  In this paper, we propose a novel leaky least mean square (leaky LMS, LLMS)
algorithm which employs a p-norm-like constraint to force the solution to be
sparse in the application of system identification. As an extension of the LMS
algorithm which is the most widely-used adaptive filtering technique, the LLMS
algorithm has been proposed for decades, due to the deteriorated performance of
the standard LMS algorithm with highly correlated input. However, both ofthem
do not consider the sparsity information to have better behaviors. As a
sparse-aware modification of the LLMS, our proposed Lplike-LLMS algorithm,
incorporates a p-norm-like penalty into the cost function of the LLMS to obtain
a shrinkage in the weight update, which then enhances the performance in sparse
system identification settings. The simulation results show that the proposed
algorithm improves the performance of the filter in sparse system settings in
the presence of noisy input signals.
