Test of independence for cooperative spectrum sensing with uncalibrated receivers

In cooperative spectrum sensing networks the sensing nodes are often assumed to have the same noise power level. However, the different secondary users (SUs) could experience different temperatures, have receiver chains with different characteristics or even with a completely different architecture. Therefore, it is unlikely that they experience exactly the same noise power. In this paper we study the problem of cooperative spectrum sensing in cognitive radio (CR) networks, focusing on the case where the receivers experience different levels of noise power (uncalibrated receivers). We propose the independence test and compare it with the popular sphericity test. The independence test is in fact the generalized likelihood ratio (GLR) when the SUs are uncalibrated. We address in particular the threshold setting problem under a Neyman-Pearson framework. In order to reduce the complexity of the analysis, we approximate the test metrics as beta distributed random variables (r.v.s), by using a moment-matching approach. We provide simple and analytically tractable expressions for the computation of the probability of false alarm and for setting the decision threshold. Numerical simulations show that these approximated forms match very well the empirical distributions, allowing a very precise estimation of the probability of false alarm. In cooperative spectrum sensing with uncalibrated receivers the independence test is shown to be robust to strong imbalances of the noise power level.