CENTRALIZED BLIND MULTIUSER DETECTION USING SICA

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(1)CENTRALIZED BLIND MULTIUSER DETECTION USING SICA . . ˜ Antonio J. Caamano, Rafael Boloix-Tortosa and Juan J. Murillo-Fuentes Universidad de Sevilla, ATSC. Paseo de los Descubrimientos sn, 41092 Sevilla, Spain. Universidad Carlos III. DTC. ATSC. Butarque, 15, 28911 Leganés, Madrid, Spain. [email protected] . A BSTRACT In this paper, a new Centralized Blind Multiuser Detector (MUD) based on the introduction of an Independent Component Analysis (ICA) matrix into the structure of the Minimum Mean Square Error (MMSE) is proposed. This approach palliates one of the main problems of the BSS/ICA algorithms, their sensitiveness to noise, and exploits the matrix structure of the blind centralized MMSE MUD. This novel solution is successfully applied to the multiuser synchronous CDMA channel.. 1. I NTRODUCTION. Interference limitation due to the simultaneous access of multiple users in Code Division Multiple Access (CDMA) systems has been the stimulus to the development of a powerful family of Signal Processing techniques, namely Multiuser Detection (MUD). In the simple memoryless synchronous case where no training sequences are available, the algorithms should cope with noise and the nearfar problem. In this sense, the minimum mean square error (MMSE) criteria (Verdú, 1998) provides a good blind linear solution to the problem. Due to its computational complexity, some other alternative algorithms have been proposed (Yang, 1995), (Wang and Poor, 1998), (A. J. Caamaño and Ramos, 2001) such as the PASTd. On the other hand, some blind source separation (BSS) algorithms have been proposed as fully blind MUD’s, in the sense that spreading codes are unknown (Murillo-Fuentes et al., 2001), (Causey and Barry, 1998), (Murillo-Fuentes and González-Serrano, 2001). However this blind techniques are not usually noise robust. We propose in this article to introduce a similar technique to BSS such as independent component analysis (ICA) (Murillo-Fuentes and González-Serrano, 2001), (Cardoso, 1998) into the structure of the MMSE MUD and its proven noise robustness. We will compare the performance of a block ICA algorithm such as SICA (Murillo-Fuentes and González-Serrano, 2001) to an adaptive method to compute the matrix such as M-EASI algorithm (Murillo-Fuentes et al., 2001). Noise robustness, efficient convergence and nearfar resistance of this new structure will be demonstrated..

(2) 2. P ROBLEM S TATEMENT. 2.1 Signal Model Let be a vector of symbols transmitted by independent finite-alphabet transmitter at time . We then denote by the

(3) vector corresponding to the receiver observation at time ,. . (1). where is an memoryless channel matrix, and the noise. This may be identified with the narrowband m-sensor linear-array application, the synchronous-CDMA case with spreading factor , or the general instantaneous BSS/ICA model. In synchronous CDMA communications, matrix may be decomposed into !!"$# , where # is a diagonal matrix with the amplitudes of each user and " is a matrix whose columns are the spreading codes. 2.2 Linear Multiuser Detection A linear multiuser detector %. gives an estimation of the original transmitted signals as. & %' %()*%'+. (2). The centralized detector minimizing the mean-square-error (MSE) for each user , , MSE -. E /0 & - 2134-56 0 798 , is the %;:<:>=4?. % :<:>=4?. . @(DEACD B "GF)"GFH"IJDF I. D "$F. (3). where K " F and IML is the decorrelating matrix for vector K . Here, as in the following, F denotes transpose-conjugate. In (Causey and Barry, 1998) the authors define a whitening–rotation detector (WR) as the %ON>P matrix that minimizes the MSE sum of MSE - , ,QG SR9TUTVTUR . A posible structure for this receiver was given as follows. %WN>P. . X)Y(I. (4). where I is a Z ; whitener, Y a Z ; rotation matrix, and J \[ ]'^`_ is O ; . In the context of the BSS, the problem consist of computing the matrix Iba that minimizes statistical dependence at the output. Other previous BSS approaches to fully blind MUD’s use a SVD decomposition. However, this involves a higher computational complexity. The natural or relative gradient (NG) has been also used as a steepest descent algorithm for adaptive approach in both BSS and MUD (A. J. Caamaño and Ramos, 2002).. 3. C ENTRALIZED MUD,. THE. BH. DETECTOR. In this paper, it is proposed to substitute the matrix product " F "cI DF I D in (3) by a matrix d makes the outputs eSf as statistically independent as possible. The new detector yields. % ahg di" F !YWI. D " DF. that. (5).

(4) where d is a whitening–rotator computed by using the SICA algorithm (Murillo-Fuentes and González-Serrano, 2001). Notice that in the centralized case the dimensional reduction is carried out by the matched filter " F , thus J ] in (4). In (Murillo-Fuentes and González-Serrano, 2001) authors prove that under whiteness constrains some fourth-order contrasts may be approximated by a sinusoid. Thus, the minimization of the contrast reduces to computing its phase. The starting point is the Minimum Entropy (ME) ICA contrast given by Comon in (Comon, 1994) so that we use the ’Jacobi optimization’ to cope with higher dimensions. This method, called SICA (Sinusoidal ICA,) has a good performance along with a low computational cost, outperforming the ME by Comon and the JADE methods (Cardoso and Souloumiac, 1993). Applying SICA to our problem, assuming inputs f have been decorrelated, this algorithm computes & !dWK minimizing the following function, denoted as contrast,. . :<?[ & _. &. [ _ . f

