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finals08soln

# finals08soln - EE 230B Final Examination Spring 2008 UCLA...

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EE 230B Final Examination, Spring 2008 NAME:_______________________ UCLA Electrical Engineering Department Prof. G. Pottie Instructions: Attempt all five questions; they are of equal weight but not necessarily of equal difficulty. A sheet of useful formulae and other facts is attached. 1. Phase Error in QAM Suppose a persistent phase error of θ occurs. a) By what factor is the effective minimum distance reduced for 4-QAM compared to perfect synchronism? Write an expression for P ( e | θ ). Solution: d 1 d r θ d 2 + d 2 = r 2 ; d = r / 2 = r sin( π /4) sin( π /4 θ ) = d 1 / r ; d 1 = r sin( π /4 θ ) P ( e | θ ) = 2 Q 2 r sin( π /4 θ ) 2 N 0 b) Repeat for the worst-case signal point in 16-QAM. Soln: Here, things are much the same except now there is a new boundary located at 2 r /3.

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