An MMSE Strategy at Relays With Partial CSI for a Multi-Layer Relay Network

We consider a relay network with a single source-destination pair and multiple layers of relays between them. We assume that these layers sequentially relay the signal transmitted by the source to the destination. Unlike existing work, we also assume that the destination and all the forward layers present between the transmitting layer and the destination receive signals during every transmission phase. We optimally combine these signals, say μ of them, using a precoder at each relay layer for onward transmission. We obtain this precoding matrix by minimizing the mean-squared error (MSE) at the relays, and do not require channel-state-information (CSI) of the forward channels at the relays unlike existing systems that minimize MSE at the destination and require CSI of the forward channels at the relays. Our closed-form solution for this matrix is valid for any K number of layers, whereas minimizing MSE at the destination does not have closed-form solution for K > 1. For K > 1, we enhance an existing scheme to obtain a sub-optimal closed-form precoder solution and use it for comparison. We show using simulations that our scheme approaches the bit-error-rate (BER) performance of this scheme, when μ is increased, even with partial CSI.