wave generation

Waveform Generation

Waveform GenerationPrepared by:

Jalal Al-Roomy 120050239

Akram Abu-Raida 120061458

Department of Electrical EngineeringThe Islamic University of Gaza

Gaza - Palestine

Submitted to: Dr. Mohammed OudaJanuary 2010ABSTRACT

Radars use different types of waveforms, each waveform with its own specifications, depending on the desired application. In this report, we will discuss the main types of waveforms used in Radar systems.

First of all, we will classify the waveforms depending on some different parameters. Then, we will discuss the importance of the proper choice of the radar waveform. After that, we will mention the factors affecting the choice. Later, we will discuss the main radar waveforms and splash their major characteristics and properties. At the end, we will introduce our software work and Matlab codes.

Table of Contents

AbstractI

Table of contents ........II

List of figures...IV

List of tables.....V

Table of abbreviations.......VI1 Introduction.1

2 Classification of waveforms ....13 Choice importance of Radar waveforms .....23.1 Performance2 3.2 Resolution33.3 Measurement33.4 Classification44 Factors of the selection of waveforms ......45 The most popular pulse shapes56 Types of Radar waveforms ....7

3.1 A continuous-wave waveform7

3.2 A simple pulse83.3 linear frequency-modulated waveform83.4 A nonlinear frequency-modulated waveform9 3.5 A phase-coded waveform107 Software work .....113.1 Matlab Code11 3.2 Simulink15References 17LIST OF FIGURES

Figure 1 : Ideal and actual pulse shapes.5

Figure 2 : CW waveform ....7

Figure 3 : A simple pulse ...8

Figure 4 : Frequency varies linearly over time ...8

Figure 5 : Symmetrical and asymmetrical NLFM waveforms...9

Figure 6 : Binary phase-coded signal .10

Figure 7 : Frank poly-phase coded waveform....10

Figure 8 : CW waveform....12

Figure 9 : The variation of frequency over time..13

Figure 10 : LFMCW waveform ....13

Figure 11 : The variation of frequency over time ..14

Figure 12 : NLFCW waveform .15

Figure 13 : Block diagram of simple pulse generator...15

Figure 14 : Sine wave ...15

Figure 15 : Train of pulses....16

Figure 16 : Simple pulse...16

LIST OF TABLES

Table 1 : List of pulse shapes ..6

Table 2 : Performance of pulse-compression waveforms ...11

TABLE OF ABBREVIATIONS

Description long nameAbbreviation

Continuous WaveformCW

Frequency ModulatedFM

Linear Frequency ModulatedLFM

Nonlinear Frequency ModulatedNLFM

Linear Frequency Modulated Continuous WaveformLFMCW

Nonlinear Frequency Modulated Continuous WaveformNLFMCW

1- Introduction:

The waveform is the shape of the graph of any varying quantity against some variable, usually, time [1]. In Radar systems, Continuous Waveforms (CW) or pulsed waveforms, with or without modulation, can be used.Choosing a specific waveform and a signal processing technique in a radar system depends on the radar's specific role since the correct choice of the waveform defines all the main characteristics and prosperities, including performance of target detection, resolution, measurement, and classification.[2]

The major factors affecting the choice of a specific waveform are the requirements of range and doppler coverage, probability of detection, measurement errors, interference rejection and the complexity and cost of waveform generation and signal-processing systems.[3]

Later, in this report, we will discuss the radar waveforms and their characteristics in some detail. 2- Classification of waveforms:

Depending on the parameter, the classification is based upon, Waveforms are divided into several groups[4]:

1- The character of variation in time domain:

Waveforms are divided into:- Continuous-wave waveforms. - Pulse waveforms.

2- Usage of intra-pulse modulation:

Pulse waveforms are divided into:- Simple (uncoded) pulses. - Pulse-compression waveforms.

3- Pulse compression technique:

Pulse-compression waveforms are divided into:- Frequency-modulated waveforms.

- Phase-coded waveforms.

4- Type of frequency coding:

Frequency-modulated waveforms are divided into:- Linear frequency-modulated waveforms.

