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ClassNotes4 - ECE595 Wireless Communications Lecture 4...

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ECE595 Wireless Communications Lecture 4 Spring 2009 [Review of previous lecture] Small-scale fading s ( t ) = Re n u ( t ) e j 2 πf c t o Send a cosine, e.g. u ( t ) = 1 r ( t ) = Re n X α n ( t ) e n ( t ) e j 2 πf c t o = X α n ( t )cos( φ n ( t ))cos( ω c t ) | {z } In-phase:zero-mean Gaussian - X α n ( t )sin( φ n ( t ))sin( ω c t ) | {z } Quadrature:zero-mean Gaussian ch ( t ) = ch I ( t ) + jch Q ( t ) Complex Gaussian random variable The autocorrelation and cross-correlation of ch I and ch Q are A ch I ( τ ) = A ch Q ( τ ) = 1 2 X α 2 n ( t ) cos(2 π Δ f n τ ) = 1 2 X α 2 n ( t ) J 0 (2 πf D τ ) A I,Q ( τ ) = 1 2 X α 2 n ( t ) sin(2 π Δ f n τ ) = 0 Power Spectrum F{ A I ( τ ) } = S I ( f ) = Ω p 2 πf D r 1 - ± f f D ² 2 , | f | < f D
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Lecture 4 What is R S I ( f ) df ? To get uncorrelated, f D τ = 0 . 4 λ . Amplitude of channel, | ch ( t ) | is Rayleigh distributed. | ch ( t ) | 2 is exponential dis- tributed. Jakes Spectrum
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ClassNotes4 - ECE595 Wireless Communications Lecture 4...

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