Modular and numerically stable multichannel FTF algorithms

The authors present scalar implementations of multichannel fast recursive least squares algorithms in transversal filter form (so-called FTF). By processing the different channels sequentially, i.e one at a time, the processing of any channel reduces to that of the single-channel algorithm. This sequential processing decomposes the multichannel algorithm into a set of intertwined single-channel algorithms. Geometrically, this corresponds to a modified Gram-Schmidt orthogonalization of multichannel error vectors. Algebraically, this technique corresponds to matrix triangularization of multichannel error covariance matrices and converts matrix operations into a regular set of scalar operations. Algorithm structures that are amenable to VLSI implementation on arrays of parallel processors follow naturally from this approach. Numerically, the resulting algorithm benefits from the advantages of triangularization techniques in block processing. Stabilization techniques for control of numerical error propagation in the update recursions are incorporated