Implementation of Sequential Algorithm in Batch Processing for Clutter and Direct Signal Cancellation in Passive Bistatic Radars

Transcription

1 Implementation of Sequential Algorithm in atch Processing for Clutter and Direct Signal Cancellation in Passive istatic Radars Farzad Ansari*, Mohammad Reza aban**, * Department of Electrical and Computer Engineering Yazd University, ansaryfarzad@stu.yazduni.ac.ir ** Department of Electrical and Computer Engineering Yazd University, mrtaban@yazduni.ac.ir Abstract: Passive bistatic radars are an important batch of scout radars that use the signals of other independent transmitters as illuminators of opportunity. Cancellation of clutter and multipath is an important problem in these radars. his problem is exacerbated as the transmitter signal is not under the control of designer. In this paper, we propose a novel algorithm for clutter and multipath cancellation in the passive radars that called sequential cancellation algorithm-batch (SCA-). Indeed, the SCA- is a generalization of some recent algorithms such as the ECA, the SCA and the ECA- that act based on projecting the received signals in a subspace orthogonal to both clutter and pre- detected targets. In this paper, the SCA- algorithm use for static and non-static clutters cancellation. he SCA- provides an admissible performance with low complexity. Keywords: Passive radar, Clutter and multipath cancellation, Ambiguity function. 1. Introduction oday, the radar systems play an important role in military applications. his causes that the radars become the permanent targets for the adversaries. Passive radars can detect aerial targets without being identified by the enemy. In this type of radar, the signals can be V [1], radio [2], and satellite signals, in the space which can be used as the transmitted signal. hese radars don t have transmitter; thus, they will stay hidden. he scenario that occurs in the passive radars is presented in Fig 1. In this scenario, the passive radar consists two receive erence and eillance antennas. he erence antenna receives only the direct signal from transmitter, while the eillance antenna receives both the direct signal and the signal lecting from the targets and clutters. Using the ambiguity function based on the matched filters [3,4], the Range-Doppler targets and clutter are detectable. efore computing the ambiguity function, there are some problems that must be solved. Some of them are the high power direct signal, the low power target signal, and the multipath effects in the channel target/clutter. Various methods have been proposed to overcome these problems. An important class of these methods is based on the projections of the received signal in a subspace orthogonal to both the clutter and the pre-.detected targets. he most important of them are the SCA 1 [5], the ECA 2 [5, 6], and the ECA- 3 [6]. Simulation results show that the proposed SCA- 4 has a better or equal performance with respect to the mentioned methods corresponding to the conditions. Furthermore, the SCA- requires less memory than the mentioned methods. he paper is organized as follows. Section 2 introduces the signal model and ambiguity function. Section 3 and 4 describes ECA and SCA algorithms. Section 5 describes the proposed SCA- technique and this section 6 two test are introduced for algorithm comparisons. Finally, Section 7 is our conclusions. 2. Signal Model And Introduce Ambiguity Function he FM radio signals used in the passive radar are in the MHz band. As seen in Fig 1, two required signals for interference cancelation algorithms are obtained from the erence and eillance antennas. he received signal s (t) from the eillance antenna is modeled as below: s 0 t 0 M j 2f C dm ( t) A d ( t) a d ( t ) e c ( t) d ( t ) n m m1 m t N i i1 Figure 1 - scenario of passive radars 1 Sequential Cancellation Algorithm 2 Extensive Cancellation Algorithm 3 Extensive Cancellation Algorithm atches 4 Sequential Cancellation Algorithm atches ci (1) ( t)

