handbook of position location (theory, practice, and advances) || positioning in lte

1081

Handbook of Position Location: Theory, Practice, and Advances, First Edition.Edited by Seyed A. (Reza) Zekavat and R. Michael Buehrer.© 2012 the Institute of Electrical and Electronics Engineers, Inc.Published 2012 by John Wiley & Sons, Inc.

CHAPTER 32

POSITIONING IN LTE Ari Kangas , 1 Iana Siomina , 2 and Torbj ö rn Wigren 1

1 WCDMA RAN System Management, Ericsson AB, Stockholm, Sweden 2 Ericsson Research, Ericsson AB, Stockholm, Sweden

THIS CHAPTER describes the positioning standard for the long - term evolution

(LTE) cellular system. First, a review of the LTE architecture and air interface is

given. The chapter then proceeds with a discussion of positioning requirements,

positioning architectures, and signaling. Service discrimination is then addressed

by a description of how positioning method sequences and prior information can

be constructed and confi gured. The coordinate systems and the transformations

used in positioning systems are described in detail. Thereafter, the backbone cell

ID method is discussed. This method is often augmented with timing advance

(TA) and angle - of - arrival (AOA) information in the enhanced cell identity

( E - CID ) class of methods. Two approaches to fi ngerprinting positioning are

described: the pattern matching method and the self - learning adaptive enhanced

cell ID ( AECID ) method. The LTE standard also supports a downlink (DL)

observed time difference of arrival ( OTDOA ) method, which performs hyperbolic

trilateration on dedicated DL signals. A related uplink (UL) method (uplink time

difference of arrival, U - TDOA ) is currently being added to the standard. Finally,

the satellite navigation functionality provided by the assisted global navigation

satellite system (A - GNSS) is discussed. Since each positioning method generates

positioning information in its own native format, the LTE system has inherited the

seven reporting formats of the Global System for Mobile Communications (GSM)

and wideband code division multiple access (WCDMA) systems. Techniques for

transformation between the formats are discussed, together with the consequences

of this. The chapter ends with a section on the predicted performance of the

methods in different environments, thereby indicating how they are best

applied.

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1082 CHAPTER 32 POSITIONING IN LTE

32.1 INTRODUCTION

LTE [1] is standardized in 3GPP as an evolution of the universal mobile telecom-munications system ( UMTS ). The chapter discusses the localization technology available in LTE.

32.1.1 System Architecture

The LTE system architecture [2] , depicted in Figure 32.1 , comprises two major functional parts: the radio access network and the core network . The design philosophy behind the LTE radio network, evolved universal terrestrial radio access network ( E - UTRAN ), has been to minimize the number of nodes, which resulted in the single eNodeB. An eNodeB can support frequency - division duplex ( FDD ) mode, time - division duplex ( TDD ) mode, or dual mode operation. The design philosophy for the LTE core network, evolved packet core ( EPC ), has been to make the LTE core network as independent of the radio access technology as possible.

32.1.2 Radio Access Network

A cell is the smallest radio network entity having its own identifi cation number, or cell ID , publicly visible for the user equipment ( UE ). Each eNodeB and each cell has a globally unique ID, which is the eNodeB ID and the evolved cell global identity ( ECGI ), respectively. An eNodeB may serve several cells, with antenna sites that are not necessarily colocated.

Figure 32.1 LTE system architecture. P - GW, packet data network (PDN) gateway; SGSN, serving GPRS support node.

SGSN

UE

Cell

Cell

Cell

Cell

Cell

E-UTRAN

UEEPC

eNodeB

eNodeB

S-GW

LTE-Uu S1-U

X2

networksExternal

OtherPLMN

Operator'sIP services(e.g., IMS)

MME

S1-MME

HSS

S6a

SGi

S11

S10

P-GW

S5/S8

S3S4

Other RAN

Gr

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32.1 INTRODUCTION 1083

Radio communication between E - UTRAN and the UE is conducted over the LTE - Uu interface. Within E - UTRAN, the eNodeBs can be interconnected through the logical X2 interface, which is mainly used for mobility and some radio resource management. The E - UTRAN is connected to the EPC through a logical interface S1.

The LTE E - UTRAN interfaces and protocol structures are organized into two logically independent planes: the control plane and the user plane . The control plane involves the application protocol, which operates over several interfaces involving different network nodes (e.g., S1 - AP is the application protocol transmitted over the S1 in interface, and X2 - AP is the application protocol transmitted over the X2 inter-face), and the signaling bearer for transporting , that is, delivering, the application protocol messages. The top protocol level in the control plane is the nonaccess stratum ( NAS ) which operates between the UE and the EPC. It uses the radio resource control ( RRC ) protocol over the LTE - Uu interface and S1 - AP over the S1 interface as transport. The user plane includes the data bearers for the data streams transported by a user - plane tunneling protocol.

32.1.3 Core Network

The mobility management entity ( MME ) is the EPC node responsible for the control - plane functionality, and it is the reference node in the EPC for NAS signaling. The user - plane functionality is implemented in the serving gateway ( S - GW ), which is separated from the MME. The S1 interface between the eNodeB and the MME, denoted S1 - MME, is used in control - plane positioning. The S1 interface between the eNodeB and the S - GW, denoted S1 - U, is involved in user - plane positioning. User subscription information, mobility, and service data are stored in the home subscriber server ( HSS ) node, which also has the authentication center functionality.

32.1.4 Air Interface

DL : The transmission scheme used in the DL of LTE is orthogonal frequency division multiplexing ( OFDM ) [1] . In OFDM, modulated symbols are transmitted on many parallel orthogonal subcarriers. In order to preserve orthogonality in mul-tipath channels, a cyclic prefi x ( CP ) is added before the OFDM symbol. The use of the CP simplifi es receiver processing in multipath channels since the subcarriers are orthogonal, as long as the channel delay spread is smaller than the CP. The structure of the OFDM modulation waveform makes it natural to use fast Fourier transform (FFT)/inverse fast Fourier transform (IFFT) in implementation, as outlined in Figure 32.2 .

In Figure 32.2 , modulated symbols a i , i = 0, … , N − 1 are mapped on to N subcarriers, starting with negative frequencies − N /2/ N fft , … , − 1/ N fft , skipping the zero subcarrier and continuing with positive frequencies 1/ N fft , … , N /2/ N fft . Since typical FFT implementations only use positive frequencies, the symbols mapped to negative frequencies ( a 0 , … , a N /2 − 1 ) are placed at the end of the IFFT input sequence. Since the FFT size N fft typically is larger than N , the central part of the FFT is

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zero - padded. The N fft - point IFFT produces an N fft - length time domain sequence s i , i = 0, … , N fft − 1. The last N cp samples of this sequence are copied and prepended to the sequence, resulting in a time domain sequence of length N fft + N cp , which is then digital - to - analog converted and mixed up to the carrier frequency and sent to the antenna port. Phase and amplitude modulation schemes are both used, for example, binary phase - shift keying ( BPSK ), quadrature phase - shift keying ( QPSK ), and quadrature amplitude modulation ( QAM ).

Figure 32.3 shows a simplifi ed block diagram of an LTE receiver. In the fi rst step, the CP is removed and the remaining N fft - length sequence is processed with an FTT. The N used subcarriers are extracted, and the received signal is multiplied with the conjugate of the channel response H i , i = 0, … , N − 1, producing an estimate ai of the transmitted signal a i .

Figure 32.4 shows an example of an allocation of different physical channels and signals in a resource block . When a normal CP is assumed, the resource grid consists of 14 OFDM symbols in time and 12 subcarriers in frequency. Each subcar-rier occupies 15 kHz and the OFDM symbol duration including the CP is 1/14 ms. The transmission bandwidth confi guration of an LTE carrier is in the range from 6 to 100 resource blocks corresponding to channel bandwidths of 1.4 – 20.0 MHz. For positioning purposes, it is desirable for the UE to be able to perform measurements

Figure 32.2 A logical block diagram for an example of an LTE transmitter.

Figure 32.3 A logical block diagram for an example of an LTE receiver.

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32.1 INTRODUCTION 1085

(e.g., time and signal strength) on signals that are known to the UE. Examples of such signals in LTE are cell - specifi c reference signal s ( CRS s) and positioning reference signal s ( PRS s) [3] . For each of the two signal types, 504 different signals exist, and different cells can use up to six different shifts in frequency. CRS and PRS symbols are transmitted on the resource elements shown in Figure 32.4 . Further details on PRSs are provided in Section 32.6.4 . CRSs are transmitted every subframe and over the entire bandwidth, being used, for example, for channel estimation.

UL : The access method of the LTE UL is single carrier frequency division multiple access ( SC - FDMA ). Similar to OFDM, SC - FDMA transmits data over the air inter-face in many subcarriers; however, it adds an additional processing step — spreading the signal over all subcarriers, which ultimately reduces the power consumption of the UE, as compared to OFDM. At the receiver end, the signal is demodulated, amplifi ed, and treated by FFT processing in the same way as in OFDM; however, an equalizer is also required due to the spreading at the transmitting end, which causes intersymbol interference. The time – frequency grid of resources is the same as the one defi ned for the DL. In the radio frequency (RF) spectrum, the DL and UL are separated when FDD is used.

Presently, only UL AOA and eNodeB Rx – Tx measurements utilize the UL radio interface. The current standardization of U - TDOA positioning will expand the use of the UL radio interface. Sounding reference signal s ( SRS s) will be used for U - TDOA measurements.

SRSs are modulated and power controlled in a way similar to those used for the physical uplink control channel ( PUCCH ). The modulated signals on SRS are based on so - called Zadoff – Chu sequences [3] and have good auto - and cross - correlation properties. An SRS can be periodic and aperiodic; the alternatives are separately confi gured. Some of the confi guration parameters are cell specifi c, some are user specifi c, and some can be both. For most subframes, the SRS is transmitted in the last symbol of the subframe. The transmission SRS bandwidth is confi gurable between 4 and 96 resource blocks in frequency (which is possible with the 40 - MHz

Figure 32.4 PRS pattern for normal CP with two transmit antennas. PCFICH, physical control format indicator channel; PDCCH, physical downlink control channel; PHICH, physical hybrid ARQ indicator channel; PDSCH, physical downlink shared channel.

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system bandwidth), and may be either cell specifi c or user specifi c. Pseudorandom frequency hopping is also possible for SRS, for example, to randomize the interfer-ence and to better adapt to frequency - selective fading. The SRS hopping may be confi gured as group hopping, which relies on a pattern of frequency – time resources on which SRSs are to be transmitted, and/or as sequence hopping, which implies SRS sequence randomization. The periodicity and the offset from the fi rst subframe in the cell may be confi gured by cell - specifi c parameters, and values are selected from a predefi ned set of values. Thus, SRS may be confi gured and transmitted in each subframe, every second, every fi fth, or every tenth subframe, while the offset, measured in terms of the number of full subframes, can be any integer between zero and nine, that is, any subframe within a radio frame.

32.2 REQUIREMENTS ON POSITIONING IN LTE

32.2.1 3 GPP Requirements

3GPP specifi es functional requirements [4] , which describe the minimum set of mechanisms for supporting and developing various location service s ( LCS s) as well as a set of the attributes to describe or characterize LCS. The 3GPP also specifi es performance requirements [5] .

32.2.2 Emergency Positioning

U.S. Federal Communication Commission ( FCC ) Phase 2 Enhanced 911 (E - 911) emergency positioning requirements [6] mandate that the cellular network operators are responsible for positioning wireless terminals with an accuracy of 50 and 150 m in 67% and 95% of all positioning attempts, respectively. These fi gures are valid for UE - based positioning methods, that is, where the positioning method involves func-tionality located in the UE, like global positioning system ( GPS ) receiver hardware. The requirements for network - based methods, without such UE functionality, are 100 m (67%) and 300 m (90%). The response time shall be less than 30 seconds after the E - 911 call is placed. Note that recent indications from the FCC may lead to the requirements for network - based methods being discontinued.

The accuracy requirements implicitly require an availability of at least 95%. This creates a diffi cult situation since much more than 50% of all mobile calls are placed indoors where the most accurate method, assisted global positioning system ( A - GPS ) [7] , has a very limited availability. As a result, cellular operators are forced to use other positioning methods as a fallback, or to select other methods than A - GPS for high - accuracy positioning [8] . The fallback methods also need to be fast to meet the overall 30 - second requirement since they are sometimes applied in a reattempt manner.

