Exploiting Low-Density Signal Structure via Approximate Message Passing With Side Information for Grant-Free NOMA

This paper studies an uplink grant-free non-orthogonal multiple access (GF-NOMA) system using low-density signature orthogonal frequency division multiplexing (LDS-OFDM), where each user transmits non-orthogonal pilots and data symbols that are mapped onto a small number of subcarriers determined by the LDS sequence. After an initial estimation based on pilot symbols, our proposed receiver utilizes the low-density signal structure to improve active user detection, channel estimation, and multi-user detection accuracy. To achieve this, a birth-death drift process is applied to model the information exchange between two estimation modules for pilot and data symbols, and a corresponding side information (SI) calculation and denoiser design are proposed for SI-aided multiple measurement vector approximate message passing (MMV-AMP). Moreover, the asymptotic performance of the proposed SI-aided MMV-AMP is analyzed based on state evolution. Numerical results confirm that the proposed method outperforms state-of-the-art methods and that it can perform predictions using the derived state evolution.