CONVERGENCE PROPERTIES OF GRAM-SCHMIDT AND SMI ADAPTIVE ALGORITHMS

The open-loop Gram-Schmidt (GS) canceler is shown to be numerically identical with the sampled matrix inversion (SMI) algorithm in the transient state if infinite numerical accuracy is assumed. Two forms of the GS canceler are discussed and analyzed: concurrent and noncurrent processing. Results for concurrent and nonconcurrent SMI cancelers have been obtained in the past by Reed, Mallet, and Brennan under the assumption that the inputs are Gaussian. Many of those results are reproduced here using the GS structures as an analysis tool. In addition, new results are obtained when the input noises are not Gaussian. The deleterous effect of “over-matching the degrees of freedom” is discussed. © 1990 IEEE