The current emergency call delivery standards in the United States put addi-tional requirements by a limitation on the allowed geometric shapes used by cellular systems for reporting of positions [9] . For LTE, the consequence is a requirement to be able to transform between the shapes in Reference 9 .

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32.3 POSITIONING ARCHITECTURE AND SIGNALING IN LTE 1087

32.2.3 Location - Based Services ( LBS s)

One consequence of the growing number of LBS is that the LTE system needs to be prepared for service - dependent positioning to a higher degree than previously. The positioning node therefore needs to be able to select the best mix of positioning technologies to meet the requested positioning quality of service ( QoS ).

The large bandwidth in LTE enables real - time video transmissions from and between terminals. More advanced terminal technology may integrate also inertial sensors [10] like accelerometers and gyros. This development may have implications for the future positioning technology of LTE. For example, it may become possible to transmit video, pictures, and directional information to positioning nodes that may use pattern matching techniques to fi nd the precise position, given only a rough initial position.

The convergence of the telecommunication and computer industries means that it will no longer be acceptable for cellular operators to mainly provide high - performance positioning services outdoors. Users will expect applications to work irrespective of where they are located, with indoor and outdoor performance not being too different.

32.3 POSITIONING ARCHITECTURE AND SIGNALING IN LTE

The three important network elements in any positioning architecture are the LCS client , the LCS target , and the LCS server . The LCS server is a physical or logical entity managing positioning for an LCS target device by obtaining measurements and other location information, providing assistance data to assist UEs in measure-ments, and computing or verifying the fi nal position estimate. An LCS client is a software and/or hardware entity that interacts with an LCS server for the purpose of obtaining location information for one or more LCS targets, that is, the entities being positioned. LCS clients may reside in the LCS targets themselves. LCS clients subscribe to LCS to obtain location information, and LCS servers process and serve the received requests and send the positioning result to the LCS target. The position-ing result comprises estimated location coordinates, although it may also include a velocity estimate or the location failure indication in case of a failure. Seven formats for reporting location coordinates are currently supported in LTE [9] : ellipsoid point, ellipsoid point with uncertainty circle, ellipsoid point with uncertainty ellipse, polygon, ellipsoid point with altitude, ellipsoid point with altitude and uncertainty ellipsoid, and ellipsoid arc.

Example 32.1 3 GPP Encoding of Position Reporting Formats

An ellipsoid point is a point on the surface of the WGS84 earth ellipsoid described by a latitude and a longitude. The latitude is the angle between the equatorial plane and the normal to the tangent plane to the ellipsoid surface at the ellipsoid point. Positive latitudes correspond to the Northern hemisphere. The longitude is the angle between the half - plane determined by the Greenwich meridian and the half - plane

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defi ned by the ellipsoid point and the polar axis, measured eastward. The coordinates of an ellipsoid point are coded with an uncertainty of less than 3 m. The latitude is coded with 24 bits: 1 bit of sign and a number between 0 and 2 23 − 1 binary coded with 23 bits. The longitude, expressed in the range [ − 180 ° , + 180 ° ], is coded as a number between − 2 23 and 2 23 − 1, using a binary 2 s complement.

Solution

The formal encoding of the ellipsoid point is performed as follows [9] :

Ellipsoid - Point :: = SEQUENCE { latitudeSign ENUMERATED {north, south},

degreesLatitude INTEGER (0..8388607),

degreesLongitude INTEGER ( - 8388608..8388607)

}

The gateway mobile location center ( GMLC ) is the fi rst node an external LCS client accesses in a public land mobile network ( PLMN ), through the Le interface. After performing registration authorization, it sends positioning requests to the MME and receives fi nal location estimates from the corresponding entity via the SLg interface. A location retrieval function ( LRF ), which may or may not be colocated with the GMLC, is responsible for retrieving or validating location information, providing routing and/or correlation information of a UE that has initiated an IP multimedia subsystem ( IMS ) emergency session.

Two new protocols have been standardized specifi cally to support positioning in LTE: the long - term evolution positioning protocol ( LPP ) [11] and the long - term evolution positioning protocol annex (LPPa) [12] . The LPP [11] is a point - to - point protocol between an LCS server and an LCS target device, used in order to position the target device. The following transactions have been specifi ed: capability transfer procedure (request/provide messages), assistance data transfer procedure (request/provide messages), and a location information transfer procedure (request/provide messages). Multiple LPP procedures of any of the aforementioned types can be used in series and/or in parallel . LPP is used both by control - plane (see, e.g., Fig. 32.5 ) and user - plane (see e.g., Fig. 32.6 ) positioning solutions.

Figure 32.5 LTE positioning architecture, control plane.

S1-AP

UE eNodeB

LTE-Uu

MME

S1-MME

E-SMLC

GMLC

SLs

SLg

LPPa LPPa

LPP LPPLPPLCS-AP

HSS

ExternalLCS Client

S6a

Le

RRC

LrLRF

SLh

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32.3 POSITIONING ARCHITECTURE AND SIGNALING IN LTE 1089

LPPa is specifi ed only for control - plane positioning procedures. However, with the user plane and the control - plane interworking, LPPa can also assist the user - plane solution by querying eNodeBs for information and eNodeB measure-ments not related to a UE connection.

32.3.1 Control Plane

To support LCS, at least two functional nodes must be present in the LTE control - plane architecture: the evolved serving mobile location center ( E - SMLC ), which controls the coordination and scheduling of the resources required to locate the mobile device, and the GMLC, which controls the delivery of position data, user authorization, charging, and more. The LPP messages are transmitted transparently to the MME, using RRC as a transport over the LTE - Uu interface between the UE and the E - SMLC, using S1 - AP over the S1 - MME interface, and using LCS - AP over the SLs interface between the eNodeB and the E - SMLC. LPPa conducts the LPPa location information transfer procedures for positioning - related information. LPPa is also transparent to the MME, which routes the LPPa packets transparently over the S1 - MME and SLs interfaces without knowledge of the involved LPPa transaction. The LTE positioning architecture for the control plane is shown in Figure 32.5 . To describe the operation of the architecture, consider the case where the MME receives a positioning request for some LCSs associated with a particular LCS target (e.g., a UE). The MME then sends an LCS request in an LCS - AP loca-tion request message [13] to an E - SMLC. The E - SMLC processes the LCSs request to perform a positioning of the target UE. The E - SMLC then returns the result of the LCS back to the MME. The MME then forwards the result at least to the request-ing node.

Figure 32.6 LTE positioning architecture, user plane.

S1-AP

SET eNodeB

LTE-Uu

MME

S1-MME

E-SMLC

GMLC

SLs

SLg

LPPa LPPa

LPP

LPPLCS-AP

HSS

ExternalLCS Client

S6a

RRC

LrLRF

SLh

SPC

SLCP-GWS-GWS1-U S5

Llp

SGi

Le

SLP

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32.3.2 User Plane

In general, secure user plane location ( SUPL ) [14, 15] supports and complements control - plane protocols to enable LBS support with the least possible impact on the control plane and the deployed network. The LTE user - plane positioning architecture is shown in Figure 32.6 . SUPL uses established data - bearing channels (i.e., the LTE user plane) and positioning protocols (i.e., LPP) for exchanging the positioning - related data between an LCS target and an LCS server. In the general user - plane protocol stack, SUPL occupies the application layer with LPP transported as another layer above SUPL. After establishing a TCP/IP connection and initiating the SUPL and then LPP sessions, the fl ow of LPP messages can be the same as in the control - plane version of LPP, just with the SUPL enabled terminal ( SET ) as the LCS target and the SUPL location platform ( SLP ) as the LCS server.

The SLP implements the SUPL location center ( SLC ) and the SUPL position-ing center ( SPC ) functions with the latter either being integrated in the E - SMLC or attached to it with a proprietary interface. The SLC system coordinates the opera-tions of SUPL in the network and implements the following SUPL functions as it interacts with the SET over the user - plane bearer: privacy function, initiation func-tion, security function (cf. Chapter 3 ), roaming support, charging function, service management, and position calculation. The SPC supports the following SUPL func-tions: security function, assistance delivery function, SUPL reference retrieval func-tion (e.g., retrieving data from a GPS reference network), and SUPL position calculation function.

32.4 POSITIONING PROCEDURES IN LTE

32.4.1 Signaling of Client Type and Q o S

The type of service is normally received in the E - SMLC in the form of a client type [13] . The client type may be determined in the MME, the GMLC, or some other node, from the knowledge of the type of service that requests positioning. Currently, there are eight client types available in LTE [13] ; this set may, however, be extended in future releases.

The most important QoS parameters are the response time, the horizontal accuracy, and the vertical accuracy. In LTE, these can be signaled to the E - SMLC from the MME node [13] . The QoS parameters can also be requested from the UE over the LPP protocol [11] , that is, after the positioning session has been estab-lished. The response time is within [1, 128] seconds. The horizontal accuracy is expressed as 128 accuracy codes, corresponding to uncertainty radii of uncertainty circles. The vertical accuracy is expressed as 128 other accuracy codes. Both the horizontal and vertical accuracy are associated with a confi dence value. This confi -dence value expresses the probability that the UE is located within the uncertainty region associated with the positioning result. The importance of the confi dence cannot be underestimated since positioning results are statistical quantities. The accuracy alone may, for example, be enhanced by a reduction of the associated confi dence.

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32.4 POSITIONING PROCEDURES IN LTE 1091

32.4.2 Positioning Method Selection

The E - SMLC uses the client type and the QoS information to determine the best possible use of the available positioning resources. One way to do this is to fi rst let the client type determine a service class, mapped to a set of LBSs, each service class with its own positioning sequence.

The Positioning Sequence and Prior Performance Information: When the method for the fi rst positioning attempt is to be determined, the positioning method selection mechanism must rely on stored, possibly preconfi gured, information regarding the performance of the different available positioning methods. A more accurate solution than preconfi guration is to build up the prior information on posi-tioning performance adaptively [16] . This may be done by registration of the obtained positioning results and the associated QoS information in the E - SMLC. This regis-tered information can then be used for online generation of histograms describing the probability density functions of the response time, the horizontal accuracy, the vertical accuracy, and the availability for each positioning method.

To determine the positioning method for the fi rst attempt, one approach is to check QoS parameters sequentially, which is used in some UMTS implementations where the order of precedence of the QoS information is specifi ed [17] . More advanced approaches, suitable for LTE, include the use of performance indices that can be used to fi nd a best fi t to the requested QoS.

Once the fi rst positioning attempt has been performed, the position method selection mechanism may proceed with one or more positioning reattempts in case the requested QoS has not been met.

Q o S Evaluation: In order to apply the above principles, methods for calculation of the achieved QoS need to be available. The achieved positioning time can be directly measured with timers. The vertical accuracy is a one - dimensional quantity, and there are no computations needed to assess it. The computation of the achieved horizontal accuracy is more intricate since the uncertainty region associated with each geographical reporting format [9] needs to be transformed to a radius of an uncertainty circle to comply with the reporting format for horizontal accuracy [11] . One common principle is to fi rst compute the area of the reported geographical region. The radius of a circle with the same area is then computed and used as the achieved horizontal accuracy.

The most important geometric shapes horizontally are the polygon, the ellipse, and the ellipsoid arc. To describe the QoS computations, the corners of the 3GPP polygon [9] are denoted ( x i y i ) T , i = 1, … , N p . It is assumed that the last corner is identical to the fi rst. Furthermore, the inner radius of the ellipsoid arc [9] is denoted by R , the thickness is denoted by Δ R , and the opening angle in radians is denoted by α . The semimajor and semiminor axes of the 3GPP ellipse [9] are denoted by a and b , respectively.

The area of the polygon can now be computed as in Reference 34 . The area of the ellipse is π ab , while the area of the ellipsoid arc is easily computed as the difference of the areas of the circle sectors limited by the outer and inner radius.

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The equivalent radius of the uncertainty circle is then computed by setting these areas equal to π r 2 and solving for r . This gives the uncertainty radii of Equation 32.1 , which are then quantized as described in Reference 9 :

r

x y x y

r R R R

i i i i

i

N p

polygon

ellipsoid arc

=−( )

= +

+ +=

−

∑ 1 1

0

1

2

22

παπ

Δ Δ(( )

=r abuncertainty ellipse .

