On the suboptimality of DDF and static QMF communication strategies in half-duplex single relay networks

The diversity-multiplexing trade-off (DMT) expresses the optimal trade-off between the transmission rate and the error probability for communications at high signal to noise ratios (SNR) in wireless networks with fading channels. For half-duplex single relay networks with quasi-static fading channels, if the average signal to noise ratio (SNR) of the source-relay (S-R) link is equal to the average SNR of the relay-destination (RD) link, quantize-map-and-forward (QMF) and dynamic decode-and-forward (DDF) strategies are DMT optimal at high and low multiplexing gains, respectively. In this paper, we show that DDF and SQMF strategies are not generally DMT optimal in half-duplex single relay networks when the average SNR of the S-R link and R-D link are not equal. We show that DMT of dynamic QMF strategy is strictly greater than DMT of DDF and static QMF strategies for a specific half-duplex single relay network at certain multiplexing gains.