Mutual Information of Amplify-and-Forward DSTBCs over the Random Set Relay Channel

We analyze amplify-and-forward (AF) distributed space-time block coded (DSTBC) cooperative relaying systems over the random set relay channel (RSRC). A two-stage operation is considered where all terminals operate in hair-duplex mode and where the source first transmits to a pool of N relays, each of which decides independently whether to relay the source's information to the destination or not, by comparing its own instantaneous received signal-to-noise ratio (SNR) to a threshold zeta. The K <= N transmitting relays do so with constant transmit power per relay, and cooperate through linearly dispersed full-rate-full-diversity DSTBCs. The system concept is interesting in which no coordination amongst relays is required, and only backward channel state information (CSI) is assumed. We derive the mutual information (MI) achieved by such a scheme with Rayleigh fading at each channel branch and assuming perfect interleaving (ergodic channel). Then, we study the effect of the selected threshold onto achievable MI in the case where the source and each relay transmits with the same power. It is found that the maximal MI is not achieved under full-time-all-relay cooperation (K = N), despite the fact that the total receive power at the receiver increases with K. The maximum MI in this case can also be fitted to a simple function of N. Next, we investigate the effect of different power balances between the two transmission stages while fixing the total average transmit power. It is shown that the optimum power allocation depends on the threshold, such that the MI is maximized not with equal power allocation (and K = N), but rather with a power balance of around 2-to-3 and K < N, again, despite the fact that the total receive power at the receiver increases with K. Finally, we compare the maximum MI against the MI achieved with QPSK and QAM modulations, which reveals that the envelope behavior of the latter follows the same trend observed with the former.