radar signal design for high resolution multiple/distributed

Mohd. Moazzam Moinuddin et. al. / International Journal of Engineering Science and Technology Vol. 2(8), 2010, 3797-3807

Radar Signal Design for High Resolution Multiple/Distributed Target Detection

Mohd. Moazzam Moinuddin Professor, Dept. of ECE, Noor college of Engg. and Technology

Shadnagar, Mahaboobnagar dt, A.P., India [email protected]

I.A.Pasha

Professor, Dept. of ECE. Dr.B.V.Raju Inst.of Technology Narsapur, Medak dt., A.P., India

[email protected]

Y. Mallikarjuna Reddy Professor, Dept. of ECE, Vasireddy Venkatadri Inst. of Technology

Nambur, Guntur dt., A.P., India [email protected]

V.M. Pandharipande

Professor, Emeritus, Dept. of ECE, Osmania University, Hyderabad, A.P., India, [email protected]

K.Lal Kishore

Professor, Dept.of ECE, Director, Research and Development, J.N.T.University Hyderabad, A.P., India

[email protected] Abstract: Side lobe suppression is extremely important in precisely determining the weak echo scattering region in the presence of range side lobes. This paper addresses the signal design problem for the detection of multiple/distributed targets in high resolution radar (HRR) application with improved side lobe suppression ratio. The simulation results indicate a significant improvement in terms of noise robustness and Doppler tolerance for HRR target detection; compared to conventional binary sequences. Keywords: Poly-semantic radar; Hamming backtrack; side lobe suppression. 1. Introduction Designing of coded radar signal for obtaining the pulse compression sequences with large non-periodic autocorrelation properties and very low side lobes is an important issue in high resolution radar (HRR) applications [1], [2]. Earlier Poly-alphabetic radars (PAR) and Poly-semantic radars (PSR) [3], [4] have been studied extensively in the context of side lobe suppression [5], [6] and detection of point targets in presence of high density additive noise and Doppler environment. Compared with conventional radars, these radars possess the advantages of high range resolution, enhanced clutter-suppression capability, improved noise immunity, Doppler tolerance etc. In PAR, only a binary sequence is transmitted, but at the receiver, through poly-gram reading, it can be interpreted as binary, quaternary and octal sequences. In this design, a bigram is viewed as a quaternary element or a trigram is viewed as an octal element. This is somewhat a constrained concept. In Hamming scan, the quaternary and octal elements as independent entities would have 3 and 7 first order Hamming neighbors, but bigrams and trigrams on the substratum of binary monograms, have only two and three first order Hamming neighbors. Thus, the higher order poly-gram interpretations have a disadvantage in Hamming scan. Also in PAR, the enlarged alphabets cause deterioration in the noise and Doppler performances at larger sequence lengths [7]. In order to overcome these drawbacks and to restrict the enlarged alphabets of poly- alphabetic sequence to binary, the poly-semantic sequences (PSS) are proposed [4]. These sequences are mono-alphabetic nature of poly-alphabetic sequences. The work presented in this

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paper is to evaluate the detection ability of binary poly-semantic sequences for multiple/ distributed targets in presence of high dense noise. The detection performance of these sequences is evaluated in terms of figure of merit.

1.1 Figure of Merit: The figure of merit is defined [8] as,

( ) ( )

( ) 0

( )

(0) max ( )

(0)

m m

m k

m

C C kF

C

(1)

Here ‘m’ represents the number of bits in error obtained in the sequence when it is received. So, the figure of merit (1) is defined in the context, when known number decoding errors are present in the detected signal. It is assume that the distortion due to propagation delay is ignored and the additive noise is independent with transmitted signal. But in real time situations, the received signal may be corrupted by random noise with unknown noise strength. The performance of the PSS by considering additive random noise will be discussed in Sec. 4.

