A global gradient descent algorithm for hierarchical FIR adaptive filters

We present an extension of the recently introduced hierarchical least mean square (HLMS) algorithm. The original algorithm suffers from two major drawbacks, namely the incapability to converge for every unknown channel and the dramatic deterioration of its performance as the number of levels increases significantly. To be able to cope with these, a novel global gradient descent algorithm is proposed. This algorithm converges for every class of unknown filters and it exhibits faster convergence than HLMS in any case.