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LMS tracking behavior under periodically changing systems

The tracking behavior of Least Mean Squares (LMS) and Recursive Least Squares (RLS) algorithms have been under considerations for several years. For system identification problems it is usually assumed that the system under consideration is of FIR type with coefficients that are statistically independent random processes with identical distribution (IID), a somewhat artificial assumption that can hardly be found in existing systems. In this article it is assumed that the system is periodically changing over time. This is an important case that occurs in every wireless system where the carrier frequency provided by the transmitter suffers an offset compared to the local oscillator of the receiver. The article presents an analysis of the algorithm tracking behavior as well as algorithms to estimate the frequency offset so that this particular corruption can be removed.