1997 IEEE Intemational Symposium on Circuits and Systems, zyxwvuts June 9-12,1997, Hong Kong zyxw A zyxwvu Network Structure Approach to Blind Source Separation using Second Order Cyclic Statistics Ying-Chang Liang, A. Rahim Leyman and Boon-Hee Soong Centre for Signal Processing School of Electrical and Electronic Engineering Nanyang Technological University Nanyang Avenue. Abstract This paper addresses the problem of blind sepa- ration of cyclostationary sources. By using the cyclostationarity property of the source signals, a new criterion based on second order cyclic statis- tics (SOCS) is established] from which a network structure (NS) approach for blind source separa- tion is proposed. Because the use of SOCS, the new approach requires few data samples and no re- strictions on the distributions of the source signals. Simulation results are given to demonstrate the ef- fectiveness of this new approach. zyxwvut I. Introduction The problem of blind source separation arises in a wide range of application fields, such as speech processing, data communication and biological sig- nal processing. To date, numerous approaches have been proposed and implemented to this problem [l- 61, [9]. For example, HJ network approach [l] and YW method [9] recover the source signals via itera- tive algorithms based on some higher order criteria. FOB1 zyxwvutsrq [a], AMUSE zyxwvutsrq [4] and EAMUSE [5] estimate the signals by using matrix transform techniques. Although these approaches are successful under certain assumed conditions, they have diverse lim- itations. To begin with, the approaches based on higher order statistics (HOS) require a large num- ber of data samples for the time-averaging estima- tion of HOS; in addition, restrictions on the dis- tributions of the source signals are imposed. Al- though AMUSE and EAMUSE exploit second or- der property of the signals, they fail to work when the processes involved are white. Finally, they are applicable only for stationary source signals. In practical applications, the signals encountered may be nonstationary processes. Especially, since almost all man-made communication signals ex- hibit cyclostationarity [7], there is a need to study Singapore 639798 the problem of blind separation of cyclostationary sources. The situation considered in this paper is similar to the communication systems, where the source signals are all cyclostationary processes. A new criterion based on second order cyclic statistics zy (SOCS) of the measurements is established] from which a new network structure (NS) approach for blind source separation is proposed. Simulation ex- amples are presented to show that the performance of the new approach. 11. Problem Statement In this paper. we consider the following model: .(TI) = Ao~o(n) + w(.) (1) where ~(n) = [~l(n).~~(n),...,5~(n)]~ is the ob- [SI zyxwvutsr (n) , s2 (n) , . . . , shf ( n)IT is the unknown source vector; and w(n) = [~)1(n),~2(n),...,w~(n)]~ is the additive noise vector; Ao = {aij}$” is the unknown parameter matrix that characterizes the medium or the channel. The zyx blind source separa- tion is to identify A0 and so(n) from ~(n) only. The following conditions are assumed to hold. (AS1) Ao has full rank; (AS2) Source signals s ~ ( n ) , s ~ ( n ) ; . . , ~ ~ ( n ) are zero mean (time-average), statistically mutually in- dependent, and second-order cyclostationary pro- cesses with nonzero and different cyclic frequencies QI, QZ, . . . , a!,!{, respectively; (AS3) Noise processes wl(n),w2(n);.. ,w~(n) are all zero mean stationary processes. They may be Gaussian or non-Gaussian, white or colored, and uncorrelated or correlated to each other; (AS4) Source signal %(n) and noise ~(n) are sta- tistically independent. Proposition 1: Under (ASl)-(AS4), the following results about the cyclic statistics are true: - - served . data vector; SO (n> ry(m) = E[sz(n)sz(n + m)e-j-] # 0 (2) (3) r:::: (m) = ~[si(n)sk(n + m)e--jain] 0, i + ]E 0-7803-3583-X/97 $10.00 01997 IEEE 2549