(32.1)

Example 32.2 Q o S of Ellipsoid Point with Uncertainty Ellipse

The QoS computations described earlier are necessary, for example, to determine if a positioning sequence can be terminated or if it needs to improve the QoS by apply-ing another positioning method. One QoS computation algorithm is needed for each of the seven reporting formats of LTE. The example code Chapter_32_Example_2.m illustrates how the QoS is computed in one such case, for an ellipsoid point with uncertainty ellipse. MATLAB codes can be found online at ftp://ftp.wiley.com/public/sci_tech_med/matlab_codes . As stated previously, the uncertainty is repre-sented by the radius of a circle that has the same area as the ellipse. The formula of Equation 32.1 is used for the computation. The example code also contains the encoding/decoding steps according to Reference 9 , thereby providing further insight and examples of this.

Solution

The example code is run from the MATLAB workspace. When executing the code, the variables positionFormat and positionFormatDescription are expected to be present in the workspace of MATLAB. positionFormat contains the name of the input reporting format, while positionFormatDescription contains a 3GPP encoded ellipsoid point with uncertainty ellipse. The 3GPP encoded format contains the fol-lowing elements (in order): the number of the format, the encoded latitude sign, the encoded latitude, the encoded longitude, the encoded semimajor axis, the encoded semiminor axis, the encoded orientation angle (clockwise from north), and the encoded confi dence. A typical MATLAB command sequence is as follows:

>> positionFormat = ‘ ELLIPSOID_POINT_WITH_UNCERTAINTY_ELLIPSE ’ ;

>> positionFormatDescription = [3 0 400 400 25 15 130 39]; >> Chapter_32_Example_2

>> AccuracyCode

AccuracyCode = 20

It can be noted that the encoded accuracy code is in between the encoded semiminor and semimajor axes, as can be expected.

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32.5 COORDINATES 1093

32.5 COORDINATES

To measure, compute, signal, and use cellular positioning results, it is necessary to agree on two basic things — the coordinate system and the time.

32.5.1 Time

The universal time code ( UTC ) and GPS system time are two common time bases used for cellular positioning. UTC is derived from two timescales, the fi rst one being defi ned by atomic clocks and the second one by the rotation of the earth. The inter-national atomic time is associated with the SI defi nition of the second. The timescale related to the rotation of the earth (UT1) helps in defi ning the so - called earth - centered earth - fi xed ( ECEF ) coordinate frame. The two timescales are merged to provide UTC time, which is aligned with solar time [18, 19] .

GPS system time is derived from atomic clocks in the GPS space vehicle s ( SV s) and in the GPS ground control segments [10] . GPS system time therefore drifts with respect to UTC, and in case the LTE system is not synchronized to GPS system time, the relation to the time base used needs to be maintained. GPS system time is expressed in terms of the GPS week number and the GPS time of week, counted from midnight Saturday/Sunday.

32.5.2 Coordinate Systems

The A - GPS and A - GNSS methods (cf. Chapter 28 ) utilize Cartesian ECEF coordi-nates for measurements and position calculation, whereas the other positioning methods of LTE utilize Cartesian earth tangential ( ET ) coordinate systems. Assistance data for A - GPS and A - GNSS, as well as results, are signaled as latitudes, longitudes, and altitudes, expressed in the WGS84 geodetic model [9] . Figure 32.7 defi nes these coordinate systems and the most important variables. The latitude of the location r

Figure 32.7 Coordinate systems and variables for LTE positioning.

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is measured as the angle between the equatorial plane of the WGS84 Earth ellipsoid, and the normal of the tangent plane, at r . The longitude is counted eastward from the Greenwich meridian.

The ECEF coordinate system has the origin in the center of the WGS84 ellip-soid, the x - axis ( xECEF) in the Greenwich meridian plane, and the y - axis ( yECEF) 90 ° to the east of xECEF. The z - axis of the ECEF coordinate frame coincides with the axis of rotation of the WGS84 ellipsoid.

The ET coordinate system has the origin on the surface of the WGS84 ellipsoid with the x - axis ( xET) pointing east, the y - axis ( yET) pointing north, and the z - axis ( zET) pointing up. The latitude at r is denoted θ , the longitude φ , the altitude h , and Cartesian coordinates in any coordinate frame are denoted ( x y z ) T .

32.5.3 Coordinate Transformations

It is assumed that the positions handled by the E - SMLC are relatively close. The vectors from the center of the Earth to r , and from the center of the Earth to the center of the ET coordinate system are then almost parallel, a fact that allows the altitude to be directly added to the ET coordinates and to be neglected when transforming from WGS84 coordinates to ECEF coordinates and to ET coordinates.

Using the ellipsoidal geometry of Figure 32.7 , the transformation of r from WGS84 latitude and longitude to Cartesian ECEF coordinates is

x N

y N

zb

aN

ECEF

ECEF

ECEF

= ( ) ( )= ( ) ( )

= ⎛⎝⎜

⎞⎠⎟

cos cos

cos sin

sin

θ ϕθ ϕ

θ2

(( )

=− ( )(

Na

e1 2 2sin θ,

(32.2)

where e , a , and b denote the eccentricity, the semimajor axis, and the semiminor axis of the WGS84 ellipsoid, respectively, and N is a help variable. Similarly, the selected center of the ET coordinate system is transformed to ECEF coordinates,

resulting in the position x y zT

ECEFETsystem

ECEFETsystem

ECEFETsystem( ) . The transformation from

ECEF to ET coordinates of the position r is then

x x x

yET

ETsystemECEF ECEF

ETsystem

ETsystemEC

= − ( ) −( )+ ( )

sin

cos

ϕϕ EEF ECEF

ETsystem

ETETsystem ETsystem

ECEF

−( )= − ( ) ( ) −

y

y xsin cosθ ϕ xx

y yECEFETsystem

ETsystem ETsystemECEF ECEF

ET

( )− ( ) ( ) −sin sinθ ϕ ssystem

ETsystemECEF ECEF

ETsystem

ET

( )+ ( ) −( )

=cos

.

θ z z

z h

(32.3)

c32.indd 1094c32.indd 1094 8/5/2011 3:46:11 PM8/5/2011 3:46:11 PM

32.5 COORDINATES 1095

In the other direction, the ET - to - ECEF transformation becomes

x x xECEF ECEFETsystem ETsystem

ET

ETsystem ET

= − ( )− ( )

sin

sin cos

ϕθ ϕ ssystem

ET

ECEF ECEFETsystem ETsystem

ET

ETsy

( )= + ( )

−

y

y y xcos

sin

ϕθ sstem ETsystem

ET

ECEF ECEFETsystem ETsystem

( ) ( )= + ( )

sin

cos

ϕθ

y

z z yyET.

(32.4)

Finally, the transformation from ECEF to geodetic coordinates is given by

θ

ϕ

= ( ) +⎛⎝⎜

⎞⎠⎟

= ⎛

sign arccos

atan

ECEFECEF ECEF

ECEF

ECEF

zx y

M

y

x

2 2

2

2⎝⎝⎜

⎞⎠⎟

=

= + + ⎛⎝⎜

⎞⎠⎟

h z

M x ua

bz

ET

ECEF ECEF ECEF22 2

4

,

(32.5)

where atan2( · ) denotes the four - quadrant inverse of the tangent function.

Example 32.3 Coordinate Transformations

The coordinate transformations described previously are used in virtually all com-putations of a cellular positioning system. The reason is that most cellular measure-ments are performed in an environment best described in an ET coordinate system; this is, for example, the case when the travel time of radio waves between base sta-tions and terminals is used. It is therefore of central importance to have a good understanding of these transformations. The example code Chapter_32_Example_3.m illustrates how the transformation from WGS84 latitude/longitude to ET coor-dinates (and back) works in one such case, for the polygon geographical format of LTE. MATLAB codes can be found online at ftp://ftp.wiley.com/public/sci_tech_med/matlab_codes . The example code includes the encoding/decoding steps accord-ing to Reference 9 , thereby providing further insight in format encoding/decoding. The example code makes use of Equations 32.2 – 32.5 , which are implemented sequentially. The code hence exploits the simplifying assumption that the altitude is handled separately in the coordinate transformations.

Solution

The example illustrates the transformation for a small four - corner polygon close to the equator. The example code is run from the MATLAB workspace. When execut-ing the code, the variable positionFormatDescription is expected to be present in the workspace of MATLAB. positionFormatDescription contains the 3GPP encoded polygon. In this case, the polygon format contains the following elements (in order): the number of the polygon format, the number of corners in the polygon, the encoded

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latitude sign of the fi rst corner, the encoded latitude of the fi rst corner, the encoded longitude of the fi rst corner, the encoded latitude sign of the second corner, the encoded latitude of the second corner, the encoded longitude of the second corner, the encoded latitude sign of the third corner, the encoded latitude of the third corner, the encoded longitude of the third corner, the encoded latitude sign of the fourth corner, the encoded latitude of the fourth corner, and the encoded longitude of the fourth corner. After defi nition of the polygon, the transformations are performed by typing Chapter_32_Example_3 in the MATLAB command window. The result is then available in the variables CellLatLong (the latitude and longitude of the four corners), CellXYZ (the ECEF coordinates of the four corners), polygonXY (the ET coordinates of the four corners, fi rst corner selected as the ET origin). The command sequence is as follows:

>> positionFormatDescription = [5 4 0 418 - 210 0 376 188 1 418 209 1 376 - 189];

>> Chapter_32_Example_3 % Execute the code

>> CellLatLong % Display the latitudes and longitudes of the

polygon corners

CellLatLong = 1.0e - 004 *

0.7827 0.7041 - 0.7827 - 0.7041

- 0.7865 0.7041 0.7827 - 0.7078.

>> CellXYZ % Display the ECEF coordinates

CellXYZ = 1.0e + 006 * 6.3781 6.3781 6.3781 6.3781

- 0.0005 0.0004 0.0005 - 0.0005

0.0005 0.0004 - 0.0005 - 0.0004,

>> polygonXY % Display the ET coordinates

polygonXY = 1.0e + 003 * 0 0.9507 1.0008 0.0502

0 - 0.0498 - 0.9918 - 0.9419

32.6 POSITIONING METHODS IN LTE

To meet LBS demands, the LTE network will deploy a range of methods that have different performances. Depending on where the measurements are con ducted and the fi nal position is calculated, the methods can be UE - based , UE - assisted , or network - based , each having specifi c advantages. The following methods are avail-able in the LTE standard for both the control plane and the user plane [20] :

• cell ID (CID);

• UE - assisted and network - based E - CID, including network - based AOA;

• UE - based and UE - assisted A - GNSS; and

• UE - assisted OTDOA,

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32.6 POSITIONING METHODS IN LTE 1097

where all methods are available from the second LTE release, with only CID being available from the fi rst LTE release. Hybrid positioning and fi ngerprinting position-ing do not require additional standardization and are therefore also possible from the second LTE release.

32.6.1 Cell Identity ( CID )

Given the cell ID of the serving cell, the UE position is associated with the cell coverage area, which can be described, for example, by a prestored polygon. The polygon format is one of the standardized positioning reporting formats in 3GPP [9] , where a polygon is defi ned as a list of 3 – 15 corners with each corner represented by latitude and longitude encoded in the WGS84 system [9] . The cell boundary is modeled by the set of nonintersecting polygon segments connecting all the corners. The UE is assumed to be within the polygon with a certain confi dence, although the polygon format as such does not contain the confi dence information. This is the fastest positioning method since no measurements are needed.

32.6.2 E - CID

E - CID methods exploit four sources of position information: the CID and the cor-responding geographical description of the serving cell, the TA of the serving cell, the CIDs, and the corresponding signal measurements of the cells (up to 32 cells in LTE, including the serving cell), as well as AOA measurements. The following measurements are available for E - CID in LTE [5, 20] :

• UE Measurements . E - UTRA carrier received signal strength indicator ( RSSI ), reference signal received power ( RSRP ), reference signal received quality ( RSRQ ), and UE Rx – Tx time difference;

• E - UTRAN Measurements . TA type 1 being (eNodeB Rx – Tx time differ-ence) + (UE Rx – Tx time difference), TA type 2 being eNodeB Rx – Tx time difference, and UL AOA,

where the UE E - CID measurements are reported by the UE to the E - SMLC over the LPP protocol, and the E - UTRAN E - CID measurements are reported by the eNodeB to the E - SMLC over the LPPa protocol (see Section 32.3 ). Next, three common techniques for E - CID are described.

