1 Introduction The Separation of Independent Sources (SIS) assumes that some unknown but independent temporal signals propagate through a mixing and/o

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1 Appeared in IEEE Trans. on Circuits and Systems, vol. 42, no. 11, pp , November 95 c Implementation and Test Results of a Chip for The Separation of Mixed Signals Ammar B. A. Gharbi and Fathi M. A. Salam Circuits, Systems and Articial Neural Networks Laboratory Department of Electrical Engineering Michigan State University, East Lansing, MI gharbi@ee.msu.edu, salam@ee.msu.edu Abstract We describe an algorithm and chip implementation for separating a mixture of unknown, but independent, temporal signals in static and dynamic environments. The proposed algorithm, which is a simple modication of the Herault and Jutten (HJ) algorithm, proved to be robust to parameter variations. Moreover, we present some chip results to quantify the performance of the modied algorithm in static and dynamic (mixing and ltering) environments. Acknowledgment: This work is supported in part by the Michigan Research Excellence Fund (REF). 1

2 1 Introduction The Separation of Independent Sources (SIS) assumes that some unknown but independent temporal signals propagate through a mixing and/or ltering natural or synthetic medium. By sensing outputs of this medium, a neural network is tailored to adaptively recover the original independent signals. Using only the property of independence, the neural network would work to counteract the eect of the mixing medium, see [1], [2], [3] and [4]. Major applications include the separation of signals received via an array of sensors in radar, sonar, pace makers, hearing aides, and medical diagnosis. (More motivation of the potential uses of this approach are relegated to the cited references.) One essential and practical limitation, however, is that the HJ algorithm and all its reported realizations, considers only static mixing environments represented by an unknown but constant matrix.dynamic environments which signify mixing and ltering are more realistic. Filtering indeed introduces a physical signal delay whichmaybecontributed by the medium and/or the sensors. One may also consider a cascade of lters to construct a delay line to provide for larger signal delays. This work introduces a modication of the Herault-Jutten (HJ) algorithm which aspires to address the eect of dynamic media in mixing and/or ltering signals. It describes the implementation and application performance of a prototype neuro-chip in static (mixing) and dynamic (mixing and ltering) environments. Moreover, it experimentally quanties the chip's capability and limitation. 2 Problem Denition The general block diagram for SIS is shown in Figure 1. The vectors s(t), e(t), and y(t) are, respectively, the unknown source vector, the measured signal vector, and the output signal vector. The network to be designed receives the signal e(t) and adaptively modies y(t) to reproduce the original signal s(t). In [1] and [2], Herault and Jutten had proposed an algorithm that assumes a static linear medium with no dynamics. The input to the network model is a measured signal vector, e(t): e(t) =As(t) (1) where A is a matrix whose components are all positive and which models the environment statically. Furthermore, A is assumed to be nonsingular. Its diagonal entries are all ones and each o diagonal element is less than one. Herault and Jutten [1, 2] used a recursive architecture made up of fully 2

3 interconnected outputs. Each output,y i (t), receives the mixed signal, e i (t), and a weighted sum of all other outputs, ; P j6=i d ij y j (t). Thus, y(t) =e(t) ; D y(t) (2) where D is an nn matrix whose main diagonal is zero. Now, the problem of separation of signals translates to retrieving the original signals. In the limit, it is thus desired to have: y(t) =P s(t) where P is a permutation matrix. From biological and intuitive inspirations, Herault and Jutten [1, 2] proposed the following update law: _ d ij = ij f(y i )g(y j ) (3) where f(:) and g(:) are two nonlinear odd functions and ij is the learning rate. This algorithm has been implemented in CMOS. Successful testing of several implementations, using static models of the environment and the network, described by (1) and (2), has been reported in [5] and [6]. However, the algorithm, and thus its implementations, lacks robustness to changes in the environment model (which may include dynamics). 3 A Modied HJ Algorithm The network of (2) can be rewritten as =;y i + e i ; X j6=i d ij y j (4) To include the eect of the transient dynamics, we consider the dynamic network i _y i (t) =;y i (t)+e i (t) ; X j6=i d ij y j (t) (5) where i, for all i, is selected to provide time-scale separation between (5) and (3). By considering the dynamic network (5) in conjunction with the update law (3), only the stable and robust solutions of (5) become feasible solutions. This robustness property is important in lieu of the fact that physical circuit realization is necessarily prone to function approximation and inaccuracies. Moreover, this modied algorithm performs smoothing and enables an integrated circuit implementation to dominate the ever-present parasitic capacitance of its transistors. In [4], simulation 3

