A Novel Iterative Discrete Estimation Algorithm for Low-Complexity Signal Detection in Uplink Massive MIMO Systems  
[PERSON]  
1 Department of Electronic Science and Technology, Tongji University, Shanghai 201804, China 1  
[PERSON]  
2 Jiangsu Provincial Engineering Laboratory of Pattern Recognition and Computational Intelligence, Jiangnan University, Wuxi 214122, China 2  
[PERSON]  
2 Jiangsu Provincial Engineering Laboratory of Pattern Recognition and Computational Intelligence, Jiangnan University, Wuxi 214122, China 2  
[PERSON]  
3 Department of Information Systems, California State University, Los Angeles, CA 90032, USA 3  
Correspondence: [PERSON]_ADDRESS]; Tel. : +86-0510-8591-063  
It is worth noting that some approaches for approximating the matrix inversion have been proposed to reduce the computational complexity [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19], among which, for example, the Neumann series (NS) approximation is used to approximate the matrix inversion by a series of truncated NS expansions [9; 10]. However, only marginal reduction in the computational complexity can be reached with the increased terms of the NS expansion. Hence, various classical iterative algorithms have been provided to approximate the inverse matrix in LMMSE detection to achieve low computational complexity, which include the Richardson (RI) algorithm [11], the Jacobi algorithm [12; 13; 14; 15], the successive over relaxation (SOR) algorithm [16], the symmetric successive over relaxation (SSOR) algorithm [17], and the Gauss-Seidel (GS) algorithm [18; 19]. The computational complexity of the matrix inverse is reduced by these approximation-based detection algorithms from \(O\left(N_{t}^{3}\right)\) to \(O\left(N_{t}^{2}\right)\). It is noted that these algorithms involving the inverse-matrix approximation in LMMSE detection (also known as the approximated LMMSE) achieve a near-LMMSE performance, but with lower computational complexity. It is well known that the approximated LMMSE detection algorithms achieve a substantial performance loss when \(N_{r}>N_{t}\) in multiuser massive MIMO systems. Various algorithms have been proposed to obtain a better BER performance than that of LMMSE detection in multiuser massive MIMO systems, which include the non-convex and the convex optimization algorithms [20; 21; 22]. For example, the alternating minimization (AltMin) algorithm is one of the non-convex optimization algorithms, which is applied to the data detection in a multiuser massive MIMO system [20]. Specifically, the AltMin algorithm converts the ML detection problem into a sum of convex functions by decomposing the received vector into multiple sub-vectors. Hence, the non-convex problem is transformed into the convex problem in the AltMin algorithm. The AltMin algorithm shows better BER performance than that of the LMMSE detector in overloaded network scenarios with relatively low computational complexity. However, it shows near-LMMSE performance with even higher computational complexity when the ratio of the number of BS antennas to the number of single-antenna users is larger. Similarly, some convex optimization algorithms are used to solve the non-convex optimization problems, which include, for example, the alternating direction method of multipliers (ADMM) detection algorithm [21; 22]. In the multiuser massive MIMO system, ADMM demonstrates better BER performance than the LMMSE detection algorithm with the relatively low computational complexity of the iterative procedure. However, the computational complexity of the preprocessing in the ADMM algorithm includes the calculation complexity of the Gram matrix and LDLdecomposition [23; 24], which results in very high computational complexity for massive MIMO systems.