Performance Analysis of Collaborative Beamforming With Outdated CSI for Multi-Relay Spectrum Sharing Networks

Prior works on performance analysis for cognitive radio networks often assume perfect channel state information (CSI), which may not be readily available. This paper investigates the effects of the outdated CSI on the performance of a dual-hop multi-antenna multi-relay spectrum sharing system. To exploit the benefits of available multiple antennas, collaborative zero-forcing beamforming is considered at the secondary user (SU) source node with the outdated CSI and maximum ratio combining diversity reception at the destination node. The $N$th best relay selection strategy is adopted at the relays. Analytical outage probability and bit-error rate expressions are derived for the SU. Moreover, we examine the high signal-to-noise ratio regime and present closed-form expressions for the asymptotic outage probability and asymptotic bit-error rate with and without feedback delay. In addition, we derive the closed-form ergodic capacity expression for the special case of our considered system, and analyze the effects of delay on the capacity. Furthermore, the closed-form outage probability expression for the primary user is obtained and the impact of delay on the interference on the primary user is investigated. Monte Carlo simulations are carried out to verify our analysis.