Iterative Order Recursive Least Square Estimation for Exploiting Frame-Wise Sparsity in Compressive Sensing-Based MTC

Abstract

In multiple measurement vectors (MMV) problems, the sparsity structure, i.e., the support of the measurement vectors, remains constant for multiple instants. For machine type communication (MTC) context, this sparsity structure may remain constant over all symbols in a frame, which can be termed as frame-wise sparsity. Instead of employing symbol-by-symbol detection based on algorithms such as orthogonal matching pursuit (OMP), group orthogonal matching pursuit (GOMP) can take advantage of this constant sparsity structure and decodes group of symbols together in order to improve the accuracy. Unfortunately, the exponential growth in computational complexity of the GOMP algorithm with the group size prohibits it from increasing the group size and fully exploiting the frame-wise sparsity. This letter presents an iterative order recursive least square (IORLS) algorithm, which can exploit the frame-wise sparsity and increase accuracy. IORLS iteratively employs a modified OMP operations over a frame to gather the sparsity support information with manageable complexity. IORLS substantially reduces complexity by avoiding the matrix inversions in OMP and GOMP algorithms. Furthermore, it has been shown that the proposed algorithm is robust against noise, achieving near-oracle estimation performance.