Signal Processing for Remote Sensing - Chapter 10

10 Blind Separation of Convolutive Mixtures for Canceling Active Sonar Reverberation Fengyu Cong, Chi Hau Chen, Shaoling Ji, Peng Jia, and Xizhi Shi CONTENTS 10.1 Introduction..................................................................................................................... 187 10.2 Problem Description....................................................................................................... 188 10.3 BSCM Algorithm............................................................................................................. 190 10.4 Experiments and Analysis ............................................................................................ 193 10.4.1 Backward Matrix of Active Sonar Data for Approximating the BSCM Model............................................................................................... 193 10.4.2 Examples of Canceling Real Sea Reverberation .......................................... 194 10.4.2.1 Example 1: Simulation 1................................................................. 194 10.4.2.2 Example 2: Simulation 2................................................................. 194 10.4.2.3 Example 3: Simulation 3................................................................. 195 10.4.2.4 Example 4: Real Target Experiment............................................. 198 10.4.2.5 Example 5: Simulation 4................................................................. 198 10.5 Conclusions...................................................................................................................... 199 References ................................................................................................................................... 200 10.1 Introduction Under heavy oceanic reverberation, it can be difficult to detect a target echo accurately with an active sonar. To resolve the problem, researchers apply two methods that use reverber-ation models and specialized processing techniques [1]. For the first method, receivers with differing range resolutions may encounter different statistics for a given waveform. Furthermore, a given receiver may encounter different statistics at different ranges [2]. Researchers have used Weibull, log-normal, Rician, multi-modal Rayleigh, and non-Rayleigh distributions to describe sonar reverberations [3,4]. For the second method, it is usually assumed that reverberation is a sum of returns issued from the transmitted signal. Under this assumption, a data matrix is first generated from the data received by the active sonar data [5,6]. The principal component inverse (PCI) [7–13] is primarily used to separate reverberation and target echoes from the data matrix. However, important prior knowledge such as the target power should be provided [11]. In Refs. [11–13], PCI and other methods have performed very well in Doppler cases, and the authors have also shown that PCI still performs well when the Doppler effect is not introduced. Provided that prior knowledge is ß 2007 by Taylor & Francis Group, LLC. hard to obtain and the Doppler effect does not exist, it becomes very desirable to ca reverberation with easily obtainable but minimal prior knowledge even in more compli-cated undersea situations. The chapter focuses on this case. The essenc e of PCI is separ ation by ran k red uction. Ne vertheles s, the pro separ ation is an old one in electri cal enginee ring and man y algorit hms exi st dep on the natur e of sign als. Blind sign al separ ation (BSS) [14] is a signif icant statisti c pro cessing me thod that has been develop ed in the past 15 years. The a dvantag e o that it does not need mu ch pri or knowle dge and make s full use of the sim appar ent statis tical proper ties, such as non- Gaussia nity, nonstati onarity, co lored cha ter, uncorr elatedne ss, inde pendence , and so on. We stu died BSS on canceling reve ation in Ref . [15] . From the per spectiv e of BSS, the data receive d by active son convo lutive mi xture [16] , wh ile the instan taneous mixtur e mode l was onl y discu Ref . [15]. Consequ ently, we perfo rm blind separati on of convolu tive mixtur es (BSC nul lify ocea nic reve rberat ion in this contrib ution. In Ref . [15], the data wave form desc ribed in time -domain , and here, we will provide mo re illustrat ions on the m filter outpu ts un der differen t sign al-to-re verberatio n ratio s (SRR). We pro vide examp les for better explanatio n. The rest of this chapter is organi zed as follo ws: Se ction 10.2 presents the pr desc ription ; Section 10.3 introduces the BSCM algor ithm, which is bas ed on the reve ation charact ers; Sectio n 10 .4 provides exa mples of canc eling real sea reverbe ration main conten t; and finall y, Se ction 10.5 sum marizes the above co ntents. 