  In this paper, we examine the outage performance of a cognitive relay
network, which is comprised of a secondary transmitter (ST), multiple
decode-and-forward (DF) relays and a secondary destination (SD). We propose a
multi-relay selection scheme for the cognitive relay network, where multiple
relays are selected and used to participate in forwarding the secondary
transmission from ST to SD. A closed-form expression of the outage probability
for the proposed multi-relay selection under imperfect spectrum sensing is
derived in Rayleigh fading environments. For comparison purposes, the
conventional direct transmission and the best-relay selection are also
considered as benchmarks. Numerical results show that as the spectrum sensing
performance improves with an increasing detection probability and/or a
decreasing false alarm probability, the outage probabilities of the proposed
multi-relay selection as well as the direct transmission and the best-relay
selection schemes all decrease accordingly. It is also demonstrated that the
proposed multi-relay selection significantly outperforms the conventional
approaches in terms of the outage probability.
