Name:GTID:ECE 6390: Satellite Communications and Navigation SystemsTEST 3 (Fall 2004)• 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 50 minutes to complete this examination. When the proctor announces a “last call”for examination papers, he will leave the r oom 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)In a state of emergency, the US government may add selective Answer to degrade thetiming precision of GPS satellites.(b)(True or False) Most of the EPIRB emissions are false alarms in the SARSAT system.(c)What type of earth orbit is a GPS satellite?(d)(True or False) The SARSAT system is capable of finding an EPIRB within 100m.(e)The Answer message is a 50 bits/sec signal modulated onto the GPS waveform.(f)A Answer GPS system uses a secondary ground station radio signal to calibrate outcommon errors within a local area.(g)Small perturbations and uncertainties in the orbital position of a satellite are calledAnswer errors.(h)A measure of how much a CDMA receiver can reject (“spread out”) noise and interferenceis called Answer gain.(i)A GPS Answer is a group of 4 active satellites in a common orbit with 55◦of inclination.(j)No matter how good the time-integration or local corrections are, a stationary D-GPSreceiver can never get rid ofAnswer errors.22. Descriptive Answer Section (20 points)Write a concise answer to each question in the spaces provided beneath each pr oblem state-ment. Note: Correct answers that are extremely verbose will be penalized.(a) SARSAT: The SARSAT system has 4 satellites with nearly polar inclination orbits.Which parts of the earth receive the most frequent scans? Why might this be a po ordesign characteristic for a general search and rescue system? Does GPS have this sameproblem? Why or why not? (10 points)(b) Heavily-Loaded CDMA system: The maximum real data capacity (in bits/sec) of asingle user in a CDMA system with processing gain M , bandwidth B, and an extremelylarge number of equal-powered users N is approximately:Capacity ≈BMN ln 2Derive this expression from first principles, assuming that the CDMA link is interference-limited, rather than noise-limited, and that a conventional spread spectrum receiver isused (no interference cancellation) with a very long m-sequence. The following r elation-ship may be used to simplify your answer:ln(1 + x) ≈ x for x < 1(10 points)33. Satellite Doppler: Doppler shift is at a maximum when a satellite is at the horizon withrespect to an earth-based receiver. The altitude of an LEO satellite is 1200 km and the spec-ified operating frequency is 1700.0 MHz. If the radius of the earth is 6380 km, what is themaximum possible Doppler-shift for this satellite? (30 points)Hints: The total Doppler s hift is the sum of the shifts at the transmitter and receiver; do notforget to consider the rotation of the earth in your calculation. Also assume that the satelliteorbits in the same direction as the rotation of the earth.44. GPS Precision: You are using a super-resolution differential GPS receiver on the highseas. A marine radiobeacon signal perfectly corrects all local GPS errors so that the dominantcontribution to position error is due to received signal quality. At your location, the receivedCNis -15 dB (spread). How many seconds will your GPS receiver have to integrate before theposition accuracy drops below 1m standard deviation error? (30 points)Hint: Recall that the spreading gain for GPS is 43.1 dB and that a typical GPS receiver uses4 satellites for location estimates. Assume no dilution of precision.5Cheat Sheetλf = c c = 3 × 108m/sChannel Capacity = B log21 +CNPR= PT+ GT+ GR− 20 log104πλ− 20 log10(r) − Additional Loss in dBPN= kT B k = 1.3807 × 10−23J K−1Doppler Shifts: fR,D op= −VRλcos θRfT,Dop=VTλcos θTCNdespread= MCNspreadCNspread=CPN+ (N − 1)Cσr= c TcsNsatTbCNdespreadTintTb= 20 ms Tc= 980 nsRotation: Vθ= R˙θ Orbits: V