  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 RZA-LMS shows robustness against this
variation in sparsity, but at the price of increased computational complexity.
The other variants such as the l 0 -LMS 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.
