Auxiliary Diffusion Strategy Against Link Noises Over Distributed Networks

Recently, the compressive diffusion strategies have been proposed to reduce the communication load of adaptive networks in the absence of link noises. In this paper, we are the first to study the compressive diffusion double normalized least mean square (CD<inline-formula><tex-math notation="LaTeX">${}^{2}$</tex-math></inline-formula>-NLMS) algorithm in the presence of noisy communication links. By means of the single update global weight error model, the transient and steady-state results of the CD<inline-formula><tex-math notation="LaTeX">${}^{2}$</tex-math></inline-formula>-NLMS algorithm are formulated analytically. One of the main findings is that the impact of link noises is well suppressed by use of small step-sizes and randomized projection vectors with a large variance in the second step of the algorithm. Taking advantage of the anti-link noise method and further combining with the traditional diffusion scheme, we ultimately design a novel auxiliary diffusion strategy to resist link noises in this paper. Different from the existing diffusion schemes, the designed auxiliary diffusion strategy consists of three steps: (i) weight update, (ii) auxiliary interaction, and (iii) weight combination, where the second step introduces an auxiliary estimation process to achieve the purpose of anti-link noise. Finally, numerical simulations are presented to demonstrate our theoretical analysis and the effectiveness of the proposed algorithms.