Analysis of generalized selection combining in cooperative networks with outdated CSI

Until now, the performance analysis of Generalized Selection Combining (GSC) applied to cooperative diversity networks in the presence of outdated channel state information (CSI) is still not available in the literature. In this paper, therefore, we derive closed-form expressions of the ergodic capacity and outage probability for amplify-and-forward GSC over independent and identically distributed Rayleigh channels. Monte-Carlo simulations are set up to corroborate the correctness of our theoretical analysis. The analytical and numerical results reveal that GSC is an effective way to combat the effect of outdated CSI. When using the perfect CSI, a full diversity on the number of all cooperating relays K is available. With the outdated CSI, where the performance of the conventional opportunistic relaying drastically degrades and its diversity order is limited to 1 (i.e., no diversity), a diversity order on the number of selected relays N can still be achieved. However, the performance gain on the diversity comes at the price of sacrifice in the spectral efficiency.