Multistep linear predictors-based blind identification and equalization of multiple-input multiple-output channels

Channel estimation and blind equalization of multiple-input multiple-output (MIMO) communications channels is considered using primarily the second-order statistics of the data. Such models arise when single receiver data from multiple sources is fractionally sampled (assuming that there is excess bandwidth) or when an antenna array is used with or without fractional sampling. We consider the estimation of (partial) channel impulse response and design of finite-length minimum mean-square error (MMSE) blind equalizers. We extend the multistep linear prediction approach to MIMO channels where the multichannel transfer function need not be column reduced. Moreover, we allow infinite impulse response (IIR) channels as well as the case where the “subchannel” transfer functions have common zeros. In the past, this approach has been confined to SIMO finite impulse response (FIR) channels with no common subchannel zeros. A related existing approach applicable to MIMO channels is restricted to FIR column-reduced systems with equal length subchannels. In our approach, the knowledge of the nature of the underlying model (FIR or IIR) or the model order is not required. Our approach works when the “subchannel” transfer functions have common zeros, as long as the common zeros are minimum-phase zeros. The sources are recovered up to a unitary mixing matrix and are further “unmixed” using higher order statistics of the data. Illustrative computer simulation examples are provided.