POSTSMOOTHING FOR THE LMS ALGORITHM AND A FIXED-POINT ROUNDOFF ERROR ANALYSIS

Digital implementations of the LMS algorithm display a stalling behavior when the input to the weight update equation falls below the least significant bit of the corresponding quantizer. The stalling range can be reduced by increasing the algorithm step size mu. However, increasing mu increases the steady-state weight fluctuations and the corresponding algorithm misadjustment. On the other hand, for increasing mu, the weight vector sequence (over time) becomes less correlated. This suggests smoothing the weights with a post-algorithm filter. The performance of this scheme is studied and shown to perform better than the digital LMS algorithm above, optimized over mu.