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# Q3-F - ECE 402 Communications Engineering Quiz 3/Final Exam...

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ECE 402 Communications Engineering 2009 Quiz 3/Final Exam NAME: STUDENT NUMBER: INSTRUCTIONS Write your name and student number in the space provided above. Questions 1-4 are Quiz 3. Questions 5-8 are the Final Exam. This quiz is closed-book and closed-notes. Three handwritten 8.5” × 11” reference sheets may be used. Conventional calculators may be used but no computers, PDAs or other wireless devices. You may not share calculators. Give step-by-step solutions that include all details. Assume the graders know only the basics. Box your final answer . GRADES (200 points possible) 1 5 2 6 3 7 4 8 Q3 Total F Total 1

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Problem 1 (25 pts): An entrepreneur wants to design a broadband wireless data link using the same unlicensed frequency band occupied by baby monitors (46-49 MHz). The plan is to transmit data using QAM bandpass modulation with a raised-cosine rolloff pulse waveform. (a) If a data rate of 14 Mbps is desired, what is the smallest QAM constellation that could be used to transmit in this band with no intersymbol interference? (b) Using the constellation from (a) , find a carrier frequency, symbol rate and raised-cosine rolloff that uses the entire band. 2
Problem 2a (13 pts): When data are transmitted over an additive white Gaussian noise channel using M -ary PAM, the bit-error-rate is well approximated by P b Q s (6 log 2 M )SNR M 2 - 1 . For 8PAM with data amplitudes ± A, ± 3 A, ± 5 A, ± 7 A , the signal-to-noise ratio is SNR = 21 A 2 T/N 0 . (a) (7 pts) If we want to transmit data with a BER of P b = 10 - 6 using 8PAM , find the required E b /N 0 in decibels . (b) (6 pts) When 8PAM is transmitted using the raised-cosine rolloff pulse with r = 1 it has a spectral efficiency of 1.5 bps/Hz. According to Shannon’s Formula, what is the smallest E b /N 0 (in decibels ) that any reliable communication system with this spectral efficiency can have? Problem 2b (12 pts): The MATLAB script below plots 30 random 8PAM pulses with a raised-cosine rolloff pulse with r = 0 . 75, a symbol rate of 3 symbol/s and a sampling rate of 6 samples/s. Fill in the missing lines. Your answers should contain no unknowns .

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