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quiz1solns09

# quiz1solns09 - Quiz 1 Solutions EE230B Prof Greg Pottie 1 2...

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EE230B Prof. Greg Pottie 1 Quiz 1 Solutions EE230B Prof. Greg Pottie 2 (a) 4-QAM s 4 s 1 s 3 s 2 φ 2 1 In phase bits 2 ( t ) 1 ( t ) Quadrature bits X X Σ 2 ( t ) 1 ( t ) X X dt T dt T Modulator Demodulator May alternatively replace correlators with matched filters.

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EE230B Prof. Greg Pottie 3 (b) 4-QAM Error Probability As discussed in Lecture 3: s 4 s 1 s 3 s 2 φ 2 1 P ( e ) 2 Q E N 0 = 2 Q 2 E b N 0 EE230B Prof. Greg Pottie 4 Error Probability for 16-QAM 2 1 Let the coordinates of the lowest energy signal in the first quadrant be ( a,a ). Then the minimum distance is 2 a , and the average number of neighbors at this distance is (4(4)+8(3)+4(2))/16=3. d min = 2 a = 2 E 10 = 2 4 E b 10 = 8 E b 5 so that P ( e ) = 3 Q 4 E b 5 N 0 E =(4( a ) 2 +4(3 a ) 2 )/4=10a 2 (using the four-fold symmetry and similarity for the two coordinates). Then:
EE230B Prof. Greg Pottie

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quiz1solns09 - Quiz 1 Solutions EE230B Prof Greg Pottie 1 2...

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