A novel heuristic for the analysis of block sign LMS algorithm

This paper presents a new heuristic for the analysis of adaptive filtering algorithms. It combines Price's Theorem (which is strictly valid when the random variables are jointly Gaussian) with a probabilistic model of the input data that assumes statistical independence between the radial and angular distributions. Moreover, the last distribution is modeled as discrete, which allows obtaining concise and useful closed-form estimates of the algorithm's performance. The proposed method directly provides a derivation of a traditional result for the steady state performance of the Sign Least Mean Squares algorithm. Furthermore, it can be used to gain new insights into the asymptotic performance of the Block Sign Least Mean Squares algorithm. The analysis results are confirmed through simulations.