Approximate sample variance analysis of exponential channel derived from SVD-based algorithm

Tufts et al. (see Proc. IEEE Int. Conf. Commun., Seattle, WA, USA, 1987) presented an algorithm for improving conventional least-squares (LS) estimates of the truncated pulse response of a communication channel. It involves oversampling of the channel output and singular value decomposition (SVD) of the data matrix before LS estimation. Here, an approximate expression for the variance of the estimate of each channel sample is derived when the algorithm is applied to the problem of identifying an exponential impulse response channel. SVD is shown to introduce discontinuities in the variance, which repeat periodically at the symbol rate, for those sample estimates outside the interval corresponding to the central tap. Experimental results confirm the validity of the approximations used in the variance computations, and that the disjoint periodic structure exists even for higher order channels.