PARAFAC-PARATUCK Semi-Blind Receivers for Two-Hop Cooperative MIMO Relay Systems

In two-hop amplify-and-forward (AF) relay systems, a source node sends information to one or several relay nodes that amplify and retransmit the received signals to a destination node, without decoding. Such AF relaying-based cooperative communications allow to improve communication reliability due to increased channel gains and space diversity at the destination node. In this paper, we consider a two-hop AF cooperative scheme, with a simplified Khatri-Rao space-time (KRST) coding at transmission (source). We show that the third-order tensor of signals received by the destination node satisfies a PARAFAC decomposition for the direct link, and a PARATUCK2 decomposition for the relay-assisted link. This tensorial modeling enables a joint semi-blind estimation of transmitted symbols and channels of both hops. Three receivers that combine these two tensor models in different ways are proposed. An identifiability study for these receivers is carried out, from which sufficient conditions for joint symbol and channel recovery are derived. The performance of these receivers is illustrated by means of simulation results, and a comparison is made with recent supervised approaches that allow to estimate channels and symbols in two separated steps. Besides a joint semi-blind channel/symbol estimation, our approach gives a better BER performance due to coding at the transmitter.