4 results had shown that the system described by (1), (3) and (5) successfully separates mixed signals more robustly. Our chip implementation of system (3) and (5), discussed below, will be tested in both the static environment case as well as the more realistic dynamic environment case. It should be noted that dynamic environment is represented by a linear mixing and ltering function, where ltering introduces a physical signal delay characteristics. 4 VLSI Implementation The modied HJ algorithm is implemented in CMOS using 2:m technology on a Tiny Chip (2:222:25mm 2 ). Equations (3) and (5) are implemented in CMOS by the circuit diagrams shown in Figure 2 using basic building blocks from [5, 7]. The governing equations are _V ij = 2wI e (V b+v ) tanh C ij 2 y i sinh y j C i V ij ; V T (V R ; V T ) _y i = e i ; y i + X j6=i V R ; V T y i Observe the explicit inclusion of the capacitor, Ci, to generate the proper dynamics necessitated by our algorithm. The table below shows the parameters in equations (3) and (5), their corresponding CMOS expressions as well as their nominal values in the course of testing. CMOS expression Nominal value i Ci (V R ;V T ) 1:2 1 ;8 s ij 2wI e (V b +V ) C ij 8: 1 4 s ;1 Using the basic building blocks, the circuit implementation of our algorithm, governed by (3) and (5), is directly realized. Observe that the ratio between i and the inverse of ij is about 4-folds, leading to a fast and slow time-scales of the dynamics of the network and the weight update. This distinct fast-slow time-scales are crucial in enabling convergence of the algorithm. 5 Test Results The resulting chip is tested to quantify its performance for static and dynamic media. The chip testing has been carried out using a two-neuron network where it is desired to separate two independent signals. Experiments have been conducted to investigate the performance of the chip for the separation of signals in three scenarios: (i) separation of prototype waveforms such as sine, triangular and square waveforms, (ii) separation of two speech segments of two dierent English 4

5 speakers, or English and Japanese speakers, and (iii) separation of white noise and an English speech segment. 5.1 The Static Medium Case It is assumed here that the mixed signals are linear combinations of the unknown sources as described in (1). The combined circuits shown in Figure 3, with C F ij combination of the original sources: e i = nx R R j=1 ij s j = s i + X j6=i R R ij s j with R ii = R =1k =, will produce a linear Thus, the coecient of the matrix A in (1), a ij = R R ij,canbevaried by using an external variable potentiometer for R ij. Such variations can be used to study the robustness of the network realized on the Tiny Chip. Successful separation was obtained in the rst two cases for mixing levels less than 8%. For the third case, perfect separation is attained only for mixing levels less than 3%. Above these levels, the outputs of the network are not separated but rather contain a mixture of the original signals. See Figure 4 for example experimental results. For the three mentioned scenarios, the level of mixing has been varied in order to study the robustness of the network to variations. For this reason, the parameters a ij are initially xed to some values. Once the network converged (and separation of signals is established), the parameters a ij are then varied in order to observe the quality of performance. Experiments for dierent starting values of the mixing matrix A were performed. The percentage of the robustness to each parameter is then recorded. Based on the experiments, the network is robust to parameter variations of about 15% (on average). As the level of mixing is varied, it was discovered that the network fails to separate the signals when the mixing reaches some level. Based on experiments, the coecients of the mixing matrix A should range between. and.8 for the rst two scenarios and. and.3 for the third scenario. 5.2 The Dynamic Modeling Case It is now assumed that the input to the network is a superposition and a ltered version of the unknown sources. This is a more realistic, real-world, mixing scenario. The circuit diagrams shown in Figure 3 (a) is used to obtain a ltered version of the original signals: e i = nx X F ij (s j )=s i + j=1 j6=n 5 F ij (s j ) with C Fij = and R ij = R