- Nonlinear frequency-modulated waveforms.

- Frequency-stepped waveforms.

5- Type of Phase coding:

Phase-coded waveforms are divided into:- Binary-coded waveforms.

- Poly-phase-coded waveforms.

6- The shape of the waveform:

The most popular shapes of waveforms are:- Sinusoidal.

- Rectangular. - Gaussian. - Sawtooth. - Triangular.- Exponential.7- Discretization state:

Waveforms are divided into:- Analog waveforms:

Continuous in both time and amplitude.

- Discrete waveforms:

Discrete in time and continuous in amplitude.

- Digital waveforms:

Discrete in both time and amplitude.

3- Choice importance of Radar waveforms: The choice of the radar waveform is so important since it determines the characteristics and the properties of the radar system. Therefore, the choice must be proper and suitable for the radar application.

Some of the radar main characteristics that depend on the radar waveform are discussed here, in some detail.3.1- Performance: Radar performance is the set of characteristics defining the quality of radar operation. It is also called tactical-technical characteristics.[5]

The performance of a radar can be defined by resolution, target detection, measurement, and classification. The tactical characteristics describe top-level performance:1- Detection range.

2- Coverage angles.

3- Resolution.

4- Measurement accuracy.5- Throughput capacity.

6- Interference immunity.

The technical characteristics describe low-level performance:1- Operating frequency.

2- Pulse repetition frequency.

3- Transmitter power. 4- Antenna gain.

5- Receiver sensitivity.

3.2- Resolution: Resolution is the ability to separate the signals from adjacent sources. The requirements for resolution depend on the radar mission.

The common measurement to resolve two targets in a specific dimension is if separated by a distance equal to or more than the half-power width of the radar response in this dimension.[6]3.2.1- Angular resolution: The angular resolution is the ability to separate targets at the same range but on different bearings.[7]

Practically, two targets at the same range can be resolved if the angular distance between them is more than the half-power beamwidth of the antenna.[8]3.2.2- Doppler resolution: Doppler resolution is the minimum separation in the radial velocities of two detected targets the radar receiver is able to distinguish. [9]3.2.3- Frequency resolution: Frequency resolution is the receiver to be able to detect two or more signals that differ separately only on frequency. The resolution is typically specified as the width of the frequency-response curve measured at -3dB (half-power) below the main response lobe.[10]

3.2.4- Range resolution: The range resolution of a radar system is the minimum resolvable separation, in range, of two targets of the same bearing.[11] Range resolution depends on the transmitted pulse-width, the target cross-section. 3.3- Measurement:

Radar measurement is the process of estimating target parameters, which are the angular coordinates, the range, the radial velocity and the radar cross-section.3.3.1- Angular measurement:

Angular measurement is the estimation of target angular coordinates. The coordinates of angular position are azimuth and elevation.[12]3.3.2- Frequency measurement:

Frequency measurement is the estimation of the radial velocity of the target by the measurement of doppler frequency shift. A common technique is to use a number of doppler filters over an interval of frequency and to determine the radial velocity in the filter with the strongest signal.[13]3.3.3- Range measurement:

Range measurement is the estimation of the range of the target. There are three basic methods used in the estimation[14]: 1- Time-related. 2- Frequency-related. 3- Phase-related.The time-related method, which is used in pulsed radars, is based on the measuring the time delay td. The target range R is then computed as:

In the frequency- related method, LFMCW signals are used. The transmitted frequency is mixed in the receiver with the echo frequency fr = f0 + a(t - td) to obtain:

The phase method, which is used in CW radars, the difference in phase between the transmitted and received waveforms, that are modulated at a frequency fm, is used:

3.3.4- Error measurement:

An error occurs when there is a difference between the accurate value of a target parameter and its measured value, which may be the time delay, the angle, the doppler frequency or the radar cross-section. The presence of random noise in the receiver is the fundamental source of measurement error.3.4- Classification:

Classification of the target is an important feature of modern radars, which not only can detect target position, but also can classify the type of the target. 4- Factors of the selection of waveforms :

There is a set of factors affecting the choice of radar waveforms. When trying to select a specific waveform, these factors must be matched. These factors include coverage, resolution, measurement, cost and complexity of the system. A detailed discussion is introduced.

