Implementation of Barker Code and Linear Frequency Modulation Pulse Compression Techniques in Matlab

Implementation of Barker Code and Linear Frequency Modulation Pulse Compression Techniques in Matlab C. S. Rawat 1, Deepak Balwani 2, Dipti Bedarkar 3, Jeetan Lotwani 4, Harpreet Kaur Saini 5 Associate Professor, Department of Electronics and Telecommunications Vivekanand Education Society s Institute of Technology, (V.E.S.I.T) Mumbai, India Student, Department of Electronics and Telecommunication, Vivekanand Education Society s Institute of Technology, (V.E.S.I.T) Mumbai, India. Abstract--Radar is a system that uses electromagnetic waves to detect, locate and measure the speed of reflecting objects such as aircraft, ships, spacecraft, vehicles, people, weather formations, and terrain. It transmits the electromagnetic waves into space and receives the echo signal reflected from objects. By applying signal processing algorithms on the reflected waveform, the reflecting objects can be detected. Furthermore, the location and the speed of the objects can also be estimated. Radar was originally an acronym for RAdio Detection and Ranging. Pulse Compression is an important signal processing technique used in Radar Systems to reduce the peak power of a radar pulse by increasing the length of the pulse, without sacrificing the range resolution associated with a shorter pulse and different techniques Barker code and LFM are implemented. Keywords -- Radar signal processing, Pulse compression, need of pulse compression, pulse compression techniques Barker code, Lfm,ambiguity function I. INTRODUCTION Radar Signal processing is a very important aspect of Radar systems. It involves Pulse Compression (PC), Adaptive Beam forming (ABF), Space-time Adaptive Processing (STAP) and all are based on the basic concept of matched filtering to achieve high signal-tointerference ratio, which in turn is a form of coherent integration. Signal processing relies on the characteristic differences between signals from targets and the interfering signals. Target signals exhibit orderliness, interferers exhibit randomness. The rate of change of the phase (d/dt) of the orderly signals is deterministic unlike the dφ/dt of the interferer signals. On the basis of Doppler content and amplitude characteristics, the signal processing separates targets from clutter and thus signalto-interference ratio and target detection is improved. The target-masking effects of clutter are reduced by Radar signal processing and hence Radar vulnerability to Electronic countermeasures is reduced. Information on target characteristics and behavior can also be extracted. This is explained very nicely in [3]. Signal integration, correlation, filtering and spectrum analysis [3] or enhancing target signals while suppressing interference signals. Figure 1.1 shows a typical signal processor possessing digital pulse Compression. [3] It mainly includes the following: A/D converter Analog signals are transformed into digital words at specific times and rates Storage Digitized signals are kept temporarily and waited for all signals required for process to be gathered Pulse compression matched filter The echo signal is correlated with delayed copy of the transmitted signal Signal filter Portion of the Doppler spectrum (slow time) is removed to reduce clutter II. NEED OF PULSE COMPRESSION A continuous waveform (CW) is the simplest radar waveform which is transmitted continuously while receiving target echoes on a separate antenna. The advantage of CW is the unambiguous Doppler measurement. However, due to continuous nature of the waveform the target range measurement is entirely ambiguous. Most of the modern radar systems employ a pulsed waveform which provides range information accurately. The primary advantage of pulsed radar is that the transmitter and receiver can share the same antenna due to pulsating nature of the waveform. A pulsed waveform is shown in Figure 2, where Tp is the pulse duration and Tr is the pulse repetition time. The unambiguous range Ru that can be measured by this waveform as described in [2] is: 105

