Lowering the SNR Wall for Energy Detection Using Cross-Correlation

Abstract

Spectrum sensing is a key enabler of cognitive radio but generally suffers from what is called a signal-to-noise ratio (SNR) wall, i.e., a minimum SNR below which it is impossible to reliably detect a signal. For energy detection, which has the advantage of not requiring knowledge of the signal, the SNR wall is caused by uncertainty in the noise level. Cross-correlation has been suggested as a possible means to obtain higher sensitivity but has received little attention in the context of noise uncertainty. The idea of cross-correlation is to have two receive paths, where each path independently processes the signal before they are combined, such that the noise added to the input signal at the individual paths is largely uncorrelated. In this paper, we mathematically quantify the SNR wall for cross-correlation, showing that it linearly scales with the amount of noise correlation. This lower noise correlation results in higher sensitivity, which is significantly better than that for autocorrelation. Equations that can be used to estimate the benefit over autocorrelation and the measurement time for a required probability of detection and false alarm are derived.