Computation of the normalized detection threshold for the FFT summation detector through eigenvalue sequence truncation

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.