Analysis of degrees of freedom under mixture Gaussian model in cognitive radio systems

We propose a mixture-Gaussian model for a cognitive radio channel to analyze the interplay between the interference in the system and the degrees-of-freedom (DOF), i.e., the average number of channel uses per transmission frame, used by the secondary user (SU) for communications in the long run. In contrast to the conventional studies, we assume that the SU receiver (SU-RX) does not precisely know whether the primary-user (PU) transmitter is on or off. Due to this assumption the resulting interference channel is mixture-Gaussian. Our objective is to find the optimal sensing threshold and sensing time for the signal detector used by the SU transmitter (SU-TX). Our formulation of the optimization problem reflects the trade-off between SU-TX’s DOF for communications and that for detection. Both the DOFs affect PU’s interference to SU, and SU’s interference to PU. The latter interference causes PU performance degradation, which is kept within tolerable range as a constraint. As a further contribution, we define interference regimes for SU performance on the basis of PU transmission power level. We also address the scenario when PU receiver uses the nearest neighbor decoding while wrongly anticipating that the channel is Gaussian. Finally, we demonstrate that even if SU-TX’s signal detector performs suboptimally, SU can still achieve the optimal detector’s performance in the high interference regime by adjusting the sensing parameters.