EFFICIENT MULTICHANNEL FIR FILTERING USING A SINGLE-STEP VERSATILE ORDER RECURSIVE ALGORITHM

In this paper two highly efficient, order recursive algorithms for lea st squares multichannel FIR filtering and multivariable system identif ication are developed. Multichannel FIR filters with different number of delay elements for each input channel are allowed. The first algori thm uses two terms Levinson type recursions. The later utilizes Schur type formulas for updating the pertinent parameters, thus being suitab le for parallel implementation. Multichannel FIR filters are described by a multi-index [m1, m2,...,m(k)] where mi equals the number of dela y elements associated with the i-input channel, i = 1, 2,...,k. The no vel feature of the proposed algorithms is that they employ updates of the form [m1, m2,...,m(i),...,m(k)] --> [m1, m2,...,m(i) + 1,...,m(k), ]. Therefore, and in contrast to existing methods, they offer the grea test possible maneuverability in the index space. This flexibility can be taken into advantage when the true index is not known, except from being an element of a set. Computationally efficient paths that searc h for the true index are described. If the true filter order [p1, p2,. ..,p(k)] is known, the filter coefficients are computed at P = (p1 + P 2 + ... + P(k)) steps, by a repetitive application of single step recu rsions. The computational complexity of the method is O(kP2), while ex ecution time could be reduced to O(1) or O(P) if the Schur type algori thm is implemented in a parallel processing environment on a rectangul ar or on a linear array, respectively. The final filter can be approac hed by p!/(p1!p2!...p(k)!) distinct order updating paths, each time pa ssing through different lower dimension filters. This feature can be u tilized for the efficient determination of the order of a multichannel process, accelerating the exhaustive searching procedure required by most of the order determination criteria. Finally, the mean squared er ror is considered with potential applications to the optimal two-dimen sional (2-D) FIR filtering and 2-D system identification.