# Diffusion L0-norm constraint improved proportionate LMS algorithm for sparse distributed estimation

## TL;DR

This paper introduces the L0-IPLMS algorithm, which combines diffusion proportionate LMS and sparsity constraints to enhance sparse system estimation, demonstrating superior performance in simulations.

## Contribution

The paper proposes a novel diffusion L0-norm constrained LMS algorithm that integrates benefits of prior methods for improved sparse system estimation.

## Key findings

- L0-IPLMS outperforms existing diffusion LMS algorithms in simulations.
- The proposed method effectively exploits system sparsity.
- Simulation results confirm enhanced convergence and accuracy.

## Abstract

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.

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Source: https://tomesphere.com/paper/1703.08284