for both MSK and 64-QAM, thedecisions in the receivers are based on the same basic principle as inBPSK, i.e. to take a phase decision of the received signal [42][43]. Thedetailed analyses are shown in Appendix D and E.

The results are shown in figure 6.7 and 6.8. In these figures, the signalto disturbance ratio SIR (instead of the disturbance level) is used on they-axis. The SIR in this case is defined as the RMS value of the desiredsignal divided by the RMS value of the disturbance signal. The RMSvalue of the disturbance signal is calculated with respect to the systembandwidth. If another bandwidth is used, the curves will be moved inthe y-axis direction. The results are for a signal to noise ratio (SNR) of12 dB for MSK and BPSK. For 64-QAM, an SNR of 20 dB is used.Furthermore, the symbol error probabilit y is used for 64-QAM. The rea-son is that a general relation between BEP and symbol error probabilit ycannot be determined. However, for certain cases, approximate relationsbetween BEP and symbol error probabilit y can be obtained. An exampleof such approximated relation is when the symbols are assigned ac-cording to Gray coding. In that case, a linear function between BEP andsymbol error probabilit y exists, see Appendix E.

The SNR is defined as 0/ NEb . Here, bE is energy per data bit and 0N isthe single-sided power spectral density [W/Hz] of the internal thermalnoise level in the receiver. If the internal noise consists of thermal noiseonly, it will be equal to kT, where k is Boltzmanns constant(= 231038.1 −× J/K) and T is the temperature in Kelvin. In section 6.5, it isshown that the tolerated disturbance level for a certain BEP value is notdependent on the pulse width of the pulses as long as the pulse width ismuch smaller than the symbol duration time. In [18][63][71], theweighting curves show strong dependence with the pulse width, see fig-ure 6.11. Thus, using the RMS value measured within the radio receiver

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bandwidth, the pulse width dependence is removed as the RMS valuerelated to a certain BEP will remain constant if the pulse width ischanged. This means that the pulse repetition frequency only has to beconsidered to determine the maximum tolerated RMS detector output in,for instance, a future emission standard. Furthermore, the pulse repeti-tion frequency below which the required SIR starts to decrease rapidly(i. e. the tolerated RMS value of the disturbance starts to increase[18][63][71]) is considerably smaller than in the weighting curves in[18][63][71]. For instance, for a pulse width of 10 sµ , this break point isapproximately 5 kHz in [18] and below 100 Hz in figure 6.7 for BEP =

310− . This means that for a large region of possible pulse repetition fre-quencies, the dependence could be regarded as linear in log units. Theslope of the curves in figures 6.7 and 6.8 is close to 7.5 dB/frequencydecade. Thus, figures 6.7 and 6.8 show a close agreement with equation(6.1). The reason why the disturbance power increases rapidly at smallpulse repetition frequencies is that only a small fraction of the data sym-bols are disturbed by the disturbance pulses. As the BEP for a singledata symbol cannot be larger than 0.5, theoretically an infinite distur-bance power level can be tolerated for each disturbance pulse.

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Pulse repetition frequency [Hz]

Sig

nal t

o in

terf

eren

ce r

atio

, rm

s−va

lues

[dB

]

BEP = 10−3

BEP = 10−4

BEP = 10−5

Figure 6.7: Required signal to disturbance ratio versus pulse repeti-tion frequency for three design levels of the BEP for the modulationscheme BPSK.

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101

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Pulse repetition frequency [Hz]

Sig

nal t

o in

terf

eren

ce r

atio

, rm

s−va

lues

[dB

]BPSK MSK 64−QAM

Figure 6.8: Signal to disturbance ratio versus pulse repetition fre-quency for a BEP of 410− . Comparison between the modulationschemes MSK, BPSK and 64-QAM. For 64-QAM the symbol errorprobability is used. The slope of the curves is close to 7.5dB/frequency decade (equation 6.1).

When the pulse repetition frequency is larger than the bandwidth of theradio receiver, only one spectral component from the Fourier series ex-pansion of the repetiti ve disturbance signal will enter the radio receiver.Thus, the tolerated disturbance power for a certain BEP will remain con-stant for all pulse repetition frequencies larger than the bandwidth of theradio receiver (as the RMS value is determined with a bandwidth equalto the bandwidth of the digital radio system). The linear behavior wasalso investigated by measurements on a real radio system. The meas-urement setup is shown in figure 6.9. A more detailed description of themeasurements is found in [67]. In figure 6.10, the RMS value resultingin constant BEP using equation (6.1) is compared with measurements onan MSK radio system working with a symbol rate of ≈16 kbit/s, and achosen 0p 3104 −⋅≈ . The measurement uncertainty for the RMS value is

estimated at a maximum of ± 2 dB. The lower theoretical li mit for equa-tion (6.1) is 130p ≈f Hz in this case. A perfect match is not possible, of

course, due to the differences between the theoretical model and thepractical consequences of an implementation in a real system.

_____________________________________________________________________________________87

A few hundred meters

Ra

BEP BEP

Disturbancesignal

MSK16 kbit/s

Ra = Radio with MSK modulationBEP = equipment for BEP measurement

Ra

To spectrum analyzer

Signalgenerator

Transmittingradio

Figure 6.9: Measurement setup.

Taking these differences into account, the agreement is considered asacceptable to confirm the linear behavior of equation (6.1). This meas-urement result is not valid, of course, for a complete justification of the

101

102

103

104

105

−5

0

5

10

15

20

25

30

Pulse repetition frequency [Hz]

RM

S−

valu

e fo

r co

nsta

nt B

EP

[dB

µV]

Measured Estimated

Figure 6.10: Comparison of measured and, by equation (6.1), esti-mated BEP. The results are for p0

3104 −⋅≈ for an MSK radio system.The pulse width of the disturbance signal is sµ10 .

_____________________________________________________________________________________88

approximated relation in equation (6.1). Together with the theoreticalresults, however, it strongly indicates that the tolerated RMS value for acertain BEP can be modeled as suggested.

6.4.3 Compar ison with results from CISPR work.

In figure 6.11 an example of a measured result [63] from the workwithin CISPR is shown for 64-QAM. In this figure, the peak value forconstant BEP is presented on the y-axis. An error correcting code withrate 7/8 has been used, which can be considered as a low level of errorprotection. The symbol rate is approximately 30 Mbit/s corresponding toa symbol rate of approximately 6.9 Msymbols/s. The strong dependenceon disturbance pulse width can be seen, as well as a much stronger de-pendence on the disturbance pulse repetition frequency, than for theRMS detector. The RMS value is proportional to the amplitude and tothe square root of the pulse repetition frequency (equation 6.12). Equa-tion (6.1) gives a slope of +7.5 dB/frequency decade for the RMS valuecorresponding to a constant BEP in the transition region

SpS02 RfRp << . As the RMS value increases with +10 dB/frequency

decade for constant disturbance pulse amplitude, a slope of +7.5 dB

0

20

40

60

80

100

120

0.1 1.0 10.0 100.0 1000.0 10000.0 100000.0 1000000.0 10000000.0

f / Hz

dB(µµV)

width 0,1E-06s

width 0,5E-06s

width 1,0E-06s

width 2,0E-06s

width 5,0E-06s

width 10,0E-06s

DVB-T f = 560,0 MHz, 64 QAM, 8k, CR 7/8, BER = 3,0 * 10-6

R S2p 0 R S

Figure 6.11: Weighting functions [63][71] of DVB-T with 64-QAM andcode rate (CR) 7/8, i.e. a low level of error protection.

_____________________________________________________________________________________89

0

20

40

60

80

100

120

0.1 1.0 10.0 100.0 1000.0 10000.0 100000.0 1000000.0 10000000.0

f / Hz

dB(µµV)

width 0,1E-06swidth 0,5E-06swidth 1,0E-06swidth 2,0E-06swidth 5,0E-06swidth 10,0E-06s

DVB-T f = 560,0 MHz, QPSK 8k, CR 1/2, BER = 3,0 * 10-6

Figure 6.12: Weighting functions [63][71] for DVB-T with QPSK andCR=1/2, i.e. a high amount of error protection.

