Efficient Distributed Multi-Task Schemes for mmWave MIMO Channel Estimation

In this study, the problem of sparse channel estimation is investigated with the employment of a fully distributed approach. We exploit the spatially joint sparsity structure of the involved channels to formulate the channel estimation problem in the angular domain. The devices collaboratively estimate their channel sparsity support sets before the local estimation of the channel values, assuming the existence of global and common support subsets. The combination of the proposed distributed scheme with the classical Simultaneous Orthogonal Matching Pursuit (SOMP) algorithm is called Weighted Distributed Simultaneous Orthogonal Matching Pursuit (WDiSOMP). The performance of WDiSOMP is assessed under a multi-task scheme considering a new weighted voting method. The new mechanism is applied at each support set index and enhances its estimation accuracy and, thus, the eventual estimation of the overall channel. The mean squared error (MSE) is utilized to derive the performance bounds and assess the efficacy of the WDiSOMP estimator. Finally, the performance and the theoretical findings are evaluated via the comparison of WDiSOMP with Distributed Simultaneous Orthogonal Matching Pursuit (DiSOMP), local SOMP, and a centralized approach based on Structured SOMP (SSOMP) in terms of the MSE.