Distributed beamforming for spectrum-sharing systems with AF cooperative two-way relaying

We consider in this paper distributed beamforming for two-way cognitive radio networks in an effort to improve the spectrum efficiency and enhance the performance of the cognitive (secondary) system. In particular, we consider a spectrum sharing system where a set of amplify-and-forward (AF) relays are employed to help a pair of secondary transceivers in the presence of multiple licensed (primary) users. The set of relays participate in the beamforming process, where the optimal beamformer weights are obtained via a linear optimization method. For this system, we investigate the transmission protocols over two and three time-slots. To study and compare the performance tradeoffs between the two transmission protocols, for both of them, we derive closed-form expressions for the cumulative distribution function (CDF) and the moment generating function (MGF) of the equivalent end-to-end signal-to-noise ratio (SNR) at the secondary receiver. We analyze the performance of the proposed methods where closed-form expressions for the user outage probability and the average error probability are derived for independent and identically distributed Rayleigh fading channels. Numerical results demonstrate the efficacy of beamforming in enhancing the secondary system performance in addition to mitigating the interference to the primary users. In addition, our results show that the three time-slot protocol outperforms the two time-slot protocol in certain scenarios where it offers a good compromise between bandwidth efficiency and system performance.