Sequential Monte Carlo methods for complexity-constrained MAP equalization of dispersive MIMO channels

The ability to perform nearly optimal equalization of multiple input multiple output (MIMO) wireless channels using sequential Monte Carlo (SMC) techniques has recently been demonstrated. SMC methods allow to recursively approximate the a posteriori probabilities of the transmitted symbols, as observations are sequentially collected, using samples from adequate probability distributions. Hence, they are a class of online (adaptive) algorithms, suitable to handle the time-varying channels typical of high speed mobile communication applications. The main drawback of the SMC-based MIMO-channel equalizers so far proposed is that their computational complexity grows exponentially with the number of input data streams and the length of the channel impulse response, rendering these methods impractical. In this paper, we introduce novel SMC schemes that overcome this limitation by the adequate design of proposal probability distribution functions that can be sampled with a lesser computational burden, yet provide a close-to-optimal performance in terms of the resulting equalizer bit error rate and channel estimation error. We show that the complexity of the resulting receivers grows polynomially with the number of input data streams and the length of the channel response, and present computer simulation results that illustrate their performance in some typical scenarios.