In this paper, the problem of joint design of spectrum sensing (SS) and receive beamforming, with reference to a cognitive radio (CR) system, is considered. The aim of the proposed design is the maximization of the achievable average uplink rate of a secondary user, subject to an outage-based quality-of-service constraint for primary communication. A hybrid CR system approach is studied, according to which the system either operates as an interweave (i.e., opportunistic) or as an underlay (i.e., spectrum sharing) CR system, based on SS results. A realistic channel state information framework is assumed, according to which the direct channel links are known by the multiple antenna receivers, while merely statistical (covariance) information is available for the interference links. A new closed-form approximation is derived for the outage probability of primary communication, and the problem of rate-optimal selection of SS parameters and receive beamformers is addressed for hybrid, interweave, and underlay CR systems. It is proved that our proposed system design outperforms both underlay and interweave CR systems for a range of system scenarios.
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