Convergence rate of adaptive line enhancer with tap failures

The adaptive line enhancer (ALE) has been applied to a variety of problems. There has been extensive analysis of the convergence, tracking, and steady state error properties of the normal ALE. Recently, the effects of tap failures on the steady state error of the ALE were investigated. Here the effect of tap failure on the mean convergence behavior of the ALE operating under general tap failure is analyzed under the independence assumption. The convergence rate is shown to be related to one of the eigenvalues of the modified autocorrelation matrix. These results are then applied to the special cases of single complex exponential, single real sinusoid, and multiple complex exponential input signals in additive white noise. Simulation results showing close agreement with theory are presented.