A signal transmission system for telephone lines over microwave links consists of of FDM-SSB and FM signaling. Each of the bandlimited signals m (t) has bandwidth of W=6 KHz and modulates carrier si

UFMF S7-15 -3 Page 1 of 8 Academic Year: 2020 /2 1 OCT /SIT Module Leader: Taleb Moazzeni Module Code: UFMFS7 -15 -3 Module Title : Communications Examination Date: 03 January , 2021 Examination Start Time: 10 AM Duration: (24 Hours Submission) Please complete your Student Number below: Standard materials required for this examination : Examination Answer Booklet Yes Multiple Choice Answer Sheet No Graph Paper Type of paper e.g. G3, G14 N/A Number of sheets per student 0 Additional materials required for this examination : Details of additional material supplied by GCET : Exam formula Sheet To be collected with Answer Booklet Yes Details of approved material supplied by Student : NONE To be collected with Answer Booklet (please delete as appropriate) University approved Calculator Yes Candidates permitted to keep Examination Question Paper No UFMF S7-15 -3 Page 2 of 8 Instructions to Students: Students must answer ALL questions. This is ‘Take Home Exam Paper’ , you have to submit it within 24 hours using UWE on line platform (Blackboard). The duration of the exam on the front page indicates the time estimated to complete the exam. You have 24 hours to complete and submit the paper. The paper must be submitted to the UFMF S7-15 -3 Blackboard site by the deadline You are reminded that to submit work that is not your own as your own, to allow others to copy your work or to collude with others in the completion of this individual assessment may constitute an assessme nt offence and will be investigate under the University's assessment offence procedure. Please refer to instructions on electronic submission of handwritten material that have been circulated to students, a copy of which is available from the UFMF S7-15 -3 Blackboard site in the Assignment content area. Note: 1. Total Marks are 100 2. Question paper has 4 pages. 3. Candidates must answer TEN questions UFMF S7-15 -3 Page 3 of 8 SECTION -I Question 1 [10 Marks] An AM modulation system generates four signals and combines them through a multiplexer as, Determine, a) i: The modulating signals [3 Marks] ii: Carrier signals [2 Marks] Hint: Split t he summation into four terms, first. b) i) Modulation index [2 Marks] ii) The ratio of the of the power in the sidebands to the power in the carrier [3 Marks] Question 2 [10 Marks] In an Angle modulation system, the signal shown in Figure Q2 modulates a carrier signal. Figure Q2 a) What is the relationship between the frequency deviation constant ( Kf) and phase deviation constant ( Kp)? [5 Marks] b) If , find the maximum instantaneous frequency for each modulation case. [5 Marks]  ) 1100 cos( 10 ) 1000 cos( 40 ) 900 cos( 10 )( 4 1 t n t n t n n t S n       4 2   f P K K UFMF S7-15 -3 Page 4 of 8 Question 3 [10 Marks] A normalized signal with 20 KHz bandwidth and 2 W power is transmitted via a channel with bandwidth of 100 KHz and loss of 50 dB by an FM modulator. Assume that the noise in the channel is additive and white with a power -spectral density of W/Hz. To get an SNR of 30 dB at the receiv er output, a) What is corresponding modulation index? [7 Marks] b) What is the minimum required transmitter power? [3 Marks] Question 4 [10 Marks] A signal transmission system for telephone lines over microwave links consists of of FDM -SSB and FM signaling. Eac h of the bandlimited signals mi(t) has bandwidth of W=6 KHz and modulates carrier signals Ci (t) = 10 cos 2 π f cit using USSB method, where fci = (i − 1) W, 1 ≤ i ≤ K. The combined FM modulated signal m(t) with a modulation index of β.is then transmitted on a carrier signal with amplitude of 20 and frequency fc (Figure Q4). Figure Q4. a) [5 Marks] Find the noise power entering the demodulators at the receiver side. Assume that the channel is additive and white with a power -spectral density of W/Hz . b) [5 Marks] Find