Closed-form capacity formula for multi-antenna cognitive radio networks with asymmetric fading

A cognitive radio network with a multiple-input single-output secondary link and a multi-antenna primary receiver is considered. The secondary transmitter steers its transmission into the direction of its intended destination in order to maximize the received signal-to-noise ratio. Under this beam-forming strategy, the power allocation is optimized to achieve the ergodic capacity under the constraint that the long-term interference, caused at the primary receiver, will not exceed a predefined threshold. Assuming line-of-sight communication (Rician fading) for the secondary link and Rayleigh fading for the secondary-to-primary link channel, we derive the exact closed-form expression for the ergodic capacity. Numerical results corroborate theoretical findings and illustrate the manifold impact of the system parameters into its performance.