Convergence bounds of an SMI/Gram-Schmidt canceler in colored noise

摘要

The performance of the sampled matrix inversion (SMI) adaptive algorithm in colored noise is investigated using the Gram-Schmidt (GS) canceler as an analysis tool. Lower and upper bounds of average convergence are derived, indicating that average convergence slows as the input time samples become correlated. When the input samples are uncorrelated, the fastest SMI algorithm convergence occurs. When the input samples are correlated then the convergence bounds depend on the number of channels N, the number of samples per channels K, and the eigenvalues associated with K*K correlation matrix of the samples in a given channel. This matrix is assumed identical for all channels.