4.1- Range coverage:

It can be described in terms of the maximum detection ranges as a function of target angle, if the detection area and the environment are correctly specified.[15]4.2- Doppler coverage: Doppler coverage includes the range of target radial velocities over which the target data can be detected and processed.[16]4.3- Probability of detection:

It is the probability that a signal will be correctly detected based on observation of the receiver output. The probability of detection is associated with the probability of the false alarm that if the detection threshold is reduced, the false-alarm probability will increase, and vice versa.[17]

4.4- Resolving capability:

It is the ability of the radar system to separate signals from adjacent sources. It includes range resolution, angular resolution and velocity resolution.

4.5- Measurement errors:

The presence of random noise in the receiver results in measurement error in the measured parameters such as range, angle and velocity.4.6- Interference rejection:

Interference having a random nature results when receiving waves other than ones produced by the transmitter or observed target. Some sources of interference are clutter, noise and jamming. 4.7- Enhanced modes of operation:

In modern radars, It is reachable to classify the target as well as detecting it. However, it is not perfect and there are many levels of classification.4.8- Complexity and cost of generation and processing:

There are different application of radars, each one has its own requirements. These application varies in complexity, in both hardware and software components, as well as in cost. For example, LFM pulses are the least complex among pulse-compression waveforms, but also are the lest efficient because of its high sidelobes.

5- The most popular pulse shapes :A pulse is a wave that has a constant state between two identical other states. In radar applications, the pulse has constant amplitude between two zero states.

Fig.1 Ideal and actual pulse shapesThe pulse as shown in figure 1 - has two edges, the leading edge and the trailing edge. The leading edge represents the transition from 0 state to a constant value whereas the trailing one represents the transition from a constant value to 0 state. In an ideal pulse, the transition time is zero and the amplitude is constant. In a practical pulse, the transition time is non-zero and the amplitude is inconstant.

The parameters of the practical pulse are the raising time, the falling time and pulse ripple. The rising time is the interval from 10% to 90% of the amplitude, whereas the falling time is the interval from 90% to 10% of the amplitude. The ripples occur when there is a variation in amplitude. A pulse with a fast rise-fall time and a sharp edges is essential for good range resolution. The duration of the pulse or the pulse-width, is defined between the half-power points of both edges.Several pulse shapes, as rectangular, triangular, saw-tooth, sinusoidal, Gaussian and exponential pulses, shown in table 1, are used in radar systems. However, except rectangular pulse, these pulses are produced by pulse compression in the receiver, because radar transmitters operate most efficiently in the saturated mode, producing constant output ( rectangular shape) between the leading and trailing edges.[18]

Table 1 List of the most popular pulse shapes The pulses shown in table 1 differs in time-bandwidth product. The time-bandwidth product is a measure of the compression ratio. If the time-bandwidth product is less than one, then it means that the pulse is expanded while if it is greater than one, as in the exponential pulse, then it is compressed. The simple pulse has a unity time-bandwidth product whereas the pulse-compression waveforms have time-bandwidth product values much greater than one.

6- Types of Radar waveforms : The radar waveforms are divided into two main categories which are continuous-wave waveforms and pulse-compression waveforms, each waveform may be modulated or un-modulated. These waveforms will be discussed, in some detail, in the following sub-chapters.6.1- A continuous-wave waveform: A continuous-wave or continuous waveform (CW) is an electromagnetic wave of constant amplitude and frequency, as shown in figure 2, and in mathematical analysis, of infinite duration.[19] In reality, continuous-waveforms have limited duration.

Fig.2 CW waveformThe continuous-waveform could be a pure sine or cosine and its equation is:

Et = E0 cosw0tWhere E0 and w0 are constants.

