In this paper, we develop and analyze a novel performance metric, called interference efficiency, which shows the number of transmitted bits per unit of interference energy imposed on the primary users (PUs) in an underlay cognitive radio network (CRN). Specifically, we develop a framework to maximize the interference efficiency of a CRN with multiple secondary users (SUs) while satisfying target constraints on the average interference power, total transmit power, and minimum ergodic rate for the SUs. In doing so, we formulate a multiobjective optimization problem (MOP) that aims to maximize ergodic sum rate of SUs and to minimize average interference power on the primary receiver. We solve the MOP by first transferring it into a single objective problem (SOP) using a weighted sum method. Considering different scenarios in terms of channel state information (CSI) availability to the SU transmitter, we investigate the effect of CSI on the performance and power allocation of the SUs. When full CSI is available, the formulated SOP is nonconvex and is solved using augmented penalty method (also known as the method of multiplier). When only statistical information of the channel gains between the SU transmitters and the PU receiver is available, the SOP is solved using Lagrangian optimization. Numerical results are conducted to corroborate our theoretical analysis.
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