The emergence of big data and the multidimensional nature of wireless communication signals present significant opportunities for exploiting the versatility of tensor decompositions in associated data analysis and signal processing. The uniqueness of tensor decompositions, unlike matrix-based methods, can be guaranteed under very mild and natural conditions. Harnessing the power of multilinear algebra through tensor analysis in wireless signal processing, channel modeling, and parametric channel estimation provides greater flexibility in the choice of constraints on data properties and permits extraction of more general latent data components than matrix-based methods. Tensor analysis has also found applications in Multiple-Input Multiple-Output (MIMO) radar because of its ability to exploit the inherent higher-dimensional signal structures therein. In this paper, we provide a broad overview of tensor analysis in wireless communications and MIMO radar. More specifically, we cover topics including basic tensor operations, common tensor decompositions via canonical polyadic and Tucker factorization models, wireless communications applications ranging from blind symbol recovery to channel parameter estimation, and transmit beamspace design and target parameter estimation in MIMO radar.

中文翻译：

---

无线通信和MIMO雷达中的张量分解

大数据的出现和无线通信信号的多维性质为在相关数据分析和信号处理中利用张量分解的多功能性提供了重大机遇。与基于矩阵的方法不同，张量分解的唯一性可以在非常温和自然的条件下得到保证。通过在无线信号处理，通道建模和参数通道估计中的张量分析来利用多线性代数的功能，可以为数据属性的约束选择提供更大的灵活性，并且可以提取比基于矩阵的方法更多的潜在数据分量。Tensor分析还发现了在多输入多输出（MIMO）雷达中的应用，因为它具有利用其中固有的高维信号结构的能力。在本文中，我们提供了无线通信和MIMO雷达中的张量分析的广泛概述。更具体地说，我们涵盖的主题包括基本张量操作，通过规范的多元和Tucker分解模型进行的常见张量分解，从盲符号恢复到信道参数估计的无线通信应用，以及MIMO雷达中的发射波束空间设计和目标参数估计。