A new analytical expression is presented for the instantaneous power Probability Density Function （PDF） of receiver signals over composite K-u/gamma fading channels. Moreover, the exact expression of channel capacit...A new analytical expression is presented for the instantaneous power Probability Density Function （PDF） of receiver signals over composite K-u/gamma fading channels. Moreover, the exact expression of channel capacity is derived in the form of an infinite series, while an accurate approximation expression is obtained in closed form. To reveal the implications of the model parameters on capacity, we provide an expression for the case of a high-SNR environment. The relationship of the presented results with previously reported results on generalised-K and K fading channels is also discussed. Finally, numerical and simulation results are presented to prove the correctness of our derived expressions.展开更多
A stochastic version of Lotka-Volterra model subjected to real noises is proposed and investigated. The approximate stationary probability densities for both predator and prey are obtained analytically. The original s...A stochastic version of Lotka-Volterra model subjected to real noises is proposed and investigated. The approximate stationary probability densities for both predator and prey are obtained analytically. The original system is firstly transformed to a pair of It6 stochastic differential equations. The It6 formula is then carried out to obtain the It6 stochastic differential equation for the period orbit function. The orbit function is considered as slowly varying process under reasonable assumptions. By applying the stochastic averaging method to the orbit function in one period, the averaged It6 stochastic differential equation of the motion orbit and the corresponding Fokker-Planck equation are derived. The probability density functions of the two species are thus formulated. Finally, a classical real noise model is given as an example to show the proposed approximate method. The accuracy of the proposed procedure is verified by Monte Carlo simulation.展开更多
基金supported by the National NatNatural Science Foundation of China under Grants No. 61132003,No. 61101237the Open Research Fund of National Mobile Communications Research Laboratory,Southeast University under Grant No. 2012D07
文摘A new analytical expression is presented for the instantaneous power Probability Density Function （PDF） of receiver signals over composite K-u/gamma fading channels. Moreover, the exact expression of channel capacity is derived in the form of an infinite series, while an accurate approximation expression is obtained in closed form. To reveal the implications of the model parameters on capacity, we provide an expression for the case of a high-SNR environment. The relationship of the presented results with previously reported results on generalised-K and K fading channels is also discussed. Finally, numerical and simulation results are presented to prove the correctness of our derived expressions.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11172233,10932009,61171155Natural Science Foundation of Shannxi Province under Grant No.2012JM8010the Doctorate Foundation of Northwestern Polytechnical University under Grant No.CX201215
文摘A stochastic version of Lotka-Volterra model subjected to real noises is proposed and investigated. The approximate stationary probability densities for both predator and prey are obtained analytically. The original system is firstly transformed to a pair of It6 stochastic differential equations. The It6 formula is then carried out to obtain the It6 stochastic differential equation for the period orbit function. The orbit function is considered as slowly varying process under reasonable assumptions. By applying the stochastic averaging method to the orbit function in one period, the averaged It6 stochastic differential equation of the motion orbit and the corresponding Fokker-Planck equation are derived. The probability density functions of the two species are thus formulated. Finally, a classical real noise model is given as an example to show the proposed approximate method. The accuracy of the proposed procedure is verified by Monte Carlo simulation.