an expression for the ratio of the input noise power of demodulator i with carrier frequency of fi to the input noise power of demodulator j with carrier frequency of f j, 1 ≤ i, j ≤ K. Also, Find the value of SNR at the output of the 4 -th demodulator, if the power of transmitted power for each USSB signal is 2 W. Question 5 [10 Marks] An AM signal is generated by modulating the carrier fc = 12 00 kHz by the signal m(t)= 2sin 600 πt + 4 cos 400 πt The AM signal 12 10 2  oN 12 10 2  oN UFMF S7-15 -3 Page 5 of 8 u(t)= 40[1 + m(t)] cos 2 π f ct is fed to a 50 Ohm load. a) Determine and sketch the spectrum of the AM signal. [4 Marks] b) Determine the average power in the carrier and in the sidebands. [6 Marks] SECTION -II Question 6 [10 Marks] It is desired to transmit a massage signal with bandwidth of 6 KHz and following probability density function (Figure Q6) us ing a pulse code modulation system. Figure Q6 a) [4 Marks] Find the signal to quantized noise ratio ( SQNR ), if we use sampling at the Nyquist rate with a uniform quantizer level of 16, b) [6 Marks] If the channel has 60 K Hz bandwidth find the highest achievable SQNR for the following case , i) Without guard band ii) With guard bound of 1 KHz Question 7 [10 Marks] A digital communication system transmits quadrature amplitude modulation ( QAM ) signal over a voice -band telephone channel at a rate 1200 symbols/second. If the signal is purported by additive white Gaussian noise, a) [6 Marks] At what bit energy to noise power ratio, an error probability of 10 −5 is achieved at the following bit rate? i) 2400 bps ii) 4800 bps Hint: Use Q(4.2649 )= 10 −5 Q: Q-Function b) [4 Marks] Compare and discuss the results obtained in part (a) in terms of bit energy to noise power ratio . UFMF S7-15 -3 Page 6 of 8 Question 8 [10 Marks] Consider the 16 -arry quadrature amplitude modulation ( QAM ) Modula tion. a) [5 Marks] Sketch 2 types of signal constellation b) [5 Marks] Find the ratio of for the same error probability. SNR: Signal to Noise Ratio, PSK: Phase Shit Keying Question 9 [10 Marks] Consider the two 8 -point QAM signal constellation shown in Figure Q 9. In Figure (a), t he distance of each point from the origin is A In Figure (b) the distance between the nearest points is A. Figure Q9 a) Determine the average transmitted power for each constellation assuming that the signal points are equally probable. [8 Marks] b) Which constellation is more power efficient? [2 Marks] Question 10 [10 Marks] Find the bandwidth efficiency (passband and baseband) for 8 -PAM , 128 -QAM and 256 -Orthogonal modulation for: a) Nyquist pulse shaping function [6 Marks] b) Rectangular pulse shaping function [2 Marks] c) Raised -Cosi ne pulse shaping function with roll -off factor of 0.75 . [2 Marks] END OF QUESTION PAPER     QAM PS K SNR SNR   16 16 UFMF S7-15 -3 Page 7 of 8 Formula Sheet - The phase of PM signal: The phase of FM signal: Carson’s rule For FM The power spectral density of the noise at the output of the FM demodulator: AM Signal: In uniform PCM, it is assumed that the range of the input samples is and the number of quantization levels N is a power of 2. The length of each quantization region is given by The signal to quantization noise ratio (SQNR) ratio is obtained by, The probability of error for BPSK signal The probability of error for an M -ary PSK signal is )(t m KP       t f t f d m K d m K t 0 ) ( 2 ) ( 2 )(        W Bc )1 (2    nM o P N S )1 ( 60 2           b M o N S P N S n              2 3 )1 ( 20 0 ,           W N P N S R thb 2 2 , ) ( f A N f S c o on  W N P P P N S P P N S R M M b M M O n n n n 0 2 2 2 2 1 1                 ] , [ max max x x 1max max 2 2 2     v x N x 2max 2 4 3 SQNR x Xv          0 2 )( N E Q e P b        M N E Q P o b M  sin 2 2 UFMF S7-15 -3 Page 8 of 8 The probability of error for an M -ary QAM system with M = 2 k: The probability of error for an M -ary QAM signal is upper bounded by: 2 )1 ( 3 1 1 1 1                        o b M N M kE Q M P         o av M N M E Q P )1 ( 3 4