Modified stochastic gradient algorithm using nonquadratic cost functions for data echo cancellation

A new stochastic gradient algorithm based on the cost function |e _k|^τ where τ⩾2 is proposed. Conditions for the convergence of means are derived. Merits of the new adaptation algorithm as compared with that of the least mean square (LMS) algorithm are demonstrated by means of simulations. Computer simulations were performed with non-Gaussian binary sequences of data in the presence of far-end signals in data echo cancellers for full duplex digital data transmission over telephone lines. Three different echo path models were used in these simulations. Convergence goals were set 20 dB below the level of the far-end signals in each case. τ was increased starting from 2.0 in steps of 0.1. It is observed that convergence time decreases with the increase in τ initially and then levels off. After levelling off for a small region of τ, convergence time starts increasing once again before the algorithm becomes unstable. These simulations indicate that a substantial reduction in convergence time can be achieved relative to the mean square algorithm