Diffusion Sparse Least-Mean Squares Over Networks

We address the problem of in-network distributed estimation for sparse vectors. In order to exploit the underlying sparsity of the vector of interest, we incorporate the ℓ
₁
- and ℓ
₀
-norm constraints into the cost function of the standard diffusion least-mean squares (LMS). This technique is equivalent to adding a zero-attracting term in the iteration of the LMS-based algorithm, which accelerates the convergence rates of the zero or near-zero components. The rules for selecting the intensity of the zero-attracting term are derived and verified. Simulation results show that the performances of the proposed schemes depend on the degree of sparsity. Provided that suitable intensities of the zero-attracting term are selected, they can outperform the standard diffusion LMS when the considered vector is sparse. In addition, a practical application of the proposed sparse algorithms in spectrum estimation for a narrow-band source is presented.