Corresponds to an amplitude decrease of 2.5 dB/frequency decade inthe transition region SpS02 RfRp << . In figure 6.11, the slope of the

curves is approximately -8 dB/frequency decade up to approximately 30kHz. This corresponds to a slope for the corresponding RMS value of +2dB/frequency decade. The suggested model (equation 6.1) indicates+7.5 dB/frequency decade for the uncoded case. In figure 6.12, weight-ing curves for DVB-T with QPSK and an error correcting code with rate½ is shown. As expected, the pulse repetition frequency from which thetransition region begins is higher when a more powerful error correctingcode is used. In this case, the transition region is no longer so notice-able. In [63][71] weighting curves for other systems are presented withapproximately the same slopes. The results in [63][71] indicate thatwhen error correction codes are involved in the weighting curve analy-ses, the RMS value corresponding to a certain BEP is approximatelyconstant with respect to the disturbance pulse repetition frequency. Thetransition region SpS02 RfRp << is not as noticeable as in the uncoded

case. The results in this thesis show that for uncoded systems, the corre-sponding RMS value has to be decreased (compared to the level allowedfor pulse repetition frequencies above the symbol rate) for pulse repeti-tion frequencies below the symbol rate. However, the results in [63][71]

_____________________________________________________________________________________90

agree with the results in this thesis for the principal behavior of theweighting curves, which can be modeled as three regions with respect tothe pulse repetition frequency. For pulse repetition frequencies abovethe symbol rate, a constant value is obtained. Below the symbol rate, wehave a transition region with a slope of a few decibels/frequency decade.At the lower pulse repetition frequencies, the allowed disturbance levelincreases rapidly when the pulse repetition frequency is decreased.Thus, even if the results in [63][71] include error correcting coding, theresults in this thesis do not contradict those results. Rather, an agree-ment can be seen between the principal behavior of the weightingcurves in this thesis and [63][71].

6.5 The relation between BEP and RMS value forBPSK

In this section we will show that the bit error probabilit y does not de-pend on the pulse width of repetiti ve pulses as long as the pulse width isconsiderably smaller than the symbol duration time. Furthermore, thedisturbance level versus pulse repetition frequency for a constant BEPwill be determined to justify the linear behavior of equation (6.1). Thisis shown for the correlation demodulator, which is commonly used indigital communication receivers supplying coherent detection of thedata symbols. Each symbol alternative is represented by a branch in thereceiver, as in figure 6.13. The function e(t) is the corresponding basefunction for the particular symbol and is typically of the form

)2cos(s

2)( tf

Tte cπ= , (6.2)

where cf is the carrier frequency and ST is the symbol duration time.Let the disturbance be

î

+=0

)2cos(2

)(S

S ϕπρ tfT

Eti c

][otherwise

Tttt WII , +∈ , (6.3)

_____________________________________________________________________________________91

∫ST

dt0

e(t)

r(t)=s(t)+i(t)

To detector

µS(TS)+ µI(TS)

Receivedsignal

Figure 6.13: Correlation demodulator.

where ϕ is assumed to be uniformly distributed between 0 and 2π and0≥ρ . SE is the desired signal energy per databit. Thus, the amplitude of

the disturbance signal is expressed as the amplitude of the desired signalbut scaled with ρ . The following analysis will show the convenience ofusing this way of expressing the amplitude of the disturbance signal.The output from the correlator at the sampling instant ST is

∫

∫∫

≈

+==

S

SS

0 S

S

0 S

S

S0SI

cos

)2cos(2

)2cos(2

)()(

T

T

cc

T

dtT

E

dttfT

Etf

Tdtte(t)iT

ϕρ

ϕπρπµ

][

][

][ SWSI

WI

WSI

S

SI

S

SIW

S

SW

,,

0,,

,0,

cos)(

cos)(

cos

TTTt

Tt

TTt

T

EtTT

EtTT

ET

S −∈

−∈

−∈

î

−

+=

ϕρ

ϕρ

ϕρ

(6.4)

The dominating contribution is from the first term in (6.4), i.e. if][ WSI ,0 TTt −∈ . Using this term only, we have

ϕρϕµ cos)(S

WS T

TET b≈ . (6.5)

_____________________________________________________________________________________92

1/fp

tI

TS-TS

TW

t

Disturbance signal

0

iI(t)

S

S

T

E2ρ

Figure 6.14: The disturbance signal.

If only the desired signal is detected, the output from the correlator willbe bE± if BPSK is used ( bEE =S for binary modulation schemes). Asthe analysis for BPSK is of fundamental importance even for MSK and64-QAM, this modulation scheme will be assumed for the followinganalysis. The bit error probabilit y bP for a mixture of the disturbancesignal and noise modeled as additive white Gaussian noise (AWGN)with the two-sided power spectral density of 0N /2 is now [60]

+=

2)( 0

SN

TEQP bb ϕµ , (6.6)

where bE is the signal energy per bit and Q(x) is )2/(21 xerfc .This is

due to the fact that the decision variable, from which the detector will

decide whether it was a “1” or “0” that was transmitted, will be normal

distributed with mean )( S ϕµ TEb + and variance 0N /2. By combining

(6.5) and (6.6), the error probabilit y when the symbol “1” is disturbed

by one pulse, can be written as

( )

+

=

+

= )cos1(2

2

cos

1S

W

00

S

W

ϕρϕρ

T

T

N

EQ

N

T

TEE

QeP b

bb

. (6.7)

_____________________________________________________________________________________93

TW

W

t

Tp

i I(t)

WS

2T

T

Ebρ

Figure 6.15: Periodic pulsed signal (bandpass representation).

If the symbol “0” is transmitted, the error probabilit y will be

( )

−

=

−

= )cos1(2

2

cos

0S

W

00

S

W

ϕρϕρ

T

T

N

EQ

N

T

TEE

QeP b

bb

. (6.8)

The average error probabilit y for a disturbed symbol is then

î

−

+

+

= )cos1(

2)cos1(

2

2

1

S

W

0S

W

0

ϕρϕρT

T

N

EQ

T

T

N

EQP bb

b . (6.9)

Now we just have to determine the relationship between )( Sϕµ T and theRMS value RMSV of the disturbance. As the RMS value should be de-termined with respect to the bandwidth RW of the radio receiver, theFourier series expansion of the disturbance signal is convenient to use.The disturbance signal )(I ti , see figure 6.15, can be written as

∑=∞

−∞=

+

k

tfjk

kecT

ti )2(

PI

1)( ϕπ . (6.10)

The amplitude spectral components within the main lobe are schemati-cally shown in figure 6.16 when the disturbance signal in figure 6.15 ispulse modulated by a sine wave with frequency cf . The power within

_____________________________________________________________________________________94

1/TW

1/Tp

ck

f

WR≈1/TS

WS

2

2T

T

Ebρ

fc

Figure 6.16: A schematic figure of the main lobe of the amplitudespectral components of iI(t) multiplied by a sine wave with frequency

cf .the bandwidth of the radio receiver can be calculated approximately asthe sum of the powers corresponding to the components within thisbandwidth. The response of an RMS detector at the output of a narrowband filter is analyzed in [34]. Here, a simpli fied analysis is used whichgives the same result. If SW TT << , the average power 2

RMSV within the

bandwidth of the radio receiver, see figure 6.16, is then approximately

2Sp

2W

22W

S2

p

2S

2P

2

2

1

2

21RMS RfTET

Tf

ER

TV b

b ρρ

=≈ . (6.11)

Equation (6.10) is obtained by summarizing the spectral componentswithin the bandwidth. The number of components is pS fR . In general

the response of an RMS detector to repetiti ve pulses filtered through anarrow band filter can be expressed as [34]

imppWIRMS ffTCAV ∆≈ , (6.12)

where C is a constant depending on how the detector is calibrated. IA isthe amplitude of the disturbance signal and impf∆ is the impulse power

bandwidth of the narrow band filter. If (6.12) is inserted in (6.7), weobtain

_____________________________________________________________________________________95

( )

+=

+

= ϕϕ cos

22)cos

21(

21

0

RMS

0

RMS

0 p

b

pb

b

fN

V

N

EQ

fE

V

N

EQeP . (6.13)

The total bit error probabilit y eP for the pulse modulated disturbance isdetermined by Bayes’ rule so that

( ) [ ] [ ][ ] [ ]

)14.6( ).1(2

cos22

cos22

2

1

only AWGNonly AWGNby disturbedrerro

pulseepuls aby disturbedrerro

p0

p0

RMS

00

RMS

0

Sb

Sp

b

p

b

e

TfN

EQ

TffN

V

N

EQ

fN

V

N

EQ

PP

PPP

−

+

î

−+

+=

+

=

ϕϕ

ϕ

Thus, using the RMS value, the bit error probabilit y is independent ofthe pulse duration time WT . If the disturbance level from the repeatedpulses is much larger than the noise level, equation (6.14) can be ap-proximated as

Sp

b

p

b TffN

V

N

EQ

fN

V

N

EQ p

0

RMS

00

RMS

0

cos22

cos22

2

1

î

−+

+ ϕϕ . (6.15)

Let the design BEP be 0p , S

W

T

Tx

ρ= and

,)cos1(2

)cos1(2

2

1

cos22

cos22

2

1

S

W

0S

W

0

0

RMS

00

RMS

0p

î

−

+

+

=

î

−+

+=

ϕρϕρ

ϕϕ

T

T

N

EQ

T

T

N

EQ

fN

V

N

EQ

fN

V

N

EQP

bb

p

b

p

b

(6.16)

which is just equation (6.15) without being divided by SpTf .

