132A_1_2001final sol

# 132A_1_2001final sol - Final Exam 2001 1. (15 points) Basic...

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Final Exam 2001

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1. (15 points) Basic communications questions. a) (5 points) In 64-QAM, how many bits per symbol are transmitted? l bits/Symbo 6 64 log 2 =
b) (10 points) Consider the matched filter setup shown below . The waveform of g(t) is as follows = otherwise , 0 2 / , 1 2 / 0 , 2 ) ( T t T T t t g Find and sketch h(t), the impulse response of a matched filter for this g(t). ( 29 = - = otherwise , 0 2 / , 2 2 / 0 , 1 ) ( T t T T t t T g t h = otherwise , 0 2 / , 1 2 / 0 , 2 ) ( T t T T t t g

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2. (10 points) A BPSK signal is transmitted over an AWGN channel. The two possible transmitted signals are: At the receiver, suppose that there is a phase error of ϕ radians, so that the receiver's version of the cosine basis function differs by ϕ radians from the transmitter’s version of the cosine basis function. Provide a mathematical expression for the probability of bit (not symbol) error. ( 29 t f T E t x c b b p 2 cos 2 ) ( ± = ) ( t x ( 29 j p + t f T c b 2 cos 2 b T 0 ) ( t y The receiver output is given by: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 [ ] j j p j j p p j p cos 2 cos cos 1 2 cos 2 2 cos 2 2 cos 2 0 0 0 b T c b b c b T c b b c b T E dt t f T E dt t f T t f T E dt t f T t x t y b b b ± = + + ± = + ± = + = j cos b
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## This note was uploaded on 07/02/2010 for the course EE EE 132A taught by Professor Villasenor during the Spring '09 term at UCLA.

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132A_1_2001final sol - Final Exam 2001 1. (15 points) Basic...

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