CID and TA : One common E - CID method combines the geographical cell description, the eNodeB position, and the distance between the eNodeB and the UE obtained from a time measurement. A previous example of this technique is round - trip time ( RTT ) positioning in the WCDMA system [17, 21, 22] . Applied to the LTE situation, the distance is obtained from the TA time measurement as

Rc

TATA= ⋅2

, (32.6)

where c is the speed of light. The uncertainty of the TA distance ( Δ R TA ) may be determined by fi eld trials [17] and can then be confi gured in the system as a

c32.indd 1097c32.indd 1097 8/5/2011 3:46:12 PM8/5/2011 3:46:12 PM


parameter. In GSM, the granularity of the TA is of the order of 1 km. In LTE, the granularity is much fi ner, of the order of 10 m. Since the bandwidth of LTE is nor-mally larger than that of WCMDA, a radial accuracy at least as good as for RTT positioning in WCDMA is expected (cf. Reference 17 ).

The combination of the TA distance with the geographical cell description can be performed in several ways. Figure 32.8 illustrates an algorithm for a case where the cell boundary is described by a 3GPP polygon [9] . In the fi gure, the resulting ellipsoid arc describes the intersection between the 3GPP polygon and the 360 ° arc corresponding to R TA with uncertainty Δ R TA . To compute the left and opening angle of the ellipsoid arc, test points are distributed uniformly within the circular strip at a distance of R TA + Δ R TA /2 from the eNodeB. Next, it is checked for each test point ( x 0 y 0 ) T whether it is in the interior of the polygon. The test exploits a test ray from the test point to infi nity, parallel to the east axis of the coordinate system. When a test point is in the interior, the cell polygon must be intersected an odd number of times when the test ray moves from the test point to infi nity. The crossings with the polygon boundary are easily determined by checking for intersections between the test ray and the line segments between two adjacent cell polygon corner points. The intersection between the horizontal ray y = y 0 , x ≥ x 0 , and the line segment between

the polygon corners with index i , x yiET

iET T( ) , and i + 1, x yi

ETiET T

+ +( )1 1 , of the cell polygon with N P corners is given by a solution to

x

y

x

y

x

yx xi

i

i

i0

1

101 0

⎛⎝⎜

⎞⎠⎟

= ⎛⎝⎜

⎞⎠⎟

+ −( )⎛⎝⎜

⎞⎠⎟

≥ ≤+

+

α α αET

ET

ET

ET, , << 1, (32.7)

when a unique solution exists. Repetition of this procedure for all line segments between corners allows for a count of the number of intersections for one specifi c test point. The complete algorithm of References 17 and 22 repeats this for all test points. In order to fi nd the angles, a search is performed for the largest set of adjacent test points that are exterior to the polygon. The complement of this set corresponds to the set of test points that defi nes the ellipsoid arc. Note that this procedure handles the case with more than one intersection between the circular strip and the cell polygon (see Fig. 32.8 ).

Signal Strength: Distance measures can also be derived from signal strengths measured in the UE and combined with cell polygons as for CID and TA. Unfortunately, signal strengths become inaccurate when shadow fading affects the signal propagation of handheld UEs. This can be illustrated by consideration of the Okumura – Hata propagation model

L L R= + ⋅ ( )0 1010η log , (32.8)

where L is the pathloss in dB, R is the distance between the eNodeB and the UE, L 0 is the attenuation constant, and η is the attenuation exponent. Differentiation of Equation 32.8 results in

dLdR

RdR RdL R=

( )⇔ = ( ) ≈ ( )10

10

10

10

10

10

ηη η

σln

ln ln,shadow (32.9)

c32.indd 1098c32.indd 1098 8/5/2011 3:46:12 PM8/5/2011 3:46:12 PM


where σ shadow is the standard deviation of the lognormal shadow fading. Inserting the values η = 3.7 and σ shadow = 10 dB for shadow fading due to head effects gives dR = 0.62 R . This means that the 1 - sigma error of a received signal strength measurement amounts to more than 60% of the measured value. The inaccuracy associated with raw signal strength measurements is demonstrated in the following example.

Example 32.4 Shadow Fading due to Head Effects

The example highlights the fact that the orientation of handheld UEs has a very signifi cant effect on the accuracy of any positioning method that relies on signal strength measurements. The reason is obvious considering the direction depen-dent damping of the head and body of the users, when different eNodeBs are considered.

Solution

In the example, the signal strength of six eNodeBs were generated with the Okumura – Hata model (Eq. 32.8 ) in multiple points of a cell. The signal strengths were quan-tized as high/low, resulting in signals strengths characterized by 1 of 64 different cases, for each point in the cell. The geographical points appear coded with gray scales according to the signal strength case in Figure 32.9 . The smearing due to shadow fading of the geographical information content in the combined signal strength measurements is very signifi cant.

Figure 32.8 Combination of TA and the serving cell polygon. The eNodeB is marked with a star in the center of the circle denoting a TA range; the cell polygon is plotted with a solid line; test points are plotted as small circles, some of which are located in the interior of the cell polygon. The resulting ellipsoid arc consists of the parts of the circle that are in the interior of the cell polygon.

2000

1500

1000

500

0

Nor

th (

m)

–500

–1000

–1500

–2000 –1500 –1000 –500 0East (m)

500

*

1000 1500 2000

c32.indd 1099c32.indd 1099 8/5/2011 3:46:12 PM8/5/2011 3:46:12 PM


Admittedly, the large uncertainty of a single signal strength measurement is reduced somewhat when several measurements with respect to different eNodeBs are combined. Relative signal strengths, using one eNodeB as the reference, can contribute to a further reduction of the errors. The use of advanced pattern matching techniques and advanced signal processing is known to improve accuracy even more [23] . Further comments are given in Chapters 11 – 15 and in the discussion on fi n-gerprinting positioning in Section 32.6.3 .

AOA : The AOA measurement standardized for LTE is defi ned as the estimated angle of a UE with respect to a reference direction, which is the geographical north, positive in a clockwise direction. AOA can improve accuracy, as compared to the CID and TA method, by reducing the angular uncertainty, as shown in Figure 32.10 . For a given beam direction φ and beam width Φ , the set of possible UE positions are all locations ( x y ) T given by Equation 32.10 , parameterized by γ and δ that each vary in the range of [0, 1]:

x

yR R

⎛⎝⎜

⎞⎠⎟

= + −⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟ ⋅

+ −⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

TA TAΔΦ

γϕ δ

1

2

1

2sin

coss

.

ϕ δ+ −⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟Φ 1

2

(32.10)

Reporting of an ellipsoid arc is anticipated for this case. Due to the geometric orthogonality of distance and AOA, this is expected to be an effi cient hybrid posi-tioning method.

AOA is traditionally measured by the eNodeB with an antenna array (see Reference 24 and Chapter 9 ), but with LTE, it may also be possible to use the so - called precoder matrix indice s ( PMI s) reported by the UE. Each precoder index corresponds to the use of an “ antenna beam, ” as indicated in Figure 32.11 . It can be seen that the reported PMI gives a useful indication of the direction to the UE.

Example 32.5 AOA Antenna Diagrams

This example illustrates the angular accuracies that can be expected when PMIs are used for positioning purposes.

Figure 32.9 Inaccuracy with shadow fading. No shadow fading (left) and 6 - dB shadow fading (right).

–400

–400

–300 –200 –100 0 100 200 300 400–400 –300

–300

–200

–200

–100

–100

0

0

100 200

100

200

–400

–300

–200

–100

0

100

200

300 400

c32.indd 1100c32.indd 1100 8/5/2011 3:46:12 PM8/5/2011 3:46:12 PM


Solution

The expected SNRs for an example 4TX antenna codebook are shown in Figure 32.12 . As can bee seen from these diagrams, the central major lobes cover approxi-mately 30 ° , making PMIs a useful source of location information, in particular, when combined with TA information in LTE as illustrated in Figure 32.10 . The radial TA uncertainty may be about 100 m. At a distance of 1 km, the region corresponding to these measurements would hence cover an area of about 100 × 500 m 2 .

32.6.3 Fingerprinting

Fingerprinting denotes a set of positioning methods that exploit detailed geographi-cal maps of radio properties for positioning (cf. Chapter 15 ). The UE measures the radio properties it experiences and sends them to the E - SMLC. The E - SMLC then

Figure 32.10 Combination of TA and AOA.

Figure 32.11 Antenna confi guration and PMI selection. The results are based on live measurements. See color insert.

c32.indd 1101c32.indd 1101 8/5/2011 3:46:12 PM8/5/2011 3:46:12 PM


searches for a best match between its stored geographical map of radio properties and the measured radio properties sent by the UE. The best match determines the position of the UE. Fingerprinting positioning has been studied relatively little for cellular applications [25] , although fi elded cellular fi ngerprinting systems exist. The LTE positioning standard is prepared for fi ngerprinting positioning and allows for signaling of CIDs, signal strengths, TA, and AOA along with OTDOA and A - GPS/A - GNSS measurements between the UE, the eNodeB and the E - SMLC. The informa-tion is carried over the LPP [11] and LPPa [12] protocols.

RF Fingerprinting: The most common technique for fi ngerprinting is denoted RF fi ngerprinting or RF pattern matching . In LTE, it would exploit UE measurements of received signal strength, from a number of eNodeBs. The geographical RF maps can be created by advanced radio signal strength prediction software, using very detailed information of the 3 - D geographical topology together with accurate infor-mation of the cell plan, tower locations, tower heights, antenna directions, antenna tilting, antenna patterns, and transmission power. To achieve a good enough accu-racy, such prediction software still may need to be complemented with surveying. Another approach would be to rely entirely on surveying, which, however, would be very costly even for normally sized cellular networks since the positioning accuracy will always be bounded by the density of the geographical grid of the RF map.

Even when accurate predictions of the signal strength can be made, another problem limits performance. This is due to the fact that the antenna diagrams of handheld UEs vary a lot with user orientation and the way the UE is held, for example, against the user ’ s head. Such effects can easily amount to more than 10 dB

Figure 32.12 SNRs for a 4TX PMI codebook.

6

4

2

0

–2

–4

Receiv

ed p

ow

er

(dB

)

Antenna diagrams using four-antenna codebooks,antenna spacing two wavelengths

Direction (degrees)

–6

–8

–10–80 –60 –40 –20 0 20 40 60 80

c32.indd 1102c32.indd 1102 8/5/2011 3:46:12 PM8/5/2011 3:46:12 PM


of uncertainty (cf. Figure 32.9 ). There is no perfect way around this situation, and this will affect any positioning technology exploiting received signal strength mea-surements, while time measurements are likely to be less sensitive (cf. Eq. 32.9 and Reference 8 ). A way to mitigate the effects of this problem is to apply averaging or to use relative signal strength measurements. Other types of signal processing can be used as well, exploiting aspects related to the signal strength [23] , possibly in combination with advanced multiple - hypothesis strategies.

AECID : Another way to enhance fi ngerprinting positioning performance is to extend the number of radio properties that are used. In LTE, at least CIDs, TA, and AOA are suitable in addition to received signal strengths. Unfortunately, the geo-graphical radio map then becomes much more diffi cult to generate. In addition, the problem with handheld UEs becomes even more complex. Furthermore, there is a need to address the accuracy of the measured position, using multiple radio proper-ties. Ideally, this requires that both an inaccuracy and an associated confi dence value are determined together with the position.

The AECID positioning method [26] addresses the above problems. It fuses geographical cell descriptions (corresponding to CIDs), received signal strengths, and TA, and can be extended to include AOA information. The method replaces the radio property prediction software and the surveying by the following self - learning mechanisms:

1. Whenever an A - GPS, A - GNSS, or OTDOA high - precision positioning is per-formed, the E - SMLC orders measurements of the radio properties, this being a subset of geographical cell descriptions, TA, signal strengths, and AOA. The radio property measurements are quantized, producing the fi ngerprint of the obtained high - precision position.

2. All high - precision positions with the same fi ngerprint are collected in clusters. These clusters describe geographical regions where the same fi ngerprint persists.

3. A model of the cluster boundaries is computed by an algorithm that generates a 3GPP polygon that contains a prespecifi ed fraction of the high - precision measurements of the cluster. An advantage with this is that the polygon is determined to have a confi dence equal to the prespecifi ed fraction. This polygon, together with its fi ngerprint and confi dence value, is stored in a database accessible by the E - SMLC.