_____________________________________________________________________________________96

10−5

10−4

10−3

10−2

10−1

−12

−10

−8

−6

−4

−2

0

Bit error probability pp

20lo

gx

Figure 6.17: 20logx versus pP averaged over ϕ for 40 10−≥p and

SNR = 12 dB.

(We use large P for error probabilit y expressed as an equation and smallp for a certain value). In figure 6.17, 20logx versus pP averaged overϕ

is shown for 40 10−≥p and SNR = 12 dB. The slope of this curve is ap-

proximately 2.5 dB per decade of 0p . As the bit error probabilit y in-creases linearly with pf , equation (6.12) shows that if the frequency in-

creases by a factor 10, then pP must decrease by a factor 10 to obtain the

same total BEP. A decrease of pP by a factor 10 requires a decrease of x

by 2.5 dB. This requires the amplitude of the disturbance signal to de-crease by 2.5 dB. Thus, as RMSV is proportional to the disturbance ampli-tude and to the square root of pf , the total change of RMSV (6.12) will

be approximately 10 – 2.5 = 7.5 dB/frequency decade. This relationshipwill be true as long as it is possible to compensate an increase in pf by

increasing pP . As 5.0p ≤P and Spp0 RfPp = , we have the condition

S0p 2 Rpf ≥ . This condition corresponds to pf ≈130 Hz for the measured

results presented in section 6.4.

_____________________________________________________________________________________97

6.6 Conclusion

The possibilit y of using the RMS detector for emission measurementswhen digital radio systems are considered is presented. It is shown thatthe tolerated RMS value of the disturbance level for a certain bit errorprobabilit y is, in practice, independent of the pulse width of a repetiti vepulsed disturbance signal. This is because the RMS value changes withthe pulse width so that the RMS value corresponding to a certain BEPwill remain constant for different pulse widths. Furthermore, the pulserepetition frequency below which the required SIR starts to decreaserapidly (i. e. the required RMS value of the disturbance starts to in-crease) is considerably smaller than earlier published weighting curvesbased on the peak value. Consequently, the variation of the toleratedRMS value with the pulse repetition frequency of the disturbance caneasily be modeled. These properties make it possible to express themaximum allowed disturbance level in terms of the output from theRMS detector. This simpli fies the issue of determining maximum al-lowed emission limits when digital radio systems are considered. Theoverall conclusion is that the RMS detector is a promising candidate forthe development of future emission standards considering digital radiosystems as the disturbance “victim” . Up to now, the RMS detector hasnot been used in EMI measurements measurements (except for out-of-band emission of radio transmitters), even if the 2nd edition (1972) ofCISPR 1 [59] states that experience has shown that an RMS voltmetermight give a more accurate assessment of the disturbance effect onanalog radio than the QP detector does. The results presented in this the-sis strongly indicate that the RMS detector might be a proper detectoreven for digital communication systems.

_____________________________________________________________________________________98

_____________________________________________________________________________________99

7 Analysis for the jamming case

N this chapter, the narrow-band method is investigated for the jam-ming case, in which the combined effect of inherent disturbance and

jamming disturbance is investigated. In a jamming situation, inherentdisturbance will contribute to the jammers’ effort to cause damage to thecommunication link. It is therefore of great importance to be able to es-timate the consequences with respect to the vulnerabilit y to jammingwhen inherent disturbance is present.

7.1 Introduction

Classical jamming analysis [47] [48] considers the impact of the com-posite disturbance of AWGN and the jamming wave form on the com-munication link. In this thesis, interest is focused on how this jammingperformance is affected when disturbance from co-located equipment isadded. If we have inherent disturbance dominated by CW signals, theproblem is to calculate the resulting BEP for the composite of thermalnoise in the receiver, the CW disturbance signal and the jamming signal.These calculations are generally too diff icult to be an eff icient tool in

I

_____________________________________________________________________________________100

engineering applications, which is why a simpli fied analysis is required.This was done in chapter 4. If both the inherent and the jamming distur-bance could be approximated with an acceptable result according to thenarrow-band method, the calculations would be greatly simpli fied. Wewill show that the narrow-band method gives a final estimated BEP thatis close enough to the calculated value to be used in system design ap-plications. Thus, a useful method for considering inherent disturbance inthe jamming situation is obtained.

7.2 Jammers

Frequency hopping (FH) systems are considered in the jamming case.The basics for the jamming game are defined in figure 7.1 [48], where

WSS bandwidth [Hz] of the spread spectrum communication sys- tem;Rb bit rate [bits/s] from the transmitter;S signal power [W] at the input to the intended receiver;J jammer power [W] at the input to the intended receiver;PG processing gain, which is W RbSS .

Jammer

Transmitter Receiver

Hostile detector

Inherentinterference

S, J, PI, PG, WSS

WSS, Rb

WJ

Figure 7.1: The game between jammer and communication system.

_____________________________________________________________________________________101

We define two fundamental types of jammers; Gaussian noise jammersand tone jammers. Furthermore, these jammers are divided into twotypes; broad band and partial band jammers. The broad band noisejammer spreads Gaussian noise of total power J evenly over the totalrange of SSW . The equivalent single-sided noise power spectral density

JN is then

NJ

WJSS

= . (7.1)

A partial band noise jammer spreads noise of total power J evenly overa frequency range JW which is a part of SSW so that

SSJ WW ρ= , (7.2)

where 10 ≤≤ ρ . This results in a noise power spectral density of ρJN . If the jamming system has knowledge of JNEb , it is possible to

optimize ρ with respect to maximum created BEP of the communicationsystem. Another, sometimes more effective, FH jamming technique ismultitone or multiple CW jamming. In this case, the jammer divides itstotal power into distinct, equal power, random phase CW tones. Thesetones are then distributed over the spread spectrum bandwidth SSW ac-cording to different strategies. Tone jammers are more effective thanpure noise jammers on non-coherent modulation schemes, as it is easierto inject energy into those demodulators by the use of sine waves [47].In this thesis, the focus is on partial band tone jammers. This is a jam-mer which spreads random phase sine waves over a fraction ρ of thefrequencies used by the FH system. At the jammed frequencies thejamming tone is located at the carrier frequency of each hop.

7.3 Impact of disturbance on the duel betweenjammer and communication system

7.3.1 The narr ow-band method in the CW tone jammingsituation

Let the inherent disturbance be

_____________________________________________________________________________________102

cos2πfct

-sin2πfct

a(t)

a(t)

2nTb

(2n+1)Tb

Decisionlogic

r(t) ;α+

iI(t)

iJ(t)

n0(t)

Figure 7.2: The composite disturbance situation.

[ ]i tE

Tf f tb

bI I c I I() cos ( )= + +

22α π ϕ∆ (7.3)

and the jamming disturbance

[ ]i tE

Tf f tb

bJ J c J J() cos ( )= + +2

2α π ϕ∆ , (7.4)

where )(I ti and )(J ti are independent with phases uniformly distributedover [ ]0 2, π . If the thermal noise in the receiver is denoted n t0(), thedisturbance situation in Figure 7.2 appears. The calculated bit errorprobability for this situation is

P P Pb = −2 1ph ph( ), (7.5)

where [Appendix B]

_____________________________________________________________________________________103

[ [ ]

[ ] ]

P E erfcE f f

N

erfcE

N

f T

f T

f T

f Td d

b

b b

b

b

b

phI I I J J J

I I I

I

J J J

JI J

=+ +

î

=î

+−

+−

∫∫

1

2

1

81

4 2

1 4

4 2

1 4

0

2 0

2

0

2

02

2

λ ϕ λ ϕ

πα ϕ π∆

π π∆

α ϕ π∆π π∆

ϕ ϕ

ππ

( , ) ( , )

cos cos

( )

cos cos

( ).

