Performance Tradeoffs Offered by Beamforming in Cognitive Radio Systems: An Analytic Approach

This paper studies the design of beamforming weights for a multi-antenna secondary transmitter in an underlay cognitive setting that simultaneously maximizes the secondary received-power while limiting the primary interference to some threshold ∈. With perfect channel state information (CSI), a closed-form expression for the maximum secondary received-power is found. Under imperfect CSI and when the beamforming weights are computed using the channel estimates, the actual secondary received-power, G, and the actual primary interference-power, I, are derived. We show that the mean E[G] has a term that grows linearly with the number of secondary antennas, N, and additional terms dependent on ∈. Consequently, we obtain tradeoffs between E[G] and c. Under perfect CSI, we show that small increases in c from zero lead to moderate enhancements in E[G] for small N. However, increasing N reduces the enhancements. Under imperfect CSI, the gain in E[G] is less compared to the perfect CSI case. Furthermore, we show that the dominant parts of E[I] are independent of N. Thus, we conclude that there is no significant loss for the secondary to perform null-steering beamforming instead. Moreover, it can employ additional antennas to improve E[G] without generating significant extra interference on the primary.