quiz2solns09 - Quiz 2 Solution Spring 09 EE230B Prof. Greg...

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EE230B Prof. Greg Pottie 1 Quiz 2 Solution Spring 09 EE230B Prof. Greg Pottie 2 a) Error Probability for BPSK For binary PSK, s 1 ( t ) = E φ 1 ( t ), s 2 ( t ) =− E 1 ( t ), where 1 ( t ) = 2/ T cos(2 π f c t ), 0 t T E E Signal space: Error probability: P ( e ) = Q 2 E N 0 dt T 1 ( t ) X Modulator Demodulator X 1 ( t ) +1 -1 +1 -1
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3 a) Coherent binary FSK Signal space φ 1 2 E b E b d min = 2 E b vs .2 E b for PSK P ( e ) = Q E b N 0 1/0 2 ( t ) 1 ( t ) Inverter X X Σ 2 ( t ) 1 ( t ) X X dt T dt T Σ + - EE230B Prof. Greg Pottie 4 b) Effect of Phase error E.g. phase offset has effect of keeping original decision boundaries, but rotated signal positions (blue) Noncoherent FSK is immune to such phase errors since the detector integrates energy. Thus, we are looking for the phase error that causes a 3 dB reduction in error performance for BPSK. For binary PSK, a 45 degree rotation causes a factor of the square root of 2 reduction in the minimum distance, making it the same as for FSK.
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quiz2solns09 - Quiz 2 Solution Spring 09 EE230B Prof. Greg...

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