  Recently, the leaky diffusion least-mean-square (DLMS) algorithm has obtained
much attention because of its good performance for high input eigenvalue spread
and low signal-to-noise ratio (SNR). However, the leaky DLMS algorithm may
suffer from performance deterioration in the sparse system. To overcome this
drawback, the leaky zero attracting DLMS (LZA-DLMS) algorithm is developed in
this paper, which adds an l1-norm penalty to the cost function to exploit the
property of sparse system. The leaky reweighted zero attracting DLMS
(LRZA-DLMS) algorithm is also put forward, which can improve the estimation
performance in the presence of time-varying sparsity. Instead of using the
l1-norm penalty, in the reweighted version, a log-sum function is employed as
the substitution. Based on the weight error variance relation and several
common assumptions, we analyze the transient behavior of our findings and
determine the stability bound of the step-size. Moreover, we implement the
steady state theoretical analysis for the proposed algorithms. Simulations in
the context of distributed network system identification illustrate that the
proposed schemes outperform various existing algorithms and validate the
accuracy of the theoretical results.
