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ClassNotes8

# ClassNotes8 - ECE595 Wireless Communications Lecture 8...

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ECE595 Wireless Communications Lecture 8 Spring 2009 [TX diversity] Channel is known at the TX. Total TX power = | α i | 2 P T , M i =1 ρ 2 i = 1. The received signal is r ( t ) = overall received signal = X r i ρ i u ( t ) + noise The SNR is γ Σ = [ r i ρ i ] 2 P T N R

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2 Lecture 8 Find max [ r i ρ i ] 2 such that ρ 2 i = 1 with Lagrange integral h X r i ρ i i 2 - λ X ρ 2 i - 1 ∂/∂ρ j = 2 h X r i ρ i i r j - 2 λρ j = 0 ρ j = r j r i ρ i λ X ρ 2 i = 1 = 1 λ 2 X r 2 i h X r j ρ j i 2 = 1 h X r j ρ j i 2 X r 2 i = λ 2 λ = X r j ρ j q X r 2 i ρ j = r j r i ρ i r i ρ i q r 2 i = r j q r 2 i SNR is similar to RX diversity γ Σ = P T N R h r 2 j i 2 r 2 j = P T N R X r 2 j = X i SNR i [Macroscopic Diversity] Microscopic diversity does not help with shadowing. α i = | ch i | ⇒ P r = | ch i | 2 P T = received power. P r dB is in normal distribution. Receive from two branches outage Probability = prob { P r 1 , dB , P r 2 , dB < P min } = prob { P r 1 , dB < P min } × prob { P r 2 , dB < P min } = " 1 - Q P
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