Impact of Improper Gaussian Signaling on the Achievable Rate of Overlay Cognitive Radio

Improper Gaussian signaling (IGS) has been recently shown to provide performance improvements in underlay cognitive radio systems as opposed to the conventional proper Gaussian signaling (PGS) scheme. For the first time, this paper implements IGS scheme in overlay cognitive radio system, where the secondary transmitter broadcasts a mixture of two different signals. The first signal is selected from the PGS scheme to support the primary message transmission. On the other hand, the second signal is chosen to be from the IGS scheme in order to reduce the interference effect on the primary receiver. We then optimally design the overlay cognitive radio that employs IGS to maximize the secondary link achievable rate while satisfying the minimum rate requirement of the primary network. In particular, we derive closed form expressions for the circularity coefficient used in the IGS scheme and the power distribution parameters. Simulation results are provided to support our theoretical derivations.