Probabilistic ODMA Receiver with Low-Complexity Algorithm for MIMO Unsourced Random Access

In this work, we present the design for both pilot-uncoupled and pilot-free on-off multiple access (ODMA) receivers in unsourced random access (URA) for multiple-input multiple-output (MIMO) systems. Unlike pilot-coupled ODMA, where on-off patterns are linked to pilot selection, pilot-uncoupled and pilot-free ODMA reduce transmission redundancy but face challenges in processing complexity and capacity performance. The joint pattern and data detector (JPDD) design is critical for these schemes, but the current JPDD algorithm has high complexity with quadratic computational costs. To address this, we propose a low-complexity detector based on approximate message passing (AMP), which offers linear complexity, providing reduced cost and improved performance in the under-determined linear regression case. Decoding is initialized via pilot-free matrix factorization through alternating minimization, resolving phase and scalar ambiguities. Compared to existing pilot-free schemes, the proposed method achieves a 13 dB improvement and favorable trade-offs in complexity and capacity performance when compared to benchmarks.