A subspace algorithm for guard interval based channel identification and source recovery requiring just two received blocks

Blind channel identification techniques usually exploit a known property of the source symbols such as a statistical or finite alphabet property. Recently, a purely algebraic approach that relies on guard intervals (sequences of zeros equal or longer in length than the channel memory) inserted between transmitted blocks has been considered. It was proved that only two received blocks suffice for channel identification and source recovery. We approach the channel identification problem from a z-domain perspective. It is shown that, in the z-domain, the channel is a common factor in all received blocks (this fundamental property appears to have gone unnoticed in the literature). This allows a subspace method for computing the greatest common divisor (GCD) to be applied to the channel estimation problem. The algorithm achieves the theoretical limit in that only two received blocks are required before the channel can be identified, but of course, the more blocks that are used, the better the performance in the presence of noise.