The clustering can be extended to perform smoothing by the clustering computation algorithms in Reference 27 . Those algorithms can also split weakly coupled parts of a cluster into subclusters that can be individually described by polygons, after which these polygons are merged into one polygon for reporting.

The polygon computation is initiated by a calculation of the center of gravity, r CG , of the cluster of high - precision reference points and by the creation of an initial polygon with all points of the cluster in the interior [26] .

Each step of the so - called contracting polygon algorithm performs tentative movements of the corners, rp

i , i = 1, … , N p of the polygon p inward toward the center of gravity of the cluster. The movement is continued until one point of the cluster becomes an exterior point of the polygon. This is repeated for all corners,

c32.indd 1103c32.indd 1103 8/5/2011 3:46:12 PM8/5/2011 3:46:12 PM


and the corner that results in the largest decrease of the polygon area is selected for the actual movement, for each iteration. The algorithm continues iteration until a prespecifi ed fraction of the points remain in the interior of the polygon.

When moving a corner inward, it needs to be checked when a specifi c refer-ence measurement point (superscript m ) of the cluster, r p

jm, , j = 1, … , N , becomes

exterior to the polygon. This check needs to be performed for all points of the cluster that remain in the interior of the polygon at the start of an iteration. Figure 32.13 shows three adjacent polygon corners rp

k , rpi , and rp

l . The middle point rpi is then

moved inward. The line segments connecting rpk and rp

i , as well as rpi and rp

l , move. At some point, r p

jm, may be intersected by either of these two line segments. To

determine the tentative points of intersection, it is noted that the movement of rpi

can be expressed as

r r r rp p p pCG

pi i iα α( ) = + −( ), (32.11)

where α p is a scalar parameter that varies between zero and one when the point moves between the original position and the center of gravity. A necessary require-ment for an intersection between the moving boundary of the polygon and r p

jm, is

that r rp p pi kα( ) − and r rp p

jm

k, − become parallel, or that r rp p p

i lα( ) − and r rp pjm

l, −

become parallel. The fact that the cross product between parallel vectors is zero allows for a computation of α p . Straightforward algebra gives

αi kj i k j

mk j

mk i k

i

x x y y x x y y

x x,,

, ,p

p p p p p p p p

CGp

=− −( ) −( ) + −( ) −( )

−( )) −( ) − −( ) −( )

=− −( ) −

y y x x y y

x x y

jm

k jm

k i

i lj i l j

m

, ,

,,

,

p p p pCG

p

pp p p

αyy x x y y

x x y y x xl j

ml i l

i jm

l jm

l

p p p p p

CGp p p p p

( ) + −( ) −( )−( ) −( ) − −(

,

, , )) −( )y yiCGp

.

(32.12)

Figure 32.13 Tentative polygon corner movement geometry for AECID.

r pi

rpi (α

p)

rpl

rpk

rm,p

rCG

j

c32.indd 1104c32.indd 1104 8/5/2011 3:46:12 PM8/5/2011 3:46:12 PM


The subscripts indicate the polygon corner points that defi ne the line segment under evaluation. The superscript denotes the index of the high - precision measurement point. Both the above are candidates for being an active constraint, for which it is required that αi k

j,, 0p > and αi l

j,, 0p > .

It remains to check if the intersection point falls between the corner points that limit the line segment of the polygon. This means that the following equations need to be fulfi lled for βi k

j,, 0, 1p ∈[ ] or βi l

j,, 0, 1p ∈[ ] :

r r r r

r r

p p p p p p

p p p

jm

i i kj

i kj

k i

jm

i i lj

i l

,,,

,,

,,,

,

= ( ) + −( )= ( ) +

α β

α β jjl i

, .p p pr r−( ) (32.13)

Since the vectors leading to the above equations are parallel, it is enough to consider one of the coordinates when solving for the β - parameters.

The conditions αi kj,, 0p > , αi l

j,, 0p > , βi k

j,, 0, 1p ∈[ ], and βi l

j,, 0, 1p ∈[ ] are then checked

for each point (for the specifi c polygon corner), and the point that meets the condi-tions and fi rst limits the inward movement is determined as the point that fi rst becomes exterior to the polygon. The procedure is then repeated for each corner. Finally, the corner that generates the largest decrease of the area of the polygon is selected for the current iteration of the algorithm. The mathematical details appear in Reference 26 .

In case TA is used, it may happen that the fi ngerprinted regions become very wide in the lateral direction and narrow in the radial direction, at the same time as they become curved. This follows since cells may be very large. Two problems then occur. First, the contraction point, given by the center of gravity of the cluster, may be located outside the cluster itself. This may prevent convergence of the algorithm to an accurate description of the boundary of the cluster. Second, all polygon corner points tend to converge toward the lateral center of the cluster. This follows since the corners move toward the center of gravity of the cluster, and since the cluster is much more wide in the lateral direction than in the radial direction. This leaves few points for modeling of the lateral end points of the cluster boundary, a fact that reduces accuracy. Reference 28 discusses this further and provides solutions to these problems.

The AECID positioning method is self - learning, using positioning attempts of opportunity. Furthermore, real - world radio conditions are captured. The problem with handheld UEs is also refl ected, which means that overoptimistic accuracies are avoided. Also, the confi dence is refl ected by real user data. The availability of OTDOA in LTE secures that the database of fi ngerprinted polygons will cover indoor locations. In fact, the OTDOA positioning method can also provide GSM and WCDMA with indoor high - precision position measurements, using the inter - radio access technology (RAT) signal strength measurements defi ned in LTE.

When a user is to be positioned by the AECID method, the E - SMLC orders radio property measurements, constructs the fi ngerprint, and looks up the fi nger-printed polygon and confi dence in its database. The position result is then reported. An example of the output is illustrated in Figure 32.14 . That fi gure is computed with a reference code for an AECID product, including the algorithms of both References 26 and 28 .

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Example 32.6 Polygon Computation Video Clip

The polygon computation algorithm is quite involved. For this reason, the algorithm was illustrated in MATLAB by creating a video clip, composed of all iterations applied in the computation of a cell boundary; that is, in this case, only CID was used for fi ngerprinting.

Solution

The video clip is available in the fi le Chapter_32_Example_6.avi. The result can be displayed by running the fi le in a suitable media player. In the video, the red dots represent the cluster points of the algorithm.

32.6.4 OTDOA

OTDOA is a DL positioning method standardized in LTE that exploits time differ-ence measurements conducted on DL reference signals received from multiple loca-tions. An OTDOA measurement, reference signal time difference ( RSTD ), is defi ned as the relative timing difference between two cells, the reference and a measured cell, calculated as the smallest time difference between two subframes received from the different cells. At least three timing measurements from geographically dispersed base stations with a good geometry are needed to solve for two coordinates of the UE, where the good geometry means that no two branches of the distinct hyperbolas intersect twice so that a unique solution can be found. In practice, a larger number of measurements, typically at least six to seven, is desirable. The position calculation is based on the multilateration approach by which an intersection of hyperbolas is

Figure 32.14 The high - precision position measurement cluster (black stars) and the computed polygon (black solid). The stars with surrounding circles represent high - precision position measurements that are exterior to the polygon after the computation using References 26 and 28 .

59.42

59.415

59.41

59.405

59.4

59.95

17.96 17.965 17.97 17.975

Longitude (degrees)

Latitu

de (

degre

es)

17.98 17.985 17.99 17.995

c32.indd 1106c32.indd 1106 8/5/2011 3:46:13 PM8/5/2011 3:46:13 PM


found, where a hyperbola for a pair of cells corresponds to a set of points with the same RSTD for the two cells. The OTDOA positioning method is illustrated in Figure 32.15 , where a UE is receiving DL signals from the eNodeBs and performing RSTD measurements τ 1,2 , τ 1,3 , and τ 2,3 , which form three intersecting hyperbolic strips, the widths of which correspond to the RSTD measurement uncertainties. The

distance equivalents of the RSTD measurements are d1,2, d1,3, and d2,3, respectively. Assuming the UE is located in ( x y ) T in an ET system, and eNodeBs are located at ( x 1 y 1 ) T , ( x 2 y 2 ) T , and ( x 3 y 3 ) T , respectively, the system of equations to be solved in the least squares sense to fi nd two - dimensional (2 - D) coordinates ( x y ) T is as follows:

x x y y x x y y d d

x x y y

12

12

22

22

1 2 1 2

22

22

−( ) + −( ) − −( ) + −( ) = −

−( ) + −( )

ˆ, ,Δ

−− −( ) + −( ) = −

−( ) + −( ) − −( ) + −(

x x y y d d

x x y y x x y y

32

32

2 3 2 3

12

12

32

3

ˆ, ,Δ

)) = −21 3 1 3

ˆ ,, ,d dΔ

(32.14)

where Δ d i , j is the distance equivalent of the transmit time difference for cells i and j ( Δ d i , j = 0 when the two cells are perfectly synchronized and Δ d i , j ≠ 0 for asynchro-nous systems, e.g., UMTS or the asynchronous mode of LTE). As follows, from the system of Equation 32.14 , the precise knowledge of the transmitter locations and timing offsets is needed to fi nd the UE coordinates. Determining transmitter timing is nontrivial at the required accuracy level. The advantage of OTDOA is that syn-chronization between the eNodeBs and the UE is not required, unlike when time - of - arrival measurements are used.

Many approaches exist for solving the system of equations (e.g., see Reference 29 ); most of them involve linearization of least squares minimization problems. With the common Taylor series - based approach, the UE coordinates ( x y ) T are found iteratively starting from an initial UE position estimate ( x 0 y 0 ) T . It is straightforward to extend the formulation to a larger set of eNodeBs and RSTD measurements for 3 - D coordinates. Please see Chapters 6 and 7 for a description of TDOA computa-tional techniques.

Figure 32.15 Multilateration in OTDOA positioning.

eNodeB3: (x3, y3)

eNodeB2: (x2, y2)

eNodeB1: (x1, y1)(x, y)

(x0, y0)

cell: PCI1

cell: PCI2

cell: PCI3

τ1, 2

τ1, 3

τ2, 3

c32.indd 1107c32.indd 1107 8/5/2011 3:46:13 PM8/5/2011 3:46:13 PM


Although RSTD measurements can be performed on a number of DL signals, for example, CRS or synchronization signals [3] , it has been recognized that the existing signals suffer from poor hearability, which is crucial for OTDOA when multiple remote neighbor cells have to be detected. Therefore, to ensure the possibil-ity of positioning measurements of a proper quality and for a suffi cient number of distinct locations, PRS [3] having transmission patterns with an effective reuse of six has been introduced in LTE.

PRSs are transmitted in certain positioning subframes grouped into positioning occasions . A positioning occasion comprises 1, 2, 4, or 6 consecutive positioning subframes and occurs periodically with 160 - , 320 - , 640 - , or 1280 - ms interval; these two parameters describe the PRS confi guration, which is a part of the assistance data signaled to the UE.

Within each positioning occasion, PRSs are transmitted with a constant power. PRS can also be transmitted with zero power, or muted , which can be utilized to avoid measuring in the presence of the strongest interferers. The PRS muting con-fi guration of the serving and neighbor cells is to be decided by the network and signaled to the UE over the LPP protocol.

To further improve hearability of PRS, positioning subframes have been designed as low - interference subframe s ( LIS s), that is, with low transmission activ-ity or without transmission on data channels. As a result, ideally in synchronous networks, PRSs are interfered by other - cell PRSs with the same PRS pattern index, that is, the same frequency shift, but not by data transmissions. To achieve good positioning performance, interference coordination for PRS is crucial in these sub-frames. Therefore, confi guring aligned positioning subframes over cells is a justifi ed PRS planning strategy giving synchronized positioning occasions in subframe - synchronized LTE networks and up to half - subframe aligned positioning subframes in asynchronous LTE networks.

The interference to PRS can be further minimized, for example, allowing simultaneous PRS transmissions for groups of cells with either orthogonal PRS patterns or low mutual interference. A PRS confi guration example for four cells is illustrated in Figure 32.16 . In OTDOA, the UE receiver has to deal with PRS from neighbor cells, much weaker than those received from the serving cell. Furthermore, without the approximate knowledge of when the measured signals are expected to arrive in time and what is the exact PRS pattern, the UE would need to search the signals blindly, which would impact the time and accuracy of the measurements. To facilitate UE measurements, the network transmits assis-tance data to the UE [11] , including, among the others, neighbor cell list with CIDs, the number of antenna ports, the number of consecutive DL subframes per position-ing occasion, PRS transmission bandwidth, expected RSTD, and the estimated uncertainty.

