Iterative LBG clustering for SIMO channel identification

This paper deals with the problem of channel identification for Single Input Multiple Output (SIMO) slow fading channels using clustering algorithms. Due to the intrinsic memory of the discrete-time model of the channel, over short observation periods, the received data vectors of the SIMO model are spread in clusters because of the AWGN noise. Each cluster is practically centered around the ideal channel output labels without noise and the noisy received vectors are distributed according to a multivariate Gaussian distribution. Starting from the Markov SIMO channel model, simultaneous maximum-likelihood estimation of the input vector and the channel coefficients reduce to one of obtaining the values of this pair that minimizes the sum of the Euclidean norms between the received and the estimated output vectors. Viterbi algorithm can be used for this purpose provided the trellis diagram of the Markov model can be labeled with the noiseless channel outputs. The problem of identification of the ideal channel outputs, which is the focus of this paper, is then equivalent to designing a Vector Quantizer (VQ) from a training set corresponding to the observed noisy channel outputs. The Linde-Buzo-Gray (LBG)-type clustering algorithms [1] could be used to obtain the noiseless channel output labels from the noisy received vectors. One problem with the use of such algorithms for blind time-varying channel identification is the codebook initialization. This paper looks at two critical issues with regards to the use of VQ for channel identification. The first has to deal with the applicability of this technique in general; we present theoretical results for the conditions under which the technique may be applicable. The second aims at overcoming the codebook initialization problem by proposing a novel approach which attempts to make the first phase of the channel estimation faster than the classical codebook initialization methods. Sample simulation results are provided confirming the effectiveness of the proposed initialization technique.