1.2 Multiple Targets Scenario: When there are N number of point targets (source of reflectors) clustered with in the sequence length period, the echoes from the reflectors arrive at the receiver at different sub-pulse delays are added in the subsequent range bins. The resultant sequence length increases as the distance between two distinct targets increases. If τ is the sub-pulse duration and N is the sequence length the maximum separation between the targets is N.τ sec. The no. of range cells required is (2N-1). Consider there are three targets separated at 2 τ and 5 τ respectively with the first target. If Barker B13 sequence is transmitted, the echoes from these targets are given by Echo from I target : 0 0 0 0 0 1 1 1 1 1 -1 -1 1 1 -1 -1 1 -1 Echo from II target: 0 0 0 1 1 1 1 1 -1-1 1 1 -1 -1 1 -1 Echo from III target : 1 1 1 1 1-1-1 1 1-1 -1 1 -1 The resultant echo is [ 1 1 1 2 2 2 2 3 2 1 1 2 -1 0 0 -2 1 -1] Therefore, the no. of range cells required are 18. Similar procedure can be followed for N no. of sequences. 1.3 Distributed Targets: The distributed targets such as cloud, thunderstorm, precipitation etc. for weather radar, consist of number point scatters, in which the target samples occupy more than the radar resolution cell. Therefore the echo sequences are added at every sub-pulse duration (SPDA). i.e., If the distributed target has k.τ sec duration, then k no. of sequences are added. For example if k=3, then the echoes from the distributed target are 0 0 1 1 1 1 1-1-1 1 1-1-1 1 -1, 0 1 1 1 1 1-1-1 1 1-1-1 1-1 and 1 1 1 1 1-1-1 1 1-1-1 1-1 The resultant sequence is [1 2 3 3 3 2 -1 -2 1 1 -1 -1 -1 0 -1 ]. The no. of range cells required are 15. 1.4 Discrimination Factor & Figure of Merit for multiple/distributed targets: Since the matched filter output has multiple peaks corresponds to the multiple/distributed targets. Discrimination Factor and Figure of merit can be redefined as

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[ ]max ( )

1( )

k ttC k

FC t

or 11t

tF

D

(2)

and

[ ]

( )

max ( )t

k t

C tD

C k

(3)

Where F is the figure of merit, D is the discrimination at given signal to noise ratio (η), t is an integer represents

target position and [t] is an array of all target positions. 1.5 Hamming backtrack algorithm for PSS Binary Hamming Backtrack algorithm [7] is modified and applied in the context of poly-semantic signatures by considering figure of merit as performance index. The main drawback with Hamming scan algorithm is it may not perform recursive search among all the Hamming neighbors and results in suboptimal solution to the signal design problem. The backtracking Hamming scan algorithm can be employed when Hamming scan for poly-semantic sequence yields no further improvement in the objective function. It considers a prescribed number 'n' called span of the best Hamming neighbors (though they are all inferior to starting sequence) and improves them separately by repeated recursive Hamming scan, say 'c' times (called climb). If some sequences superior to the starting poly-semantic sequence results, the best among them is selected. A span of 10 and a climb of 4 are used in the proposed algorithm. 2. Coded Waveform Design for PSS The generation of poly-semantic sequences is completed in two steps: first one using restricted (selective) Hamming backtracking scan for interspersed binary sequences and the second, using a complete Hamming backtracking scan with an appropriate joint objective function, which takes into the account of correlation properties between the received sequence R and predefined interleaved sequences in the process of signal design. The block schematic diagram of poly-semantic radar signal processor at the transmitter is shown in Fig. 1. Consider, optimal binary codes or randomly generated binary codes of length N, given by S1= A= [aj] (4) B = [bj] (5) and C= [ cj ] (6) Where, j = 0, 1 ,2, 3 , …, N-1. The elements of these sequences are drawn from alphabet {-1, +1}. The sequence S1 is mutated viz. +1 -1, - 1 +1 using Hamming backtracking scan algorithm to get optimum figure of merit. The sequences S2 of length 2N and S3 of length 3N are generated by interleaving the elements of S1&B and S2&C respectively. Therefore S2=[ajbj] (7) And S3=[ajbjcj] (8) Where, j= 0, 1 ,2, 3 , …, N-1. A selective Hamming backtracking scan algorithm [7] is applied on the sequences S2 and S3 , so that the figure of merit of the output sequence is optimized. This algorithm performs mutations only on the embedded elements, i.e., b0, b1, b2, b3 … of the sequence S2, and c0, c1, c2, c3 … of the sequence S3, without disturbing the other elements. The sequence S3 is interspersed by binary sequences S1 and S2. It is equivalent to three sequences with good autocorrelation properties being transmitted in the form of S3.

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Fig. 1 Block schematic diagram of poly-semantic radar signal processor (a) Transmitter (b) Receiver.

