Characteristics of $p$-Norm Signal Detection in Gaussian Mixture Noise

Performance of the p-norm detector has been analyzed recently in additive white Gaussian noise and several analytical solutions were obtained. We have developed these solutions for the case of non-Gaussian noise. Expressions for the false alarm probability PF and the detection probability P
_D
were found in series-form for an arbitrary index of power p using an analysis based on the moment generating function. Series-form expressions for the average detection probability P̅
_D
in the non-Gaussian environment for Nakagami-m, k-μ, and η-μ fading channels were derived as well. Recently proposed p-law selection and p-law combining schemes for antenna diversity reception were analyzed. The detection characteristics of a p-norm detector were compared with a traditional energy detector and with an optimal detector. All analytical results were verified with a statistic simulation.