Detection of Narrow-Band Signals Through the FFT and Polyphase FFT Filter Banks: Noncoherent Versus Coherent Integration

Formulas are derived for computing performance gain that is achieved by coherent integration over noncoherent integration in detection schemes based on polyphase fast Fourier transform (FFT) and FFT filter banks. Numerical computation of the processing gain is then discussed. The crucial role that is played by window energy normalization in detection performance comparisons, which has never been recognized in the literature, is emphasized and analyzed. The numerical results provided for typical implementation parameters are useful for making appropriate tradeoffs in the design of solutions for practical signal detection problems.