In several signal processing applications for wireless communications, the transmitted and received signals and the communication channel have a multidimensional nature and may exhibit a multilinear algebraic structure. Tensor decompositions have been the subject of numerous works in the past two decades. The key characteristics of signal processing based on tensor decompositions, not covered by matrix-based signal processing, are the following. It does not require the use of training sequences nor the knowledge of channel impulse responses and antenna array responses. Moreover, it does not rely on statistical independence between the transmitted signals.
Instead, tensor-based receiver algorithms are usually deterministic and exploit the multilinear algebraic structure of the signals. Tensor-based algorithms act on data blocks (instead of using a sample-by-sample processing approach). They are generally based on a joint detection of the transmitted signals (either from different users/sources or multiple transmit antennas).