CW waveforms are widely used in CW radars, Doppler radars and Bistatic radars. The Usage of CW waveforms results in a simplification in the radar design. In addition, they provide high average power at low operating voltages whereas a higher voltages are needed in pulsed systems.On the other hand, dual antennas are required when the transmitted power is more than a few watts to protect the receiver. In addition, The receiver must be isolated from the transmitter, when high power waveforms are used, to minimize transmitted noise sidebands so that the target detection is not affected.[20]6.2- An un-coded (simple) pulse: A simple pulse is an amplitude modulated waveform, on-off, with constant carrier frequency f0. The simple pulse waveform has a rectangular envelope, as shown in figure 3.

Fig. 3 A simple pulse

There are two types of the simple pulse, short pulse and long pulse. The long pulse is a narrowband waveform with long pulse-width and has poor range but good Doppler resolution. On the other hand, the short pulse is a wideband waveform with short pulse-width and has poor range but good Doppler resolution. The usage of these pulses reduces the cost of the radar system.[21]

6.3- linear frequency-modulated waveform: A linear frequency-modulated waveform is a frequency-modulated waveform with a carrier frequency varying linearly with time, as shown in figure 4, for some specified period (in CW radar) or within the pulse-width (in pulsed radar). The phase must have a quadratic dependence on time to obtain this waveform.The waveform voltage can be written as:

where v0 is the amplitude, w0 is the carrier frequency, and q(t)is the phase. When

the instantaneous frequency is:

Fig. 4 Frequency varies linearly over timeThis waveform was widely used, and is still used, in both CW and pulse radar applications. In FMCW radars, it is used to enable the detection of the target range beside its radial velocity.

In pulse radars, two methods to generate LFM waveforms are used: active and passive. A special generator is used in active methods, as a voltage-controlled oscillator, in which the desired linear ramp can be obtained by applying a ramp input voltage. However, in the passive method, the waveform is generated by exciting a the system with an impulse.[22]

The LFM waveform is quite insensitive to doppler shifts. Also, it is the easiest to generate. However, It has range-doppler cross coupling, which can be avoided when the range or the radial velocity is pre-determined. In addition, its range sidelobes, which appear after correlation process at the receiver, are high so that weighting is required to reduce the range sidelobes and in signal-to-noise ratio ( in a 1- to 2-dB loss ). [23][24]

6.4- A nonlinear frequency-modulated waveform: A nonlinear frequency-modulated waveform: is a frequency- modulated waveform with a carrier frequency varying nonlinearly, either symmetrical or asymmetrical, with time, as shown in figure 5. Asymmetrical waveform has a frequency that varies in one direction over all time while the frequency of the symmetrical waveform increases during the first half of the pulse and decreases during the second half of the pulse. The phase variation for this waveform can be written as:

where wn(t) is a nonlinear function, and may be sin(t) or cos(t).

Fig. 5 Symmetrical and asymmetrical NLFM waveforms

The nonlinear variation in time is equivalent to amplitude weighting, which also is a nonlinear function and is used to reduce the range sidelobes. Therefore, the NLFM waveform has very low range sidelobes. However, it is more sensitive to doppler frequency shifts, and more complex than the other pulse-compression waveforms.[25][26]

6.5- A phase-coded waveform:

A phase-coded waveform is a waveform in which the pulse is subdivided into subpulses of equal duration, each with a specific phase. The phase of each subpulse is owed to a given code sequence. Phase-coded wave-forms may be binary-coded or poly-phase coded.The binary-coded waveform is a waveform with two levels of phase-shift keying, 0 for positive amplitude and 180 for negative amplitude, as shown in figure 6. The Barker codes and the allomorphic codes are the common binary-coded waveforms.[27]

Fig. 6 Binary phase-coded signal

The poly-phase coded waveform has more than two phases as the Frank-coded waveform, shown in figure 7, quadric-phase-coded waveform, and waveforms using P-codes.

Fig. 7 Frank poly-phase coded waveformPhase-coded waveforms have low range sidelobes. They are preferred when operating in jamming conditions in that the coding reduce interference with other electromagnetic waveforms. On the other hand, their resolution is poor, in presence of distributed clutter and they are more complex than LFM waveform.[28]

A comparison between the main pulse-compression waveforms - the LFM waveform, the NLFM waveform and the phase coded waveform is introduced in table 2.[29]

Table 2 Performance of pulse-compression waveforms7- Software work:

The software work was performed using Matlab. The work is of two parts, the m-file code and the simulink. Both are introduced and discussed here.

