Beamspace processing is an emerging technique to reduce baseband complexity in massive multiuser (MU) multiple-input multiple-output (MIMO) communication systems operating at millimeter-wave (mmWave) and terahertz frequencies. The high directionality of wave propagation at such high frequencies ensures that only a small number of transmission paths exist between user equipments and basestation (BS). In order to resolve the sparse nature of wave propagation, beamspace processing traditionally computes a spatial discrete Fourier transform (DFT) across a uniform linear antenna array at the BS where each DFT output is associated with a specific beam. In this paper, we study optimality conditions of the DFT for sparsity-based beamspace processing with idealistic mmWave channel models and realistic channels. To this end, we propose two algorithms that learn unitary beamspace transforms using an $\ell^4$-norm-based sparsity measure, and we investigate their optimality theoretically and via simulations.

翻译：光束处理是一种新兴技术,可以降低在毫米波(mmWave)和千兆赫频率上运行的大型多用户(MU)多投入多输出(MIMO)通信系统的基带复杂性。在这种高频率上波波传播的高度方向性确保了用户设备和基站之间只有少量传输路径。为了解决波传播的稀疏性质,光束处理传统上在BS的一条统一的线性天线阵列上计算出一种空间离散的Fourier变形(DFT),每个DFT输出都与一个特定的波束相关。我们在本文件中研究DFT的最佳性条件,以便利用理想的mmWave频道模型和现实的频道进行基于宽度的波束空间处理。为此,我们建议采用两种算法,即使用$\ell4美元-诺尔米基的微粒度测量法来学习单一波空间变,我们从理论上和模拟角度研究其最佳性。