Performance Analysis of Non-Orthogonal AF Relaying in Cognitive Radio Networks

In this letter, we address the problem of maximizing the throughput of underlay cognitive networks, through optimal power allocation of non-orthogonal amplify-and-forward relays. The optimization problem is formulated and transformed to a quadratically constrained quadratic problem (QCQP). The optimal power allocation is obtained through an eigen-solution of a channel-dependent matrix where the corresponding signal-to-noise ratio (SNR) is shown to be the dominant eigenvalue of this matrix. Our optimal power allocation is shown to transform the transmission over the non-orthogonal relays into parallel channels, resulting in the received SNR to be the sum of the SNRs over the relaying channels. While closed-form expressions for statistics of the received SNR are mathematically intractable, we propose an approximation for the probability density function of the received SNR based on Gamma random distribution. The outage probability of the cognitive network is analyzed where the Gamma approximation is shown to be accurate and insightful.