Overview of tensor decompositions with applications to communications

International audienceTensors decompositions are powerful tools for modeling wireless communication systems and for solving problems such as blind/semi-blind equalization, source/user separation, and channel estimation. Tensors have received great attention over the past decade. In the context of communication systems, the basic motivation for resorting to tensor-based signal processing comes from the multidimensional nature of transmitted and received signals (typical dimensions are symbol periods, time blocks, space, frequency, coding, etc) which translates into more powerful uniqueness and identifiability properties compared with matrix-based signal processing. This chapter has overviewed tensor signal models for three types of systems. First, we have discussed a tensor-based space-time-frequency (TSTF) coding model for MIMO systems, which unifies the model of different space-time and space-time-frequency schemes derived previously. Second, we have presented some tensor models for cooperative communication systems with AF-based relaying. Third, the application of tensors to multidimensional array processing has been discussed, with a focus on the problems of multidimensional model order selection, prewhitening, and parameter estimation. As already said, tensor models/decompositions are very useful for representing multidimensional data in various fields of application. Among the hot research topics on tensors for future works, we can mention the development of methods for sparse low-rank tensor approximation using compressive sensing techniques, with possible application to sparse massive MIMO channel estimation in the context of cooperative communications