Multichannel estimation by blind MMSE ZF equalization

We investigate a new multichannel estimation method based on blind MMSE ZF equalization. The recently proposed method by Tsatsanis et al. (1997) corresponds to unbiased MMSE equalization. We interpret this approach in terms of two-sided linear prediction (TSLP), also called smoothing by Tong (1998). We establish the links between MMSE, minimum output energy (MOE) and MMSE ZF and we prove equivalence under the unbiasedness constraint in the noiseless case. Our analysis shows how to properly apply Capon's principle (1969) for linearly constrained minimum variance (LCMV) beamforming to multichannel equalization. Furthermore, we show that Tsatsanis's application of Capon's principle becomes only correct, and Tong's channel estimate becomes only unbiased, at high SNR. Whereas the goal is to do MMSE ZF, it is easier to approach the problem via unbiased MMSE (UMMSE) on noiseless data. Hence, the covariance matrix of the received signal has to be "denoised" before using it in the blind estimation method. We provide an approach without eigen-decomposition that shows excellent performance. Simulation results are presented to support our claims.