An accurate model for periodogram-based energy detection over Nakagami fading

Spectrum sensing is a major function within a cognitive radio system, and it is recently shown that the frequency-domain implementation of the energy detector yields a lower probability of false alarm when compared with the timedomain model. In this paper, an accurate mathematical model is presented for spectrum sensing using the periodogram-based energy detector over for independent and identically distributed (i.i.d.) Nakagami fading channels. By exploiting the quadratic form representation of the periodogram, the eigenvalue of the product of the sample covariance matrix of the observed vector and the matrix of the quadratic form is investigated for the case of transmission over Nakagami fading. Hence accurate closed forms are derived for the average probability of missed detection as a function of the sensing threshold and the signal-to-noise ratio (SNR). The results show that the derived equations are accurate and the performance is enhanced with any increase of the eigenvalue or the SNR. However, it is also found that for a given signal and fading parameters, the detector is not affected with any change of the length of observations.