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# lecture4 - Lecture 4 EE 359 Wireless Communications Autumn...

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Lecture 4 - EE 359: Wireless Communications - Autumn 2011 Statistical Fading Models. Narrowband Models Lecture Outline Model Parameters from Empirical Data Random Multipath Model. Time Varying Channel Impulse Response. Narrowband Fading Approximation. In-Phase and Quad Signal Components under LLN. Mean, Autocorrelation, and Cross Correlation in Narrowband Fading. 1. Model Parameters from Empirical Data: Constant K obtained from measurement at distance d 0 . Power falloff exponent γ obtained by minimizing the MSE of the predicted model versus the data. The resulting path loss model will include average attenuation, so μ ψ dB = 0. The shadowing variance σ 2 ψ dB obtained by determining MSE of the data versus the empirical path loss model with the optimizing γ . 2. Statistical Multipath Model: At each time instant there are a random number N ( t ) of multipath signal components. Each component has a random amplitude α n , phase θ n , Doppler shift f D n = v λ cos θ n , and path delay τ n = ( d n - d ) /c . Thus, received signal is r ( t ) = Rfractur N ( t ) summationdisplay n =0 α n ( t ) e - n ( t ) u ( t - τ n ( t )) e j 2 πf c t .

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