Energy Detection Based Spectrum Sensing Over $\kappa{-}\mu$ and $\kappa{-}\mu$ Extreme Fading Channels

Abstract

Energy detection (ED) is a simple and popular method of spectrum sensing in cognitive radio systems. It is also widely known that the performance of sensing techniques is largely affected when users experience fading effects. This paper investigates the performance of an energy detector over generalized <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\kappa{-}\mu$</tex></formula> and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\kappa{-} \mu$</tex></formula> extreme fading channels, which have been shown to provide remarkably accurate fading characterization. Novel analytic expressions are firstly derived for the corresponding average probability of detection for the case of single-user detection. These results are subsequently extended to the case of square-law selection (SLS) diversity and for collaborative detection scenarios. As expected, the performance of the detector is highly dependent upon the severity of fading since even small variations of the fading conditions affect significantly the value of the average probability of detection. Furthermore, the performance of the detector improves substantially as the number of branches or collaborating users increase in both severe and moderate fading conditions, whereas it is shown that the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\kappa{-} \mu$</tex></formula> extreme model is capable of accounting for fading variations even at low signal-to-noise values. The offered results are particularly useful in assessing the effect of fading in ED-based cognitive radio communication systems; therefore, they can be used in quantifying the associated tradeoffs between sensing performance and energy efficiency in cognitive radio networks.