Exact expectation analysis of the LMS adaptive identification of non‐linear systems

Abstract

Most adaptive filtering schemes employ the tapped-delay line. In part, such a fact can be explained by the assumption that the plant they intend to estimate is linear. Although such a hypothesis can be reasonable if the input signal is constrained to a certain range, sometimes it may not be valid. In this last case, the performance and stability guarantees provided by stochastic models that presume linearity of the ideal system are no longer valid. This Letter advances an analytic model of the least-mean-square (LMS) learning capabilities when the ideal system is not linear, with the additive noise including non-linear functions of the input samples. The proposed analysis does not assume neither that the excitation signal is statistically independent of the adaptive weights, nor that the additive noise is white and/or independent of input data. Furthermore, it can be applied to non-Gaussian and/or non-white input signals. Simulations show that the advanced model is more accurate than traditional approaches.