Diversity-multiplexing-delay tradeoff of a DDF protocol on a half-duplex ARQ relay channel

The diversity-multiplexing-delay tradeoff (DMDT) of the dynamic decode-and-forward (DDF) protocol on a half-duplex (HD) relay channel is analyzed, where the source uses an automatic retransmission request (ARQ) protocol. Our analysis for short-term static (STS) channels, where each of the retransmissions go through an independent and identically distributed channel state than the original one, shows that diversity gains keep increasing with maximum number of ARQ rounds L, for all multiplexing gains. The optimal DMDT for the long-term static (LTS) channel ( where all the retransmissions take place in the same channel state ) derived, shows that diversity gains can be obtained only at higher multiplexing gains and that too bounded by the diversity order at zero multiplexing gain of the basic DDF protocol. To circumvent this limitation, different ARQ rounds are allowed to use different power level keeping the long term average power constant and dramatic improvement in the diversity order has been observed. Closed form solution for the L = 2 case is provide however the DMDT with long-term power control for a general L can be computed using numerical methods. Throughout the paper, the performance of our scheme is compared with another ARQ relay scheme considered (hereafter mentioned as TDK-scheme). In all of the above discussed scenarios, the optimal diversity orders of our scheme are shown to be higher than those of the TDK-scheme, for all multiplexing gains. Further, we derive an exact expression for the optimal DMDT of the TDK-scheme for the STS channel condition (since only an upper bound was derived) and a closed form expressions for the DMDT of the TDK-schemes under long term power constraint for L = 2 case, which enable us to analytically quantify the performance gain of our scheme over that of the TDK-scheme.