6 F ij (:) isalow pass lter with gain g ij = R =R ij and cuto frequency! ij =1=R C Fij, namely F ij (V in )= g ij s! cij +1 V in The goal now is to study whether the modied algorithm can still update the parameters where the parameters d ij will adaptively counter the eect of g ij and! cij, and thus recover the original signals. The three previous scenarios are repeated in studying this problem. Exhaustive experimentation and testing led to the conclusion that separation of the signals occurs in the rst two scenarios when g ij < :4 and also in the third scenario when g ij < :15. See Figure 5 for example results. It is noted that the interval range over which the separation occured had shrunk considerably in comparison to the linear static medium case. Nonetheless, the chip was able to achieve signal separation in this dynamic medium as well. 6 Conclusion We have tested chip implementation of the modied HJ algorithm and explored its validity range. The modication produces robust performance to parameter variations and to dynamic media eects. Limits were also experimentally quantied. The fact that realistic sensors have their own inherent dynamics underlines the need for such consideration. We showed that the modied algorithm has a potential in solving the problem of SIS in more realistic real-world environments. References [1] J. Herault and C. Jutten. Blind separation of sources, part 1: An adaptive algorithm based on neuromimetic architecture. Signal Processing, 24:1{1, July [2] J. Herault and C. Jutten. Blind separation of sources, part 2: Problem statement. Signal Processing, 24:11{2, July [3] J. C. Platt and F. Faggin. Networks for the separation sources that are superimposed and delayed. Advances in Neural Information Processing systems, 1:73{737, [4] F. M. A. Salam. An adaptive network for blind separation of independent signals. International Symposium on Circuits and Systems, 1:431{434, May

7 [5] E. Vittoz and X. Arreguit. Cmos integration of herault-jutten cells for separation of sources. Proceedings Workshop on Analog VLSI and Neural Systems, May [6] M. H. Cohen and G. Andreou. Current-mode subthreshold mos implementation of heraultjutten autoadaptive network. IEEE Journal of Solid-State Circuits, 27(5):714{727, May [7] C. Mead. Analog VLSI and Neural Systems. Prentice Hall, New York, s(t) - Environment Model e(t) - Network Model y(t) - Figure 1: Block diagram Vr -ei Ci yi Vin Vij Vi1 yn yj Figure 2: Summing Unit Vin Ro CFij Ro sj Low Pass : Ri1 : Rij Low Pass. : sn Low Rin Pass Vout (1) Ro ei V out = ;1 s V!cij +1 in (a) Low pass lter e i = P n j=i F ij(s j ) (b) Mixing/ltering circuit Figure 3: Mixing Circuit 7

8 1 5 5 s2 () () e e y error: (ms) error: y2-s (ms) (a) sine and triangular functions 5 5 s e1 61 e y y2 s ms ms (b) White signal and English segment Figure 4: Static Mixing 8

9 () delayed 1 () e s delayed s e2 1 () y2 () error: error: y2-s2 2 () (ms) (ms) (a) Two sine functions 5 5 s e1 57 e y y2 s ms ms (b) Both English segments Figure 5: Dynamic Mixing 9

BLIND SEPARATION OF SOURCES: A NON-LINEAR NEURAL ALGORITHM

BLIND SEPARATION OF SOURCES: A NON-LINEAR NEURAL ALGORITHM Gilles BUREL Thomson CSF, Laboratoires Electroniques de Rennes, Avenue de Belle Fontaine, F-35510 CESSON-SEVIGNE, France My new address is: Prof.