2 where d (t) is the direct signal multiplied by the complex amplitude A ; a m, m, and f dm are the complex amplitude, delay and Doppler frequency of the m-th target signal (m=1,..,m), and ci is the delay of the i- th clutter (i =1,.., N ). All delays are calculated with c respect to the direct signal. n (t) is the thermal noise contribution at the receiver antenna. he complex amplitudes c i (t) are considered slowly varying functions of time, so that they can be represented by only a few frequency components around zero Doppler: j 2 f t c cl i ( t) ci e (2) where f and cl ci are the Doppler shift and complex amplitude of the i-th clutter (i =1,.., N ). Also, the received signal s (t) at the erence antenna is: s ( t) A d( t) n ( t) (3) where A is a complex amplitude and (t) is the c n thermal noise contribution. he samples collected at the receiving channel at time instants ti is, are arranged in a N1 vector s : s ( t0), s( t1), s( t2),..., s( t N 1 )] s [ (4) where N is the number of samples to be integrated. Similarly, we collect (N+R-1) samples of the signal at the erence channel in the following vector s : [ s ( tr1),..., s ( t0),..., s ( tn 1) ] s (5). We use the ambiguity function for evaluation of the interference cancelation algorithms and target detection. Discrete ambiguity function equation is as follows [4]: N 1 i0 j2 pi [ l, p] s [ ] [ ] N i s i l e l 0,..., R 1 (6) where s [i] and s [i] denote s ( t i ) and s ( t i ) respectively. Consider that the discrete delay l corresponds to the delay [ l] ls. Similarly, the discrete Doppler frequency bin, p corresponds to the Doppler frequency f [ p] p. d N s Fig 2 shows a Doppler-Delay scenario that has nine clutters in the form of blue stars and three targets in the form of red circles. he clutter and target specifications are shown in able I and able II respectively. Also, the SNR 5 of the direct signal is assumed to be 60d. able I- clutter Echoes Parameters clutter #1 #2 #3 #4 #5 #6 #7 #8 #9 Delay (msec) Doppler (Hz) SNR (d) 5 Signal to Noise Ratio able II- clutter Echoes Parameters target #1 #2 #3 Delay(msec) Doppler(Hz) SNR(d) Figure 2: Scenario of the study case Fig 3 shows the ambiguity function of the received signal in a two dimensional mode (2-D) without removing the direct signal and clutter. In Fig 3 peak of targets are masked by peaks of direct signal and clutters. In Fig 3 output of ambiguity function for l 0 is drown. In this figure strong peak corresponding to direct signal (Doppler zero and delay zero) is presented obviously. Figure 3: 2-D ambiguity function output in d before cancellation, section at delay 0

3 3 Extensive Cancellation Algorithm (ECA) [5] One effective way to clutter and direct signal cancellation in passive radars is based on the L.S 6 estimation. he optimization expression of the LS estimation is as follows: min s Hθ (7) θ where H [Λ ps Λ 1S S Λ1S Λ ps ], is an incidence matrix that selects only the last N rows of the following matrix, Λ p is a diagonal matrix that applies the phase shift corresponding to the p-th Doppler bin. D is a 0/1 permutation matrix that applies a delay of 2 k1 a single sample and S [ s Ds D s... D s ] whose columns are the zero-doppler, delayed versions of the erence signal. he columns of matrix H define a basis for the M-dimensional clutter subspace, where M=(2p+1)k. Solving (7) yields θˆ H 1 H ( H H) H s. heore, the received signal after cancellation becomes: seca s Hθˆ H 1 H ( I N H( H H) H ) s P0s (8) where the projection matrix P 0 projects the received vector s in the subspace orthogonal to the clutter subspace. According to the scenario in Fig 2, we evaluate the ECA algorithm performance by substituting s ECA to s in equation 6 and computing the ambiguity function of s ECA. Fig. 4 shows the 2-D ambiguity function after clutter and direct signal cancellation. his figure has been obtained by k=50 and p=0 (namely the sizes of H S and θ are N k and k 1 respectively). Apparently, a deep null appears at zero Doppler, however clutter echoes are still present at low Doppler frequencies and the target echo cannot be identified. Fig 4 shows the ambiguity function output versus delay in Doppler l 0. In this figure, the peak corresponding to the direct signal (Doppler zero and delay zero) has been removed. Fig 5 shows the 2-D ambiguity function after direct signal and all echoes of clutter cancellation. he simulation conditions are k=50 and Doppler bin (-1, 0, 1), where p is 1 (namely the sizes of H and θ are N M and M 1 respectively). In Fig 5, the two strong targets now appear but the weak target is not detectable. Fig 5 shows the ambiguity function versus delay in Doppler l 0. It is shown that the direct signal and all clutters corresponding to the delays inside the first k bins are removed. he computational complexity of the ECA algorithm 2 3 is ( NM M ). his complexity is high because the estimation of vector θ requires the inversion of the matrix H H H with dimensions M M. 4 Sequential Cancellation Algorithm (SCA) [5] Aiming at reducing the computational load of the ECA algorithm described in Section 3, the SCA offers a sequential solution algorithm for clutter and direct signal cancellation. 6 Least Square Figure 4 : 2-D ambiguity function output after direct signal and zero-doppler clutter cancellation (k=50) with ECA algorithm section at l 0. Figure 5 : 2-D ambiguity function output after direct signal and all clutters cancellation (k=50, p=1 and M=150) with ECA algorithm section at Doppler 0.