∆ ∆

(7.6)

The disturbance contribution to the decision variable is the functions λ I

and λ J .

7.3.2 The narr ow-band method and Gaussian approxi-

mated jamming signal

If all disturbance wave forms are approximated as Gaussian distributed,we obtain (appendix B)

P erfcE

N E E

erfcSNR

SNRSIR SJR

b

b b

ph

I J

=+ +

=+ +

1

2

1

21

1 1

02 2α α

. (7.7)

Here SJR is the signal to jamming ratio which is

2J

1

α=SJR . (7.8)

SIR is the signal to disturbance ratio which is

_____________________________________________________________________________________104

2I

1

α=SIR . (7.9)

7.4 Results for the jamming case

In Figure 7.4, the BEP corresponding to equation (7.6) and (7.7) is com-pared for different relations between SNR, SIR and SJR. This is done forthe same system parameters as in chapter 5. The inherent disturbance isassumed to equal the Class B limit, which gives the desired variation inSIR. Figure 7.4 shows how the difference between estimated and calcu-lated BEP depends on the relation between SNR, SIR and SJR. The dif-ference at large separation distances is in agreement with the results inchapter 5. The difference between estimated and calculated BEP iswithin acceptable limits irrespective of the relation between SNR, SIRand SJR. Thus, approximating the two CW disturbance signals as Gaus-sian distributed gives a useful result. The conclusion is that applying

0 50 100 150 200 250 30010

−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Separation distance [m]

BE

P

SJR [dB]:

6

9

12

15

18

CalculatedEstimated

Figure 7.4: Comparison of calculated and estimated BEP for SNR =12 dB and SJR = 6, 9, 12, 15 and 18 dB. The comparison is made fordifferent separation distances to a disturbance source that equals theClass B limit.

_____________________________________________________________________________________105

the narrow-band method to the jamming situation gives satisfactoryagreement with the calculated solution. These results will be used in thenext chapter for analyzing a system example covering a jamming situa-tion.

_____________________________________________________________________________________106

_____________________________________________________________________________________107

8 Performance measures for tacticalconsiderations

N a milit ary application, the increase in BEP due to disturbance sig-nals must be interpreted to a measure that can be used for tactical con-

siderations. In this chapter, the estimated BEP is related to suggestedevaluation parameters that are useful for tactical considerations in mil i-tary applications. These evaluation parameters are applied to system ex-amples to show the usefulness of such parameters and to produce resultsthat are applicable to existing systems.

8.1 Background

In a milit ary application, the increased bit error probabilit y caused bythe inherent disturbance is not generally a measure that provides usefulinformation for a tactician. An increased BEP will always, in one way oranother, cause practical problems for the communication link. The ac-tual system application determines how these consequences will appearto the user. In a milit ary situation, the consequences for the tacticalsituation are crucial as they will degrade the combat capabilit y of a cer-tain unit [49]. Thus, to provide such useful information from an analy-sis, the BEP obtained must be related to a measure that is interpretableto tactical terms, such as operating ranges for the communication linkand the jammer. In the following sections, such measures are proposed

I

_____________________________________________________________________________________108

and applied to an example with realistic system parameters. The purposeis to suggest and apply convenient measures for tactical considerations.Furthermore, the analyses are performed on system examples with pa-rameters that are comparable to real systems. Thus, conclusions con-cerning real systems are also provided.

8.2 The impact on operating range as a measure ofperformance degradation

If no hostile jamming is present, the impact on operating range causedby inherent disturbance is a measure which can be used for tactical con-siderations. As the disturbance will cause an increase in BEP, the SNR inthe receiver must be increased to compensate for this degradation. Thiscan be done by either an increase in the output power of the transmitteror by moving the transmitter closer to the receiver. If the transmitter al-ready working with the highest available output power, a decreased dis-tance to the receiver is the only available solution. With knowledge ofthe transmission loss for the wave propagation, the reduction in operat-ing range can be estimated when the BEP caused by the disturbancesource has been determined. In [2], the reduction of operating range hasbeen determined for some typical cases. Here, some of the results arereviewed. In figures 8.1 and 8.2, examples of this measure are shownwhere the same system parameters as in chapter 5.4 are used. By as-suming that the electric field strength has a 1 2r decay, the range re-

duction to obtain a BEP of 10 3− is shown. The reduction factor R is de-termined as

Rr

r= I

0

, (8.1)

where Ir is the operating range when inherent disturbance is present,and 0r is the range in the undisturbed case. A comparison is made forSNR values 9 and 12 dB. These diagrams should be of great interest fortactical considerations as the consequences of an increased BEP in theradio receiver are shown in terms directly transferable to a real situation.The conclusion of these results is that disturbance that equals the civil-ian radiated emission limits can cause significant reductions in the oper-ating range of a digital radio system link. The milit ary emission limit,

_____________________________________________________________________________________109

0 50 100 150 2000.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Separation distance [m]

R

SNR = 12 dBSNR = 9 dB

Figure 8.1: Range reduction caused by disturbance from a distur-bance source that equals the EN55022 Class B limit.

0 50 100 150 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Separation distance [m]

R

SNR = 12 dBSNR = 9 dB

Figure 8.2: Range reduction caused by disturbance from a distur-bance source that equals the EN55022 Class A limit.

_____________________________________________________________________________________110

0 50 100 150 2000.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Separation distance [m]

R

SNR = 12 dBSNR = 9 dB

Figure 8.3: Range reduction caused by disturbance from a distur-bance source that equals the RE102 limit.

however, will not cause any problems until the separation distance be-comes very small . Furthermore, it is obvious that if disturbance sourceswith levels close to the civili an emission limits are to be co-located withdigital radio systems, some kind of shielding device is required to re-duce the disturbance. Thus, saving money by using civili an electronicswill create new costs which can be paid for in two ways; either in mate-rial or in performance degradation of the communication system.

8.3 The ” jamming loss” as a measure of an in-creased vulnerabili ty to a hostile jammer

8.3.1 Definition of j amming loss

In a jamming situation, the increased bit error probabilit y caused by theinherent disturbance is not generally a measure that gives useful infor-mation for tactical considerations. A measure which is interpretable totactical terms, such as operating ranges for the jammer, is needed.Therefore, we introduce a measure denoted jamming loss for the situa-

_____________________________________________________________________________________111

tion where both jamming and inherent disturbance are present. Thejamming loss is defined as the required increase in E Nb J to achieve aspecific bit error probabilit y in the communication system [3]. Thejamming loss should not be interpreted as a coding gain, which is usu-ally defined as the difference in the required SNR for a certain BEP be-tween the uncoded and coded system. However, the jamming loss is de-rived from two SNR values for the coded case, which is different fromhow the coding gain is derived. The jamming loss, schematically shownin figure 8.4, can, with knowledge of the wave propagation propertiesfor the specific situation, be interpreted to how much the jammer’s op-erating range can increase compared to the case where no disturbance ispresent. This increase will be referred to as an increase factor. For ex-ample, a jamming loss of 10 dB would increase the operating range ofthe hostile jammer by about 78 % if a 1 4r decay for the power is used.Of course, the jamming loss could also be used to derive the corre-sponding decrease in operating range for the communication link. Thedecision as to how the jamming loss should be used in system designdepends on how the system specification is written. In this thesis, theapplication to the jammer’s operating range is used. In the next section,the use of the jamming loss parameter is shown by an example in whichthe radio system uses an error correcting code to handle a hostile jam-mer.

Jamming loss

BEP

Eb/NJ

With interference

Without interference

Figure. 8.4: The definition of jamming loss.

_____________________________________________________________________________________112

8.3.2 Example of j amming loss for a system using errorcorrecting code

To ill ustrate the use of the jamming loss evaluation parameter, an exam-ple with realistic system parameters is analyzed. The system example isbased on a common model of the duel between jammer and communi-cation system [47]. The various system parameters for this example,shown in figure 8.5, are comparable to those for present combat radiosin the frequency band 30 - 88 MHz, such as the Ra 180 used in theSwedish armed forces. For each value of SJR, the jammer chooses tojam a fraction ρ of the total frequency band. In each 25 kHz radio chan-nel, a sine tone with random phase is transmitted as jamming distur-bance. In this example the terms SNR, SIR and SJR will be used in cer-tain cases to improve the readabilit y. All these ratios are defined perdata bit, see equation (8.3)

Two decoding cases are compared. The first occurs when side informa-tion is not available, i.e. the receiver does not know if a specific hop wasjammed or not. The other case is when side information is available, i.e.the receiver knows if a specific hop was jammed or not.

