Doubly coupled nested tensor decompositions with application to multirelay multicarrier MIMO communication networks

Abstract

Coupled tensor decompositions have emerged as a promising approach to analyze large dimensional datasets in the context of signal processing applications. In this paper, the general concept of doubly coupled decomposition (DCD) for high-order tensors is first proposed, extending the idea of coupled decompositions to doubly coupled nested structures which result from the contraction of two sets of tensors, each set depending on a specific mode. Two new decompositions are defined, the so-called doubly coupled nested Tucker decomposition (DCNTD) and doubly coupled nested PARAFAC decomposition (DCNPD). Uniqueness of these DCDs is analyzed. In a second part, we show how these DCDs can be used to model multirelay multicarrier MIMO cooperative communication networks with two different tensor codings at the source and relay nodes. Exploiting the multilinear structure of the received signals and assuming the coding tensors are known at the destination, semi-blind closed-form receivers are developed for jointly estimating the channels and transmitted symbols. The proposed receivers use Khatri-Rao and Kronecker product factorization algorithms. Identifiability conditions for system parameter estimation and design of the tensor codes are also addressed. Monte Carlo simulation results illustrate the performance improvement of the proposed DCD-based systems over existing state-of-the-art ones.