  To exploit the sparsity of the considered system, the diffusion
proportionate-type least mean square (PtLMS) algorithms assign different gains
to each tap in the convergence stage while the diffusion sparsity-constrained
LMS (ScLMS) algorithms pull the components towards zeros in the steady-state
stage. In this paper, by minimizing a differentiable cost function that
utilizes the Riemannian distance between the updated and previous weight
vectors as well as the L0 norm of the weighted updated weight vector, we
propose a diffusion L0-norm constraint improved proportionate LMS (L0-IPLMS)
algorithm, which combines the benefits of the diffusion PtLMS and diffusion
ScLMS algorithms and performs the best performance among them. Simulations in a
system identification context confirm the improvement of the proposed
algorithm.
