Criteria for blind deconvolution of multichannel linear time-invariant systems

Shalvi and Weinstein (1990) proposed certain criteria for blind deconvolution of nonminimum-phase linear time-invariant systems. Their work is, however, restricted to the single-channel (or scalar) case. This paper extends the Shalvi-Weinstein approach to the multichannel case. We propose a multistage maximization criterion and a single-stage maximization criterion for attaining multichannel blind deconvolution. Under a normalized condition, they are shown to be equivalent. We derive also a necessary and sufficient condition for multichannel blind deconvolution. A simulation example is included to demonstrate the effectiveness of the proposed criteria