Optimization of Channel Sensing Time and Order for Cognitive Radios Ahmed Ewaisha, Ahmed Sultan, Tamer ElBatt Wireless Intelligent Networks Center (WINC) School of Communication and Information Technology Nile University Cairo, Egypt, 12677 ahmed.ewaisha@nileu.edu.eg Abstract—In this paper we consider a single cognitive radio seeking a transmission opportunity by sequentially sensing a number of statistically independent primary channels. We study the joint optimization of the time spent to sense a channel, the decision threshold to determine whether the channel is free or busy, together with the order with which the channels are sensed. The sensing time and decision threshold are assumed to be the same for all channels. The design objective is to maximize the expected secondary throughput taking sensing errors into account and penalizing for collisions that may dis- rupt the primary transmission. Motivated by the computational complexity of the problem, we propose suboptimal solutions that significantly reduce the complexity without sacrificing accuracy. Our results reveal a fundamental trade-off between minimizing the probability of collision with the primary user via reducing the sensing errors, which favors a longer sensing time, and increasing the secondary user’s throughput, which favors shorter sensing time. The suboptimal approach, for plausible simulation scenarios, is found to reduce the computational complexity by more than 89%, while maintaining a near- optimal throughput within 0.28% of the optimal performance. 1 I. I NTRODUCTION The rapid growth in wireless communications and net- working, evidenced by the wide proliferation of mobile devices, variety of standards and new use cases, gives rise to the problem of spectrum scarcity. However, recent spectrum measurement studies [1] have revealed that the assigned spectrum is used sporadically and, hence, remains largely under-utilized. This, in turn, has led to the concept of Dynamic Spectrum Access (DSA), or alternatively cognitive radios (CRs), which received recent attention in an attempt to remedy this problem. The notion of DSA hinges on the assumption that unlicensed users (secondary users) could access the spectrum, opportunistically, at times and locations where licensed users (primary users) are inactive. Spectrum sensing is a major building block in such sys- tems in order to enable the secondary users to detect the inactivity of primary users on a particular frequency channel (i.e., to discover spectrum holes). In this paper, we consider a secondary terminal that senses a specific number of primary channels, one at a time, to find a transmission opportunity as quickly and reliably as possible. The secondary transmitter relies on conventional energy detection to determine the 1 This work was funded by the Egyptian National Telecommunication Regulatory Authority (NTRA). occupancy state of a certain primary channel. Accordingly, the cognitive transmitter decides, jointly, the optimal order at which channels has to be sensed, the optimal sensing time, and the optimal sensing energy threshold based on which the channel is determined to be busy or free. The problem of optimal channel selection in cognitive radio networks has received recent attention in the literature, e.g., [2]–[6]. In [3], given different channel availability probabilities and sensing times, the optimal sensing sequence is to sort the channels in ascending order of the ratio of the channel sensing time to the channel availability probability. This result is for the homogeneous channel capacity case, where all the channels have the exact same capacity. Note that in [3], the sensing times are fixed for each channel, i.e., they are not considered as optimization variables. In addition, the channel capacities are not considered to be time-varying. For heterogeneous channel capacities, the problem becomes NP-hard and is solved via exhaustive search. In [4], the authors investigate the optimal channel selection problem assuming error-free sensing. Given a set of channels and their probing costs, the sender’s objective is to choose the strategy that maximizes transmission reward minus the sensing costs. The strategies available to the cognitive ter- minal are either to transmit on a free channel, or to transmit on a previously found free channel, or to randomly select an unprobed channel and use it for transmission. The authors of [5] build upon the work in [4] by incorporating the possibility of sensing errors. Although the optimization of the sensing time is included in [5], the order by which the channels are sensed is random. When a cognitive radio wishes to transmit, it starts scanning the channels in a sequential manner. It randomly picks a channel and samples it for some time, and then decides whether the channel is idle or busy. If it is busy, another channel is randomly selected, otherwise the channel is probed to determine its quality. Depending on this quality, the channel is either used for transmission or is skipped in search for a better opportunity. Perhaps the closest to our work is [2], where a dynamic programming approach is adopted for finding the optimal order due to the sequential decision nature of the problem at hand. In [2], the time incurred for sensing a primary channel is assumed given and fixed. Although the authors tackle the issue of imperfect sensing via incorporating the probabilities of false alarm and misdetection, their formulation does not IEEE WCNC 2011 - PHY 978-1-61284-254-7/11/$26.00 ©2011 IEEE 1414