Generalized Khatri-Rao and Kronecker space-time coding for MIMO relay systems with closed-form semi-blind receivers

In this paper, we propose two new space-time (ST) coding schemes for multiple-antenna signalling based on multiple Khatri-Rao and Kronecker products of symbol matrices, denoted MKRST and MKronST codings, respectively. These new coding schemes generalize the standard Khatri-Rao coding by introducing extra space/time diversities due to a mutual space-time spreading of the transmitted data streams, induced by Khatri-Rao and Kronecker products between symbol matrices. Parallel non-iterative decoding methods are proposed for estimating each symbol matrix. We consider a one-way two-hop multi-input multi-output (MIMO) relay system using the MKRST and MKronST codings at both the source and relay nodes, and three different relaying protocols, namely, amplify-and-forward (AF), decode-and-forward (DF) and estimate-and-forward (EF). For the DF and EF protocols, the channel and symbol estimation is split into two successive phases, one at the relay and the other one at the destination. Exploiting parallel factor (PARAFAC) models for the tensors of signals received at the relay and the destination, closed-form semi-blind receivers are derived for joint symbol and channel estimation. System parameters identifiability is also discussed, and the computational cost of the proposed receivers and decoders is detailed. Monte Carlo simulation results are provided to assess the performance of the proposed coding schemes, and semi-blind receivers.