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ABSTRACT: The problem of sequentially finding an independent and identically distributed sequence that is drawn from a probability distribution Q <sub>1</sub> by searching over multiple sequences, some of which are drawn from Q <sub>1</sub> and the others of which are drawn from a different distribution Q <sub>0</sub>, is considered. In the problem considered, the number of sequences with distribution Q <sub>1</sub> is assumed to be a random variable whose value is unknown. Within a Bayesian formulation, a sequential decision rule is derived that optimizes a trade-off between the probability of false alarm and the number of samples needed for the decision. In the case in which one can observe one sequence at a time, it is shown that the cumulative sum (CUSUM) test, which is well-known to be optimal for a non-Bayesian statistical change-point detection formulation, is optimal for the problem under study. Specifically, the CUSUM test is run on the first sequence. If a reset event occurs in the CUSUM test, then the sequence under examination is abandoned and the rule switches to the next sequence. If the CUSUM test stops, then the rule declares that the sequence under examination when the test stops is generated by Q <sub>1</sub> . The result is derived by assuming that there are infinitely many sequences so that a sequence that has been examined once is not retested. If there are finitely many sequences, the result is also valid under a memorylessness condition. Expressions for the performance of the optimal sequential decision rule are also developed. The general case in which multiple sequences can be examined simultaneously is considered. The optimal solution for this general scenario is derived.
IEEE Transactions on Information Theory 09/2011; · 3.01 Impact Factor
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ABSTRACT: In a cognitive radio (CR) network, secondary users (SUs) are allowed to opportunistically access a licensed spectrum that is not currently being occupied by primary users. This paper is concerned with the problem of how to quickly and accurately locate an unoccupied channel or determine that there is no unoccupied channel, from multiple (yet finite) candidate channels for a SU with a single detector. To design channel search algorithms, we propose a design criterion that minimizes average searching time subject to constraints on the error probabilities for a multichannel system. Relying on the proposed design criterion, we develop two efficient channel search algorithms that are based on a sequential application of the sequential probability ratio test and energy detection to the candidate channels.
Global Telecommunications Conference (GLOBECOM 2010), 2010 IEEE; 01/2011
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IEEE Transactions on Information Theory. 01/2011; 57:5375-5386.
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ABSTRACT: This paper considers how to scan a wideband spectrum for a multi-channel cognitive radio system with small delay and small error probabilities. Two scenarios are particularly investigated. In the first scenario, the spectrum scanning needs to be complete within a certain period of time, which we call the finite-horizon case. In the second scenario, the spectrum scanning continues until the completion of the detection process, which we call the infinite-horizon case. In both scenarios, spectrum scanning algorithms are developed to minimize a cost function, which strikes a desirable tradeoff between detection error probabilities and the detection delay. In the finite-horizon case, the optimal algorithm requires large look-up tables and frequent update of posterior probabilities, thus incurring a prohibitively high implementation complexity. In the infinite-horizon case, the optimal algorithm is nothing but a concatenated sequential probability ratio test (C-SPRT). The truncated C-SPRT is proposed as a reduced complexity scanning algorithm for the finite-horizon case. Several truncation methods are proposed and investigated. Simulation examples are provided to illustrate the effectiveness of the proposed algorithms.
Information Sciences and Systems (CISS), 2010 44th Annual Conference on; 04/2010
