# Efficient Massive MIMO Detection for M-QAM Symbols
## 1 Introduction
However, a sufficient number of receive antennas may not be available in a practical system due to the constraints of antenna size, cost, and power consumption. Systems with \(\rho\) close to one can achieve better spectral efficiency when attaining large \(K_{t}\) and \(K_{r}\). However, the performance of the linear detectors degrades dramatically. Excessive dimensionality reduction for the sake of computational reduction results information loss, and substantial performance degradation is unavoidable due to interference, particularly when \(K_{t}\) is of the same order as \(K_{r}\). Furthermore, multiplication and division operations are required for these iterative methods. Numerical instability may occur during division operations [13]. These operations are all thought to be difficult to implement in hardware [14]. The dichotomous coordinate descent (DCD) algorithm is based on the coordinate descent method. It solves the normal equation by using variable step sizes with a power of two. With this algorithm, a linear system of equations can be solved with high computational efficiency. The algorithm is easy to implement in hardware because it does not require multiplications and divisions [15]. DCD-based multiuser detectors have demonstrated a detection accuracy close to the single-user bound for binary phase shift keying (BPSK) symbols [16; 17]. Better detection performance is achieved using box-constrained optimization [18]. In [19], a box-constrained DCD detector and its hardware architecture were proposed for complex-valued detection. Nevertheless, this architecture design was based on a serial structure and can only be suitable for small-scale systems. In [20], a parallel FPGA architecture for a box-constrained MIMO detector based on DCD iteration is proposed for MIMO detection with tens/hundreds of antennas. The complexity of these DCD-like detection methods mainly depends on the number of antennas and the number of successful update iterations \(N_{u}\). With a high \(N_{u}\), DCD-based detectors show good performance for large-scale systems. However, the complexity burden requirement will become severe as the system size increases. To further reduce complexity without sacrificing detection capability, designing suboptimal detection algorithms with low complexity and high performance is still needed to construct practical MIMO systems. To address this problem, a massive MIMO detector based on an iterated box-constrained DCD (BOXDCD) with a negative diagonal loading regularization is proposed. The idea is that the output of the BOXDCD algorithm with negative diagonal loading regularization provides a rough estimation of the m-ary quadrature amplitude modulation (M-QAM) symbols for massive MIMO systems and is taken as the initial input to the BOXDCD algorithm when updating the received signal vector. This procedure is repeated iteratively,achieving a significant performance improvement and an overall complexity reduction compared to the MMSE detector. Moreover, the proposed detector achieves much higher performance than the BOXDCD detector with the same \(N_{u}\). We provide a complexity-performance tradeoff for the proposed efficient massive MIMO detector compared with suboptimal MIMO detectors under a fully loaded system and show that the proposed method outperforms existing suboptimal detectors. The remainder of the paper is organized as follows: Section 2 describes the system model for the MIMO transmission system and briefly overviews the MMSE detector and iterated MMSE detector. The proposed detector based on an iterated box-constrained DCD algorithm with negative diagonal loading is presented in Section 3. Numerical simulations are shown in Section 4. Section 5 concludes the work. Mathematical notations: matrices and column vectors are denoted by bold uppercase and lowercase letters, respectively. The elements of the matrix and vector are denoted as \(R_{i,j}\) and \(r_{j}\), respectively. The \(j\)-th column of \(\mathbf{R}\) is denoted as \(\mathbf{R}_{:,j}\).