Performance analysis of cooperative cognitive MIMO multiuser downlink transmission with perfect and imperfect CSI over Rayleigh fading channels

In this paper, a comprehensive comparison analysis in terms of outage probability and average symbol error ratio (SER) is presented for cooperative cognitive multiple-input and multiple-output (CC-MIMO) multiuser systems with amplify-and-forward (AF) protocol. Specially, we consider two scenarios where the CC-MIMO multiuser systems have the perfect and imperfect channel state information (CSI). The CC-MIMO multiuser systems consist of one multi-antenna source, one single-antenna relay, and multiple multi-antenna destinations. At the secondary source and destinations, the maximal ratio transmission (MRT) and maximal ratio combining (MRC) are employed, respectively. For such CC-MIMO multiuser systems, we first obtain the exact closed-form expressions of outage probability under the two cases where the CC-MIMO multiuser systems have the perfect and imperfect CSI. Then, to reduce the implementation complexity, the tight lower bounds of outage probability and average SER are derived. Finally, to obtain insight, by using the high signal-to-noise ratio (SNR) approximation, the asymptotic estimations of outage probability are achieved. The numerical results show that the derivations are agreed with the simulations, which validate our derivations. At the same time, the results show that, for the systems without perfect CSI, the achievable diversity order reduces to one, regardless of the number of antennas at the cognitive source and destinations as well as the number of the cognitive destinations. Nevertheless, these key parameters affect the coding gain of the CC-MIMO multiuser systems. When the systems have the perfect CSI (or without feedback delay), the achievable diversity gain is determined by the minimum between the number of source's antennas and the product of the number of destinations and the number of destination's antennas. For the effect of PU's parameters, our results indicate that primary systems only affect the coding gain but not the diversity gain.