tailieunhanh - Stochastic Controledited Part 9

Tham khảo tài liệu 'stochastic controledited part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 312 Stochastic Control Equation 23 has three arbitrary parameters O n KJ which can be adjusted such that the approximate curve coincides with the actual curve at different points. The reason for presenting 4th order approximation of the DPSD is that we can compute explicit expressions for the constants K O kJ as functions of specific points on the data-graphs of the DPSD. In fact if the approximate density S f coincides with the exact density S f at f 0 and f fmax then the arbitrary parameters K O kJ are computed explicitly as c 1Í1 - 1 - J 0 Ì O 2 fmax K 2JS 0 V 1 S fmax Ị n yf1 2C 24 Figure 6 shows S f and its approximation S f via a 4th order even function. In the next section the approximated DPSD is used to develop stochastic STF channel models. Stochastic STF Channel Models A stochastic realization is used here to obtain a state space representation for the inphase and quadrature components 32 . The SDE which corresponds to H s in 23 is d2x t 2ộữndx i O 2x t dt KdW t x 0 x 0 aregiven 25 where dW t is a white-noise process. Equation 25 can be rewritten in terms of inphase and quadrature components as d2Xj t 2 ữndXj t O Xj t dt KdWj t Xj 0 Xj 0 aregiven d2xQ t 2ộsndXQ t O2XQ t dt KdWQ t XQ 0 XQ 0 aregiven 26 where dWj t Jt 0 and dWQ t t 0 are two independent and identically distributed . white Gaussian noises. Wireless fading channel models from classical to stochastic differential equations 313 Fig. 6. DPSD SD f and its approximation S m H jai 2 via a 4th order transfer function for mobile speed of a 5 km hr and b 120 km hr. Several stochastic realizations 32 can be used to obtain a state space representation for the inphase and quadrature components of STF channel models. For example the stochastic observable canonical form OCF realization 33 can be used to realize 26 for the inphase and quadrature components for the jth path as t 1 0 1 - íXi t 1 dt 0 - W t B 1 d - t J _- - 2 _ xỉ t J K J Ixx J t X1 0- Kj t Xt- t fJ t 1 0 1 IX t dt 0 dw Q t 0 -

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