The normalized detection threshold, T n, for the widely used FFT summation detector, is usually computed by solving a nonlinear equation. However, when the number of input data blocks, L, or the number of FFT bins, N, used for channel power estimation is large, a substantial number of eigenvalues used in the computation of T n can become extremely small with the result that function evaluations in numerical procedures often break down. This is especially the case for overlapped input data. Since small eigenvalues should make relatively small contributions to the normalized detection threshold T n, it is reasonable to expect that a close lower bound for T n can be obtained by truncating the small eigenvalues. This paper confirms that, for normalized windows, when either L or N is large, good estimates of the normalized detection threshold, T n, can be obtained under most practical conditions using the eigenvalues which are greater than or equal to 0.01.

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Keywords constant probability of false alarm, detection and estimation, FFT filter bank, normalized detection threshold, power spectrum density, spectrum analysis, spectrum sensing
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Conference 2011 IEEE Military Communications Conference, MILCOM 2011
Wang, S. (Sichun), Inkol, R. (Robert), Patenaude, F. (François), & Rajan, S. (2011). Computation of the normalized detection threshold for the FFT summation detector through eigenvalue sequence truncation. In Proceedings - IEEE Military Communications Conference MILCOM (pp. 131–136). doi:10.1109/MILCOM.2011.6127485