Enhanced Ultra-Massive MIMO Implicit Detection: A Weighted Cauchy-Barzilai-Borwein-Neumann Series Approach

For ultra-massive multiple-input multiple-output (MIMO) systems, minimum mean square error (MMSE)-based detection suffers from prohibitive complexity due to the large-dimension matrix operations. Among various low-complexity variants of the MMSE, the implicit detection is promising as it omits the explicit computation of Gram matrix and its associated inversion. However, the performance degradation is non-negligible when the system loading factor increases and the correlated channel is considered. To address this issue, this letter proposes an enhanced implicit detector which combines Cauchy-Barzilai-Borwein (CBB) iteration and Neumann series (NS) iteration by means of a dynamic weighted factor, named W-CBBNS. A simple approach to determine the weighted factor by maximizing the estimated symbol vector reliability is developed. Besides, the complexity is remarkably reduced by exploiting scalar-vector and matrix-vector multiplication compared to the CBB-based explicit detection. Numerical results show that the W-CBBNS significantly outperforms the existing implicit detectors such as the weighted NS and steepest descent-non-stationary Richardson, while at a similar magnitude of complexity, and also outperforms the state-of-the-art CBB-based detector.