Performance Analysis of Spectrum Sensing Schemes Based on Fractional Lower Order Moments for Cognitive Radios in Alpha- Stable Noise Environments

Natural and manmade noise signals tend to exhibit impulsive behaviors. Therefore modeling those signals as α-stable processes is better suited towards the development of a practical spectrum sensing scheme. However, the performances of detectors operating in an α-stable noise environment are difficult to evaluate. This is because an α-stable random variable can usually only be modeled by the characteristic function since closed-form expressions are usually not available except for the special values of the characteristic exponent that correspond to the Cauchy and Gaussian noise distributions. In this thesis, we derive a general closed-form expression for the probability density function (PDF) of symmetric alpha stable processes having rational characteristic exponent (0<α≤2). Consequently, we obtain analytical expressions for the PDF and corresponding complementary cumulative distribution function (CCDF) of the proposed fractional lower order moment (FLOM) detector. Utilizing false alarm and detection probabilities, the performance analysis of the proposed spectrum sensing scheme is conducted with the assumption that the cognitive radio (CR) users are operating in non-fading channels. We validate the analytical results with Monte Carlo simulations. The effect of the distribution parameters on the receiver operating characteristic (ROC) curves is verified.