(1) Where c is the speed of light. Two important factors to be considered for radar waveform design are range resolution and maximum range detection. Figure 2: Pulsed Radar Waveform Range resolution is the ability of the radar to separate closely spaced targets and it is related to the pulse width of the waveform. The narrower the pulse width the better is the range resolution. But, if the pulse width is decreased, the amount of energy in the pulse is decreased and hence maximum range detection gets reduced. To overcome this problem pulse compression techniques are used in the radar systems. [8][6] The maximum detection range depends upon the strength of the received echo. To get high strength reflected echo the transmitted pulse should have more energy for long distance transmission since it gets attenuated during the course of transmission. The energy content in the pulse is proportional to the duration as well as the peak power of the pulse. The product of peak power and duration of the pulse gives an estimate of the energy of the signal. A low peak power pulse with long duration provides the same energy as achieved in case of high peak power and short duration pulse. Shorter duration pulses achieve better range resolution. The range resolution Rres is expressed [2] as: Where B is the bandwidth of the pulse. For modulated pulse the time duration is inversely proportional to the bandwidth. If the bandwidth is high, then the duration of the pulse is short and hence this offers a superior range resolution. Practically, the pulse duration cannot be reduced indefinitely. According to Fourier theory a signal with bandwidth B cannot have duration shorter than 1/B i.e. its time-bandwidth (TB) product cannot be less than unity. A very short pulse requires high peak power to get adequate energy for large distance transmission. However, to handle high peak power the radar equipment become heavier, bigger and hence cost of this system increases. Therefore peak power of the pulse is always limited by the transmitter. A pulse having low peak power and longer duration is required at the transmitter for long range detection. At the output of the receiver, the pulse should have short width and high peak power to get better range resolution. (2) Figure 3Transmitter and Receiver ultimate signals. Figure 3 illustrates two pulses having same energy with different pulse width and peak power. To get the advantages of larger range detection ability of long pulse and better range resolution ability of short pulse, pulse compression [3] techniques are used in radar systems. The range resolution depends on the bandwidth of a pulse but not necessarily on the duration of the pulse [4]. Some modulation techniques such as frequency and phase modulation are used to increase the bandwidth of a long duration pulse to get high range resolution having limited peak power. In pulse compression technique a pulse having long duration and low peak power is modulated either in frequency or phase before transmission and the received signal is passed through a filter to accumulate the energy in a short pulse. 2.1 Pulse Compression [2][8] The reduction in the peak power of a pulse can be achieved by increasing the length of the Pulse. But, an increase in the length of the pulse reduces range resolution. To avoid the compromise in range resolution, some form of encoding must be done within the transmitted pulse, so that it is possible to compress" a longer pulse into a shorter one in the receiver using suitable signal processing operations. The easiest form of such encoding is to allow the radar pulse to modulate a waveform or a sequence that is uncorrelated in time but known at the receiver. A cross-correlation operation at the receiver (using the known transmitted waveform/sequence) will compress the long received waveform/sequence into a short one. This is due to the time auto-correlation properties of the transmitted waveform/sequence, which is maximum at zero-lag and almost zero at lags other than zero. The time autocorrelation of a deterministic function f(t) of time is given by: (3) And, for a random signal X(t), it is given by, (4) 106

The objective of designing a good Pulse Compression scheme is now to choose an encoding signal that has a very narrow auto-correlation function. Another important effect of Pulse Compression is the increase in the bandwidth of the signal. Without Pulse Compression, a longer pulse has a lesser bandwidth than a shorter pulse. But, due to the encoding associated with Pulse Compression, the bandwidth of the longer pulse increases. In fact, to have higher range resolution using pulse compression, the waveform/sequence encoding should be highly uncorrelated and thus use a larger bandwidth. Thus, it is obvious that we do not gain any resources (energy/bandwidth) for \free" using Pulse Compression. The only accomplishment of Pulse Compression is the reduction in the Peak Power. Figure 4: Received Radar Signal before Pulse Compression [13] Figure 5: Received Radar Signal after Pulse Compression [13] 2.2 Pulse Compression Techniques[4] 2.2.1analog Pulse Compression: Correlation Processing:[4][6] This technique is dominantly used for narrow band operations. 107 In this case, pulse compression is accomplished by adding frequency modulation to a long pulse at transmission, and by using a matched filter receiver in order to compress the received signal. Using LFM within a rectangular pulse compresses the matched filter output by a factor, which is directly proportional to the pulse width and bandwidth. Thus, by using long pulses and wideband LFM modulation we can achieve large compression ratios. This form of pulse compression is known as correlation processing. Stretch Processor: Stretch processing, also known as active correlation, is normally used to process extremely high bandwidth LFM waveforms. 2.2.2 digital Pulse Compression:[4] Costas Codes: Costas codes illustrate frequency coding. In this technique a relatively long pulse of length is divided into N sub pulses, each of width. Each group of N sub pulses is called a burst. Here the frequencies for the sub pulses are selected in a random fashion, according to some predetermined rule or logic. The compression ratio of a Costas code is approximately N. Barker Code: Barker codes illustrate binary phase coding. In this case, a relatively long pulse of width is divided into N smaller pulses; each is of width. Then, the phase of each sub-pulse is randomly chosen as either 0 or π radians relative to some CW reference signal. The compression ratio associated with binary phase codes is equal to, and the peak value is N times larger than that of the long pulse. Frank Codes: Frank codes illustrate poly-phase coding. Codes that use any harmonically related phases based on a certain fundamental phase increment are called poly-phase codes. In this case, a single pulse of width is divided into N equal groups; each group is subsequently divided into other N sub-pulses each of width. Therefore, the total number of sub-pulses within each pulse is, and the compression ratio is. As before, the phase within each sub-pulse is held constant with respect to some CW reference signal. III. LINEAR FREQUENCY MODULATION[4] LFM pulse compression technique is a kind of technique in which the frequency of the transmitted signal is varied over pulse duration of T.

