Convergence properties of Gram-Schmidt and SMI adaptive algorithms

The open-loop Gram-Schmidt (GS) canceler is shown to be numerically identical to 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 nonconcurrent processing. Results for concurrent and nonconcurrent SMI cancelers have been obtained in the past by I.S. Reed, J.D. Mallet, and E. Brennan (see ibid., AES-10, p.853-63, 1974) 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 deleterious effect of overmatching the degrees of freedom is discussed