Convergence and steady state analysis of a tap-length optimization algorithm for linear adaptive filters

An adaptive filter with a large number of coefficients or taps results in slow convergence and increases the computational load. To overcome this problem, optimum tap-length selection algorithms for automatic structure adaption in linear adaptive filters have been proposed, which provide improved convergence rate without degrading the steady state performance. The most recent variable-tap length, variable step normalized least mean square algorithm with variable error spacing (VT-VSNLMSVE), employs a sliding window weight update and achieves better results in reducing the structural as well as computational complexity compared to its predecessors. But it does not present a convergence and steady-state analysis of the proposed algorithm. In the present paper, we have made a convergence and steady state analysis of the VT-VSNLMSVE algorithm. A mathematical formulation of the variable step-size, mean square equations and steady state tap-length is obtained that provides an idea regarding the applicability of the variable tap-length algorithm for many applications using higher-order adaptive filters. Computer simulations are presented in support of the algorithm analysis under predefined assumptions.