  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.
