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Satellite Tracking and Communication Lecture
- 3. • Satellite communicaNon runs in Sep-Oct – Lectures • Exercises in preparaNon for wriSen examinaNon – PracNcal • Assignment satellite communicaNon • Satellite tracking runs in Nov-Jan – Lectures • Exercises in preparaNon for wriSen examinaNon – PracNcal • Assignment satellite tracking • The total work-load is 4 ECTS 06/10/17 TU Del3 class ae3535-16 3
- 5. • There are assignments – Group report of Satellite CommunicaNon – Group report of Satellite Tracking • There is a wriSen examinaNon • Final grade is determined by the weighted average assignments and examinaNon • A rounded grade goes into OSIRIS 06/10/17 TU Del3 class ae3535-16 5
- 6. • Exercises – They are introduced during the contact hours. – Exercises are typical for exam problems • Assignments – Groups will be formed before in week 1.6 – Group assignment will be issued in week 1.6 – Due dates are menNoned in the assignment text – Assignment reports do yield credits • Maneesh Verma deals with all assignments and exercises for satellite communicaNons, for satellite tracking Bart Root is your guide. 06/10/17 TU Del3 class ae3535-16 6
- 7. • Preference for MATLAB during exercises/assignments • Structure of a report • Explain the problem and the soluNon • Include MATLAB results • Explain task distribuNon in your group (if applicable) • Explain how you validated your results? • HandwriSen reports are fine as long as we can read them • Copied and pasNng from lecture notes, the internet and other sources is not allowed • Convert your report to an unsigned PDF file • Submit your reports to brightspace, there are individual and groups folders for assignment or exercise, consult your TA. 06/10/17 TU Del3 class ae3535-16 7
- 8. 06/10/17 TU Del3 class ae3535-16 8 Week Topics 1.1 IntroducNon to radio technology in spaceflight, Nme and frequency domain, Fourier transformaNon, FFT 1.2 ProperNes of the Fourier transform, schemaNcs transmiSer and receiver, superheterodyne receiver, intermodulaNon, so3ware defined receiver (SDR) 1.3 LC networks, admiSance of inductors and capacitors, RC constant, LC circuit, π filters, LCR circuits, Q factor, transmission lines, antenna’s 1.4 Impedance matching, modulaNon, propagaNon, signal and noise, link margin 1.5 Digital modulaNon, radio astronomy, GNSS 1.6 PracNcal 1.7 PracNcal
- 9. • IntroducNon radio technology in spaceflight, • Time and frequency domain, • Fourier transformaNon, • Fast Fourier TransformaNon
- 10. • Satellites, rockets, parts of rockets, etc, all is nowadays tracked by radio • Visual contact: – maybe for several kilometer, and only for verificaNon purposes – In the past we relied on opNcal tracking • Radio-range depends on: – Frequencies used – Antenna characterisNcs – Transmit power and receiver sensisiNvity – Antenna horizon and field of view • CommunicaNon and navigaNon are closely related, in fact, there is hardly any difference 06/10/17 TU Del3 class ae3535-16 10 Baker-Nunn camera S-band tracking system
- 11. What to do beyond point of radio-contact (antenna horizon) • Rely on autonomity of the space vehicle – Occasional contact (most satellites) – Some space vehicles don’t need contact at all • Antenna in the sky concept – Tracking and data relay satellite system (TDRSS) • High Earth orbit implementaNon – GeostaNonary orbits (all telecom satellites + TDRSS) – GNSS orbits – High inclinaNon, high eccentricity orbits • Low Earth orbit implementaNon – Swarm of low earth orbiters 06/10/17 TU Del3 class ae3535-16 11
- 14. From this point on we call a radio a device that is able to either send or receive informaNon within a defined range of frequencies info info ether info info ether Half duplex set-up Full duplex set-up 06/10/17 TU Del3 class ae3535-16 14
- 15. • Modulated signal – music, voice, television, images, telex, e-mail – finite bandwidth – finite length record – sampling at a defined Nmesteps • Carrier frequency >> modulated signal • ElectromagneNc wave propagaNon • Antenna’s and Transmission lines • Receivers, transmiSers, amplifiers, filters • Test equipment 06/10/17 TU Del3 class ae3535-16 15
- 16. • This is the 20 meter radio amateur band running from 14000 kHz to 14350 kHz • Do it yourself on the University of Twente web SDR hSp://websdr.ewi.utwente.nl:8901/ • The slider under the graph is used to adjust your radio receiver. • Waterfall plots are not “spectra”, instead they are derived from the spectra of a received signal. Frequency Time
- 17. Normally signals appear in the time domain: v(t) with t ∈ [0,T] where T is the length of a record. If we assume that: v(t +T) = v(t) then the function is said to be periodic. Furthermore if v(t) has a finite number of oscillations in [0,T] then we can develop v(t) in a series: v(t) = Ai i=0 N/2 ∑ cos(ωit)+ Bi sin(ωit) which is known as a Fourier series and where Ai and Bi denote the Euler coefficients. 06/10/17 TU Del3 class ae3535-16 17
