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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.
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