Performance Analysis Of Energy Detection Over Fading Channels

As a non-coherent detection,energy detection does not require any prior information of authorized users.Because of the low complexity,energy detection becomes one of the most promising and effective methods of spectrum sensing.To solve the problem of "hidden terminal" and instability of detection performance caused by channel fading,the proposed research project studying the influence of fading channels on energy detection and analyzing the factors that affect the detection performance,and using diversity techniques to improve the detection performance.The main research contents and results are summarized as follows:First,to solve the computational complexity caused by the performance analysis of energy detection based on probability density function(PDF),a method based on moment generation function(MGF)is proposed.The influence of channel fading on the detection performance is analyzed by using ROC(receiver operating characteristic)curve and AUC(area under the ROC curve)curve.First,the closed-form expressions for both average detection probability and average AUC are derived.Moreover,In order to mitigate the performance deterioration caused by channel fading,the analysis is then extended to the cases with equal gain combining(EGC).With the aid of Padé approximants theory,approximate closed-form expressions of MGF of the received instantaneous signal-to-noise ratio with equal gain combining(EGC)are derived.Further,approximate and closed-form analytic expressions for both average detection probability and the average AUC curve are derived.The proposed mathematical analysis is verified by various numerical results and computer simulations.The theoretical results agree well with Monte Carlo simulation,and the probability of missed detection is reduced as the merged branches increase.Moreover,the performance of detection with MRC is better than EGC.Then,in order to combine spectrum sensing with new technologies such as MIMO,a general and novel fading model,called cascaded fading channels is given.The cumulative distribution and probability density functions of the cascaded fading channels are derived in closed form.Using these formulas,the average AUC over cascaded fading channels is given.The derived expression for the average AUC includes as special cases,cascaded Nakagami-m,cascaded Weibull,cascaded Rayleigh and one-sided Gaussian.Furthermore,a closed-form upper-bound for average AUC with equal gain combining receivers over fading channels is also obtained.Different factors affecting energy detection over cascaded fading channels has been analyzed,which can be readily used in cognitive radio.The simulation results show that: unlike single multipath fading,the number of N in the cascaded fading channels is a key factor affecting the performance of energy detection,and the larger of N,the worse performance of detection.Finally,considering the practical wireless communication channels,the performance of energy detection over the composite fading channels is discussed.Here,the composite fading channel refers to the presence of both the fading and shadowing,where multipath fading superimposed on shadowing.First,we present the closed-form expression of composite(Weibull-lognormal shadowed)fading using the efficient tool proposed by Holtzman,where Weibull distribution represents multipath fading and Lognormal distribution represents shadowed fading.The approximate expression of the probability density function of the Weibull-Lognormal distribution is given by using Holtzman approximation.Using this result,the amount of fading(AF),the approximate average detection probability and approximate average AUC are analyzed and expressed in closed form.Numerical results show that: Both shadowing and multipath fading affect the detection performance,the smaller the multipath fading parameter c,the severer the fading and the worse the detection performance.The larger the shading parameter ?,the severer the fading,the lower the detection probability.Furthermore,the parameter u has little effect on detection performance.