This variation of the frequency from low to high or vice a versa is known as chirping. Changing the frequency from low to high is called up-chirp or upsweep. Similarly, changing the frequency from high to low is called down-chirp. The technique of applying a different chirp rate for each pulse is known as chirp diversity. Figure 7 Matlab outputs for a. The real part of the transmitted signal b. Frequency spectrum of transmitted signal Figure 6 Typical LFM waveforms.(a) up chirp (b) down-chirp. A typical LFM waveform can be expressed in complex notation by [2] (5) Where rect (1/ T) represents rectangular pulse of width T, fo represents radar center frequency and µ is LFM co efficient given by µ = 2π B where B = Bandwidth Figure 8 shows the received echo signal from three targets before compressionfrom above figure it is clear that targets are not separated in the time domain prior to the compression 108

Figure 9 shows the compressed output with distance slightly greater than range resolution between targets. Thus third target has started appearing as the distance will increase further the target will be clearly separate. IV. BARKER CODE Barker codes are one of the binary phase codes that produce compressed waveforms with constant side lobe levels equal to unity. A Barker code of length is denoted as BN. There are only seven known Barker codes namely B2, B3, B4, B5, B7, B11 & B13. In this paper Barker code length 7 has been implemented in matlabr2008a.optimal binary sequences are those whose autocorrelation peak sidelobe is the minimum possible for a given code length. A special class of binary codes is known as Barker codes. The benefit is that auto correlating or match filtering for these codes gives a main lobe peak of N and a minimum peak sidelobe of 1, where N is the number of sub pulses (length of the code). Only a small number of these codes exist. Table 1 lists all known Barker codes and those having a minimum peak sidelobe of 1. Ideally, these codes could be used for pulse compression radars if longer lengths existed. However, the longest known Barker codes are of length 13, so pulse compression radar using these Barker codes would be limited to a maximum compression ratio of 13 [5][6][7]. Table 1: Barker code of various lengths CODE CODE CODE SIDE LOBE SYMBOL LENGTH ELEMENT REDUCTION (db) B2 2 +- 6.0 ++ B3 3 ++- 9.5 Figure 10 shows the compressed output with the sufficient distance between three targets. Thus targets are easily detectable. In LFM, the frequency is swept linearly across the pulse width, either upward (up-chirp) or downward (down-chirp). Increase in frequency from T = 0 to T = τ is known as up chirp and decrease in frequency from T = 0to T = τ is known as down chirp. LFM is implemented using Matlab. From the simulations it is clear that prior to compression the targets are not separated in time domain. After compression the targets are easily detectable. Moreover the targets are not distinguished if the distance between them is kept less than the range resolution. As the distance increase then the range resolution between the targets, the targets get separated in time domain and are easily detectable. Also to reduce the side lobe noise different windows were used at the output of the match filter. Output using no window, Hamming window, Kaiser window and Chebychev window was implemented. When no window was used the side lobe noise was observed in the output. B4 4 ++-+ 12.0 +++- B5 5 +++-+ 14.0 B7 7 +++--+- 16.9 B11 11 +++---+--+- 20.8 B13 13 +++++--++- +-+ 22.3 The Barker code is fed to the mixer to which other input is a pulse. At the output we get barker encoded pulse. This Barker encoded pulse is fed to other mixer to which second input comes from carrier oscillator. This mixer gives BPSK modulated signal at the output. This BPSK signal is transmitted towards the target. For simulation pulse width of 1 Nano sec and carrier frequency of 20 GHz is chosen. as in Figure9 109