7.1 Matlab Code:

This code is to plot the CW waveform, LFMCW waveform and NLFMCW waveform.

1- CW waveform:

* The code:%%%%%%%%%%%%% CW %%%%%%%%%%%%%%t =input('time range t (*:*:*) = ');f=input('fundamental frequency f = ');s1=sin(2*pi*f.*t);figure(1)plot(t,s1)* Explaining the code:

This code asks the user to define a range to plot the signal over it, and the frequency of the CW waveform.

time range t (*:*:*) = 0:0.02:2

fundamental frequency f = 10* The output:

If the user defined the range of time as 2 seconds and the frequency as 10 Hz, the output will be as follows:

Fig. 8 CW waveform2- LFMCW waveform:

* The code:%%%%%%%%%%%% LFMCW %%%%%%%%%%%%t =input('time range t (*:*:*) = ');f0=input('fundamental frequency f0 = ');k =input('slope K = ');f =f0+k*t;s2=sin(2*pi*f.*t);figure(2)plot(t,f)figure(3)plot(t,s2)* Explaining the code:

This code asks the user to define a range to plot the signal over it, the fundamental frequency, and the slope of the variation.

time range t (*:*:*) = 0:0.02:4

fundamental frequency f0 = 0

slope K = 1

* The output:

If the user defined the range of time as 4 seconds, zero frequency and unity slope, the output will be as follows:

Fig. 9 The variation of frequency over time

Fig. 10 LFMCW waveform3- NLFMCW waveform:

* The code:%%%%%%%%%%%% NLFMCW %%%%%%%%%%%t =input('time range t (*:*:*) = ');f0=input('fundamental frequency f0 = ');k =input('slope K = ');f =f0+k*t+cos(t);s3=sin(2*pi*f.*t);figure(3)plot(t,f)figure(4)plot(t,s3)* Explaining the code:

This code asks the user to define a range to plot the signal over it, the fundamental frequency, and the slope of the variation. The frequency depends on time within a nonlinear law.time range t (*:*:*) = 0:0.02:3

fundamental frequency f0 = 0

slope K = 2slope K = 1

* The output:

If the user defined the range of time as 3 seconds, zero frequency and the slope to be 2, the output will be as follows:

Fig. 11 The variation of frequency over time

Fig. 12 NLFCW waveform7.2 Simulink:

The block diagram built using simulink is to simulate a simple pulse. For this purpose, a pulse generator is used to generate a train of pulses which is modulated by a sine wave.

* The block:

Fig. 13 Block diagram of simple pulse generator* Scope:

Fig. 14 Sine wave* Scope 1:

Fig. 15 Train of pulses* Scope 2:

Fig. 16 Simple pulseReferences [1] http://en.wikipedia.org/wiki/Waveform.

[2] Barton, D. K., and Leonov, S. A., Radar Technology Encyclopedia, Artech House, 1998, page 472.

[3] Skolnik, M. I., Radar Handbook, 2nd edition, McGraw-Hill, 1990, page 10.3.



[6] Barton, D. K., and Leonov, S. A., Radar Technology Encyclopedia, Artech House, 1998, pages 401-402.

[7] US Navy, Aviation Electricity And Electronics, NAVEDTRA 14339, Page 1-2.




[11] US Navy, Aviation Electricity And Electronics, NAVEDTRA 14339, Page 1.2.








[19] http://en.wikipedia.org/wiki/Continuous_wave.


[21] Barton, D. K., and Leonov, S. A., Radar Technology Encyclopedia, Artech House, 1998, pages 314-315.







[28] Barton, D. K., and Leonov, S. A., Radar Technology Encyclopedia, Artech House, 1998, pages 475-476 .


wave generation

Documents

specific waveform

list of figures figure

main radar waveforms

classification of waveforms

nlfcw waveform

lfmcw waveform

continuous waveforms

pulsed waveforms