A QPSK modulator produces a phase-imbalanced signal of the form (a) Show that the integrator outputs of

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A QPSK modulator produces a phase-imbalanced signal of the form
x.(t) = Ad, (t) cos ( 27f t- -Ad, (1) sin ( 2af.1 - 5) 2

(a) Show that the integrator outputs of Figure 10.2, instead of (10.5) and (10.7), are now given by

= Ar, (zcos sin - AT, V; = AT, ± sin ± cos 2

where the ± signs depend on whether the data bits d1 (t) and d2 (t) are + 1 or -1.


Figure 10.2


(b) Show that the probability of error per quadrature channel is 

For no phase imbalance, the correlator outputs were V1, V2 = ± 1/2 ATs = ± ATb giving Eb = V2/ Tb = V22 / Tb and 

With phase imbalance, the best- and worst-case values for E'are 

and

These occur with equal probability.

(c) Plot PE given by (10.16) and the above result for P'E,quad chan on the same plot for β = 0, 2.5, 5, 7.5, and 10 degrees. Estimate and plot the degradation in Eb / N0, expressed in dB, due to phase imbalance at a symbol error probability of 10-4 and 10-6 from these curves.

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Related Book For  book-img-for-question

Principles of Communications Systems, Modulation and Noise

ISBN: 978-8126556793

7th edition

Authors: Rodger E. Ziemer, William H. Tranter

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