A New Minimum Peak Side Lobe Codes In Radar Systems

A New Minimum Peak Side Lobe Codes In Radar Systems Mohamed Abdel-Latif, El-Sayed A. Youssef, Amr Mokhtar, Mohamed Madkour, Faculty of Engineering. Alexandria University-Egypt E-mail: Mohamed @madkour.net Abstract A New Minimum Peak Side Lobe Codes (MPSC) has been investigated to be applied in radar systems. In radar terminology extraction the high resolution spatial profile from received signal is known as pulse compression. The problem inherent to pulse compression is the small targets masking through the large nearby targets resulted from the standard matched filter side lobes. In this paper, the proposed scheme introduces several biphase pulse compression codes with minimum peak side lobes. Code lengths up to 34 were discussed. A genetic algorithm optimization tool is used to get a set of codes with minimum peak and median side lobes to increase the probability of detection and reduce the probability of false alarm. The optimization results show an optimum codes for lengths 12, 23 than there published before. Also the results carried out a different optimum codes at the same length that satisfy the design flexibility.

I- INTRODUCTION In order to improve the range resolution in radar systems while maintaining a good signal to noise ratio (SNR), it is necessary to decrease the pulsewidth, otherwise increasing the pulsewidth is required to achieve large radiated energy. Pulse compression technique has been investigated as a remedy in such cases [1]. However, unnecessary side lobes produced by the autocorrelation process yield ghost echoes of targets, which have a negative influence on the radar detection performance. In regards to the pulse compression technique it is very important in pulse compression radar to minimize the peak side lobes (PSL) and median side lobes (MSL), it is also vital to minimize the complexity of the digital correlator to reduce the cost and increase the speed of pulse compression hardware consequently. There have recently been many studies that are concerned with minimizing the complexity of the digital correlator [2]. A pulse compression is performed using a biphase codes which have a considerable interest due to their simple realization, the goodness of compressed biphase code waveform depends heavily on the random sequence of the phase for the individual sup-pulse. In this paper we introduce an optimum biphase codes with minimum PSL and MSL. Optimization results provide about 3.56dB improvement in MSL for code length 12 and 0.77 dB for code length 23.Aanother important advantage, we carry out a group of biphase pulse compression codes which have an optimum autocorrelation function for different code lengths, these sets of biphase pulse compression codes can be assigned to each radar so that several radars can share the same spectrum [3]. Also these families of codes make the design process more flexible. Optimization results ensure that there is a group of codes with a specific PSL and MSL. Biphase pulse compression codes had been discussed in references [4-7] and still under research for optimum results accomplishment.

II- BIPHASE PULSE COMPRESSION CODES One of the early methods for pulse compression is the phase coding. A pulse with duration T is divided into M bits of identical duration tb =T / M, each bit is assigned (coded) with different phase value .The complex envelope of the phase coded pulse is given by: t − ( m − 1)t b 1 M (1) ] u (t ) = ∑ u m rect [ tb T m =1

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Where, um = exp ( jφ m ) and the set of M phases { φ1 , φ 2 ....φ m } is the phase code associated with u (t) . The criteria for selecting a specific code are the resolution properties of the resulting waveform (the autocorrelation properties), frequency spectrum and the ease with which the system can be implemented. The most widely used phase-coded waveform employs two phases and is called binary (biphase) coding. One family of biphase codes that produced compressed waveforms with constant side lobe levels equal to unity is the Barker code. The binary code consists of a sequence of either 0 s or 1s or +1 s and -1s. The phase of the transmitted signal alternates between 0° and 180° in accordance with the sequence of code elements, as shown in Fig.1.

