Sensing/throughput trade-off for cognitive radio under outage constraints over frequency- selective fading channels

The most widely used detector in spectrum sensing for cognitive radio is the energy detector, due to its simplicity. The performance of an energy detector technique is normally investigated by determining the probabilities of both false alarm (P_FA) and detection (P_D). Due to the fading wireless channel, P_D (unlike P_FA) is itself a random variable and we call the probability of P_D falling below a certain predefined target detection probability threshold the outage probability (p_out). Also, we define outage constraint to mean the imposition of an upper bound on p_out. In this paper, we evaluate the sensing/throughput trade-off under outage constraints over a frequency-selective fading channel. We will show how the secondary user may exploit the existence of multipath propagation (over the primary to secondary wireless channel) to improve the secondary throughput. First, we derive expressions for both P_FA and P_D over a Rayleigh fading frequency-selective channel which rely upon a new closed form spectrum sensing threshold which takes into account the outage constraint. Second, we derive a closed form expression for the secondary throughput. The simulation results show that there exists an optimum sensing time (under outage constraint) that will maximise this secondary throughput. Also, our simulation results show that the throughput improves dramatically with an initial increase in the number of channel multipaths and then levels out. Finally, we show there exists an optimum signal to noise ratio for which the secondary throughput is maximised.