The signaled expected RSTD and the estimated uncertainty defi nes the search window. Given the distance between the UE and the reference cell 1 (e.g., R TA obtained from Eq. 32.6 when the reference cell is the serving cell) and the distance d 1,2 between the reference cell 1 and the measured cell 2, the search window for signals from the measured cell is the range [ − R TA / c , R TA / c ] centered at ( Δ d 2,1 + d 1,2 − R TA )/ c with respect to the reference cell, where c is the speed of light.

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The PRS signal is transmitted in N prs consecutive subframes. The total number of OFDM symbols containing PRS resource elements over all the consecutive sub-frames is N l . Let the time domain signal transmitted in the l th OFDM symbol be denoted

s n n N N l Nl l( ) = − − = −, , , 1, 0, , 1,cp … … (32.15)

where N cp is the CP length, N is an OFDM symbol length in time samples, and where

s n s n N n Nl l( ) = +( ) = − −, , , 1.cp … (32.16)

Let a multipath channel characterized by a discrete fi nite length time impulse response be ( h (0) … h ( K − 1)) T , with h ( i ) = 0, i < 0, I ≥ K . Then the signal propa-gated through the channel becomes

y n h i s n i n n N N Kl l l

i

K

( ) = ( ) − −( ) + ( ) − + + −=

−

∑ τ ε τ0

1

, = , , 2,cp … (32.17)

where ε l ( n ) is additive complex Gaussian noise with variance N 0 , and τ is the propa-gation delay, for simplicity assumed to be an integer number of samples. The problem is to estimate the arrival time τ of the fi rst path of the channel.

For OFDM, the reference signal is specifi ed in the frequency domain. It is well - known that the circular convolution of two sequences is equal to multiplication of the FFTs of the signals in the frequency domain. In the circular convolution, the linear convolution (Eq. 32.17 ) is replaced with

y n h i s n i n n Nl l N l

i

K

( ) = ( ) − −( ) + ( ) = −=

−

∑ τ ε0

1

, 0, , 1… , (32.18)

Figure 32.16 A PRS confi guration example for three subframe - synchronized cells, which are half - subframe aligned with the fourth cell. The dashed rectangles are the positioning occasions with a transmitted PRS which are otherwise muted in other positioning occasions. A positioning occasion comprises six consecutive PRS subframes.

PCI = 6 ... ... ... ...

PCI = 0

PCI = 1

...

...

...

...

...

...

...

...

PCI = 7 ... ... ... ...

positioningoccasion withmuted PRS

positioningoccasion withmuted PRS

positioningoccasion with

transmitted PRS

positioningoccasion with

transmitted PRS

...... time

frequency

c32.indd 1109c32.indd 1109 8/5/2011 3:46:13 PM8/5/2011 3:46:13 PM


where s l ( · ) N means that the index is taken modulo N . Due to the use of a CP of length N cp , s l ( − n ) = s l ( N − n ), for n = 1 … , N cp . Hence, as long as K + τ − 1 ≤ N cp , the circular convolution is equal to the linear convolution. To exploit this, the FFT of Equation 32.18 is

Y k

Nh i s n i n e

H

l l N l

i

Ki nk N

n

N

( ) = ( ) − −( ) + ( )⎛⎝⎜

⎞⎠⎟

==

−−

=

−

∑∑1

0

12

0

1

τ ε π

ll li k N

lk S k e E k k N( ) ( ) + ( ) = −− 2 , 0, , 1.πτ …

(32.19)

Since S l ( k ) is known, multiplication in frequency domain yields an estimate of the channel in the frequency domain as

H k Y k S k H k e S k E kl l l li k N

l l( ) = ( ) ( ) = ( ) + ( ) ( )−* 2 * .πτ (32.20)

The PRS signal spans several OFDM symbols, so the processing is repeated for a number of consecutive OFDM symbols containing PRS, resulting in

ˆ ˆH kN

H k k Nk

l

l

Nk

( ) = ( ) = −=

−

∑1, 0, , 1,

0

1

… (32.21)

where N k is the number of coherently accumulated PRS symbols in subcarrier k . If N k and/or the Doppler spread are large, the terms in the complex sum (Eq. 32.21 ) may start to cancel each other. In such a case, it is necessary to divide the coherent accumulation into M segments, and perform an IFFT on each, resulting in

ˆ ˆh n H km ( ) = ( )( )IFFT , (32.22)

which is the time domain complex channel estimate for the m th segment. Finally the M channel estimates are noncoherently added. The resulting correlator output can then be written as

ˆ ˆr n h nm

m

M

( ) = ( )=

−

∑ 2

0

1

. (32.23)

The values of r n( ) are compared to a threshold and if any values fall above the threshold, then a fi ne search is performed to interpolate the position of the fi rst peak.

Since there is no guarantee that the signal has enough power to be detected, the threshold should be selected so as to avoid false alarms. Assuming only complex Gaussian noise as input in Equation 32.22 , the terms are complex Gaussian distrib-uted with variance

N N Nk

k

N

0 0

0

1

==

−

∑ .

Hence r n( ) of Equation 32.23 is the sum of squares of Gaussian variables. Therefore, it is convenient to modify the detection variable to be

λ = ( )2 0r n N

c32.indd 1110c32.indd 1110 8/5/2011 3:46:13 PM8/5/2011 3:46:13 PM


which is χ 2 (2 M ) distributed. This can be used to determine an appropriate threshold for a desired false alarm rate.

Assuming the PRS pattern in Figure 32.4 , a system using N RB resource blocks, N prs positioning subframes, and coherent accumulation over N c subframes, it can be readily determined that

1 70

1

N N Nk

k

N

c

=

−

∑ = RB .

Furthermore, when the signal part dominates over the noise in Equation 32.23 , this expression becomes r n h n L M( ) ≈ −( )τ 2 2

prs , where L prs = 10 N RB is the number of subcarriers occupied by PRS, and M = N prs / N c .

Therefore, λ ≈ (200 N RB N prs /7)| h ( n − τ )| 2 / N 0 . The factor

γ prs RB prs= 200 7N N (32.24)

can be interpreted as the processing gain of the PRS detector. For the CRS pattern in Figure 32.4 , it can similarly be verifi ed that

1 30

1

N N Nk

k

N

c

=

−

∑ = RB .

Furthermore, the signal part in Equation 32.23 becomes r n h n L M( ) ≈ −( )τ 2crs2 ,

where L crs = 4 N RB is the number of subcarriers occupied by CRS. Therefore λ ≈ γ crs | h ( n − τ )| 2 / N 0 with

γ crs RB prs= 32 3.N N (32.25)

The probability of false alarm assuming threshold λ * can be computed as

P chi cdf Mfa = − ( )1 2 , 2λ* . (32.26)

The above discussion provides the tools needed to assess the probability of detection of a certain number of base stations. This translates into predictions of the avail-ability of the OTDOA method, which, together with accuracy, is the most important performance characteristic.

Example 32.7 OTDOA Coverage

The expected coverage of OTDOA, that is, the probability that at least three base stations can be measured, is evaluated for a simulated case in this example. The use of PRS and CRS is compared. It should be noted that the detection of three eNodeBs is a bare minimum; in practice, excess detections are often necessary to be able to suppress outliers in the measurements. Such outliers can, for example, arise due to non - line - of - sight (NLOS) propagation. For the above reason, the detection capability of a TDOA method can often be the limiting factor, which makes it important to understand how the detection performance is computed.

c32.indd 1111c32.indd 1111 8/5/2011 3:46:14 PM8/5/2011 3:46:14 PM


Solution

In Figure 32.17 , the false alarm probability is plotted versus SINR * = λ * / γ prs,crs , for M = 1, 2, 3, 6 using Equation 32.26 . For the calculation of γ prs,crs using Equations 32.24 and 32.25 , N RB = 6 and N prs = MN c = 6 was assumed. It can, for example, be seen that if the desired P fa = 10 − 4 , then for PRS and M = 1, the threshold SINR * is roughly − 17.5 dB, whereas for M = 6, the threshold becomes roughly − 14 dB. The corresponding numbers for CRS are − 13 and − 10 dB, respectively. Thus, the detec-tion probability of CRS is approximately 3.5 – 4.0 dB worse than that for PRS. Furthermore, higher UE speed (larger M ) requires higher SINR * . In Figure 32.18 , cumulative distribution function s ( CDF s) of simulated signal - to - interference - plus - noise ratio s ( SINR s) are shown for the best fi rst, second, third, and fourth sites, respectively, for a system using CRS and PRS. The presented results are for uni-formly distributed users in a network of 19 sites with an intersite distance of 500 m, three - sector realistic 3 - D antennas, and 25% data load. When interference is not specifi cally handled, the CRS also gets interfered by data transmitted in cells that are not in the same frequency reuse group as the measured cell. By comparing Figure 32.17 with Figure 32.18 , it can be concluded that the probability to be able to measure three or more base stations is close to 100% for PRS for all choices of M . For CRS, the probability is around 91% when using M = 1 and 88% when using M = 6. Note that these calculations assume a single - tap channel h ( n ). In reality, the channel energy is usually spread over several lags, meaning that the probability to detect three base stations is lower.

32.6.5 U - TDOA

The major conceptual difference between U - TDOA [13] and OTDOA is that the latter requires multiple transmit points, while the former utilizes multiple receive points at different locations, although the position calculation principle is the same.

Figure 32.17 Probability of false alarm as a function of detection threshold.

100

10–1

10–2

10–3

Pfa

10–4

10–5

10–6

–28 –26 –24 –22 –20 –18

SINR* threshold (dB)

–16 –14 –12 –10 –8

PRS, M = 1PRS, M = 2PRS, M = 3PRS, M = 6CRS, M = 1CRS, M = 2CRS, M = 3CRS, M = 6

c32.indd 1112c32.indd 1112 8/5/2011 3:46:14 PM8/5/2011 3:46:14 PM


To perform U - TDOA timing measurements on user data, one reference receiver decodes the UE signals and forwards the sequence to cooperating receivers. This procedure is relatively complex and requires a signifi cant amount of signaling. Therefore, SRSs [3] have been selected for U - TDOA measurements. For U - TDOA positioning, periodically transmitted SRSs are scheduled in a nondynamic way to allow a suffi ciently long time for the measurements. This reduces the need for sig-naling of the full scheduling information to communicate the SRS confi guration parameters. SRSs occupy a selected part of the last OFDM symbol in a subframe. The used bandwidth and the periodicity can be confi gured to meet the demands for positioning. SRS measurements for positioning may either be performed and pro-cessed directly at a radio base station or the operation may be performed by specifi c measurement units that may or may not share the antennas with the radio base sta-tions. The main disadvantage with U - TDOA, as compared to OTDOA, is a hearabil-ity problem due to the power control of the UE transmissions. UEs close to their own base station transmit at a low power level to avoid creation of unnecessarily high levels of interference — this is denoted the near - far problem. The consequence is that such signals may not be strong enough to reach the required UL signal strength for U - TDOA measurements at neighbor sites.

At the time of writing, U - TDOA has been approved for standardization in a later LTE release; the reader is referred to future revisions of Reference 20 for details.

32.6.6 A - GNSS

GNSS is a generic name for satellite - based positioning systems with global cover-age, see Chapter 28 . Examples of GNSS systems include the U.S. GPS [10] , the European Galileo, the Russian Glonass, and the Chinese Compass. In addition, there

Figure 32.18 SINR CDFs with CRS and PRS.

4th best site

CRS, 1TX:

PRS, aligned LIS:

3rd best site2nd best site

1st best site

4th best site3rd best site

2nd best site1st best site

–300

0.1

0.2

0.3

0.4

0.5

CD

F

0.6

0.7

0.8

0.9

1.0

–20 –10 0 10

SINR (dB)

20 30 40 50

c32.indd 1113c32.indd 1113 8/5/2011 3:46:14 PM8/5/2011 3:46:14 PM


exist regional satellite - based augmentation system s ( SBAS ), including Wide Area Augmentation System (WAAS, United States), European Geostationary Navigation Overlay Service (EGNOS, European Union), Multi-functional Satellite Augmentation System (MSAS, Japan), and Aided Geo Augmented Navigation (GAGAN, India). SBAS typically use a few satellites to provide improved ionospheric models and real - time integrity monitoring. The SBAS satellite signals can also be used as an additional satellite in computing the receiver position.