4 Consider the matrix H as form H [ x0 x1... xm 1], where x i is its (i-1)-th column. he sequential equation of the SCA algorithm is as follow: ( i) x i1 Pi xi1 M,...,2, 1 i (9) H (i) (i) xi1 xi1 Q i I N H (i) (i) xi 1 xi1 i M,...,2, 1 (10) P i 1 QiQi1... Q M M I i M,...,2, 1 (11) and: (i) Pi s s i M,...,2, 1. (12) Now using the projection matrix P 0, the output vector s SCA is obtained as follow: P. (13) ssca 0s A schematic plan of the SCA algorithm containing the clutter cancellation and direct signal path is shown in Fig 6. his figure almost shows all steps of a SCA algorithm. It is possible to limit the computational of the cancellation algorithm by arresting it after stage S (S < M). he computational complexity of the SCA algorithm limited to S stage is O (NMS ), which can be significantly smaller than the computational cost of the corresponding complete ECA algorithm. 5 Sequential Cancellation Algorithm -atch (SCA-) In order to improve the cancellation performance with a limited computational load, a modification of the SCA is proposed, called SCA-. he received signal at the eillance antenna is divided into sections with length. If the entire length of the eillance antenna signal is int, the total number of samples of the signal at the antenna will be N int fs where f s is the sampling frequency. he signal is divided into b packets with N N b available samples. he SCA algorithm is applied to each of these packets distinctly. he output of the SCA algorithm on the each packet is a vector removed of the clutter and direct signal. he main cleaned vector is obtained from the union of these subvectors. Finally, the main vector can be used for plotting the ambiguity diagram and target detection. In this manner, vectors s (i ) and s (i ) corresponding to the (i-1)-th packet, are defined as follows: s (i) s (i) [ s [ in ] s [ in 1]... s [( i 1) N 1]] i 0,1,2,..., b 1 (14) [ s [ in R 1] s [ in R]... s [( i 1) N 1]] i 0,1,2,..., b 1, (15) If the output of the SCA algorithm on the i-th packet denotes vector S SCA(i), the total output SSCA with cancelled clutter and direct signal, is obtained as: SCA [ SSCA(0) SSCA(1)... SSCA(b1) S ] (16) A schematic plan of the SCA- algorithm is shown in Fig 7. his algorithm is also simulated based on the scenario presented in Fig 2. Information required for the simulation is shown in able III. Fig 8 shows the 2-D ambiguity function after cancelling the all clutters and direct signal using the SCA- algorithm. his simulation has been prepared with S=100, Doppler bin (-1, 0, 1) and k=50. Cancellation of the direct signal and clutter causes that the strong targets can be seen better and by using a simple detector such as the CA-CFAR detector, they can simply be detected. Nonetheless, the weak target has not been detected. Figs 8 and 8(c) show the ambiguity function versus delay for Doppler -50 and 100 respectively. In these two figures, the locations of two strong targets are shown obviously Figure 7:. Sketch of SCA-batches approach able III- SCA- algorithm parameters required for simulation Figure 6- Sketch of the sequential cancellation algorithm[5] ime ime Sampling atch int s b msec 1 sec 10

5 1 ambiguity function of s ( t), the weak target can be appeared. he observation algorithm is repeated until the expression (18) occurs. max ( d, fd ) min ( d, fd ) max ( d, fd (18) where ( d, fd ) is the value of ambiguity function in the all positions ( d, f d ) and is a small value where in our simulations has been selected between zero and one. Fig 9 shows the 2-D ambiguity function output after removing the direct signal, all clutters, and the strongest target using the observation algorithm. Here, the weak target now appears as a strong peak. Fig 9 shows the ambiguity function versus delay for Doppler 50. In this figure, the location of weak target is shown obviously. he computational complexity of the SCA- algorithm in each batch is O( N MS). his means that the SCA- (c) Figure 8-2-D ambiguity function output after direct signal and all clutters cancellation with SCA- algorithm with Doppler bin (- (1,0,1) section at Doppler -50 (c) section at Doppler 100 We use the observation algorithm for detection of the weak target. he Doppler frequency ( fˆ d ), delay ( ˆ d ) and amplitude ( Â d ) of each strong target can be extracted based on the information of location of this strong target in the ambiguity function. hen, the echo of the strong target is subtracted from ssca (t) as follow: ssca ( t) Aˆ d d( t j fˆ ˆ 2 d t 1) e 1 s ( t) (17) where ssca (t) is the signal with removed clutter and direct signal by the SCA- algorithm. y computing the Figure 9-2-D ambiguity function output after direct signal and all clutters and strong targets is removed with SCA- algorithm section at Doppler 50, algorithm requires less memory than that of ECA and SCA algorithms. When the SCA algorithm is run on b batch, the computational complexity will be O( bn MS)