Jammer

Transmitter Receiver

Hostile detector

Inherentinterference

WSS, Rb

WJ

MSK25 kHzNoise figure ==10 dB30 - 88 MHz(9,1) repetitioncode. No sideinformationavailable.SNR = 15 dB

Multitonepartial banduses SJR foroptimization

Knowledge of SJR

Interference levels equal the limitsin an emission standard

SJR

SIR

SNR

Figure 8.5: System parameters for the example.

_____________________________________________________________________________________113

We use the narrow-band method extended to the jamming case (eq. 8.7)to estimate BEP. This gives a total BEP of

P P P P Pb = ′ − ′ + − ′′ − ′′ρ γ γ ρ γ γ2 1 1 2 1ph ph ph ph( )( ( )) ( ) ( )( ( ), (8.2)

where

P erfcE

N N N

erfcSNR

SNRSIR SJR

bph

I J

( )′ =+ +

=+ +

γ 1

2

1

21

1 1

0

, (8.3)

and

P erfcSNR

SNR

SIR

ph( )′′ =+

γ 1

21

. (8.4)

Furthermore, the jammer is assumed to optimize the value of ρ for eachvalue of SJR. For non-coherent binary frequency shift keying, this opti-mized value ∗ρ can be determined analytically [3]. This is not possible

for MSK, thus ∗ρ has to be determined numerically. The resulting *ρ is[50]

8201

82082.0

î

≤=∗

.SJR

.SJR> SJR

ρ (8.5)

Slow frequency hopping is assumed, which means that at least one datasymbol is transmitted per frequency hop. Interleaving is used so thateach symbol will have an independent chance of being jammed. Each

_____________________________________________________________________________________114

code word consists of nine symbols. The symbol error probabilit y PS isthus according to equation (8.2), but with

P erfc

SNR

SNR

SIR SJR

ph( )′ =+ +

γ 1

29

19

1 1, (8.6)

and

P erfc

SNR

SNRSIR

ph( )′′ =+ ⋅

γ 1

29

19

. (8.7)

In a repeat code, only two 9-symbol codewords are available. In the(9,1) repeat code these codewords are 000000000 and 111111111 . Ifno side information is available, i.e. the receiver does not know whethera specific hop (codeword symbol) was jammed, a majority decision ismade over the demodulated codeword symbols. If a codeword is sub-jected to disturbance, the decoder selects the codeword within the clos-est Hamming distance. If the symbol error probabilit y is denoted PS,then the bit error probabilit y for the (9,1) repeat code is

Pi

P Pbi

i i=

−=

−∑9

15

99

S S( ) (8.8)

If side information is available, the receiver knows if a specific hop wasjammed. Here, the assumed strategy is to make the decision on the un-jammed codeword symbols only. If all symbols are jammed, a decisionis made over all codeword symbols. If a symbol is jammed, the phaseerror probabilit y for that symbol is

++

=ρJI0

phj9

2

1

NNN

EerfcP b . (8.9)

If a symbol is not jammed, the phase error probabilit y for that symbol is

_____________________________________________________________________________________115

P erfcE

N Nb

phuI

=+

1

2

9

0

. (8.10)

If an even amount of the symbols is not jammed, and we have an equalHamming distance between the two alternative codewords, the decodermakes the decision randomly. Let Ai denote the event that i of 9 sym-bols are not jammed. This gives the resulting bit error probabilit y as

[ ] [ ] [ ] [ ]

[ ] [ ]

P A A A A

A A

b ii

i

ii

i

= =

=

=

=

∑

∑

Pr error Pr Pr error Pr

Pr error Pr

0

9

0 0

1

9

.

(8.11)

Inserting the variables gives [4]

[

[ ] ].)1(22

12mod)1(

)1()1(9

)1(9

2/2

5

9

1

9

99

5

9

iphu

iphu

jii

j

ji

i

j

jphj

j

jphjb

PPi

ii

j

i

j

PPj

P

−

⋅++

−

−

+

−

=

−

==

−

−

=

∑∑

∑

ρρρρ

ρ

(8.12)

The two decoding cases are compared in figure 8.6 when no inherentdisturbance is present. Having side information, of course, improves theperformance against the jammer. The bit error probabilit y averaged overall channels is presented in figure 8.7 and 8.8 when inherent disturbanceis present. The disturbance source equals the RE102 limit and is located30 m from the radio receiver.

The inherent disturbance source gives an increased BEP which can beinterpreted as a degradation of the signal protection device, i.e. the errorcorrecting code. The disturbance also increases the level of non-reducible bit error probabilit y for high values of the SJR. In figure 8.9,the jamming loss in dB is presented for the same situation. The increaseof the non-reducible BEP causes the jamming loss to go to infinity as it

_____________________________________________________________________________________116

is our inherent disturbance that gives the BEP limit when the jammer isfar away from the radio receiver. The jamming loss is larger when sideinformation is available. This is due to the fact that the relationship be-tween BEP and SJR becomes steeper when the signal protection be-comes more advanced. It is, however, important to note that the totalSJR required to obtain a certain BEP is, of course, lower when side in-formation is available.

The tactical consequence is analyzed by the use of an increase factor forthe jammer. The increase factor is defined as

equipment locatedco from ceinterferen no with Range

elctronics locatedco from ceinterferen with RangeD -

-R = (8.13)

The increase factor of the operating range for the jammer is shown infigure 8.10. The results are for a 1 4r decay of the received jammingpower.

Thus, the jamming loss gives a measure of the degradation of the signalprotection devices. This jamming loss can be related to a correspondingincrease in the operating range for the jammer, which affects the tacticalsituation.

Of course, the jamming loss could also be used to derive the corre-sponding decrease in operating range for the communication link. Thiscould be of interest if the system´s specification specifies the jammingthreat in terms of a particular physical geometry. In that case, the dis-tance between the radio receiver and the jammer is fixed and an analysisof how the range of the communication link will be reduced is of inter-est to the system designer.

The conclusion is that relating the BEP to jamming loss and the in-crease in the operating jamming range gives valuable information whenevaluating the tactical consequences of how inherent radiated distur-bance will affect the duel between jammer and communication system.Thus, with these evaluation parameters it is possible to compare the im-pact of different standard emission limits and, for instance, make atrade-off between economics and the tactical demands on a complexsystem.

_____________________________________________________________________________________117

0 5 10 15 20 25 30 35 4010

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

SJR [dB]

bit e

rror

pro

babi

lity

no side informationside information

Figure 8.6: Average bit error probability without inherent disturbancefor the two decoding cases.

0 5 10 15 20 25 30 35 4010

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

SJR [dB]

Bit

erro

r pr

obab

ility

Figure 8.7: Average bit error probability with and without (dashed) in-herent disturbance for the system example. The disturbance source islocated 30 m from the radio receiver. No side information available.

_____________________________________________________________________________________118

0 5 10 15 20 25 30 35 40

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

SJR [dB]

Bit

erro

r pr

obab

ility

Figure 8.8: Average bit error probability with and without (dashed) in-herent disturbance for the system example. The disturbance source islocated 30 m from the radio receiver. Side information available.

10−7

10−6

10−5

10−4

10−3

10−2

10−1

0

5

10

15

20

25

30

35

BEP requirement

Jam

min

g Lo

ss [d

B]

no side informationside information

Figure 8.9: Comparison of jamming loss for the two decoding cases.

_____________________________________________________________________________________119

RD

10−7

10−6

10−5

10−4

10−3

10−2

10−1

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

no side informationside information

BEP requirementFigure 8.10: The increase in operating range for the jammer is shownfor the two decoding cases.

