ML-Decoder and Criterion of Designing Codebook for a Relay Network

For a relay network system with amplify and forward (AF) protocol, in this paper, analysis of performance is conducted and an upper bound of pair-wise error probability is obtained under assumptions that (i) relays only forward received signals (do not perform signal processing), (ii) the receiver only knows Channel State Information (CSI) from relays to the receiver, (iii) the transmitter and relays do not have any CSI. Based on this upper bound, a criterion of designing codebook is proposed. Surprisedly, this bound also shows that increasing number of relays can hardly improve performance, and furthermore, the error probability is decreasing with a speed of P^-1, no matter how large the relay´s number is, where P is the total energy. These results are all confirmed by simulations.