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Unformatted text preview: ECE 402 Communications Engineering 2009 Quiz 3/Final Exam KEY NAME: STUDENT NUMBER: INSTRUCTIONS • Write your name and student number in the space provided above. • Questions 14 are Quiz 3. Questions 58 are the Final Exam. • This quiz is closedbook and closednotes. • 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 stepbystep 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 Problem 1 (25 pts): An entrepreneur wants to design a broadband wireless data link using the same unlicensed frequency band occupied by baby monitors (4649 MHz). The plan is to transmit data using QAM bandpass modulation with a raisedcosine 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 raisedcosine rolloff that uses the entire band. Solution: (a) The channel bandwidth is W = 49 46 = 3 MHz and the minimum bandwidth needed to transmit a bandpass signal without ISI is 2 × W N = f b . Thus we must have f b = R/k ≤ W or equivalently k ≥ R/W = 4 . 66. It follows that k ≥ 5 is needed, so the smallest constellation is 32QAM . (b) The carrier frequency is the center of the band, f c = 4.75 MHz . For k = 5, we have f b = R/k = 2.8 Msps and W N = f b / 2 = 1 . 4 MHz. Since W = 2(1 + r ) W N we have r = W/ (2 W N ) 1 = 0.071 . 2 Problem 2a (13 pts): When data are transmitted over an additive white Gaussian noise channel using Mary PAM, the biterrorrate is well approximated by P b ≈ Q s (6log 2 M )SNR M 2 1 . For 8PAM with data amplitudes ± A, ± 3 A, ± 5 A, ± 7 A , the signaltonoise ratio is SNR = 21 A 2 T/N . (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 in decibels . (b) (6 pts) When 8PAM is transmitted using the raisedcosine 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 (in decibels ) that any reliable communication system with this spectral efficiency can have? Solution: (a) From the reference sheet Q (4 . 753) = 10 6 . Thus for M = 8 and k = log 2 M = 3, the SNR must satisfy s (6log 2 M )SNR M 2 1 = s 18 × SNR 63 = 4 . 753 or SNR= (4 . 753) 2 × 63 / 18 = 79 . 07. Thus E b /N = SNR /k = 26 . 36 or 14 . 21 dB . (b) For η = 1 . 5 bps/Hz, Shannon’s Formula yields E b /N ≥ (2 η 1) /η = 1 . 22 or 0.860 dB Problem 2b (12 pts): The MATLAB script below plots 30 random 8PAM pulses with a raisedcosine 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 containmissing lines....
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This note was uploaded on 01/28/2012 for the course ECE 402 taught by Professor Townsend during the Fall '08 term at N.C. State.
 Fall '08
 Townsend

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