To Sense or Not To Sense
  A longer sensing time improves the sensing performance; however, with a fixed frame size, the longer sensing time will reduce the allowable data transmission time of the secondary user (SU). In this paper, we try to address the tradeoff between sensing the primary channel for $\tau$ seconds of the time slot proceeded by randomly accessing it and randomly accessing primary channel without sensing to avoid wasting $\tau$ seconds in sensing. The SU senses primary channel to exploit the periods of silence, if the primary user (PU) is declared to be idle the SU randomly accesses the channel with some access probability $a_s$. In addition to randomly accesses the channel if the PU is sensed to be idle, it possibly accesses it if the channel is declared to be busy with some access probability $b_s$. This is because the probability of false alarm and misdetection cause significant secondary throughput degradation and affect the PU QoS. We propose variable sensing duration schemes where the SU optimizes over the optimal sensing time to achieve the maximum stable throughput for both primary and secondary queues. The results reveal the performance gains of the proposed schemes over the conventional sensing scheme, i.e., the SU senses the primary channel for $\tau$ seconds and accesses with probability 1 if the PU is declared to be idle. Also, the proposed schemes overcome random access without sensing scheme.   The theoretical and numerical results show that pairs of misdetection and false alarm probabilities may exist such that sensing the primary channel for very small duration overcomes sensing it for large portion of the time slot. In addition, for certain average arrival rate to the primary queue pairs of misdetection and false alarm probabilities may exist such that the random access without sensing overcomes the random access with long sensing duration. 
Ahmed El Shafie
cs.IT cs.NI math.IT