PARATUCK-N semi-blind receivers for multi-hop cooperative MIMO relay systems

Abstract

Cooperative communication systems is a promising research field nowadays due to its advantages, like the increase of the received power, better quality of signal, and spatial diversity gains. Specifically, multi-hop systems are a very important part of cooperative communications, since they have the advantage of needing less transmission power than the direct systems. Also, multiple-input multiple-output (MIMO) systems are present in several standards of communications, providing some advantages, like the spatial multiplexing gains. Based on this scenario, this work proposes two semi-blind receivers based on the Kronecker product, that jointly estimate the symbol and the channels in a multi-hop Amplify-and-Forward (AF) MIMO relay-assisted system (AF protocol is widely used, due to its great performance and easy implementation). We consider a transmission scheme using a simplified Khatri-Rao space-time (KRST) coding at the source node, combined with an AF scheme at the relay nodes. We show that the third-order tensor of signals received by the destination node satisfies a PARATUCK-(K+1) decomposition, where K is the number of relays. This tensorial modeling enables a semi-blind estimation of symbols and channels with the use of a few pilot symbols. The first receiver called Least-Squares Kronecker-Factorization (LS-KF) is based on a factorization of the Kronecker product matrix between the symbols and the channel matrices. The other receiver called Least-Squares Kronecker-Rearrangement (LS-KR) is based on a rearrangement of this Kronecker product matrix, in order to achieve a rank-1 matrix. The performance of these receivers is evaluated by means of computational simulation results proving their efficiency in estimating the channels and, hence, providing a low Symbol Error Rate (SER). The proposed algorithms in the multi-hop scenario were compared to each other and with the two-hop and three-hop scenarios. The proposed algorithms in the multi-hop scenario were better at all simulations, providing a lower SER and better channels estimations.