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).
Figure 2: Tensor decompositions in the wireless communications transmit-channel-receive chain.
Why use tensor signal processing?
- Fully exploits multiple forms of signal diversity (e.g., time, space, oversampling, spreading, frequency, etc);
- Affords blind/semi-blind signal detection, separation, and estimation thanks to the powerful uniqueness properties of tensor decompositions
- Allows for transceiver designs operating under more flexible system setups compared to conventional (matrix-based) signal processing methods
- Complexity reduction of large filter optimizations (e.g., massive MIMO & large-scale beamforming filters and equalizers)
- Noise-resilient multidimensional constellation designs
Figure 2 depicts the connection of tensor decompositions to signal processing for wireless communications. It shows tensor structures at both ends of the communication chain and highlights the usual signal dimensions that generally appear in current systems.
The key research lines that use tensor decompositions are:
- Multiuser signal separation/equalization/detection
- Multiple-antenna transmission structures
- Channel modeling and estimation
- Complexity reduction in large-scale systems
[1] A. L. F. de Almeida, “Tensor modeling and signal processing for wireless communication systems,” Ph.D. dissertation, Université de Nice-Sophia Antipolis, 2007.
[2] A. L. F. de Almeida, G. Favier, J. C.M. Mota, “PARAFAC-based unified tensor modeling for wireless communication systems with application to blind multiuser equalization,” Signal Processing, vol. 87, no. 2, pp. 337-351, Feb. 2007.
[3] A. L. F. de Almeida, G. Favier, J. P. da Costa, and J. C. M. Mota, “Overview of tensor decompositions with applications to communications,” in Signals and Images: Adv. Results in Speech, Estimation, Compression, Recognition, Filtering, and Processing. CRC-Press, 2016, no. Chapter 12, pp. 325–356.
