Blind MIMO channel identification from second order statistics using rank deficient channel convolution matrix

For multiuser systems, several direct blind identification algorithms require that the linear multiple-input multiple-output (MIMO) system have a full rank convolution matrix. This condition requires that the system transfer function be irreducible and column reduced. We show that this restrictive identification condition can be relaxed for some direct blind identification methods to accommodate more practical scenarios. Algorithms such as the outer-product decomposition algorithm only require minor length adjustment to its processing window without the column-reduced condition. This result allows direct blind identification methods to be applicable to MIMO without requiring a full-rank channel convolution matrix.

I. Introduction

Blind channel identification and equalization of single user linear systems traditionally require high-order statistics [8], [9]. However, the well known work of Tong et al. [10] led a new direction in exploiting multichannel diversity that makes it possible to utilize only second order statistics (SOS) of channel outputs for direct blind identification of single input multiple output (SIMO) systems. Since then, a number of SOS blind equalization and identification algorithms have been proposed, including [11], [12], [14], and [19]. It has been well understood that for SIMO systems, unknown channel is blindly identifiable from SOS if and only if all SIMO sub-channels share no common zeros. This condition permits a full-rank channel convolution matrix [10], [14].