Blind multichannel estimation and joint order detection by MMSE ZF equalization

Previously, we presented 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 and/or in the noiseless case. Our analysis shows how to properly apply Capon's principle for linearly constrained minimum variance (LCMV) beamforming to blind 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 Capon dictates to do MMSE ZF, it is easier but equivalent 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 a denoising approach without eigen decomposition that gives excellent performance. Furthermore, we present a simple and efficient procedure to simultaneously detect the channel order. Simulation results are presented to support our claims