_____________________________________________________________________________________120

_____________________________________________________________________________________121

9 Discussion

N this thesis, a method of estimating the performance of digital radioreceivers in the presence of inherent electromagnetic disturbance has

been suggested. Current standard emission measurement methods aredeveloped with respect to analog receivers, thus a connection to digitalradio receivers has to be established. For milit ary applications, the needof such a method has increased as a consequence of the desire to usecheap civili an electronics in the armed forces. Disturbance levels fromcivili an electronics are considerably higher than from milit ary-specifiedelectronics. However, the financial realiti es favor dual use, which iswhy the disturbance problem with these electronics has to be quantified,not only realized. This quantification is necessary in system design ap-plications so that the consequences of co-locating civili an electronicswith milit ary digital radio systems can be analyzed in the early designphase. This is a complex problem for which a solution is suggested forsystem design applications, where more or less rough estimations areneeded in the early design process. In that case, the question is how tochoose maximum allowed radiated emission levels on electronic equip-ment co-located to digital radio systems. It has been shown that themethod gives useful results for disturbance sources dominated by peri-odic signals. A disturbance source model has been proposed for thedominating radiated disturbance signals from personal computers. It isshown that the dominating disturbance wave form characteristics arise

I

_____________________________________________________________________________________122

from periodic signals from local oscill ators in the circuit boards. Themodel has been justified with measurements, and the overall conclusionis that personal computers designed with current technology can betreated with this model. With current technology we mean the way ofusing local oscill ators to generate the different clock signals in the com-puters. The method solves the problem of translating a disturbance levelexpressed in terms of a detector output from a standard radiated emis-sion measurement, to the bit error probabilit y of a digital radio receiverexposed to this disturbance. It is shown that for disturbance dominatedby periodic signals with pulse repetition frequencies greater than thebandwidth of the radio receiver, the estimated BEP is close enough tothe real value to be useful in system design applications. It has also beenshown that for the disturbance wave forms studied, the estimated BEPfor most cases can be considered as a worst case value. This conclusionis not only limited to MSK but holds at least for non-coherent FSK andDPSK.

By the application of the suggested method on realistic system exam-ples, several practical conclusions can be drawn. Firstly, the resultsshow large differences in performance degradation between levels thatequal milit ary and civili an radiated emission limits. Levels that equalcivili an limits start to affect the radio receiver at separation distances inthe order of one hundred meters, whereas levels that equal milit ary lim-its will not cause any problems until the separation distances becomesmaller than approximately ten meters. Secondly, another practical con-sequence is that some kind of shielding device will be needed if civili anelectronics have to be co-located to digital radio systems. This will i n-crease the cost of the total system, which means that the expected sav-ings from using civili an instead of milit ary electronics could be heavilyreduced or, in some cases, negligible.

Furthermore, a contribution has been made to the work of developingradiated emission standards for digital communication receivers as thedisturbance “victim” . A key issue for the next generation emission stan-dards is the choice of EMI detector. A detector with a response that canbe related to the bit error probabilit y is preferable. We have shown thatthe RMS detector is a promising candidate for this purpose. The RMSvalue for a repetiti ve disturbance signal corresponding to a certain BEPcan easily be modeled. This has been shown for BPSK, MSK and 64-QAM. It is shown that the tolerated RMS value of the disturbance levelfor a certain bit error probabilit y is, in practice, independent of the pulse

_____________________________________________________________________________________123

width of a repetiti ve pulsed disturbance signal. This is because the RMSvalue changes with the pulse width so that the RMS value correspondingto a certain BEP will remain constant for different pulse widths. Fur-thermore, the pulse repetition frequency below which the required SIRstarts to decrease rapidly (i. e. the required RMS value of the distur-bance starts to increase) is considerably smaller than earlier publishedweighting curves based on the peak value. Consequently, the variationof the tolerated RMS value with the pulse repetition frequency of thedisturbance can easily be modeled. Further investigations have to bemade to see if this is true even for other interesting modulation schemes.However, the overall conclusion is that the RMS detector is a promisingcandidate for the development of future emission standards consideringdigital radio systems as the disturbance “victim” . Up to now, the RMSdetector has not been used in EMI measurements (except for out-of-band emission of radio transmitters) even if the 2nd edition (1972) ofCISPR 1 [59] states that experience has shown that an RMS voltmetermight give a more accurate assessment of the disturbance effect onanalog radio than the QP detector does. The results presented in this pa-per strongly indicate that the RMS detector might be a proper detectoreven for digital communication systems.

In a milit ary application, the increased bit error probabilit y caused bythe inherent disturbance is not generally a measure that provides usefulinformation for a tactician. An increased BEP will always, in one way oranother, cause practical problems for the communication link. There-fore, suggestions for how to interpret the BEP to measures useful fortactical considerations have been made for situations both with andwithout hostile jamming present. The conclusion is that relating the BEPto jamming loss and the increase of the operating jamming range givesvaluable information when evaluating the tactical consequences of howinherent radiated disturbance will affect the duel between jammer andcommunication system. If no hostile jamming is present, the range re-duction of the communication link is suggested as an evaluation pa-rameter of tactical interest. It is shown that disturbance that equals thecivili an radiated emission limits can cause significant reductions in theoperating range of a digital radio system link. The milit ary emissionlimit, however, will not cause any problems until the separation distancebecomes very small . By relating the estimated BEP to the suggestedevaluation parameters, a useful tool for system design is created. Withthese evaluation parameters, it is possible to compare the impact of dif-ferent standard emission limits and, for instance, make a trade-off be-

_____________________________________________________________________________________124

tween economics and the tactical demands on a complex system. Thesuggested method of estimating the BEP is based on the approximationof the disturbance as having a Gaussian amplitude distribution. Even ifthis is a widely used approximation, no general conclusions can bedrawn if the bit error probabilit y is the parameter of interest. Thus theconsequences of using this approximation must be investigated forevery case it is used in. The Gaussian approximation of other distur-bance wave forms than those used in this thesis is not investigated,therefore great care must be taken in using the suggested method onother wave forms than those treated in this thesis. On the other hand,electronics whose disturbance is dominated by periodic signals consti-tute an important category of disturbance sources that are co-located inthe vicinity of milit ary radio systems. This fact should make the methodwell suited for widespread use in systems design applications. So far,the method suggested has only been investigated for narrow band radioreceivers, i. e when the bandwidth of the radio receiver is smaller thanthe pulse repetition of the periodic disturbance. The development to-wards wide band radio systems will require an investigation of themethod suggested for the case when the bandwidth of the radio receiveris greater than the pulse repetition frequency.

The BEP has been chosen as a performance measure of the digital radiosystem. In real systems other measures can be of interest, such as desen-sitization and reciprocal mixing. These hardware-related effects havenot been taken into account in the analyses. However, methods analyz-ing such effects are widely known, therefore such analyses can be per-formed whenever required. Thus, the BEP as a performance measure isuseful when the hardware effects can be either treated separately or ne-glected. The overall conclusion of the results in the thesis is that amethod of dealing with current emission standards as well as a sugges-tion for future emission standards have been proposed.

Suggested topics for future work

From the discussion above, several topics for further research can besuggested. Firstly, the limitations of the method proposed could be fur-ther investigated. Here, the sensitivity to other disturbance models thanthose used should be of special interest. Secondly, the application of themethod on broad band radio systems should be of interest to create use-ful knowledge for the coming development of the next generation of

_____________________________________________________________________________________125

milit ary radio systems. As a consequence of dual use, it is li kely to as-sume that the third generation of civili an mobile radio systems will playan important role even for future milit ary radio systems. Here, it couldbe of interest to focus on how the access method rather than a modula-tion scheme is affected by inherent disturbance from co-located elec-tronics. Therefore, it could be of particular interest to investigate theconsequences of co-locating radiated disturbance sources with wideband code division multiple access (W-CDMA) systems.

Furthermore, the contribution to the work of developing next generationradiated emission standards could be further investigated for othermodulation schemes of interest. Another question is how error correct-ing codes should be handled in the work of determining maximum al-lowed limits for radiated disturbance. Throughout this thesis only un-coded systems have been considered. The reason for this is that it isdoubtful whether the error correcting capacity should be used for thiskind of disturbance. The error correcting codes are implemented to han-dle other kinds of interference, which is why it is hazardous to take thatcapacity into account for treating inherent interference. If the contribu-tion from error correcting codes should be considered, a measure of howmuch of the error correcting capacity has been used must be developed.This is necessary to avoid that no margin to other disturbance is leftwhen inherent interference is present. This is a hot topic for future re-search.

_____________________________________________________________________________________126

_____________________________________________________________________________________127

Appendix A

BEP FOR MSK SUBJECTED TO A MIXTUREOF CW

AND AWGN DISTURBANCE

r(t)

a(t)

cos2πfct

-sin2πfct

a(t)

2nTb

(2n+1)Tb

Decisionlogic

<α

Figure A1: Parallel differential MSK receiver.

