Among various massive multiple-input multiple-output (MIMO) signal detection schemes, expectation propagation (EP) achieves superior performance in high-dimensional systems with high-order modulations and flexible antenna configurations. However, the inevitable matrix inversion in each iteration of EP brings unbearable computational burden, which hinders the efficient implementation. Several reduced-complexity variants of EP are proposed recently, which effectively alleviate the computational cost but at the expense of unacceptable performance loss. In this paper, a low-complexity massive MIMO detection is first proposed based on approximate EP, which relieves the computational complexity of the exact EP while maintaining the good performance. Particularly, the EP moment matching equations are reformulated to simplify the sequential updating procedure. In addition, an approximation based on the channel-hardening phenomenon is proposed to eliminate the matrix inversion at each iteration. Numerical results show that, for high-dimensional MIMO the proposed detector approaches the exact EP in term of bit-error-rate (BER) by a small number of iterations. No matter with symmetric or asymmetric antenna configuration, it outperforms other EP variants, Gaussian tree approximation (GTA), and channel-hardening exploiting message passing (CHEMP). An analysis of computational complexity reveals the high efficiency of the proposed detection compared to the state-of-the-art (SOA) with flexible antenna configurations.

In this paper, deep neural network (DNN) is utilized to improve message passing detectors (MPDs) for massive multiple-input multiple-output (MIMO) systems. A general framework to construct DNN architecture for MIMO detection is first introduced by unfolding iterative MPDs. DNN MIMO detectors are then proposed based on modified MPDs including damped belief propagation (BP), max-sum (MS) BP, and simplified channel hardening-exploiting message passing (CHEMP). The correction factors are optimized via deep learning for better performance. Numerical results demonstrate that, compared with state-of-the-art (SOA) detectors including minimum mean-squared error (MMSE), BP, and CHEMP, the proposed DNN detectors can achieve better bit-error-rate (BER) and improve robustness against various antenna and channel conditions with similar complexity. The DNN is required to be trained only once and can be reused for multiple detections, which assures its high efficiency. The corresponding hardware architecture is also proposed. Implementation results with 65 nm CMOS technology approve the efficiency and flexibility of the proposed DNN framework.

Massive multiple-input and multiple-output (MIMO) is considered as an advanced technique in wireless communication due to its high spectral efficiency, data rates, and transmission reliability. However, the large number of antennas makes it challenging to design efficient detectors since computational complexity is much higher. Thus, conventional linear methods like minimum mean square error (MMSE) detection suffer from prohibitive complexity. To balance complexity and performance, a class of iterative linear methods are considered to approach MMSE performance with O(NT2) complexity, where NT is the number of transmit antennas. Among them, successive over relaxation (SOR) detector is promising since it achieves near MMSE performance with affordable complexity and fast convergence. However, error performance of previously proposed SOR detectors is sensitive to a relaxation factor ω, especially when the channel varies. To address this issue, two detectors are proposed in this paper: non-adaptive SOR (NA-SOR) detector (with fixed ω) and adaptive SOR (A-SOR) detector (with iteratively changed ω). Compared to prior SOR detectors, the performance of the NA-SOR detector is more robust to ω, and the A-SOR detector achieves better performance, especially in highly correlated channels. An efficient pipelined hardware architecture of the A-SOR detector is proposed. Implementation results show advantages when compared to the state-of-the-art (SOA).

This paper presents deep learning (DL) methods to optimize polar belief propagation (BP) decoding and concatenated LDPC-polar codes. First, two-dimensional offset Min- Sum (2-D OMS) decoding is proposed to improve the errorcorrection performance of existing normalized Min-Sum (NMS) decoding. Two optimization methods used in DL, namely backpropagation and stochastic gradient descent, are exploited to derive the parameters of proposed algorithms. Numerical results demonstrate that there is no performance gap between 2-D OMS and exact BP on various code lengths. Then the concatenated OMS algorithms with low complexity are presented for concatenated LDPC-polar codes. As a result, the optimized concatenated OMS decoding yields error-correction performance with CRCaided successive cancellation list (CA-SCL) decoder of list size 2 on length-1024 polar codes. In addition, the efficient hardware architectures of scalable polar OMS decoder are described and the proposed decoder is reconfigurable to support three code lengths (N = 256, 512, 1024) and two decoding algorithms (2- D OMS and concatenated OMS). The polar OMS decoder implemented on 65 nm CMOS technology achieves a maximum coded throughput of 5.4 Gb/s at Eb/N0 = 4 dB for code length 1024 and 7.5 Gb/s at Eb/N0 = 3.5 dB for code length 256, which are comparable to the state-of-the-art polar BP decoders. Moreover, a 5.1 Gb/s throughput at Eb/N0 = 4 dB is achieved under concatenated OMS decoding mode for code length 1024 with a latency of 200 ns, which is superior to existing CA-SCL decoders that have similar error-correction performance.

Expectation propagation (EP) attains near-optimal performance for massive multiple-input multiple-output (MIMO) detection. However, the inevitable matrix inversions and exponentiations at each EP iteration bring great challenges to realistic hardware implementation. To address these issues, a low-complexity EP with iterative Neumann-series Approximation (EP-INSA) detector is proposed by employing INSA to estimate the inverse matrices. Further approximations are applied to avoid the exponentiations, which makes EP-INSA an efficient, feasible, and hardware-friendly detector for massive MIMO with various modulations. Simulation results show that EP-INSA attains similar performance as exact EP with only a few INSA terms, which assures enhanced performance and complexity trade-off. The associated hardware architectures of EP-INSA detector are also presented. The implementation results on 65 nm CMOS technology show that our design yields a throughput of 0.62 Gb/s with 2.63× area efficiency of existing EP detector.

For massive multiuser multiple-input multiple-output (MIMO) systems, linear detectors, such as minimum mean square error (MMSE), suffer from unbearable computational pressure due to the large-scale matrix inversions. Various iterative detectors, such as Jacobi and steepest descent (SD) as well as their enhanced variants, are applied to improve the performance and complexity trade-off. However, their benefits would not maintain when: 1) the number of users is close to that of the base station antennas and 2) channel correlation is considered. To address this problem, an iterative detector based on SD and Barzilai-Borwein (BB) algorithms entitled SDBB is introduced in this paper. Furthermore, a novel enhanced SDBB (ESDBB) detector is proposed, which combines SDBB with SD to achieve better performance in the challenging scenarios. Both theoretical and numerical results are detailed to demonstrate the advantages of ESDBB in balancing the performance and complexity. Specifically, attaining faster convergence and better bit error rate (BER) results, ESDBB outperforms methods, including adaptive Jacobi and successive over relaxation (SOR). An efficient hardware architecture for the ESDBB detector is also proposed. Implementation results on a Xilinx Virtex-7 XC7VX690T FPGA show the advantages of the proposed ESDBB detector compared to the state of the art (SOA) in terms of throughput (31.3 Mb/s) and efficiency.