Impact of partial relay selection on the capacity of communications systems with outdated CSI and adaptive transmission techniques

The impact of outdated channel state information (CSI) on the capacity of amplify-and-forward (AF) partial relay selection systems is studied in this paper. The closed-form expressions for the distribution of received signal-to-noise ratio (SNR) in a multi-relay cooperative communications system is first derived, with independent and identically distributed (i.i.d.) Rayleigh fading channels being assumed in each wireless link. After that, the theoretical closed-form expressions for both outage probability and channel capacity of partial relay selection are derived, with four classical adaptive transmission techniques, including the constant power with optimal rate adaption (ORA), the optimal power and rate adaption (OPRA), the channel inversion with fixed rate (CIFR) and truncated channel inversion with fixed rate (TIFR), being considered. Numerical analysis proves that the channel capacity of partial relay selection is impacted considerably by some critical parameters, including the number of relays, the channel correlation coefficient and the end-to-end SNR, etc. It's also exhibited in the numerical results that among the four adaptive transmission techniques, the diversity order of OPRA is larger than that of TIFR, and the OPRA outperforms TIFR with about 0.15 bits/s/Hz in terms of average channel capacity.