In [51], MSK modulation is analyzed for AWGN and CW disturbance,without considering the memory introduced, and with an MSK receiverthat does not use differential encoding. For instance, the BEP obtainedin [51] for AWGN disturbance only is the same as for binary-shift-keying (BPSK), which differs from the BEP presented in [44].

Let the CW disturbance be expressed as

[ ]i tE

Tf f tb() cos ( )= + +

22α π ϕc i∆ , (A1)

_____________________________________________________________________________________128

where α is a scaling factor related to the MSK signal amplitude. A fre-quency shift, ∆f , from the carrier frequency is incorporated in additionto an arbitrary phase shift ϕ i which is a stochastic variable uniformlydistributed over [0, 2π]. The interfering signal i(t) at the input to the fil-ter a(t) see figure A1, will be

.)24cos(

)2cos(2

2

1

2cos))(2cos(2

)(

ic

i

cic

+∆++

+∆=

+∆+=′

ϕππϕπ

α

πϕπα

ftf

ft

T

E

tftffT

Eti

b

b

b

b

(A.2)

When this signal is passed through the filter, the last term will vanishduring the convolution as long as bTf 1

c >> . The impulse response of the

filter is

a t T

t

Tt T

b bb()

cos= ≤

î

2

20

π

otherwise. (A.3)

The disturbance contribution, λ ϕ( , )∆f i , after the filter, a(t), at the sam-pling time t = 0, will t hen be

.cos2cos)161(

4

2cos

2

1)2cos(

2),(

i22

ii

ϕππ

α

τπτϕτπαϕλ

b

b

b

bb

T

Tb

b

fTTf

E

dTT

fT

Ef

b

b

∆∆−

=

+∆=∆ ∫− (A.4)

If we also have AWGN disturbance (such as thermal noise in the re-ceiver), the decision variable for the phase decision will be normallydistributed with mean µ λ ϕ= +E fb ( , )∆ i and variance N0 2. The

resulting average phase error probabilit y is the mean value over [0, 2π],which gives

_____________________________________________________________________________________129

[ ] ,)4(1

2coscos41erfc

41

),(erfc

2

1

i2i2

00

0

iph

ϕππ

πϕαπ

ϕλ

πd

fT

fT

N

E

N

fEEP

b

bb

b

∆−

∆+=

î

∆+=

∫(A5)

which finally gives the bit error probabilit y as P P Pb = −2 1ph ph( ).

_____________________________________________________________________________________130

_____________________________________________________________________________________131

Appendix B

BEP FOR THE JAMM ING SITUATION

Let the inherent disturbance be

[ ]i tE

Tf f tb

bI I c I I() cos ( )= + +2

2α π ϕ∆ , (B.1)

and the jamming disturbance

[ ]i tE

Tf f tb

bJ J c J J() cos ( )= + +

22α π ϕ∆ , (B.2)

where i tI() and i tJ() are independent with phases uniformly distributedover [ ]02, π . If the thermal noise in the receiver is denoted n t0(), thedisturbance situation in Figure B.1 appears. The calculated bit errorprobabilit y for this situation is

P P Pb = −2 1ph ph( ), (B.3)

where

[ [ ]

[ ] ] .)4(1

2coscos4

)4(1

2coscos41erfc

41

),(),(erf

2

1

JI2J

JJJ

2I

III

0

2

0

2

0

0

JJJIIIph

ϕϕππ

πϕα

πππϕα

π

ϕλϕλ

π π

ddTf

Tf

Tf

Tf

N

E

N

ffEcEP

b

b

b

bb

b

∆−∆+

∆−∆+

î

=

î

∆+∆+=

∫ ∫ (B.4)

The disturbance contribution to the decision variable is the functions λ I

and λ J .

_____________________________________________________________________________________132

cos2πfct

-sin2πfct

a(t)

a(t)

2nTb

(2n+1)Tb

Decisionlogic

r(t) =α+

iI(t)

iJ(t)

n0(t)

Figure B.1: The composite disturbance situation.

The corresponding BEP is denoted Pb CWCW, . If )(I ti is approximated as

additive white Gaussian noise with the same average power, the averagephase error probabilit y is

[ ]

[ ] .)4(1

2coscos41

1erfc

4

1

)4(1

2coscos41erfc

4

1

),(erfc

2

1

J2I

IIJ2

0

J2I

IIJ2I0

2

0

2I0

IIIph

ϕππ

πϕαπ

ϕππ

πϕααπ

α

ϕλ

π

π

dTf

Tf

SIR

SNRSNR

dTf

Tf

EN

E

EN

fEEP

b

b

b

b

b

b

b

b

î

∆−

∆++

=

î

∆−

∆++

=

î

+

∆++=

∫

∫

(B.5)

In equation (B.5), the average disturbance power is Ebα I2 . However, the

true contribution to the decision variable at the sampling instant, for asine wave with frequency equal to the MSK carrier frequency (equation(A.3), is

λ ϕα

πϕ( , ) cos0

4I

II=

Eb , (B.6)

_____________________________________________________________________________________133

with the average power α πI2 22Eb . However, the Gaussian approxima-

tion uses the average power measured before demodulation. We assumethat the EMI detector is calibrated in terms of the RMS value of a sinewave. This means that the output from the EMI detector for i tI() isα I E Tb b , which gives an average power of α I

2 E Tb b . The corre-sponding approximated disturbance power spectral density within theMSK receiving filter a(t) is therefore Ebα I

2 if the bandwidth of a(t) isapproximated as 1 Tb . This approximation can be justified by studyingthe Fourier transform A(f) of a(t). Using the definition of the Fouriertransform gives

( )

A fT

t

Te dt

T

e

fT

j ft

T T

t

T

Tb

Tb

T T

fT

fT

bTb

Tb

b

j ft

b

j ft

b

b b b

b b

b

b

( ) cos

cos sin

cos.

=

=−

− +

=−

−

−

−

−

∫2

2

2

44

22 2 2

1

2

2

44

2

2

2 22

2

2 22

2

π

ππ

ππ π π

π π

ππ

π

π

(B.7)

In figure B.2, the normalized A f( )2 is shown in decibels. If the band-

width is approximated as f Tb= 1 , the first and half of the second lobeare covered, therefore the approximation is considered reasonable. If alldisturbance wave forms are approximated according to the narrow-bandmethod, we obtain

.11

1

erfc2

1

erfc2

12J

2I0

ph

++

=

++=

SJRSIRSNR

SNR

EEN

EP

bb

b

αα

(B.8)

_____________________________________________________________________________________134

A f( )2 [dB]

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−80

−70

−60

−50

−40

−30

−20

−10

0

10

f Tb/

Figure B.2: The power transfer function of a(t).

Here SJR is the signal to jamming ratio which is

SJR =12α J

. (B.9)

SIR is the signal to disturbance ratio which is

SIR =12α I

. (B.10)

_____________________________________________________________________________________135

Appendix C

LIMITS FOR MAXIMUM ALL OWED ELEC-TRIC FIELD STRENGTHS IN STANDARDS

USED

Electric field strength [ ]dB V / mµ

104

106

108

1010

0

10

20

30

40

50

60

70

Class A

Class B

RE102

frequency [Hz]

Figure C.1: EN55022 radiated emission limits at 10 m distance fromthe device [14]. RE102, army (internal and external) and navy and airforce (external) transformed from r = 1 m [38] to 10 m by 1 r decay.

_____________________________________________________________________________________136

_____________________________________________________________________________________137

Appendix D

ANALYSIS OF PULSED DISTURBANCE WITHPULSE REPETITION FREQUENCY < WR FOR MSK

tI

Tb-Tb

TW

t

Interference signal > 2Tb

Figure D1: Pulsed sine wave disturbance, with pulse duration lessthan the bit duration and a pulse repetition frequency less than the bitrate.

