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lab4_wireless

# lab4_wireless - Spring 2010 UCSB ECE 146B Laboratory...

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UCSB Spring 2010 ECE146B: Laboratory Assignment 4 Lab Objectives: Introduction to modeling and performance evaluation for signaling on wireless fading channels. Let us consider the following simple model of a wireless channel (obtained after filtering and sampling at the symbol rate, and assuming that there is no ISI). If { b [ n ] } is the transmitted symbol sequence, then the complex-valued received sequence is given by y [ n ] = h [ n ] b [ n ] + w [ n ] (1) where { w [ n ] = w c [ n ] + jw s [ n ] } is an iid complex Gaussian noise sequence with w c [ n ], w s [ n ] i.i.d. N (0 , σ 2 = N 0 2 ) random variables. We say that w [ n ] has variance σ 2 per dimension. The channel sequence { h [ n ] } is a time-varying sequence of complex gains. Rayleigh fading: The channel gain sequence { h [ n ] = h c [ n ] + jh s [ n ] } , where { h c [ n ] } and { h s [ n ] } are zero mean, independent and identically distributed colored Gaussian random processes. The reason this is called Rayleigh fading is that | h [ n ] | = radicalbig h 2 c [ n ] + h 2 s [ n ] is a Rayleigh random variable. Remark: The Gaussianity arises because the overall channel gain results from a superposition of gains from multiple reflections off scatterers. Simulation of Rayleigh fading: We will use a simple first-order autoregressive (AR(1)) model, wherein the colored channel gain sequence { h [ n ] } is obtained by passing white Gaussian noise through a first-order recursive filter, as follows: h c [ n ] = ρh c [ n - 1] + u [ n ] h s [ n ] = ρh s [ n - 1] + v [ n ] (2) where { u [ n ] } and { v [ n ] } are independent real-valued white Gaussian sequences, with i.i.d. N (0 , β 2 ) elements. The parameter ρ (0 < ρ < 1) determines how rapidly the channel varies. Setting up fading simulator (a) Set up the AR(1) Rayleigh fading model in matlab, with ρ and β 2 as programmable parameters. (b) Calculate E [ | h [ n ] | 2 ] = 2 E bracketleftbig h 2 c [ n ] bracketrightbig = 2 v 2 analytically as a function of ρ and β 2 . Use simulation to verify your results, setting ρ = . 99 and β = . 01. You may choose to initialize h c [0] and h s [0] as iid N (0 , v 2 ) in your simulation. Use at least 10,000 samples.

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lab4_wireless - Spring 2010 UCSB ECE 146B Laboratory...

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