Low-Complexity Detectors for Uplink Massive MIMO Systems Leveraging Truncated Polynomial Expansion

In this work, we propose low-complexity detectors for massive multiple-input multiple-output (MIMO) systems. Particularly, we leverage variants of truncated polynomial expansion (TPE) in order to reduce the computational complexity of the signal detection in the uplink direction. Linear detectors such as zero-forcing (ZF) and minimum mean square error (MMSE) involve expensive matrix-matrix multiplication and matrix inversion operations. TPE-based detectors are appropriate candidates for approximating these linear detectors. However, tuning the normalization factor of TPE-based detectors may require calculating the minimum and the maximum eigenvalues of the channel Gram matrix. These calculations become computationally expensive for some massive MIMO systems, especially for systems with a large ratio of single-antenna user terminals to the number of antennas at the base station, i.e., loading factor. We propose to tune the normalization factor using appropriate approximations for the extreme eigenvalues. The proposed TPE-based detectors exhibit a bit error performance similar to that of the TPE-based detector with the optimal normalization factor. Moreover, our proposed detectors achieve the error performance of ZF and MMSE for different loading factors of spatially correlated and uncorrelated massive MIMO channels. The computational complexity of the proposed detector is proportional to the number of base station antennas and the number of users.