In the case where a pulsed disturbance is disturbing several informationsymbols per disturbance pulse, equation (5.10) can be used. This as-sumption, however, is valid only when the disturbance pulse duration

WT is either equal to or much greater than the bit duration bT . If thedisturbance pulses are shorter than the bit duration bT , and the pulserepetition frequency is lower than the bit rate, the bit error probabilit ycannot be determined so easily. Instead it has to be determined through amore detailed analysis of how the decision variable in the detector is af-fected. Furthermore, the output from the emission measurement is alsoconsiderably more complex to determine for this kind of pulsed distur-bance. Hence, the combined effects in the radio and in the EMI receiver

_____________________________________________________________________________________138

are a complex problem. For simplicity, we assume ∆f = 0. Let the dis-turbance signal be

[ ]

î

+≤≤+−=otherwise0

)(2cos2

)( WIIIIcII

TtttttfT

Eti

b

b ϕπα , (D.1)

where It is the starting time for the pulse and is assumed to be a sto-chastic variable equally distributed [ ]bb TTT ,W −− , see figure. D.1. Aftermultiplication with tfcπ2cos , the disturbance contribution ),( II ϕλ t tothe decision variable at the output of the filter a(t), at the sampling in-stant t = 0, will be

[ ]

î

≤≤−

−<<−

−−

−+−

−≤≤−++−

=

−∫≈

+∫ −=

−

∞∞−

∞∞−

bTtTbT

TbTtbT

T

ttf

E

T

t

T

Tttf

E

bTtTbTT

Tttf

E

dTT

tfT

E

dTT

ftfT

Et

b

b

bb

b

b

b

bbb

b

bbb

b

I

I

IIcI

I

IWIIcI

I

IWI

IcII

IcII

cIIcIII

W

W

],2

sin1)[2cos(2

],2

sin2

)()[sin2cos(

2

W],2

)(sin1)[2cos(

2

2cos

1)2(cos

2cos

2

12cos2)(2cos

2),(

ππϕπ

α

πππϕπ

α

ππϕπ

α

τπτπϕα

τπτπϕτπαϕλ

(D.2)

The corresponding average phase error probabilit y for a mixture ofAWGN and the pulsed CW is

_____________________________________________________________________________________139

.),(

erfc

),(erfc

),(erf

)2(4

1

),(erf

2

1

2

0II

0

II

2

0II

0

II

2

0II

0

II

W

0

IIph

W

W

W

∫ ∫

∫ ∫

∫ ∫

−

−

−

−

−−

++

++

î

+−

=

î

+=

π

π

π

ϕϕλ

ϕϕλ

ϕϕλ

π

ϕλ

b

b

b

b

b

b

T

TT

b

TT

T

b

T

TT

b

b

b

ddtN

tE

ddtN

tE

ddtN

tEc

TT

N

tEcEP

(D.3)

As the disturbance pulse does not cover a whole bit interval, we willhave different phase error probabiliti es depending on the relation be-tween pulse repetition frequency pf and bit duration bT . In general, the

bit error probabilit y can be determined as P P Pb = −2 1ph ph( ). In our

0 Tb 2Tb 3Tb 4Tb 5Tb 6Tb 7Tb 8Tb

Pf1 Pf2 PfSNR Pf2 Pf1 Pf2 PfSNR Pf2 Pf1

Phaseerrorproba-bil ities

Disturbance pulse

Figure D2: The phase error probability depends on the ratio between

pf and R.

_____________________________________________________________________________________140

Bit error pro babili ty EquationP12 Pf1(1- Pf2)+ Pf2(1- Pf1)

P22 2 Pf2(1- Pf2)

P2SNR Pf2(1- PfSNR)+ PfSNR(1- Pf2)

PSNR 2 PfSNR(1- PfSNR)

Table D1: Definition of phase error probabilities.

case, the phase error probabiliti es will depend on the sampling instant,see figure D2. Recalli ng that a bit error occurs if one of two successivephase decisions are in error, the bit error probabiliti es for the differentcombinations of phase error probabiliti es are defined as in table D1. De-pending on the relation between the pulse repetition frequency pf and

the bit rate R, the average bit error probabilit y can be expressed as a lin-ear combination of the error probabiliti es in table D.1 such as

( )SNR2SNR2212

1dPcPbPaP

ePb +++= , (D.4)

where the constants are according to table D.2. The output from the EMImeasurement for repetiti ve pulses is shown in table 2.1. The underlyinganalysis [33] for these equations is rather complex and requires certainassumptions to be made. The basic assumption is that the pulse duration ismuch less than the time period of the repetiti ve interference. Under thisassumption, the relation between the output from the EMI measurement andthe amplitude of the disturbance signal )(I ti is

fp a b c d e

R/2 2 0 0 0 2R/3 2 1 0 0 3R/4 2 0 2 0 4R/5 2 0 2 1 5R/6 2 0 2 2 6R/n 2 0 2 n-4 n

Table D2: The constants in equation (D.4) for different pf >

_____________________________________________________________________________________141

2 2 2E

T T P WEb

b W

ααI

Mimp R≈

( ), (D.5)

where RE is the output of the EMI measurement using the quasi-peakdetector. The other variables are defined in chapter 2. By combiningequation (D.4) and (D.5), the bit error probabilit y can be estimated.

_____________________________________________________________________________________142

_____________________________________________________________________________________143

Appendix E

ANALYSIS OF PULSED DISTURBANCE WITHPULSE REPETITION FREQUENCY < WR

FOR 64-QAM

In [42], the basic principles of determining the error probabilit y for co-herent detection of rectangular M-ary QAM is presented. The key is totreat the QAM signal as generated by two PAM signals impressed onphase-quadrature carriers. Rectangular QAM-signal constellation isused as this is the most frequently used in practice [42]. In the case inwhich kM 2= and k is even, the QAM signal constellation is equivalentto two PAM signals on quadrature carriers, each having 2/2kM = sig-nal points. The symbol error probabilit y MP of M-ary QAM withAWGN with two-sided power spectral density 20N is

2)1(1MM PP −−= , (E.1)

where

−

−=0

av

1

3)

11(2

N

E

MQ

MP

M (E.2)

is the error probabilit y of M -PAM and avE is the average symbolenergy. It is assumed that all amplitude levels are equally li kely a priori,which gives an error if the disturbance contribution to the decision vari-able exceeds half the distance between too amplitude levels. The sametechnique as in section 7.5 for BPSK is used to obtain the contribution

)( Sϕµ T from the pulsed disturbance to the decision variable after thedemodulator. Using the result from equation (7.4), the contribution

)( Sϕµ T from the pulsed disturbance gives an error probabilit y of

+

−−=0

Sav )(1

3

)1

1(2N

TM

E

QM

PM

ϕµ, (E.3)

_____________________________________________________________________________________144

where

][

][

][ .,,

0,,

,0,

cos)(

cos)(

cos

)(

SWSI

WI

WSI

S

avIIS

S

avIIW

S

avIW

S

TTTt

Tt

TTt

T

EtTT

EtTT

ET

T

−∈

−∈

−∈

î

−

+=

ϕα

ϕα

ϕα

ϕµ (E.4)

The disturbance signal )(ti is defined as

î

+=0

)2cos(2

)(S

avI ϕπα tf

T

Eti c

][otherwise

Tttt WII , +∈ . (E.5)

Using the properties for M -PAM, each signal is represented geometri-cally as M one-dimensional signal points with values

mgm AEs2

1= , m = 1,2,………, M (E.6)

where dMmAm )12( −−= and 2d is the distance between two adjacentsignal points. The demodulator is assumed to consist of a matched filterfollowed by a quantizer from which the received signal amplitude is es-timated. The estimate is compared to ( 1−M ) thresholds with a euclid-ean distance of gEd 2 , where gE is the energy of the basic signal pulse

g(t). The output from the demodulator when disturbance is present is

)()(2

1S tnTAEr mg ++= ϕµ , (E.7)

where n(t) is the contribution from the thermal noise in the receiver.Here, n(t) is modeled as AWGN. An error occurs if the quantity

)()( S tnT +ϕµ is greater than half the distance between signal points. Thisgives equation (E.3). The relation between bit error probabilit y bP andsymbol error probabilit y cannot be obtained in general. However, for

_____________________________________________________________________________________145

certain cases approximate results can be obtained. If the symbols are as-signed according to Gray coding, such a result can be determined ob-serving that for each symbol error in the set, all adjacent symbol errorscause only a single bit error [66]. Thus, since the number of bits/symbolis M2log , then for large SNR we have the simple approximate resultthat

k

P

M

PPb 2log

S

2

S =≅ . (E.7)

Consequently, bP is approximately a linear function of SP .

_____________________________________________________________________________________146

_____________________________________________________________________________________147

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_____________________________________________________________________________________155

Radio Communications Systems Lab.Dept. Of Signals, Sensors and SystemsRoyal Institute of TechnologyS-100 44 STOCKHOLMSWEDEN

TRITA-S3-RST-0007ISSN 1400-9137ISRN KTH/RST/R -- 00/07 --SE