1

1

1 1

-1

1 -1

-1

-1

Time

Time Fig. 1 Seven bits biphase pulse compression code Upon reception, the compressed pulse is obtained by either matched filtering or correlation processing. The width of the compressed pulse at the half amplitude point is nominally equal to the sub-pulse width. The range resolution is hence proportional to the time duration of one element of the code. The compression ratio is equal to the number of sub-pulses in the waveform, i.e., the number of elements in the code. Large peak side lobes leads to increasing the portability of false alarm and decreasing the probability of detection while large value of main lobe peak is required to increase the probability of detection. Finding additional minimum peak side lobe biphase codes involves an exhaustive search with a size growing exponentially with code length [8]. If a transmitted pulse u (t) with Mu phase elements defined by u m (1 ≤ m ≤ M u ) and a reference pulse v(t) with Mv elements defined by vn (1 ≤ n ≤ M v ) . The cross-correlation function of the two phase-coded pulses is defined as: ∞

(2)

Ruv ( τ) = ∫ u (t )v * (t + τ) dτ −∞

∞

=

∫

−∞

1 M utb

Mu

∑u m =1

m rect [

t − ( m − 1) t b 1 ]. tb M v tb

Mv

∑v n =1

* n

rect [

t + τ − ( n − 1)t b ]d τ tb

(3)

III- OPTIMIZIATION PROCESS Genetic algorithm has been used to optimize the pulse compression codes parameters by changing The code value .Binary encoding scheme is used in this algorithm to encode the code elements [9-11].The chromosome contains the biphase pulse compression code elements, each gene encoded as 1 bit to represent the code element . Elitism is used to save the best solution to improve the performance of genetic algorithm. The algorithm started with a set of solutions called population solutions, one population is used to form a new population, this is motivated by hope that the new population will be better than the old one .Solutions that are selected to form new off springs are selected according to their fitness .The fitness of pulse compression codes is determined according to two main parameters the PSL and MSL levels. The crossover rate used is randomly selected between 10-90 % , the mutation rate is equal to 3% , the population size is selected to be 256 . The optimization process proceeds to obtain the minimum PSL and MSL of the biphase pulse compression codes.

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IV-OPTIMIZIATION RESULTS In this paper, biphase pulse compression codes with lengths up to 34 have been addressed. New optimized codes are obtained using genetic algorithm optimization tool. We focus on the major contributions as follows: (a) We introduce a new group of optimum biphase codes with different lengths. In table.1 a sample of these codes is listed in the third column while the conventional biphase codes [1213] are reported in column 2 .our new optimum codes have the same peak and median side lobes for each code length. (b) Through Fig.3, we perform the optimized biphase pulse compression codes obtained versus the different code lengths , it is clear that the maximum number of codes obtained is 8 for code length 8 , also for code length 19 we found a new optimum code rather than the two optimum codes mentioned in [8,14] ,these codes are:{1011011101110001111}, {1110001000100100101},{0000111000100010010}. Otherwise, we did not find any additional optimum codes for lengths {20,22,,24,25,26,27.28,29,30,31,32,33,34}. (c) Figure.4 shows a novel optimized biphase pulse compression codes with lengths (12,23)which have a MSL of (-24.4 and -26.85 dB) respectively with MSL improvement of 3.56dB for code length 12 and 0.77 dB for code length 23 compared to optimum biphase codes in [12-13]. The optimum codes for code length 12 are: {000010100110},{010110011111} and for length 23 {10101000111001001000000}, {1100111101110100001 0110}. (d) Figure.5 clarify the biphase pulse compression codes with different lengths versus the value of peak side lobes, there is a limit of the maximal value of code length for which a biphase sequence with that side lobe level exists. The max code length for peak side lobe level of 1 is 13, while the max code length for peak side lobe level of 2 is 28 ….etc.

