A fast block FIR adaptive digital filtering algorithm with individual adaptation of parameters

A general formulation for developing a fast-block least-mean-square (LMS) adaptive algorithm is presented. In this algorithm, a convergence factor is obtained that is tailored for each adaptive filter coefficient and is updated at each block iteration. These convergence factors are chosen to minimize the mean-squared error in the processed block and are easily computed from readily available signals. The algorithm is called the optimum block adaptive algorithm with individual adaptation of parameters (OBAI). It is shown that the new coefficient vector obtained from the OBAI algorithm is an estimate of the Wiener solution at each iteration. Implementation aspects of OBAI are examined and a technique is presented that eliminates matrix inversion by processing signals in overlapping blocks and applying the matrix inversion lemma. When the coefficients are updated once per input data sample, the resulting OBAI algorithm requires 7N/sup 2/-5N+9 multiplications and divisions (MAD) per iteration, where N is the number of estimated parameters. The convergence properties of OBAI are investigated and compared with several recently proposed algorithms.<>