2.1 Coincidence detection strategy:

For further optimization, the following three sequences are derived from the sequence S3= [aj bj cj] T1 = [a0, 0, 0, a1, 0, 0, a2, 0, 0 … aN-1, 0, 0] (9) T2 = [ a0, b0, 0, a1, b1, 0, a2, b2, 0… aN-1, bN-1, 0 ] (10) T3 = [ a0, b0, c0, a1, b1, c1, a2, … aN-1, bN-1, cN-1 ] (11) These sequences T1 and T2 of length 3N are derived from the optimized sequences S1 and S2 embedded with zeros. The sequence T3 is same as S3. The full Hamming scan algorithm is applied on the binary sequence S3 and three derived sequences T1, T2 and T3 for finding the pseudo-discriminations d1, d2 and d3. The pseudo-discriminations d1, d2 and d3 are defined on the basis of cross correlation of the sequences S3 & T1, S3 & T2 and S3 & T3 respectively. The pseudo-discrimination is the ratio of the peak when the sequences match lengthwise to the largest side lobe amplitude in the cross correlation. This facilitates coincidence detection of the target as discussed in Sec. 4. The binary poly-semantic Hamming scan induces mutations in the elements of binary sequence S3, viz., +1 -,1 - 1 +1 and looks at the first order Hamming neighbors of all the elements in the sequence. A mutation in the element of S3, in turn induces mutation in the corresponding elements of the sequences T1, T2 and T3. The algorithm

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computes the sum (d) of pseudo-discriminations d1, d2 and d3 (i.e d = d1+ d2+ d3) of all the first order Hamming neighbors of S3 and picks up the binary sequence which results in largest value of d. The autocorrelation due to each perturbation of the binary sequence is calculated by merely taking into account the changes required in the original autocorrelation instead of calculating the aperiodic autocorrelation of the Hamming neighbors ab initio. This facilitates the expedition of the process of binary poly-semantic Hamming scan algorithm to obtain sequences of larger lengths. The joint figure of merit F = (F1+F2+F3) /3. Here, F1, F2, and F3 are obtained from d1, d2, and d3 respectively. The good figure of merit properties of these three interpretations are jointly used through coincidence detection for the detection of target. The binary sequence S3 (T3) is transmitted as a waveform. 3. Simulation Results and Performance Evaluation

3.1 Noise Robustness

Two targets are considered with different sub-pulse delay apart. The noise effect on figure of merit at different sequence lengths is considered. The noise performance is examined for different values of SNR (η) ranging between 0 dB to -20 dB. The noise performance results clearly show that the PSS exhibits high noise robustness at the higher sequence lengths. 3.2 Range Resolution Consider the multiple/distributed targets, which are moving within the resolution volume. Since the point reflectors are very close, assume that all are at same velocity. The following target model (Fig. 2) for N sources is developed with Doppler shift in noisy environment. This model is simulated using MATLAB functions. Also consider the targets, which are separated from different sub-pulses delay apart (SPDA) with sub-pulse duration ‘τ’ of 50 ns (range resolution 7.5 m). The sources are separated from one SPDA to a maximum of (N-1) SPDA. When targets are within the sub-pulse range, the resultant echo signal is the addition of all the echo signals from the targets. Depending on the delay between the echo signals, the length of the resultant sequence increases. As a simulated target model for generating received code SR, when targets are at n1,n2,n3…..nN SPDA with Doppler phase shifts Φ1, Φ2, Φ3,… ΦN in noisy environment. The binary code Sb is clocked (2N-1) times into the target model to get the received code SR of fixed length (2N-1). A limiter is used to limit the amplitude levels between ±1.

Fig. 2 Target model when two targets are at n- SPDA.

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For range resolution ability, consider a target model when a dispersed echo is reflected from targets located at sub-pulse duration apart (SPDA) of zero to (N-1). When the targets are stationary, Fig. 3 gives the Range Resolution ability between two targets. 3.3 . Detection Performance Let us consider a Ka-band 30 GHz radar, transmitting a poly-semantic sequence of length N=3000 with pulse interval of 36.25 μs. The sub-pulse time interval is 50 ns (signal bandwidth is 20 MHz and range resolution is 7.5 m). At the receiver, the resultant waveform is multiply interpreted for coincidence detection. Fig. 4 shows the output waveforms of Poly-semantic sequences of length N= 3000 when the stationary ( zero Doppler phase shift) multiple /distributed targets are located at different SPDA. 3.4 Doppler Tolerance Consider a moving distributed target in which the point targets at n1,n2,n3…..nN SPDA are moving with same velocity ie. Doppler phase shifts Φ1, Φ2, Φ3,… ΦN are all equal to Φ in noisy environment. So Φ1 = Φ2 = Φ3 =… ΦN = Φ. Fig. 5 shows the output response of Poly-semantic sequences of length N= 3000 when 10 point targets are located at 20 SPDA moving with same velocity of Doppler shift and Fig. 6 shows the output response of Poly-semantic sequences of length N= 3000 with SNR = 0 dB at Doppler shift 0.6pi/N. when a target is distributed with length 20 SPDA.

