Training beam design for channel estimation with infinite-resolution and low-resolution phase shifters (PSs) in hybrid analog-digital milimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems is considered in this paper. By exploiting the sparsity of mmWave channels, the optimization of the sensing matrices (corresponding to training beams) is formulated according to the compressive sensing (CS) theory. Under the condition of infinite-resolution PSs, we propose relevant algorithms to construct the sensing matrix, where the theory of convex optimization and the gradient descent in Riemannian manifold is used to design the digital and analog part, respectively. Furthermore, a block-wise alternating hybrid analog-digital algorithm is proposed to tackle the design of training beams with low-resolution PSs, where the performance degeneration caused by non-convex constant modulus and discrete phase constraints is effectively compensated to some extent thanks to the iterations among blocks. Finally, the orthogonal matching pursuit (OMP) based estimator is adopted for achieving an effective recovery of the sparse mmWave channel. Simulation results demonstrate the performance advantages of proposed algorithms compared with some existing schemes.

中文翻译：

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混合毫米波 MIMO 系统中信道估计的训练波束设计

本文考虑了在混合模数毫米波 (mmWave) 大规模多输入多输出 (MIMO) 系统中使用无限分辨率和低分辨率移相器 (PS) 进行信道估计的训练波束设计。通过利用毫米波信道的稀疏性，根据压缩感知（CS）理论制定感知矩阵（对应于训练波束）的优化。在无限分辨率PS的条件下，我们提出了相关的算法来构建传感矩阵，其中凸优化理论和黎曼流形中的梯度下降理论分别用于设计数字部分和模拟部分。此外，提出了一种逐块交替混合模数算法来解决具有低分辨率 PS 的训练波束的设计问题，其中，由于块之间的迭代，非凸恒模和离散相位约束引起的性能退化在一定程度上得到了有效补偿。最后，采用基于正交匹配追踪（OMP）的估计器来实现稀疏毫米波信道的有效恢复。仿真结果表明，与一些现有方案相比，所提出算法的性能优势。