Sparse Channel Modelling in IoT Networks using Diffusion β-Divergence based Block Proportionate NLMS Algorithm

Estimation of sparse parameters in presence of non-Gaussian noise is a challenge in Internet of Things (IoT) networks. This paper introduces a novel diffusion $\beta$-divergence based block proportionate normalized least mean squares (D $\beta$ BPNLMS) algorithm tailored for distributed estimation in Internet of Things (IoT) networks. The proposed algorithm incorporates $\beta$-divergence measure to enhance robustness against non-Gaussian noise. Further, it employs block proportionate normalization to reduce computational complexity while maintaining high estimation accuracy. The algorithm also utilizes a coefficient re-ordering strategy and uniform weighting within blocks to efficiently prioritize significant coefficients. An adapt-then-combine (ATC) diffusion strategy is implemented to improve robustness and convergence speed in distributed parameter estimation. The performance of the proposed $\mathbf{D} \beta$ BPNLMS algorithm is validated through simulation study on two critical IoT applications: acoustic echo path estimation and urban microcell wireless channel estimation. The results demonstrate that the proposed algorithm significantly outperforms state-of-the-art algorithms, achieving lower steady-state error across various noise conditions, thereby proving its effectiveness and practical applicability in real-time IoT networks.