In several signal processing applications for wireless communications, the received signal is multidimensional in nature and may exhibit a multilinear algebraic structure. In this context, tensor decompositions have been the subject of several works in the past ten years and new (generalized) tensor decompositions have been developed and studied for modeling a wider class of wireless communication systems with more flexible transmission structures, more realistic channel models and more efficient receiver signal processing. Figure 1 depicts the role of tensor signal processing in the communications chain.

Below, I briefly describe the main lines of my current research involving tensor decompositions and their applications:

**Multiple-antenna communication systems**

We have been investigating new tensor based approaches for desiging multiple-antenna (MIMO) transmission schemes and also for blind and semi-blind signal processing at the receiver. More specifically, we have shown that the algebraic structure of tensor decompositions can be exploited for designing space-time/space-time-frequency coding schemes enjoying blind/semi-blind detection with a joint symbol and channel estimation by capitalizing on the uniqueness properties of these tensor models.

**Modeling and estimation of wireless communication channels**

The problem of interest is that of parametric modeling/estimation of multipath propagation channels. In this context, we have solved the problem of estimating multipath parameters of single-input multiple-output (SIMO) and multiple-input multipl-output (MIMO) channels by recasting the model using the tensor formalism. Interestingly, the choice of the tensor model is linked to the structure of the propagation channel.

**Blind identification of underdetermined mixtures**

Blind identification and blind source separation methods have been successfully applied in multidisciplinary contexts including radiocommunications, sonar, radar, biomedical signal processing and data analysis, just to mention a few. This subject has been at the center of many theoretical works while related methods and algorithms have been used in a variety of application fields. We have investigated new methods for blind identification of underdetermined mixtures by exploiting higher-order statistics. The proposed methods rely on PARAFAC and CONFAC decompositions of the second characteristic function of the observations.

**Distributed signal processing for collaborative networks**

By combining tensor modeling with the idea of cooperative signal processing, we have shown that blind information recovery can be carried out in a distributed way in a wireless sensor network (WSN). We have been investigating distributed tensor signal processing algorithms based on average consensus for blind channel and symbol estimation in collaborative WSNs. More recently, we have investigated distributed large-scale tensor decomposition algorithms for "big data" problems.

**Blind receivers for cooperative diversity communications**

Cooperative diversity systems emulate an antenna array in a distributed manner by allowing one or more mobile terminals to relay the information transmitted from a source node to the destination node. In this research line, we study new tensor models for cooperative diversity systems under different cooperation protocols. Thanks to the uniqueness properties of tensor decompositions, our goal is to devise blind and semi-blind receivers for cooperative communication systems that perform well the tasks of channel estimation and information recovery with no (or very reduced amout of) pilot information.

The conception of the tensor model has two viewpoints from a signal processing perspective in communication problems. The first one is related primarily to receiver signal processing (e.g. multiuser signal separation, equalization, decoding and channel estimation, etc). The second one is related to transmitter signal processing (e.g. space-time multiplexing/spreading, space-time-frequency block coding, etc). Figure 2 illustrates both viewpoints, by highlighting the multiple signal dimensions that generally appear in each case.

- Blind source separation and identification
- Space-time processing /coding/ decoding
- Channel estimation and equalization
- MIMO communication systems

- Tensor-based modeling and signal processing
- Blind sensor array processing
- Cooperative communications
- Distributed signal processing