6 which is equal to the SCA algorithm because bn equals N. 6 ECA, SCA and SCA- algorithms comparison Here, the CA 7 and A 8 tests are introduced for comparison algorithms of clutter and direct signal cancellation. Initially, CA and A tests are written as follow: input clutter amplitude peak CA 10log( ) (19) output clutteramplitude peak input target amplitude peak A 10log ( ) (20) output target amplitude peak where, the amplitudes of clutter and target are indicated by "input clutter amplitude peak" and "input target amplitude peak" before the clutter/direct signal cancellation, and by "output clutter amplitude peak" and "output target amplitude peak" after clutter/direct signal cancellation. For calculating the CA and A, one target and one clutter are introduced with characteristics tabulated in able IV. In Fig 10, a simulated CA curve of the SCA- algorithm versus the number of batches is shown in comparison of the CA of the ECA and SCA algorithms. It is seen that the CA for the SCA- with ten batches ( b 10 ) is similar to that of ECA and SCA. Fig 11 shows a A diagram of the SCA- algorithm versus the number of batches. It is seen that in the SCA- algorithm with less than ten batches, similar to the ECA and SCA, the amplitude of the target in the ambiguity function is never reduced after clutter/direct signal cancellation. Nevertheless, as be seen in Fig 11, the amplitude of the target after cancellation will be reduced by increasing the number of batches from ten. his may cause that the target cannot detected in ambiguity function. Figure 11: Diagram of A versus the number of batches 6 Conclusion In this paper, the SCA- algorithm was proposed for both static and non-static clutters and direct signal cancellation and target detection for passive bistatic radars based on the projections of the received signals in a subspace orthogonal to the clutter and previously detected targets. At first, the SCA- algorithm was used for clutter and direct signal cancellation and strong targets detection. hen, the observation algorithm was applied for detection of weak targets. he simulation results showed that the SCA- algorithm has good performance in the detection of targets. he A and CA tests were used for comparison the SCA- with the ECA and SCA algorithms. hese tests showed that targets may hide in the ambiguity function when the number of batches increases. he SCA- algorithm has less computational complexity than that of ECA algorithm, also requires less memory than that of SCA algorithm. Figure 10- Diagram of CA versus the number of batches able IV- Scenario of one target and one clutter for calculation CA and A Delay(msec) Doppler(Hz) SNR(d) Clutter arget References [1] H. A. Harms, L. M. Davis, and J. Palmer, Understanding the signal structure in DV- signals for passive radar detection, Proc. Int. IEEE. Conf. on Radar, pp , May 10-14, [2] A. Lauri, F. Colone, R. Cardinali, and P. Lombardo, Analysis and emulation of FM radio signals for passive radar, Proc. Int. IEEE Conf. on Aerospace, pp X, March 3-10, [3] M. L. Skolnik, Introduction to Radar System, McGraw-Hill, 2001, pp [4]. sao, M. Slamani, P. Varshney, D. Weiner, and H. Schwarzlande, Ambiguity function for a bistatic radar, IEEE rans. on Aerospace and Electronic Systems, Vol. 33, No. 3, pp , [5] F. Colone, R. Cardinali, and P. Lombardo, Cancellation of clutter and multipath in passive radar using a sequential approach, Proc. Int. IEEE Conf. on Radar, pp , April 24-27, [6] F. Colone, D. W. O Hahan, P. Lombardo, and C. J. aker, A multistage processing algorithm for disturbance removal and target detection in passive bistatic radar, IEEE rans. on Aerospace and Electronic Systems, Vol. 45, No.2, pp , Clutter Attenuation 8 arget Attenuation