The FFT filter bank-based summation detector is well suited for detecting narrowband signals embedded in wideband noise and has numerous applications in areas such as civilian spectrum monitoring, electronic warfare, and spectrum sensing in cognitive radio networks. In practical implementations, the detection threshold is obtained as the product of the channel noise power, which is adaptively estimated from the FFT filter bank output, and the theoretical normalized detection threshold Tn corresponding to the desired probability of false alarm. Since the probability of false alarm Pfa is a strictly decreasing function of Tn, Tn is usually computed by finding the root of a non-linear equation using the Newton-Ralphson or golden section search algorithm. The initialization of the numerical procedures, however, hinges on good a priori knowledge of lower and upper bounds for Tn. In this article, a new and easily computable lower bound for Tn, the Okamoto lower bound, is derived. This lower bound is larger than the lower bounds derived earlier by the authors and hence should be preferred when initializing the numerical procedures in the computation of Tn.

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Keywords Constant false alarm rate, Detection and estimation, Detection threshold, FFT filter bank, Probability of false alarm, Spectral analysis
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Conference 2010 23rd Canadian Conference on Electrical and Computer Engineering, CCECE 2010
Wang, S. (Sichun), Inkol, R. (Robert), Rajan, S, & Patenaude, F. (François). (2010). The Okamoto lower bound for the normalized detection threshold of the FFT filter bank-based summation detector. In Canadian Conference on Electrical and Computer Engineering. doi:10.1109/CCECE.2010.5575259