Identification of Unknown Uncorrelated Colored Signals Distorted by Unknown Convolutive Channels

A fundamental problem in adaptive sensor array processing is to identify unknown uncorrelated colored signals that are distorted by unknown convolutive channels. This problem is also known as blind identification of MIMO (multi-input-multioutput) systems. In this paper, we present a novel approach called BIDS (blind identification by decorrelating subchannels). The BIDS can identify an FIR (finite impulse response) MIMO system up to a scaling and permutation if the channel matrix (a polynomial matrix) of the system has a normal full rank and is column-wise coprime. This condition is weaker than that the channel matrix is irreducible and columnreduced. The latter condition is required by many other approaches such as the subspace approach by Loubaton et al. As a result, the BIDS has a much better performance against noise. The BIDS first partitions the channel output signals into clusters of subgroups. For each group, the BIDS constructs a decorrelation filter that yields decorrelated signals. Under a (weak) condition, each of the decorrelated signals directly corresponds to one of the desired signals except for a convolutional distortion (without mixing). The output signals of the decorrelation filters can then be regrouped into a bank of SIMO (single-input-multiple-output) systems. The SIMO systems can be identified by an efficient maximum likelihood algorithm or other SIMO algorithms. Alternatively, the decorrelation filters can be directly exploited to yield the original MIMO channel matrix. This matrix can then be used in the recovery of the desired signals. The latter algorithm (named BIDS-2) is more robust than the former (named BIDS1). The BIDS algorithms are built upon a series of newly developed algebraic insights into the MIMO systems. These insights (associated with polynomial matrices) should be useful for further development of blind system identification.