A reduced computation multichannel adaptive equalizer based on HMM

This paper describes a non-linear adaptive equalizer based on a sub-optimal HMM formulation leading to a small computational complexity. A similar approach was already proposed in the monochannel case, and we show that, in a multichannel context, large improvements are obtainable. It is well known that maximum likelihood methods are subject to local minima problems. Although of reduced importance in our previous approach (due to the on-line adaptation), the problem was still present. Since it is now well known that in the multichannel case, the blind equalization problem has a unique minimum, one can hope that the local minima problems can be solved in this context. However, a straightforward formulation of the previous algorithm in the multichannel case does not solve it. Hence, we propose a new algorithm allowing conditional means estimates of the emitted symbols and blind identification of each impulse response of the channels, involving altogether a maximum likelihood formulation (by means of an approximate EM algorithm) and a criterion making use of the spatial diversity of the multichannel system. Simulations are provided, showing the identification of the impulse responses of the various channels, as well as the symbol estimation performance in terms of bit error rate (BER). The improvements over the single channel case are highlighted