Final - University of Illinois Spring 2011 ECE 361: Final...

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Unformatted text preview: University of Illinois Spring 2011 ECE 361: Final Examination Friday May 6, 2011, 1:30 p.m. 4:30 p.m. This is a closed-book closed-notes examination except that three 8.5 11 sheets of notes are permitted: both sides may be used. 1. [45 points] Consider a binary digital communication system operating over an AWGN chan- nel with two-sided power spectral density N / 2 per Hz. Four possible transmitted signal sets { s ( t ) ,s 1 ( t ) } of duration T are shown below where all eight signals have value for t < and t > T . The constants A , B , C , and D are to be chosen by you to satisfy various constraints as specified in parts (a)-(c). The question to be answered in each case is: Subject to the stated constraint, which signal set has the smallest error probability (when the appropriate optimum receiver is used) and what is this smallest error probability? E and E 1 denote the signal energies, and P = E /T and P 1 = E 1 /T denote the average signal powers in the two signals. Set I s ( t ) = A, s 1 ( t ) =- 3 A ( t/T ) , Set II s ( t ) = 2 B cos( t/T ) , s 1 ( t ) = 2 B sin( t/T ) Set III s ( t ) = 2 C cos( t/T ) , s 1 ( t ) =- 2 C cos( t/T ) Set IV s ( t ) = D, s 1 ( t ) =- D ( 2)- 1 and all signals have value 0 for t < 0 and t > T ....
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Final - University of Illinois Spring 2011 ECE 361: Final...

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