Optimal detector randomization in cognitive radio receivers in the presence of imperfect sensing decisions

In cognitive radio systems, spectrum sensing is one of the crucial tasks to be performed by secondary users in order to limit the interference to primary users. Therefore various spectrum sensing methods have been proposed in the literature. Once secondary users make a sensing decision, they adapt their communication parameters accordingly, which means that they perform communications when the channel is sensed as idle whereas they either do not transmit at all or transmit at a reduced power when the channel is sensed as busy. However, in practical systems, sensing decisions of secondary users are never perfect; hence, there can be cases in which the sensing decision is idle (busy) but primary user activity actually exists (does not exist). Therefore, the optimal design of secondary systems requires the consideration of imperfect sensing decisions. In this thesis, optimal detector randomization is developed for secondary users in a cognitive radio system in the presence of imperfect spectrum sensing decisions. Also, suboptimal detector randomization is proposed under the assumption of perfect sensing decisions. It is shown that the minimum average probability of error can be achieved by employing no more than four maximum a-posteriori probability (MAP) detectors at the secondary receiver. Optimal and suboptimal MAP detectors and generic expressions for their average probability of error are derived in the presence of possible sensing errors. Numerical results are presented and the importance of taking possible sensing errors into account is illustrated in terms of average probability of error optimization.