M ed ia nsid elo b ele v e ld B

-5

Minimum pe ak and me dian side lobe s biphase code s Minimum pe ak side lobe biphase code s

-10

-15

-20

-25

-30

-35

0

5

10

15

20

25

30

35

Code length

Fig.4 Biphase pulse compression codes versus median side lobe level 3

8

7

2.5

Peak sid e lob e

No of co des

6

5

4

3

2

1.5

1

2

0.5 1

0

0 0

5

10

15

20

25

30

35

0

5

10

15

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Code length

code length

Fig.3 Optimum biphase pulse compression codes versus number of similar codes

Fig.5 Minimum peak side lobes versus biphase code lengths

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30

35

Table.1 Sample of optimized biphase pulse compression codes. Code length

Optimum biphase codes in references [ 12-13]

8

{10010111}

9

{011010111}

10

{0101100111}

14

{01010010000011}

New optimized pulse compression codes {00001101),{00010110} {00011010},{00111101} {11110010},{10110000} {11100101},{01011000} {000101100),{010000011} {001101000},{011000010} {100101000} {1011001111},{0000011010} {0000110010},{1001000111} {1111001101},{0100100011} {0000101100} {11001100000101}, {00000110010100} {10101001100000}, {10000001100101}

PSL (dB)

MSL ( dB)

-12.04

-19.22

-13.06

-19.08

-13.97

-20

-16.9

-22.92

V - CONCLUSIONS In this paper, a new Optimized Biphase Pulse Compression Codes (OBPCC) with minimum peak and median side lobes has been presented .A set of different biphase pulse compression codes with minimum peak side lobe levels is performed. Genetic algorithm is used as a powerful optimization tool. A comparative study performs optimum codes of lengths 12, 23 with minimum median side lobe levels especially for code length 12; we also give a new optimum biphase pulse compression code with length 19. In addition, the maximum code lengths that results a specific peak side lobe levels are reported .The new optimum biphase pulse compression codes with different code lengths make the design and realization processes in radar systems more ease and reliable.

REFERENCES [1]-Reiji.Sato and Masanori Shinriki "Simple mismatched filter for binary pulse compression code with small PSL and small S/N",IEEE transaction on Areospace and electronic systems, vol.39, no.2 April. 2003, pp.711-718. [2]-Blinchikoff, H.j "Range sidelobe reduction for the quadriphase", IEEE transaction on Areospace and electronic systems, vol.32, no.2 April.1996, pp.668-675. [3]-Skolnik,M.I " Introduction to radar systems" (second addition): New York:Mc Graw-Hill, 1984. [4]-Frank F. Kretschmer and Karl Jerlach " Low side lobe radar waveforms derived from orthogonal matrices ",IEEE transaction on Areospace and electronic systems, vol.27, no.1 January. 1991, pp.92-101. [5]-Yuping Cheng and Zhiping Lin "Doppler compression for binary phase- coded waveforms",IEEE transaction on Areospace and electronic systems, vol.38, no.3 July. 2002, pp.1068-1072. [6]-Shannon D.Blunt and Karl Gerlach " Adaptive pulse compression via MMSE estimation "",IEEE transaction on Areospace and electronic systems, vol.42, no.2 April. 2006, pp.572-583. [7]-Nadav Levanon" Non coherent pulse compression" ,IEEE transaction on Areospace and electronic systems, vol.42, no.2 April. 2006, pp.756-765. [8]-Levanon, N,Mozeson,Eli Radar signals, New York: Wiley,2004. [9]-Zbigniew Michalewiez" Genetic algorithms + Data strcture = Evolution programs", Springer, Verlag Berlin Heidelberg, New York ,1996. [10]-"Genetic Algorithm", Nov.2006. Available at :, :http://cs.felk.cvut.cz/xobtiko/ga.com, [11]-Randy L .Haupt "An introduction to genetic algorithm for electromagnetics ", IEEE, Antennas and propagation magazine, Vol.37, no2, 1995. [12]-Cohen,M.N and Baden,J.M "Biphase codes with minimum peak side lobes", IEEE Radar conference,Mar. 1989,pp.62-66. [13]-Coxson,G.E and Hirschel,A. "New results on optimum PSL binary codes", IEEE Radar conference,May.2001,pp.153-156. [14]-Skolnik, M.I Radar Handbook (second addition): New York:Mc Graw-Hill, 1990.

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