Partial update and sparse adaptive filters

There has been increasing research interest in developing adaptive filters with partial update (PU) and adaptive filters for sparse impulse responses. On the basis of maximum a posteriori (MAP) estimation, new adaptive filters are developed by determining the update when a new set of training data is received. The MAP estimation formulation permits the study of a number of different prior distributions which naturally incorporate the sparse property of the filter coefficients. First, the Gaussian prior is studied, and a new adaptive filter with PU is proposed. A theoretical basis for an existing PU adaptive filter is also studied. Then new adaptive filters that directly exploit the sparsity of the filter are developed by using the scale mixture Gaussian distribution as the prior. Two new algorithms based on the Student´s-t and power-exponential distributions are presented. The minorisation-maximisation algorithm is employed as an optimisation tool. Simulation results show that the learning performance of the proposed algorithms is better than or similar to that of some recently published algorithms