Of these systems, only GPS is fully operational. The basic characteristics of the transmitted signals from GPS satellites is shown in Figure 32.19 . The signal is transmitted on the L1 frequency (1175.28 MHz), and it is a code division multiple access (CDMA) signal characterized by a coarse acquisition (C/A) pseudorandom code that is unique to each satellite. A simplifi ed model of the received, sampled baseband signal at time sample t k is

y t Pc t d t e n tk k tr k trj t

ktr k( ) = +( ) +( ) + ( )− +( )τ τ ω φ , (32.27)

where P is the received SV signal power and c ( t ) is the C/A code of the satellite, a known sequence of − 1 and + 1 values that switch with a rate of 1/ T c = 1.023 MHz. The C/A code repeats itself every 1 ms. The quantity τ tr is the code phase; d ( t ) is a sequence of − 1 and + 1 values containing navigation data, which switches at a rate of 20 ms; ω tr is the unknown Doppler shift; and ϕ is an unknown phase offset. The noise n ( t ) is assumed to be white with spectral density N F k B T 0 , where N F is the receiver noise fi gure, k B = 1.38 · 10 − 23 J/K, and T 0 is the receiver noise temperature. Interference from other satellites is not modeled here. Since the multiple access interference adds of the order of 0.1 dB to the noise power, GPS is essentially a noise - limited CDMA system. The task of the GPS receiver is to fi nd the correct code phase and doppler frequency, detect the data bit edges, and perform navigation data decoding. When the GPS receiver has acquired the timing and decoded the naviga-tion signal from at least four satellites, it can determine its location. The A - GPS receiver attempts to improve or eliminate some of the steps above. In order to do

Figure 32.19 The GPS signal structure.

1 navigation data bit20 ms

20 C/A codes

1 C/A code1 ms

A·cos(ω0t)

A·c(t)·d(t)·cos(ω0t)

1 C/A code = 1023 chips1 chip = 1/1,023,000 s

d(t)

c(t)

c32.indd 1114c32.indd 1114 8/5/2011 3:46:14 PM8/5/2011 3:46:14 PM


so, assistance data are collected from a network of GPS reference receivers. These reference receivers are located at sites with favorable signal conditions. The receiv-ers continuously track visible SVs, decode their messages, and transfer the informa-tion to the cellular network for further distribution to the GPS receivers in the UEs. In this way, the decoding may be avoided and the GPS receiver in the UE gets access to complete navigation models and correction parameters.

Assistance data are also helpful in reducing the time to fi nd the correct code phase and doppler [30] . By using knowledge of the approximate receiver location, the Doppler shift of each visible SV can be predicted and the search space in the Doppler domain can be reduced (see Fig. 32.20 ). It is also possible to provide the GPS receiver with GPS time information, accurate to a few microseconds, by exploiting, for example, a GPS receiver in the base stations of the cellular network [30] . With such information, only coherent code and Doppler search over a small search window would remain (see Fig. 32.20 ). Further information on A - GNSS signal processing appears in Chapters 22 and 29 .

A comparison of the time to fi rst fi x and sensitivity performance of different A - GPS variants is shown in Table 32.1 (see also Reference 7 ).

Figure 32.20 Search window reduction.

5

0

–5 0200

400600

8001000

0

0.2

0.4

Norm

aliz

ed c

orr

ela

tor

outp

ut

Frequency offset (kHz) Code delays (chips)

0.6

0.8

1.0

TABLE 32.1. A - GPS Comparison ( A Noise Figure of 5 d B is Assumed)

A - GPS Variant Assistance Data Response Time (s) Sensitivity (dBm)

Stand - alone FR 20 – 40 − 171 Basic FR, NM, CT ( ≈ 2 seconds) 8 – 15 − 178 Synchronized FR, NM, AT ( ≈ 10 μ s) 1 – 8 − 185

FR, frequency reference; NM, navigation models; CT, location coarse time; AT, location accurate time.

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32.7 SHAPE CONVERSION

The term shape conversion denotes the geometric transformations between the 3GPP geographical shapes [9] . Such algorithms are needed for three main reasons. First, the Public Safety Answer Point ( PSAP s) in the United States expect E - 911 position results in the form of an ellipsoid point with uncertainty circle. Second, similar restrictions may be in place for certain LBSs. Third, it is common that E - UTRAN and EPC vendors only support a restricted set of positioning reporting formats, and then interoperability requires shape conversions.

Although shape conversions enhance the fl exibility of positioning solutions, they have a distinct drawback in that they destroy information. This actually makes some E - 911 reporting standards in the United States major bottlenecks as far as E - 911 compliance is concerned.

In order to understand why, the conversion between the ellipsoid arc and the point with uncertainty circle formats is considered — this transformation is highly likely to be needed for E - 911 reporting when the E - CID positioning method is used. The transformation is depicted in Figure 32.21 . In this transformation it is assumed that the underlying probability density function of the ellipsoid arc is uniform [31] since the extension of this region is normally dependent on radio propagation proper-ties rather than random measurement errors. It is also assumed that the required confi dence of the transformed shape, that is, the circle, shall be the same as for the ellipsoid arc. The consequence is that the circle needs to cover the entire ellipsoid

Figure 32.21 Shape conversion between the ellipsoid arc and the ellipsoid point with uncertainty. The radio base station (RBS), that is, the eNodeB (asterisk), is in the origin. The ellipsoid arc and the circle are shown solid.

*

*

500

0

–500

–1000

Dis

tance (

m)

Distance (m)

–1000 –500 0 500 1000 1500 2000 2500 3000

–1500

–2000

–2500

–3000

1000

c32.indd 1116c32.indd 1116 8/5/2011 3:46:14 PM8/5/2011 3:46:14 PM

32.7 SHAPE CONVERSION 1117

arc, a fact that is exploited by the algorithm of Reference 31 . It is evident that the area of the circle can become much larger than the area of the original shape, in particular, in rural regions where the lateral extension of the ellipsoid arc may be tens of kilometers. As discussed in Reference 31 , the loss of accuracy expressed as an area may exceed a factor of 100 for E - CID E - 911 reporting in such cases. A typical E - SMLC may need more than 15 shape conversions in order to be fl exible enough [17, 22] .

Example 32.8 Shape Conversion Accuracy Loss

The example illustrates the severe loss of accuracy caused by the need to perform a shape conversion when doing E - 911 positioning, using CID + TA E - CID positioning.

Solution

Figure 32.22 illustrates the loss of accuracy when the ellipsoid arc is transformed to an ellipsoid point with uncertainty circle. The loss of accuracy was calculated in terms of the quotient of the areas of the two reported regions. The TA uncertainty was 200 m. The calculations used cell shapes that were roughly hexagonal. Similar but less severe results occur for A - GPS positioning (see Reference 31 and the example code fi le Chapter_32_Example_9.m for that case. MATLAB codes can be found online at ftp://ftp.wiley.com/public/sci_tech_med/matlab_codes ).

Figure 32.22 Accuracy loss due to E - 911 reporting for CID + TA positioning. Values for urban (left curve), suburban (middle curve), and rural (right curve) cells with radii of 500, 5000, and 50,000 m, respectively.

E-911 reporting accuracy lossra

tio b

etw

een u

ncert

ain

ty c

ircle

are

a a

nd e

llipsoid

arc

are

a

100100

101

101

102

102

103

distance RBS–>UE (m)

103 104 105

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Example 32.9 Ellipse to Circle Shape Conversion

The shape conversion from the ellipsoid point with uncertainty ellipse to the ellip-soid point with uncertainty circle, based on a Gaussian distribution, is described in Reference 31 . This transformation is typically used for E - 911 reporting when A - GPS positioning has been performed. The fi le Chapter_32_Example_9.m contains a com-plete MATLAB code for this case. The example code also contains the 3GPP encoding/decoding needed.

Solution

The example code is run from the MATLAB workspace. When executing the code, the variable positionFormatDescription is expected to be present in the workspace of MATLAB. positionFormatDescription contains a 3GPP encoded ellipsoid point with uncertainty ellipse. The 3GPP encoded format contains the following elements (in order): the number of the format, the encoded latitude sign, the encoded latitude, the encoded longitude, the encoded semimajor axis, the encoded semiminor axis, the encoded orientation angle (clockwise from north), and the encoded confi dence. In order to execute the code, the reporting confi dence of 0.95 also needs to be defi ned in the MATLAB workspace. The encoded result is stored in encodedEllipsoid-PointWithUncertaintyCircle. This variable stores the following elements (in order): The number of the format, the encoded latitude sign, the encoded latitude, the encoded longitude, and the encoded accuracy code. A typical MATLAB command sequence is as follows:

>> positionFormatDescription = [3 0 400 400 25 15 130 39]; >> confi denceAfterTransformation = 0.95; % Change the confi dence level

>> Chapter_32_Example_9 % Perform transformation

>> encodedEllipsoidPointWithUncertaintyCircle % Display the

result

encodedEllipsoidPointWithUncertaintyCircle = 1 0 400 400 32

It can be noted that the accuracy code is larger than both the semimajor axis and the semiminor axis. This follows since the reporting confi dence is larger than the input confi dence.

32.8 POSITIONING PERFORMANCE IN LTE

32.8.1 Limiting Factors

A fi rst factor that infl uences the availability of a positioning method is the UE support since large parts of the 3GPP specifi cations are optional. Other critical parameters affecting availability include the detection performance of the UE, the link budgets, and the geometry of the cellular network. For example, it is well - known that the weak link budget for A - GNSS makes indoor positioning availability poor

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32.8 POSITIONING PERFORMANCE IN LTE 1119

[7] , whereas the geometry in rural areas may limit the number of detectable eNodeBs for OTDOA.

The response time is affected by the complexity of the positioning measure-ments and the prior knowledge of the UE position and time. For time measurement - based positioning methods like A - GNSS and OTDOA, the two last parameters affect the size of the search window over which correlations need to be evaluated to fi nd the pseudorange or time of arrival. It can be noted that for A - GPS, the availability of fi ne time assistance [7, 30] can substantially reduce the positioning time and enhance the availability.

In the literature, positioning accuracy has often been addressed by a combina-tion of geometric effects and pure measurement inaccuracy, using linearization [10] and theoretical performance measures like the Cramer – Rao lower bound. However, in particular, for terrestrial time measurement - based methods, like OTDOA, this is seldom true. Positioning accuracy is rather dominated by NLOS propagation (Chapter 16 ) and the ability to detect a large enough number of eNodeBs to handle outlier measurements.

32.8.2 Accuracy Metrics

Due to the factors that limit practical positioning performance, it is preferred to evaluate positioning performance in fi eld trials. Both availability and response time can be directly measured, whereas it is more diffi cult to address the horizontal accuracy.

Since the geographical reporting shapes are geometrically very different, a common method to address the horizontal accuracy for a specifi c positioning method is to compute the area of the reported region, followed by a computation of the radius, r uncertainty , of a circle that covers the same area, A reported , as the reported geo-graphical shape. Averaging over the results gives the performance metric

rN

A i

i

N

uncertaintyreported=

=∑1

.,

1 π (32.28)

The metric (Eq. 32.28 ) does measure the uncertainty, but the relation to the actual UE position is not captured. To defi ne such a metric, it is assumed that a number of accurately surveyed truth points, ( x truth, j y truth, j ) T , j = 1, … , M , are available in a Cartesian ET coordinate system. A number of measurements, ( x i , j y i , j ) T , i = 1, … , N , j = 1, … , M , are then performed at each of these truth points. The average 2 - D error, duncertainty, can then be computed as

dMN

x x y yi j j i j j

i

N

j

M

uncertainty truth truth= −( ) + −( )==

∑1, ,

2, ,

2

11∑∑ . (32.29)

32.8.3 Expected Performance

CID : The CID positioning method is based on preconfi gured geographical cell information, ranging from a point to a complete polygon. The method thus consists

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of reporting the cell ID to the E - SMLC, followed by a database lookup and reporting to the end user. The CID method is therefore available wherever there is LTE cover-age. The response time can be expected to be very short, signifi cantly less than 1 second. The drawback is the accuracy that is determined by the size of the cell. Typical values for cell sizes, that is, the largest distance from the base station to the cell edge, are 150 – 400 m (urban), and 1000 – 3000 m (suburban).

