An Accurate Model for Periodogram-Based Energy Detection Over Nakagami Fading

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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 time-domain 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 eigen-value 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.