(5) - fVfUfUf. f

(6) - 7. (6). where f - is the fourth order cumulant of outputs e f Re Re - and e . Thus, this ICA algorithm may be seen as a fourth order decorrelation, and we go further than the second order based MMSE to find a new solution to the problem. The algorithm SICA is a block method that computes matrix d from a whole set of observations, similar to the MMSE method. As the spreading codes are usually available (at least at the base station), it is straightforward to introduce them as a subspace algorithm at a null complexity cost [3]. Besides, the structure of the MMSE detector has been used to cope with noise. We will compare the performance of this algorithm to that of the M-EASI algorithm, an adaptive method to compute matrix d that try to minimize a similar fourth order based contrast by using the natural gradient (Murillo-Fuentes et al., 2001).. 4. E XPERIMENTAL R ESULTS. As experiment we face the MUD in a synchronous CDMA system. The BPSK symbols were spread using GOLD codes with spreading factor . The number of users in the simulations was * , * and \* ^ . We study in Fig. 1 the convergence of the method for different numbers of users by computing the signal to interference ratio (SIR) along the number of samples for a signal to noise ratio (SNR) of 15 dB and average multiaccess interference (MAI) of 30 dB. On the other hand, we simulated the same scenario to depict, in Fig. 2, the bit error rate (BER) for different signal to noise ratios (SNR). This BER was computed for a training sequence of 4500 samples. The MF is included as reference along with the exact MMSE solution at every time (sample). The PASTd algorithm is also included in Fig. 1. The method presented within this paper exhibits a good performance, in comparison to the MMSE, even when the near-far problem is present. Under these conditions, other methods such as the PASTd have a poor behaviour. Besides, for a large enough number of training samples the method have a similar BER compared to that of the MMSE. We also compare the SICA to the adaptive M-EASI based method. We see how the algorithm presented here outperforms all of them although it increases the computational burden due to the block structure..

(7) 15. SIR. 10. 5. 0 0. 500. 1000. 1500. 2000. 1500. 2000. Samples (a). . users. 16 14 12. SIR. 10 8 6 4 2 0 0. 500. 1000. Samples. (b). . users. 16 14 12. SIR. 10 8 6 4 2 0 0. 500. 1000. 1500. 2000. Samples. (c). .

(8) . users. . . Figure 1: Convergence for MMSE ( ), SICA based MUD ( ), M-EASI based ( ), MF (*) and PASTd ( ) for synchronous CDMA with MAI=30 dB and SNR=15 dB.. .

(9) 0. BER. 10. −5. 10. 0. 5. 10. 15. 10. 15. 10. 15. SNR. . (a). users. 0. 10. −2. BER. 10. −4. 10. −6. 10. 0. 5. SNR (b). . users. 0. BER. 10. −5. 10. 0. 5. SNR (c). . . users. Figure 2: Bit Error Rate for MMSE ( ), SICA based MUD ( ), M-EASI based ( ) and MF (*) for synchronous CDMA with MAI=30 dB..

(10) 5. C ONCLUSIONS. In this paper the authors propose the ICA as a technique to exploit the matrix estructure of the parameters involved in the MUD problem, an application of the more general narrowband m-sensor linear-array case. Here, we propose a novel MUD by introducing an ICA matrix into the structure of the blind centralized MMSE MUD. This way we palliate one of the main problems of the BSS/ICA algorithms, their sensitiveness to noise. The results included here show a good near-far resistant performance in synchronous CDMA. References A. J. Caamaño, D. S.-V. and Ramos, J. (2001). Blind adaptive krylov subspace multiuser detection. In IEEE 54th Vehicular Technology Conference. A. J. Caamaño, J. J. Murillo-Fuentes, F. G.-S. and Ramos, J. (2002). Natural gradient based multiuser detection. In IEEE Proc PIRMC’2002 Lisbon. Cardoso, J. F. (1998). Blind signal separation: Statistical principles. Proceedings of the IEEE, 86(10):2009–2025. Cardoso, J. F. and Souloumiac, A. (1993). Blind beamforming for non gaussian signals. Proceedings IEE F, 140(6):362–370. Causey, R. T. and Barry, J. R. (1998). Blind multiuser detection using linear prediction. IEEE Journal on Selected Areas in Communications, 16(9):1702–1710. Comon, P. (1994). Independent component analysis, a new concept? Signal Processing, 36(3):287– 314. Murillo-Fuentes, J. and González-Serrano, F. (2001). Independent component analysis with sinusoidal fouth-order contrast. In International Conference on Audio, Speech and Signal Processing, volume V, pages 2785–2788, Salt Lake City, USA. Murillo-Fuentes, J. and González-Serrano, F. (2001). Median equivariant adaptive separation via independence: application to communications. Neurocomputing, (Accepted for publication). Murillo-Fuentes, J. J., Sánchez-Fernández, M., Caamano-Fernández, A., and González-Serrano, F. J. (2001). Adaptive blind joint source-phase separation in digital communications. In IEEE International Conference on Communications, Helsinki, Finland. Verdú, S. (1998). Multiuser Detection. Cambridge University Press. Wang, X. and Poor, H. V. (1998). Blind multiuser detection: A subspace approach. IEEE Transactions on Information Theory, 44(2):677–690. Yang, B. (1995). Proyection approximation subspace tracking. IEEE Transactions on Signal Processing, 43(1):95–107..

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