10.2 Problem D escription In this chapter , we assum e that re verberatio n is a sum of returns generated fro trans mitted signal . In Ref. [16], the active sonar d(att)a isserexieps ressed as K d(t) ¼ |fflfflfflfflfflffl{zfflfflfflfflfflffl}e(t) þ |fflfflfflfflfflffl{zfflfflfflfflffl} e(t) þ |{z} (10:1) targ et reverbera tion noise wh eretk is the pro pagation delhay(t,) is the pat h impul se resp ones(et), aisndthe trans mitted signal. In the reverbe ration dom inant circumst ance, we can decomp ose active sonar data into the target echo comdp(to)neanntd the reverberat ion component r(t), as define d in Equation 10.2. Extr acting the targe t and nullifyin g the reverbe rat done simulta neously d(t) ¼ |fflfflfflfflfflffl{zfflfflfflfflfflffl} e(t) þ|{z} tar get noise K r(t) ¼ hffl(t ÿtfflffl) e(t) þ n(t) (10:2) reverberatio n noise It is appare nt tdh(at)t andr(t) are of differe nt no n-Gauss ianity. Ne xt, we show a examp le of real sea reve rberat ion. For simplicity, we do not introduce the experimental detail in this section. The transm ted signal is sinusoid with a frequency of 1750 Hz, a duration of 200 msec, and a sam frequency of 6000 Hz. Figure 10.1 contains only the target echo and the background no ß 2007 by Taylor & Francis Group, LLC. 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 0 0.5 1 Samples 1.5 FIGURE 10.1 2 2.5 3 104 Target echo waveform. and most reverberation generated by a sine wave is included in Figure 10.2 where no ta echo exists and the background noise is embedded. The two waveforms in Figure 10.1 a Figure 10.2 are the time-domain descriptiodn(st) aonfd r(t) with corresponding standard kurtosis [17] 4.1 and 1.6, respectively. Here, the time-domain non-Gaussianity is enough to discriminated(t) and r(t). It may appear that detectiodn(t)fomr us t b e e vi de nt . H ow ev in the real world problem, it is not simple to cancel the reverberation to the degree Figure 10.1. To explore different effects of reverberation on detection in different SRRs, w give several examples of real sea reverberation as follows. In Figure 10.3 , the first upp er plot is reve rberat ion, and in the remain ing thr differen t targets are sim ulated and ad ded to the reverbe ration ¼wi0th dtBh,ÿe 7SR R dB, andÿ14 dB, respec tively, from the uppe r to low er plots. The target ec ho is lo betwee n the 9,00 0th and 11,000th samp les. The target does not mo ve, hence no Do effect is produc ed. The matc hed filter outputs follow in the next figure . In Figure 10.4, the middle two plots show that the matched filter results are satisfacto even in the case that the SRR is quite small, and the lowest plot gives too many false The task for us is to cancel the reverberation to the degree that the detection is possible, s to the middle two plots. In Equationd(t)10.d2o, es not contain any reverberation and just covers only the target echo and the background noise. In real world case, that is imposs However, it does not harm the detection. Figure 10.4 also reminds us that even if K d(t) ¼ |fflfflfflfflfflffl{zfflfflfflfflfflffl}e(t) þ |fflfflfflfflfflffl{zfflfflfflfflffl} e(t) þ |{z} (10:3) tar get rev erberation noise where K < K, and as long as the reverbe ration is redu ced to some sati sfactory level, detec tion can also be reliable. Af ter co mparin g the first and the third plots in Figu and Figure 10.4, resp ectively, we find that Figu re 10.3 sho ws that the reverb tion wavef orm with small SRR target add ed is nearly iden tical to the wavefor 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 0 0.5 1 Samples 1.5 FIGURE 10.2 Reverberation waveform. 2 2.5 3 104 ß 2007 by Taylor & Francis Group, LLC. 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.80 0.5 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 Waveform: reverberation only 1.5 2 2.5 3 104 Waveform: SRR = 0 dB −0.80 0.5 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.80 0.5 1 1.5 2 2.5 3 10 Waveform: SRR = −7 dB 1.5 2 2.5 3 104 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.80 0.5 1 FIGURE 10.3 Waveform: SRR = −14 dB 1.5 2 2.5 3 104 Real reverberation with different simulated targets. reve rberation , but Figu re 10.4 implie s that the correspo nding matched defini tely of dif ferent non-Gau ssianity. This informati on is useful to distin guishin g the target echoe s from the reverberat ion echoe s. filter outputs our method 10 .3 BSCM Algorit hm In the past sever al years , differen t research ers develo ped sever al BSCM algor accordi ng to sign al pro perties. Genera lly speaking, for a given sour ce–recei ver pai wavef orm arr ives at dif ferent travel time s, ow ing to varying pat h lengths [18] these make reve rberat ions nonsta tionary. The transmi tted signal is sin usoid here, so ß 2007 by Taylor & Francis Group, LLC. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 00 0.5 1 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 00 0.5 1 MF output: reverberation only 1.5 2 3104 2.5 MF output: SRR = 0 dB 1.5 2 2.5 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 00 0.5 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 00 0.5 FIGURE 10.4 1 1 Samples 3104 MF output: SRR = −7 dB 1.5 2 2.5 3104 MF output: SRR = −14 dB 1.5 2 2.5 3104 Outputs of matched filter on the data in Figure 10.3. reverbe rations must retai n the co lored feature. There fore, we say reve rberat ions nonsta tionary and colored. In this section, we will give onl y a bri ef introduct ion BSCM algor ithm. Consid er a speech scenar io, wJ hmiecrreop hones recei ve mult iple filter ed copie s of statisti cally uncorr elated or ind ependen t sign als. Mathe matically , the receive d signal be exp ressed as a convol ution, that is, I Pÿ1 xj(t) ¼ hji(p)si(t ÿ p), j ¼ 1,...,J0; t ¼ 1,...,L (10:4) i¼1 p¼0 where hji(p) mod els tPh-epo int impulse resp onse from source to mi cropLhoisn teheand leng th of the recei ved sign al. In a mo re co mpact matr ix–vector notation, Equati on be state d as Pÿ1 x(t) ¼ H(p)s(t ÿ p) p¼0 ß 2007 by Taylor & Francis Group, LLC. ... - tailieumienphi.vn