Analysis of detection performance of modified periodogram over fading channels

In this article, we investigate the performance of classical and modified periodogram based on the Neyman-Pearson (NP) criterion in terms of the false alarm and detection probabilities. We derive analytical expressions that allow us to compare the performance of the classical periodogram with the Bartlett's and the Welch's modified periodogram over generalized fading channels. Our analytical framework also captures the effect zero padding (more FFT points than the length of input sequence) on the detection performance. We show that an unpadded classical periodogram gives the same detection performance as the time domain (TD) equivalent. However, the use of zero padding leads to better energy detection performance. The Welch's overlapping periodogram averages is also shown to outperform Bartlett's method (non-overlapping periodogram). Thus we conclude that, it is advantageous to implement the energy detection in the frequency domain (FD) than in the TD. Numerical results have been generated for several representative cases and a careful review of previous works reveals that this is a new contribution to the performance analysis of modified periodogram over fading channels.