| Summary: | This paper proposes a distributed estimation technique utilizing the diffusion least mean-square (LMS) algorithm, specifically designed for sparse systems in which many coefficients of the system are zeros. To efficiently utilize the sparse representation of the system and achieve a promising performance, we have incorporated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mn>0</mn></msub></semantics></math></inline-formula>-norm regularization into the diffusion LMS algorithm. This integration is accomplished by employing hard thresholding through a variable splitting method into the update equation. The efficacy of our approach is validated by comprehensive theoretical analysis, rigorously examining the mean stability as well as the transient and steady-state behaviors of the proposed algorithm. The proposed algorithm preserves the behavior of large coefficients and strongly enforces smaller coefficients toward zero through the relaxation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mn>0</mn></msub></semantics></math></inline-formula>-norm regularization. Experimental results show that the proposed algorithm achieves superior convergence performance compared with conventional sparse algorithms.
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