This concept covers the convergence-in-mean analysis of the Complex Least Mean Squares (LMS) adaptive filtering algorithm, in which the weight-error vector (the deviation of the filter weights from the optimal Wiener solution) is shown to converge in expectation to zero under a stability condition on the step-size parameter relative to the eigenvalues of the input autocorrelation matrix. The analysis relies on the "independence assumption" — treating the weight vector as statistically independent of the current input vector (and, for deeper mean-square analysis, the desired-response scalar) — which is a stronger condition than mere uncorrelatedness and is required to factor expectations of products of dependent random quantities. This belongs to the domain of adaptive signal processing / statistical signal analysis, and generalizes the real-valued LMS convergence theory as a special case of the complex-valued treatment, extending the offline steepest-descent method to a stochastic, online gradient approximation whose exact statistics (R and p) are replaced by instantaneous estimates.
This concept covers the convergence-in-mean analysis of the Complex Least Mean Squares (LMS) adaptive filtering algorithm, in which the weight-error vector (the deviation of the filter weights from t…