Effects of Noise Power Estimation on Energy Detection for Cognitive Radio Applications

An uncertain knowledge of the noise power level can severely limit the energy detector (ED) spectrum sensing capability. In some situations this uncertainty can cause signal-to-noise ratio (SNR) penalties or even the rise of the SNR wall phenomenon. In this paper we analyze the performance of the ED with estimated noise power (ENP), addressing the threshold design and giving the conditions for the existence of the SNR wall. We derive analytical expressions for the design curves (SNR vs. observation time for a target performance) for the ENP-ED. Then we apply our analysis to cognitive radio (CR) systems where energy detection is used for fast sensing. For example it is shown that the SNR penalty with respect to ideal ED is of 5 log
₁₀
(1+λ/λ) dB, when the time dedicated to noise power estimation is a multiple λ of the ED observation interval.