Generalized Selection Combining for Cognitive Relay Networks Over Nakagami-$m$ Fading

We consider transmit antenna selection with receive generalized selection combining (TAS/GSC) for cognitive decode-and-forward (DF) relaying in Nakagami- m fading channels. In an effort to assess the performance, the probability density function and the cumulative distribution function of the end-to-end SNR are derived using the moment generating function, from which new exact closed-form expressions for the outage probability and the symbol error rate are derived. We then derive a new closed-form expression for the ergodic capacity. More important, by deriving the asymptotic expressions for the outage probability and the symbol error rate, as well as the high SNR approximations of the ergodic capacity, we establish new design insights under the two distinct constraint scenarios: 1) proportional interference power constraint, and 2) fixed interference power constraint. Several pivotal conclusions are reached. For the first scenario, the full diversity order of the outage probability and the symbol error rate is achieved, and the high SNR slope of the ergodic capacity is 1/2. For the second scenario, the diversity order of the outage probability and the symbol error rate is zero with error floors, and the high SNR slope of the ergodic capacity is zero with capacity ceiling.