Nested tensor decomposition applied to cooperative MIMO communication systems

Abstract

Multiple-input multiple-output (MIMO) systems are often used to increase the diversity and/or multiplexing gains, by transmitting multiple versions of the same signal or independent data onto the communication channels. As another way to exploit spatial diversity, cooperative communications have emerged as a promising technique for the new generations of wireless communication systems, yielding significant improvements in the performance and reliability of these systems. In this context, in the last decades, tensor decompositions have been exploited in the processing of multidimensional signals in MIMO systems and, more recently, coope- rative networks, allowing the design of effective receivers for estimation of the transmission parameters. In particular, nested decompositions have allowed the modeling of signals from systems that benefit from multiple diversities, yielding high-order tensors represented in a com- pact way. This thesis presents developments carried out within the framework of new nested tensor decompositions applied to cooperative wireless communication systems with multiple antennas. Indeed, the theoretical contributions of the present thesis rely on the proposition of new nested tensor decompositions, along with the corresponding uniqueness analysis, as well as the proposition of new cooperative MIMO communication systems that are modeled using the presented nested tensor models. In the first part of this thesis, two new tensor models based on nested Tucker decompositions (NTD) are introduced. The first model, called high-order nested Tucker decomposition (HONTD), extends NTD by considering higher order tensors resulting from the contraction of several Tucker models in a train format. The second model, called coupled nested Tucker decomposition (CNTD), can be viewed as a coupling of multiple NTDs that share a common factor, associating the nesting and coupling concepts initially defined for PARAFAC models, extending them to Tucker-based ones. In the subsequent parts of the thesis, these tensor decompositions are used in the modeling of three new cooperative MIMO systems. Two of them consider multiple relay cases (with sequential and parallel relaying, respectively) and the other one considers a single-relay multicarrier network. All the proposed systems consider tensor codings in the transmit nodes. For each proposed system, the tensor models are exploited to obtain semi-blind estimation algorithms, allowing to design receivers that jointly estimate the channels and transmitted symbols. Necessary conditions required to the uniqueness of the tensor decompositions and identifiability of the proposed algorithms are also discussed. Finally, computational simulation results are presented in order to evaluate the behavior of the proposed systems/receivers, illustrating the effectiveness of signal processing based on nested tensor decompositions.