EFFICIENT ORDER RECURSIVE ALGORITHMS FOR MULTICHANNEL LEAST-SQUARES FILTERING

In this paper four efficient order recursive algorithms for least squares (LS) multichannel FIR filtering and multivariable system identification are developed. The need for such algorithms rises when the system model assigns an unequal number of delay elements to each input channel. All proposed schemes provide considerable improvements over over-parameterization, or the zero padding approach, which simply equalizes coefficients lengths of all channels by inserting zeros and then solves the extended problem via a fast least squares algorithm. First, a block-structured algorithm is derived. It operates on boxes, or blocks, whose dimensions successively increase until their size equals the number of input channels. As a result, it requires linear system solvers and matrix multiplications. The second algorithm manages to get free of block operations by proper decomposition of each block step involved in the first method, into a number of scalar steps equal to the size of the block. The third and the fourth algorithms provide highly concurrent alternatives, and if a parallel processing environment is available, they reduce processing time by an order of magnitude. All proposed methods include a primary module, a secondary module, and a management scheme. The primary module constitutes the main body of the algorithm and is responsible for all functions required to deal with a multichannel setup. The secondary module provides all operations needed to effect the passage from a multichannel problem of i input channels to the next case involving i + 1 channels. The management scheme integrates the primary and the secondary module to achieve overall efficiency. An illustrative example from multichannel autoregressive spectral estimation is supplied.