Performance Analysis of the Gradient Comparator LMS Algorithm

The sparsity-aware zero attractor least mean square (ZA-LMS) algorithm manifests much lower misadjustment in strongly sparse environment than its sparsity-agnostic counterpart, the least mean square (LMS), but is shown to perform worse than the LMS when sparsity of the impulse response decreases. The reweighted variant of the ZA-LMS, namely RZALMS shows robustness against this variation in sparsity, but at the price of increased computational complexity. The other variants such as the l0LMS and the improved proportionate normalized LMS (IPNLMS), though perform satisfactorily, are also computationally intensive. The gradient comparator LMS (GC-LMS) is a practical solution of this trade-off when hardware constraint is to be considered. In this paper, we analyse the mean and the mean square convergence performance of the GC-LMS algorithm in detail. The analyses satisfactorily match with the simulation results.