Minimum-mean-square-error (MMSE) detection is increasingly relevant for massive multiple-input multiple-output (MIMO) systems. MMSE suffers from high computational complexity and low parallelism because of the increasing number of users and antennas in massive MIMO systems. This paper proposes a recursive conjugate gradient (RCG) method to iteratively estimate signals. First, a recursive conjugate gradient detection algorithm is proposed that achieves high parallelism and low complexity through iteration. Second, a quadrant-certain-based initial method that improves detection accuracy without added complexity is proposed. Third, an approximated log likelihood ratio (LLR) computation method is proposed to achieve simplified calculation. The analyses show that compared with related methods, the proposed RCG algorithm reduces computational complexity and exploits the potential parallelism. RCG is mathematically demonstrated to achieve low approximated error. Based on the RCG method, an architecture is proposed in a 128 × 8 64-QAM massive MIMO system. First, a parallel processing element array with single-sided input is adopted; this array eliminates the throughput limitation. Second, a deeply pipelined user-level method based on the recursive conjugate gradient method is proposed. Third, an approximated architecture is proposed to compute the soft output. The architecture is verified on an FPGA and fabricated on 1.87 × 1.87 mm$^2$ silicon with TSMC 65 nm CMOS technology. The chip achieves 2.69 Mbps/mW and 1.09 Mbps/kG energy efficiency (throughput/power) and area efficiency (throughput/area), respectively, which are 2.39 to 10.60× and 1.15 to 8.81× those of the normalized state-of-the-art designs.

中文翻译：

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用于大规模 MIMO 系统的基于能量和面积效率的递归共轭梯度 MMSE 检测器

最小均方误差 (MMSE) 检测与大规模多输入多输出 (MIMO) 系统越来越相关。由于大规模 MIMO 系统中用户和天线数量的增加，MMSE 面临着高计算复杂度和低并行度的问题。本文提出了一种递归共轭梯度（RCG）方法来迭代估计信号。首先，提出了一种通过迭代实现高并行度和低复杂度的递归共轭梯度检测算法。其次，提出了一种基于象限确定的初始方法，可以在不增加复杂性的情况下提高检测精度。第三，提出了一种近似对数似然比（LLR）计算方法来实现简化计算。分析表明，与相关方法相比，所提出的 RCG 算法降低了计算复杂度并利用了潜在的并行性。RCG 在数学上被证明可以实现低近似误差。基于RCG方法，在128×8 64-QAM大规模MIMO系统中提出了一种架构。首先，采用单边输入的并行处理单元阵列；该阵列消除了吞吐量限制。其次，提出了一种基于递归共轭梯度法的深度流水线用户级方法。第三，提出了一种近似架构来计算软输出。该架构在 FPGA 上进行了验证，并在采用 TSMC 65 nm CMOS 技术的 1.87 × 1.87 mm$^2$ 硅片上制造。该芯片分别实现了 2.69 Mbps/mW 和 1.09 Mbps/kG 能效（吞吐量/功率）和面积效率（吞吐量/面积），分别为 2.39 至 10。