4. Conclusion In this paper poly-semantic sequences are analyzed for the detection of multiple/distributed target in high density additive noise. When there is N number of point targets (source of reflectors) clustered within the sequence length period, the echo from the reflectors arrives at the receiver at different sub-pulse delays are added in the subsequent range bins. The resultant sequence length increases as the distance between two distinct targets increases. The simulation results in Fig. 4 provide evidence that the PSS at larger pulse compression ratios achieve the range side lobe level below 18.78 dB. This is significance improvement over conventional pulse compression sequences and poly-phase alphabetic sequences [9]; which provide side lobe level of 13.42 dB at length N > 1638 under noise free environment. The poly-semantic sequences at higher lengths with coincidence detection has noise tolerance of η = -10dB. While compared with poly- phase sequences, a poly-semantic sequence has achieved better noise rejection ability, higher range resolution, and improved side lobe suppression ratio. Figs. 5 and 6 provide better detection performance at SNR, η = 0 dB when ten targets at 20 SPDA moving with same velocity at Doppler shift 0.6pi/N and a target distributed with length 20 SPDA moving with velocity at Doppler shift 0.6pi/N.

These examining results lead PSS to be very suitable for the high resolution radar systems. However, these advantages will be achieved with an additional affordable signal processing at the receiver.

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0 1000 2000 3000 4000 5000 6000-1

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o S

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Rat

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Comparision of distance between two targets at -5dB Noise

0 1000 2000 3000 4000 5000 6000-5

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Target2

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SPDA = 0SPDA = 1SPDA = 2SPDA = 10SPDA = 35

SPDA = 0SPDA = 1SPDA = 2SPDA = 10SPDA = 35

Fig. 3 Range Resolution ability between two targets.

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Poly Semantic Signal of lengh N=3000,when 30 targets are at 100 SPDA

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Poly Semantic Signal of lengh N=3000,when 30 targets are at 100 SPDA at -5dB noise

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Poly Semantic Signal of lengh N=3000,when a distributed target of duration 20 SPDA

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Fig. 4 Poly-semantic sequences of length N= 3000 when (a) ten targets at 100 SPDA with no noise. (b) 30 targets at 100 SPDA. (c) 30 targets

at 100 SPDA at -5dB noise (d) distributed target of duration 20 SPDA

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(b) Fig. 5 Poly-semantic sequences of length N= 3000 with SNR = 0 dB when ten targets at 20 SPDA (a) at Doppler shift 0.3pi/N. (b) Doppler

shift 0.6pi/N.

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Fig. 6 Poly-semantic sequences of length N= 3000 with SNR = 0 dB at Doppler shift 0.6pi/N. when a target is distributed with length 20 SPDA.

Reference

[1] A.W.Rihaczek and R.M.Golden, “Range sidelobe suppression for Barker codes”, IEEE Trans. Aerospace and Electronic Systems,vol.7, 1971, pp.1087-1092.

[2] M.H Ackroyd and F.Ghani, “Optimum mismatched filters for sidelobe suppression”, IEEE Trans. Aerospace and Electronic Systems, vol.9, 1973, pp.214-218.

[3] Y. Mallikarjuna Reddy, I. A. Pasha, and S. Vasthsal, “Poly-alphabetic radar signal processor for efficient target detection”, International radar Symposium I, Bangalore, 2007, pp. 30-34.

[4] I.A. Pasha, P. S. Moharir, and V. M. Pandharipande, “Poly-semantic binary pulse compression radar sequences”, IEEE TENCON 2003, IEEE technical conference on convergent technologies for the Asia-Pacific, 2003.

[5] P. Z. Peebles, J. R., “Radar Principles”, John Wiley and Sons, Inc., 2004. [6] M.I.Skolnik, “Radar Handbook”, 2nd ed., McGrawHill, 2001. [7] I.A. Pasha, N. Sudershan Rao, and P. S. Moharir, “Poly-alphabetic Pulse Compression Radar Signal Design”, Modeling, Measurement &

Control, Journal of AMSE, vol. 74, no. 4, 2001, pp. 57-64. [8] P. S. Moharir, K. RajaRajeswari, and K. Venkata Rao, “New figures of merit for pulse compression sequences”, Journal of IETE, vol. 38,

no. 4, 1992, pp. 209-216. [9] K. RajaRajeswari. et al, “New figures of merit for range resolution radar using hamming and Euclidean distance concepts”, Proceedings of

the 7th WSEAS International Conference on Multimedia Systems & Signal Processing, Hangzhou, China, April 15-17, 2007, pp. 139-145.

ISSN: 0975-5462 3807

radar signal design for high resolution multiple/distributed

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