PS10 - University of Illinois Spring 2011 ECE 361 Problem...

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University of Illinois Spring 2011 ECE 361: Problem Set 10 Receivers for Passband Signals Due: Tuesday May 3, 9:30 a.m. 1. [Phase error in BPSK communication] Antipodal signaling over an AWGN channel with bit energy E achieves bit error probability Q ( p 2 E /N 0 ) with an optimum receiver. Now consider antipodal BPSK signaling with signals ± p 2 E /T cos(2 πf c t ) of duration T , and assume that the local oscillator (LO) is not perfectly synchronized to the carrier in the incoming signal. Thus, instead of the LO signal being 2 cos(2 πf c t ), it is 2 cos(2 πf c t + θ ) instead. Everything else is unchanged. Show that the bit error probability is increased from Q ( p 2 E b /N 0 ) to Q (cos θ p 2 E b /N 0 ). 2. [Phase error in QPSK communication] The transmitted symbol in a QPSK communication system is X I + j X Q where X I , X Q ∈ { + E b , - E b } are independent and equally likely to take on both values. Because of a phase error in the receiver, the received symbol is ( X I + j X Q ) exp( ) + ( N I + j N Q ) where θ is small and N I and N Q
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