Improper Signaling for OFDM Underlay Cognitive Radio Systems

Improper signaling, where real and imaginary parts of the transmit signal are correlated and/or have unequal power, has received a lot of attention lately because it has been shown to increase achievable rates in many interference-limited communication systems. In this paper, we study whether improper signaling can also benefit an orthogonal frequency-division multiplexing (OFDM) underlay cognitive radio (UCR) system. We assume that the primary user (PU) transmits proper signals, while the secondary user (SU) is allowed to employ improper signaling. We consider two different rate constraints for the rate of the PU: i) the total rate of the PU, and ii) the rate of the PU in each subband. We propose an algorithm to implement improper signaling for each constraint. In both cases, we show that the benefits of improper signaling are relatively small and decrease rapidly with increasing number of subbands. This rather negative result shows that the use of improper signaling in interference scenarios needs to be justified on a case-by-case basis.