Massive MIMO Detection based on Barzilai-Borwein Algorithm

For a massive multiple-input multiple-output (MI-MO) system, how to cope with the detection difficulties brought by increasing antennas is intractable. Linear methods such as zero-forcing (ZF) and minimum mean square error (MMSE) can achieve sub-optimal performance while suffer from high complexity because of large-scale matrix inversion. Recently, some iterative detectors such as steepest descent (SD) and conjugate gradient (CG) have been proposed to balance the complexity and performance. However, their fast convergence would not maintain when the system loading factor increases. To address the aforementioned issues, this paper 1) introduces a new iterative algorithm called Barzilai-Borwein (BB) that outperforms SD with inexpensive operations and 2) proposes its improved form entitled SDBB to accelerate the convergence even in bad conditions. Both theoretical and numerical results have demonstrated its advantages over the state-of-the-art ones. More specifically, SDBB can surpass the existing split pre-conditioned conjugate gradient (SPCG) detector by more than 2 dB at the bit error rate (BER) of 103 when the number of users is relatively large, and reach a complexity reduction of 10%.