标题： 通过$\ell^4$-范数最大化学习稀疏化变换用于毫米波通信 显示英文标题

标题： Learning Sparsifying Transforms for mmWave Communication via $\ell^4$-Norm Maximization

摘要： 毫米波（mmWave）载波频率下波传播的高方向性导致用户设备和基站（BS）之间只有少量显著的传输路径。这种波传播的稀疏性在波束空间域中被揭示出来，该域传统上是通过在基站的均匀线性天线阵列上进行空间离散傅里叶变换（DFT）获得的，其中每个DFT输出与一个不同的波束相关联。近年来，波束空间处理作为一种有前景的技术出现，用于减少在毫米波频率下运行的全数字大规模多用户（MU）多输入多输出（MIMO）系统中的基带复杂度和功耗。然而，尚不清楚DFT是否是有限维天线阵列的最佳稀疏化变换。在本文中，我们将Zhai等人关于通过$\ell^4$-范数最大化进行完整字典学习的框架扩展到复数情况，以学习新的稀疏化变换。我们为$\ell^4$-范数最大化提供了理论基础，并提出了两种合适的学习算法。然后，我们利用这些算法（i）从理论上并通过仿真评估DFT在稀疏化信道向量方面的最优性，以及（ii）学习改进的稀疏化变换用于现实世界和合成生成的信道向量。 显示英文摘要

摘要： The high directionality of wave propagation at millimeter-wave (mmWave) carrier frequencies results in only a small number of significant transmission paths between user equipments and the basestation (BS). This sparse nature of wave propagation is revealed in the beamspace domain, which is traditionally obtained by taking the spatial discrete Fourier transform (DFT) across a uniform linear antenna array at the BS, where each DFT output is associated with a distinct beam. In recent years, beamspace processing has emerged as a promising technique to reduce baseband complexity and power consumption in all-digital massive multiuser (MU) multiple-input multiple-output (MIMO) systems operating at mmWave frequencies. However, it remains unclear whether the DFT is the optimal sparsifying transform for finite-dimensional antenna arrays. In this paper, we extend the framework of Zhai et al. for complete dictionary learning via $\ell^4$-norm maximization to the complex case in order to learn new sparsifying transforms. We provide a theoretical foundation for $\ell^4$-norm maximization and propose two suitable learning algorithms. We then utilize these algorithms (i) to assess the optimality of the DFT for sparsifying channel vectors theoretically and via simulations and (ii) to learn improved sparsifying transforms for real-world and synthetically generated channel vectors.