SNR wall for generalized energy detector in the presence of noise uncertainty and fading

Abstract

The performance of energy detection (ED) degrades under low SNR, noise uncertainty (NU) and fading. The generalized energy detector (GED) is obtained by changing the squaring operation in ED by an arbitrary positive number p. In this paper, we investigate the signal to noise ratio (SNR) wall for GED under diversity considering NU as well as fading by considering p-Law combining (pLC) and p−law selection (pLS) diversity. First, the SNR walls considering AWGN channel are derived. It is shown that for pLC diversity, increasing p results in lower SNR wall. It is also shown that under no diversity and pLS diversity, the SNR wall is independent of p. The analysis is then extended to the channel with Nakagami fading where it is shown that the SNR wall increases significantly. As a byproduct of this work, we also study the effect of NU and fading on the detection performance and show that above certain value, the effect of NU is more severe when compared to the fading. The effect of p on the performance is analyzed and it is shown that the performance is the best for values of p close to 2. The performance of pLC and pLS is also compared.