In millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, 1 bit analog-to-digital converters (ADCs) are employed to reduce the impractically high power consumption, which is incurred by the wide bandwidth and large arrays. In practice, the mmWave band consists of a small number of paths, thereby rendering sparse virtual channels. Then, the resulting maximum a posteriori (MAP) channel estimation problem is a sparsity-constrained optimization problem, which is NP-hard to solve. In this paper, iterative approximate MAP channel estimators for mmWave massive MIMO systems with 1 bit ADCs are proposed, which are based on the gradient support pursuit (GraSP) and gradient hard thresholding pursuit (GraHTP) algorithms. The GraSP and GraHTP algorithms iteratively pursue the gradient of the objective function to approximately optimize convex objective functions with sparsity constraints, which are the generalizations of the compressive sampling matching pursuit (CoSaMP) and hard thresholding pursuit (HTP) algorithms, respectively, in compressive sensing (CS). However, the performance of the GraSP and GraHTP algorithms is not guaranteed when the objective function is ill-conditioned, which may be incurred by the highly coherent sensing matrix. In this paper, the band maximum selecting (BMS) hard thresholding technique is proposed to modify the GraSP and GraHTP algorithms, namely, the BMSGraSP and BMSGraHTP algorithms, respectively. The BMSGraSP and BMSGraHTP algorithms pursue the gradient of the objective function based on the band maximum criterion instead of the naive hard thresholding. In addition, a fast Fourier transform-based (FFT-based) fast implementation is developed to reduce the complexity. The BMSGraSP and BMSGraHTP algorithms are shown to be both accurate and efficient, whose performance is verified through extensive simulations.

中文翻译：

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具有1位ADC的mmWave大规模MIMO系统通过梯度追踪进行信道估计

在毫米波（mmWave）大规模多输入多输出（MIMO）系统中，采用1位模数转换器（ADC）来降低宽带宽和大阵列引起的不切实际的高功耗。实际上，毫米波频段由少量路径组成，因此呈现了稀疏的虚拟通道。然后，所产生的最大后验（MAP）信道估计问题是稀疏约束的优化问题，这是NP难以解决的。本文基于梯度支持追踪（GraSP）和梯度硬阈值追踪（GraHTP）算法，提出了具有1位ADC的mmWave大规模MIMO系统的迭代近似MAP信道估计器。GraSP和GraHTP算法迭代地追求目标函数的梯度以近似优化具有稀疏约束的凸目标函数，这分别是压缩感知中的压缩采样匹配追踪（CoSaMP）和硬阈值追踪（HTP）算法的概括（CS）。但是，当目标函数条件不佳时，就不能保证GraSP和GraHTP算法的性能，这可能是由高度相干的感测矩阵引起的。本文提出了一种频带最大选择（BMS）硬阈值技术，分别对GraSP和GraHTP算法进行了修改，分别是BMSGraSP和BMSGraHTP算法。BMSGraSP和BMSGraHTP算法基于带最大准则而不是单纯的硬阈值来追求目标函数的梯度。此外，开发了一种基于快速傅立叶变换（基于FFT）的快速实现方案，以降低复杂性。事实证明BMSGraSP和BMSGraHTP算法既准确又有效，其性能已通过广泛的仿真验证。