Figure 11: Block diagram of Barker code encoded carrier signal Figure 14Matlab output for : The correlation of transmitted signal and received signal added with Gaussian noise Figure 12matlab outputs for : a) One Nano sec pulse. b) One Nano sec pulse divided as per barker code. c) Carrier signal BPSK modulated as per barker code. d) Received signal with added Gaussian noise and delay V. AMBIGUITY FUNCTION The radar ambiguity function represents the output of the matched filter, and it describes the interference caused by range and/or Doppler of a target when compared to a reference target of equal RCS. The ambiguity function evaluated ( ) ( )at is equal to the matched filter output that is matched perfectly to the signal reflected from the target of interest. In other words, returns from the nominal target are located at the origin of the ambiguity function. Thus, the ambiguity function at nonzero τ and represents returns from some range and Doppler different from those for the nominal target. The radar ambiguity function is normally used by radar designers as a means of studying different waveforms. It can provide insight about how different radar waveforms may be suitable for the various radar applications. It is also used to determine the range and Doppler resolutions for a specific radar waveform. The three-dimensional (3-D) plot of the ambiguity function versus frequency and time delay is called the radar ambiguity diagram. The radar ambiguity function for the signal s (t) is defined as the modulus squared of its 2-D correlation function, i.e. ( ) χ(τ;fd)= ( ) ( ) (6) Denote as the energy of the signal E ( ) (7) Figure 13matlab outputs for : The transmitted signal and received signal used for barker code length 7 Single Pulse Ambiguity Function Consider the normalized rectangular pulse S(t) defined by ( ) ( ) (8) 110

Time-frequency analysis such as short time Fourier transform, wavelet transform and S-transform can be used for LFM signals to extract Doppler information. The LFM signal can be replaced by Doppler tolerant hyperbolic frequency modulated pulse in the pulse train and the multi objective algorithms can be employed to enhance side lobe suppression.this techniques has been for implemented the techniques for stationary target. Fig 15 shows ideal ambiguity Function Figure 16: ambiguity function for barker length = 7 Barker code length 7 pulse compression technique is analyzed and simulated using Matlab. Barker codes are one of the binary phase codes that produce compressed waveforms with constant side lobe levels equal to unity. The radar ambiguity function represents the output of the matched filter, and it describes the interference caused by range and/or Doppler of a target when compared to a reference target of equal RCS. Ambiguity Function for various Barker code length 7 was simulated using MATLAB. VI. FUTURE PROSPECTS Implementation of barker code of length 7, and LFM are done it can be further extended and can be implemented for different lengths such as 11,13,19. VII. CONCLUSION The paper discusses about radar signal processing, pulse compression and its need. The various pulse compression techniques are also discussed. Pulse Compression improves SNR and rangeresolution even for targets having very low RCS. This is done withthe help of its several analog and digital techniques. Implementation of barker code length 7 (Digital) and linear frequency modulation (Analog) has been implemented and results of same are shown in paper. REFERENCES [1 ] A.W. Rihaczek, Principle of high resolution radar. McGraw Hill, New York, 1969. [2 ] Ajit Kumar Sahoo, Development of Radar Pulse Compression Techniques Using Computational Intelligence Tools, thesis for degree of PhD with National Institute of Technology Rourkela. [3 ] B Edde, Radar Principles, Technologies, Applications, Prentice Hall, 1995. [4 ] Bassem R. Mahafza, Huntsville, Alabama Radar System Design and Analysis using Matlab, Chapman & Hall/CRC, Ph.D. COLSA Corporation Huntsville, Alabama, 2000. [5 ] C. E. Cook and M. Bernfeld, Radar signals: An introduction to theory and application, Academic Press, New York, 1967. [6 ] Chris Allen, Radar Signal Processing, available online at (callen@eecs.ku.edu) and people.eecs.ku.edu/~callen/725/eecs725.htm, 1999. [7 ] D.K. Barton, Pulse Compression. Artech House, 1975. [8 ] M. I. Skolnik, Introduction to radar system. New York: McGraw- Hill, 1980. [9 ] Mehrdad, S., Synthetic Aperture Radar Signal Processing. John Wiley & Sons, Inc., New York, 1999. [10 ] S. Apple baum, Adaptive arrays, IEEE Trans. Antennas Propagate.,vol. AP-24, pp. 585 598, Sept. 1976. [11 ] Uttam K. Majumder, Linear Frequency Modulation Pulse Compression Technique on Generic Signal Model. [12 ] VijayaChandranRamasami, Principle of the Pulse Compression Radar, University of Kansas, December 6, 2006. [13 ] Schoenig, G.N. ; SAIC, VA, USA ; Picciolo, M.L. ; Mili, L., Improved detection of strong nonhomogeneities for STAP via projection statistics Radar Conference, 2005 IEEE International, 2005 111