Name:GTID:ECE 6390: Satellite Communications and Navigation SystemsTEST 3 (Fall 2008)• Please read all instructions before continuing with the test.• This is a closed notes, closed book, closed friend, open mind test. On your desk you shouldonly have writing instruments and a calculator.• Show all work. (It helps me to give partial credit.) Work all problems in the spaces below theproblem statement. If you need more room, use the back of the page. DO NOT use or attachextra sheets of paper for work.• Work intelligently – read through the exam and do the easiest problems first. Save the hardones for last.• All necessary mathematical formulas are included either in the problem statements or the lastpage of this test.• You have 75 minutes to complete this examination. When the proctor announces a “last call”for examination papers, he will leave the room in 5 minutes. The fact that the proctor doesnot have your examination in hand will not stop him.• I will not grade your examination if you fail to 1) put your name and GTID number in theupper left-hand blanks on this page or 2) sign the blank below acknowledging the terms of thistest and the honor code policy.• Have a nice day!Pledge Signature:I acknowledge the above terms for taking this examination. I have neither given nor received unau-thorized help on this test. I have followed the Georgia Tech honor code in preparing and submittingthe test.11. Short Answer Section (20 points)(a)The idea of a rigorously-defined communications channel capacity was invented by Answer .(b)True or False: MPEG1, MPEG2, and MPEG4 are the moving pictures expert guild’sprotocol specifications for digital video modems.(c)Unlike Lempel-Ziv style compression protocols, the method for storing images in JPEGformat is Answer compression.(d)Sets of optical spectra that result in the same perceived color in the human eye are calledAnswer .(e) (1) (2)The colors cyan, magenta, and yellow are Answer 1 primaries while the colors red, green,and blue are Answer 2 primaries.(f)True or False: the human eye contains a higher density of rods (intensity-sensing cells)than cones (color-sensing cells).(g)A Answer may be used to change the first-order statistics of an analog signal beforesampling so that it is better suited for uniform quantization.(h) (1) (2)Adding forward error correction to a satellite link allows the spacecraft to travel fartherfrom earth, and/or operate with less transmit Answer 1 , and/or reduce the Answer 2in the received signal.22. Analog Video: Terrestrial analog video relies on VSB analog modulation, while satelliteanalog video uses FM. Why? (10 points)3. Digital Video: Terrestrial digital video relies on schemes such as 16-QAM and 8-VSB, whilesatellite digital video most commonly uses BPSK or QPSK. Why? (10 points)4. Pulse Shaping: What is the maximum symbol rate for a QPSK communication link thatuses an ideal raised-cosine pulse with roll-off factor κ = 0.5 that must fit within a 30 MHz RFchannel? (10 points)35. Digital Transmission: You are digitizing a 5-MHz baseband analog video signal. Yourquantizer has 12-bits per sample, you use Lempel-Ziv compression to provide a 75% reductionon the bit stream (compressed rate is 1/4 of uncompressed rate), and you plan on using arate 1/2-Turbo code for forward error correction coding. If your final transmitted symbol rateis 6 Mbaud, what is the minimum constellation size required by a system using M-QAM totransmit this signal. (10 points)6. Quantization: The output of an MPEG codec is a raw 120 Mbit/sec bit stream thatrepresents uncoded, uniformly-quantized RGB pixel levels. If the digital resolution is 500×400pixels at 20 picture frames/sec, what is the quantization SNR of each pixel? (10 points)7. Forward Error Correction: Below is a convolutional enco der with sample binary input.Write the binary output of this coder. Assume that the registers are all initialized with 0before the data is sent. For this problem, read and write binary sequences with the rightmostbit being the earliest bit. What is the rate and constraint length of this encoder? (10 points)SShiftRegisterShiftRegisterInput:11010111ShiftRegisterShiftRegisterSOutput48. Constellations: Based on the following in-phase and quadrature signals for the binarydata sequence below, sketch the signal constellation in the space below, labeling the bitscorresponding to each constellation point. (10 points)90PhaseShifteroModulatedRFSignalOscillatorcos(2 )pf tCS++ttVoltageVoltageIn-PhaseQuadratureBinaryData:000111001110010101011100t9. BER: If CINR is 10 dB for the signal transmission in the previous problem, make a roughestimate of the BER of the demodulated, uncoded signal by approximating it as a generic formof M-QAM. Would you expect this BER approximation to be pessimistic (BER higher thanactuality) or optimistic (BER lower than actuality). What is the drawback of using the abovesignal constellation? (10 points)5Cheat SheetChannel Capacity = B log2µ1 +CN¶BER for M-QAM ≈ 4µ1 −1√M¶Q³p3 CINR/(M − 1)´N-bit Uniform Quantization: SNR = 6NPN= kT B k = 1.3807 × 10−23J K−1Q(x) ≈1x√2πexpµ−x22¶for x > 3sn(x) =sin(πx)πxxQ(x )xQ(x )xQ(x )xQ(x )xQ(x )0.00 0.5000 1.00 0.1587 2.00 0.02275 3.00 0.001350 4.00 0.000031670.05 0.4801 1.05 0.1469 2.05 0.02018 3.05 0.001144 4.05 0.000025610.10 0.4602 1.10 0.1357 2.10 0.01786 3.10 0.0009676 4.10 0.000020660.15 0.4404 1.15 0.1251 2.15 0.01578 3.15 0.0008164 4.15 0.000016620.20 0.4207 1.20 0.1151 2.20 0.01390 3.20 0.0006871 4.20 0.000013350.25 0.4013 1.25 0.1056 2.25 0.01222 3.25 0.0005770 4.25 0.000010690.30 0.3821 1.30 0.09680 2.30 0.01072 3.30 0.0004834 4.30 0.0000085400.35 0.3632 1.35 0.08851 2.35 0.009387 3.35 0.0004041 4.35 0.0000068070.40 0.3446 1.40 0.08076 2.40 0.008198 3.40 0.0003369 4.40 0.0000054130.45 0.3264 1.45 0.07353 2.45 0.007143 3.45 0.0002803 4.45 0.0000042940.50 0.3085 1.50 0.06681 2.50 0.006210 3.50 0.0002326 4.50 0.0000033980.55 0.2912 1.55 0.06057 2.55 0.005386 3.55 0.0001926 4.55 0.0000026820.60 0.2743 1.60 0.05480 2.60 0.004661 3.60 0.0001591 4.60 0.0000021120.65 0.2578 1.65 0.04947 2.65 0.004025 3.65 0.0001311 4.65 0.0000016600.70 0.2420 1.70 0.04457 2.70 0.003467 3.70 0.0001078 4.70 0.0000013010.75 0.2266 1.75 0.04006 2.75 0.002980 3.75 0.00008842 4.75 0.0000010170.80 0.2119 1.80 0.03593 2.80 0.002555 3.80 0.00007235 4.80 0.00000079330.85 0.1977 1.85 0.03216 2.85 0.002186 3.85 0.00005906 4.85 0.00000061730.90 0.1841 1.90 0.02872