E - CID : The basic E - CID method augments the CID method by TA and signal strength measurements. These measurements are available almost anywhere where there is cellular coverage, resulting in almost the same availability as for CID. The response time is increased somewhat due to the need to perform measurements and reporting these, but it is expected to be below 1 – 2 seconds.

The radial accuracy can be estimated from fi eld trials performed for the RTT positioning method in WCDMA [17] . These results indicate a radial accuracy of about 80 m (67%) and 170 m (95%), with the nominal (90%) measurement accuracy of that method being 78 m according to 3GPP specifi cations. The distribution of the radial error appears in Figure 32.23 . This means that propagation conditions are starting to dominate the radial error at the WCDMA bandwidth of 3.84 MHz. For LTE, the specifi ed reporting quantization of the TA corresponds to 10 – 40 m [5] , which means that the quantization is comparable to the one used for RTT positioning in WCDMA. Since the bandwidth of the LTE system is normally higher than that of WCDMA, it seems safe to conclude that E - CID in LTE is likely to perform at least slightly better than RTT positioning in WCDMA.

The lateral inaccuracy is mainly determined by the right and left limits of the geographical extension of the cell [22] . When signal strength measurements are

Figure 32.23 Cumulative distribution of the absolute radial distance error in all radio environments. The middle black curve represents the results with all measurements from all terminals included, whereas the other curves show results for each of three terminal types.

100

90

80

70

60

50

0 50 100 150 200

Absolute Radial Error (m)

250 300 350 400

(%)

40

30

20

10

0

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combined with the cell description and the TA, the lateral accuracy can be further improved.

AOA measurements may improve the positioning accuracy in some scenarios, reducing the lateral inaccuracy. The performance of AOA - based E - CID depends on the antenna confi gurations as discussed in Section 32.6.2 (see Fig. 32.12 ). Another important factor is the radio environment. In urban areas, where the angular spread is large, one can expect large AOA errors. However, in rural areas with less angular spread and sparse deployment, or along highways, the combination of AOA and TA from one site may be attractive.

Fingerprinting: The availability and response time for fi ngerprinting in LTE can be expected to be comparable to the availability and response time of the E - CID method since the positioning step requires similar measurements.

It is not straightforward to state the accuracy for RF fi ngerprinting since algo-rithmic refi nements like the use of differential signals strengths can signifi cantly improve the accuracy beyond what is predicted by Equation 32.9 . Vendors claim that E - 911 requirements can be met, at least in rural areas. What is clear is that the error will scale with the cell size as shown by Equation 32.9 .

For the AECID positioning method, fi eld trial results for GSM have been presented in Reference 32 . Those results indicate that the adaptation to measured reference positions of opportunity from A - GPS improves the performance by a factor of about two (measured by Eq. 32.29 ) as compared to an E - CID method using the same measurements (see Fig. 32.24 ) This scaling is expected to carry over to LTE,

Figure 32.24 Cumulative radial inaccuracy (solid), TA distances (stars), and confi dence (dashed), for AECID (left) and CGI - TA (right). Note that CID + TA are the main sources of information and that the AECID results include effects of the shape conversion of Reference 34 .

100

90

80

70

60

50

Fra

ction (

%)

and c

onfidence (

%)

40

30

20

10

00 500 1000

Inaccuracy (m)

Cumulative 2—D inaccuracy and confidence -

dense urban environment

**

*

*

1500

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also when AOA information is included in the fi ngerprint. It is further expected that the sensitivity to NLOS propagation of AOA will be mitigated by the AECID adaptation.

OTDOA : The OTDOA position accuracy depends mainly on RSTD measurement quality and geometry. The best accuracy is achieved with the PRS transmission bandwidth of 10 MHz and larger. The minimum required measurement accuracy [5] of about 50 m is achieved after measuring over one positioning subframe at the PRS SINR of − 6 and − 13 dB for the reference and measured cells, respectively. The RSTD reporting granularity is about 10 m for the largest part of the feasible range. Example results for simulated OTDOA accuracy are shown in Figure 32.25 using extended typical urban (ETU) and extended pedestrian A (EPA) channel models for synchronous (1.4 MHz) and asynchronous (10 MHz) networks. The number of posi-tioning occasions were one and three, respectively, and the signals are coherently accumulated within N prs = 6. The impact of real measured propagation channels on OTDOA positioning has been studied in Reference 33 , where highly accurate and well - calibrated channel measurement data from a measurement campaign in an urban macrocellular LTE scenario showed that a positioning accuracy better than 20 m for 50% and 63 m for 95% of the time may be achieved. Note that in more diffi cult radio environments, accuracy may be further degraded as compared to Figure 32.25 .

U - TDOA : The U - TDOA method is discussed at length in Reference 8 . Due to the larger bandwidth of the LTE system, the expected performance of U - TDOA in LTE is expected to be better than reported in Reference 8 for GSM.

A - GNSS : The fi eld performance of A - GPS and A - GNSS have been discussed in many publications, and these methods are known to be very accurate in clear - sky conditions (see Fig. 32.26 ). Here, it should be noted, though, that in dense urban canyons, the cell plan may in fact give a CID accuracy that is comparable to A - GNSS

Figure 32.25 OTDOA accuracy for an intersite distance of 500, case 1 [35] .

1

0.8

0.6

CD

F

0.4

0.2

00 20 40 60 80

Positioning error, (m)100 120 140 160

EPA, synch, 1.4 MHz, 1 pos. acc: 100.00% (50 m), 100.00% (150 m)

ETU, synch, 1.4 MHz, 1 pos. acc: 88.50% (50 m), 95.98% (150 m)

EPA, asynch, 10 MHz, 3 pos. acc: 97.59% (50 m), 98.15% (150 m)

ETU, asynch, 10 MHz, 3 pos. acc: 95.67% (50 m), 98.08% (150 m)

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due to the NLOS propagation caused by very tall buildings, which deteriorates A - GNSS accuracy (see Fig. 32.27 ).

Comparison of the Expected Performance for Different Methods: The main characteristics of the different positioning methods in LTE and their expected positioning performance are summarized in Tables 32.2 and 32.3 . The footnotes in Table 32.2 give an indication of the dominating factors behind the described impacts, when there are such. Note that the impact on UEs, base stations (sites), and the

Figure 32.26 A - GPS accuracy in a rural environment.

50

40

30

20

10

–50 –50 –10 10 30 50

0

Nort

h (

m)

East (m)

–10

–20

–30

–40

–50

Figure 32.27 A - GPS accuracy in a dense urban environment.

800

600

400

200

Nort

h (

m)

0

–200

–400

–600–800 –600 –400 –200

East (m)

0 200 400

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TABLE 32.2. Typical Characteristics of Different Positioning Methods in LTE

Positioning Method

Earliest LTE Release/Optional

Environment Limitations UE Impact Site Impact System Impact

CID All/no No No No Small d E - CID Rel - 9/yes No/medium c Small Small/large c Medium e RF fi ngerprinting Rel - 9/yes (Rural) a Small Small Large e , f AECID Rel - 9/yes No Small Small Medium OTDOA Rel - 9/yes (Rural) a Medium Medium Medium g U - TDOA Rel - 11/yes (Rural) a , h Small Large Large A - GNSS Rel - 9/yes Indoors Large b Small Medium g

a No limitation if a suffi cient number of sites with a good joint geometry are detectable (for DL) or can detect the signal (for UL).

b An A - GNSS receiver is necessary.

c AOA measurements may suffer from NLOS conditions and require antenna arrays.

d Mainly confi guration, since coordinates of all cells need to be confi gured.

e Large database maintenance.

f Advanced signal processing, fi ltering over time and test drives.

g Assistance data build up, by the network (OTDOA) or by external providers (A - GNSS).

h Unlike with OTDOA, the U - TDOA performance is further subject to hearability limitations due to the UL power control and the maximum UE transmit power.

TABLE 32.3. Typical Accuracy of Different Positioning Methods Available in LTE , Subject to Restrictions of Table 32.2

Positioning Method Availability

Response Time (in RAN)

Horizontal Result Uncertainty

Vertical Result Uncertainty

CID 100% Very low High, α = 1 a n.a. E - CID Very high Low Medium α < 1 a n.a. RF fi ngerprinting High Low/medium Low/medium, α < 1 a Medium b AECID High Low Low/medium, α < 1 a Medium b OTDOA High Medium < 100 m Medium b U - TDOA High Medium < 100 m c Medium b A - GNSS High Medium/high < 5 m < 20 m

a Proportional to the cell range, with a proportionality constant α .

b Optional support.

c Only for a large SRS bandwidth and only with special processing in the receiver.

RAN, radio access network.

positioning system (mainly the positioning node) described in Table 32.2 also include the efforts associated with the implementation of new interfaces, new pro-tocols (e.g., LPP and LPPa), and their transport over the lower - layer protocols.

The accuracy and the response time, as indicated in Table 32.3 , may vary signifi cantly and are highly dependent on the network deployment and implementation. In general, the response time of CID is the lowest (mainly table

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REFERENCES 1125

lookup), and the response time of A - GNSS is the longest (mainly due to the long signal accumulation time needed to cope with low received powers at cold starts). For OTDOA, the measurement time depends mainly on the number of cells in the neighbor cell list. For RF fi ngerprinting, advanced signal processing and the use of measurements during time intervals of several seconds probably contribute the most, which impacts both the UE and the positioning node complexity. The availability aspect covered in Table 32.3 refers to the average success rate of the corresponding method in different networks and their parts. In general, a high availability is required, especially in networks where regulatory positioning requirements apply, for example, in the United States.

For all the methods, the reported result contains at least the horizontal position. Although the uncertainty of the horizontal position, that is, the estimated positioning error, cannot always be reported to the requesting node using the native shape of the positioning method, the uncertainty can always be reported after a suit-able shape converting transformation. A vertical positioning result is not always available, for example, for CID and E - CID. It may, however, be obtained for AECID, OTDOA, and U - TDOA and is of a practical use when the uncertainty is not too large. Vertical information and uncertainty are almost always reported when A - GPS is used.

32.9 SUMMARY

This chapter discussed the positioning functionality standardized in 3GPP for the LTE system. The LTE architecture was reviewed, emphasizing aspects of nodes, signaling, and air interface properties that are important for positioning. A discussion of requirements was used to highlight the need and techniques for LBS discrimina-tion in the E - SMLC. The backbone positioning method in LTE is the cell ID method, which is augmented, for example, by TA and AOA information in the E - CID class of methods. The LTE system is also prepared for fi ngerprinting positioning. The OTDOA method performs hyperbolic trilateration on DL PRSs, while the satellite navigation functionality provided by A - GNSS is similar to that in other cellular systems. A U - TDOA method is under standardization. The LTE system uses the seven reporting formats defi ned by 3GPP for the GSM and WCDMA systems. Techniques for conversions between these shapes were reviewed. The predicted performance of the positioning methods were discussed, thereby indicating how they can be applied to address different positioning services.

REFERENCES

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[2] 3GPP , 3GPP TS 36.401, “ Evolved Universal Terrestrial Radio Access Network (E - UTRAN); Architecture description , ” Release 9 (V9.1.0), 2010 .

[3] 3GPP , 3GPP TS 36.211, “ Evolved Universal Terrestrial Radio Access (EUTRA); Physical Channels and Modulation , ” Release 9, 2010 .

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[4] 3GPP , 3GPP TS 22.071, “ Technical Specifi cation Group Services and System Aspects; Location Services (LCS); Service description; Stage 1 , ” Release 9 (V9.0.0), 2009 .

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[9] 3GPP , 3GPP TS 23.032, “ Universal Geographical Area Description (GAD) , ” Release 9 (V9.0.0), 2009 .

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Protocol (LPP) , ” Release 9 (V9.0.0), 2010 . [12] 3GPP , 3GPP TS 36.455, “ Evolved Universal Terrestrial Radio Access (EUTRA); LTE Positioning

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[32] L. Shi and T. Wigren , “ AECID fi ngerprinting positioning performance , ” Proc. Globecomm 2009 , Honolulu, USA, 2009 .

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[35] 3GPP , 3GPP TS 36.814, “ Evolved Universal Terrestrial Radio Access (EUTRA); Further advance-ments for E - UTRA physical layer aspects , ” Release 9 (V9.0.0), 2010 .

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handbook of position location (theory, practice, and advances) || positioning in lte

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