Capacity and Spectral Efficiency of Interference Avoiding Cognitive   Radio with Imperfect Detection
  In this paper, we consider a model in which the unlicensed or the Secondary User (SU) equipped with a Cognitive Radio (CR) (together referred to as CR) interweaves its transmission with that of the licensed or the Primary User (PU). In this model, when the CR detects the PU to be (i) busy it does not transmit and; (ii) PU to be idle it transmits. Two situations based on CR's detection of PU are considered, where the CR detects PU (i) perfectly - referred to as the "ideal case" and; (ii) imperfectly - referred to as "non ideal case". For both the cases we bring out the rate region, sum capacity of PU and CR and spectral efficiency factor - the ratio of sum capacity of PU and CR to the capacity of PU without CR. We consider the Rayleigh fading channel to provide insight to our results. For the ideal case we study the effect of PU occupancy on spectral efficiency factor. For the non ideal case, in addition to the effect of occupancy, we study the effect of false alarm and missed detection on the rate region and spectral efficiency factor. We characterize the set of values of false alarm and missed detection probabilities for which the system benefits, in the form of admissible regions. We show that false alarm has a more profound effect on the spectral efficiency factor than missed detection. We also show that when PU occupancy is small, the effects of both false alarm and missed detection decrease. Finally, for the standard detection techniques viz. energy detection, matched filter and magnitude squared coherence, we show that that the matched filter performs best followed by magnitude squared coherence followed by energy detection with respect to spectral efficiency factor. 
Aaqib Patel, Md. Zafar Ali Khan, S. N. Merchant, U. B. Desai
cs.IT math.IT