- 18. • The variable ωi expresses an angular rate as in the formula: ωi =i.Δω where Δω=2π/T • The frequency associated with Δω = 2π/T is 1/T Hertz (Hz) when T is specified in seconds. • Otherwise we rescale frequencies to “cycles per period” and period should be defined. • For a conNnuous funcNon v(t) there are an infinite number of frequencies, in this case N is unbounded • Yet all those frequencies are mulNples of the base frequency 1/T, except for i=0 • This frequency resoluNon Δf=1/T is determined by the record length T (and not the sampling) 06/10/17 TU Del3 class ae3535-16 18
- 19. In order to calculate Ai and Bi from v(t) defined on [0,T] we exploit the orthogonality properNes sin(mx)cos(nx)dx = 0 x=0 2π ∫ regardless of m and n cos(mx)cos(nx)dx = 0 2π ∫ 0 : m ≠ n π : m = n > 0 2π : m = n = 0 # $ % & % % sin(mx)sin(nx)dx = 0 2π ∫ π : m = n > 0 0 : m ≠ n, m = n = 0 # $ % &% 06/10/17 TU Del3 class ae3535-16 19
- 20. v(x) cos(mx) sin(mx) ! " # $# % & # '#0 2π ∫ dx ⇒ An cos(nx)+ Bn sin(nx){ } n=0 N/2 ∑ cos(mx) sin(mx) ! " # $# % & # '#0 2π ∫ dx ⇒ A0 = 1 2π v(x)dx, B0 = 0 0 2π ∫ Ai = 1 π v(x)cos(ix)dx, i > 0 0 2π ∫ Bi = 1 π v(x)sin(ix)dx, i > 0 0 2π ∫ 06/10/17 TU Del3 class ae3535-16 20
- 21. • Conversion from Nme domain v(t) to frequency domain (Euler coefficients) via integrals • When we speak about “the spectrum” we speak about the existence of Euler coefficients • There are efficient algorithms that greatly speed up the computaNon of the integrals, this is what is called the Fast Fourier Transform, short FFT • Euler coefficient pairs are o3en wriSen as complex numbers • The inverse operator also exists, this is the iFFT operator. Both FFT and iFFT exist in MATLAB. 06/10/17 TU Del3 class ae3535-16 21
- 22. • EssenNally y=FFT(x) carries out a Fourier transform • FFT algorithm input – Real vector x(0..N-1) with N datasamples – The record starts at 0 and is filled to N-1 • FFT algorithm output – Euler coefficients are stored in the form of complex numbers – Stored in y(i) are: y(0) = A0 + I.B0 , y(1) = A1+ I.B1 , …, y(N/2) = AN/2 + I.BN/2 – I is a complex number: – Be careful with scaling factors, check this always with a test funcNon of which you now the Euler coefficients in advance – Suitable test funcNons are for instance linear sin and cos expressions • FFT algorithms exploit symmetries of sin and cos funcNons, please use MATLAB because it is thoroughly debugged. • Be aware that indices in MATLAB vectors start at 1 (and not 0) I = −1 06/10/17 TU Del3 class ae3535-16 22
- 25. • Go to brightspace and find three exercises for week 1.1 • Check with the TA how your reports should be submiSed • These reports do not count for your grade, but they help you in preparing for the final examinaNon • Feedback on the exercises comes in week 1.2 06/10/17 TU Del3 class ae3535-16 25
- 28. During the lecture it was explained that the University of Twente has a WebSDR that allows you to receive shortwave radio signals via a website. In this exercise you are asked to explain some characterisNcs of radio staNons in the 20m and the 40m amateur band, the 40m broadcast band, and the medium wave broadcast band. InstrucNons: • Go to the WebSDR website and make sure that you get to see the waterfall plot • Adjust the WebSDR receiver (the controls are below the waterfall plot). Make sure that you can understand a spoken radio transmission for at least three different staNons in each band Describe the se}ngs of the WebSDR receiver to demodulate a radio staNon in different bands: • The 20m amateur band between 14130 kHz and 14350 kHz, • The 40m amateur band between 7050 to 7200 kHz • The 40m broadcast band between 7200 and 7450 kHz • The medium wave broadcast band between 550kHz and 1606.5 kHz Secondly we ask you to comment on propagaNon of shortwave signals which depends on the ability of a radiosignal to reflect on ionospheric layers: • At what Nme of the day is any band crowded, and when is it quiet? • What could be the reason that propagaNon differs so much for each band? • What is the furthest staNon you heard in any band? (to do this for amateur staNons you need to decode their call sign and look up which country issued the callsign, for broadcast staNons simply listen, or check the internet). Note that the WebSDR has the possibility to show an overview of the compressed waterfall informaNon during a full day, you don’t need to listen for 24 hours. 06/10/17 TU Del3 class ae3535-16 28
- 29. • Express a sawtooth funcNon in a Fourier series • Sawtooth: at the start of the interval with length T the funcNon is 0, at the end of the interval it is 1, the interval runs from t=0 to t=T, the funcNon is linear on this interval • Make a table of the amplitude and phase values up to the 10th harmonic with MATLAB • Each overtone of the base period (between 0 and T) is called a harmonic, the first harmonic is periodic between 0 and T, the second between 0 and T/2, etc. • How many harmonics do you need to get the amplitude below 0.01? 06/10/17 TU Del3 class ae3535-16 29
- 31. • ProperNes of the Fourier transform – Nyquist limit – ConvoluNon – Parseval idenNty – Sampling – Aliasing – Filtering • Block schemaNc – TransmiSer – Several receivers
- 32. • The FFT operator implements the discrete version of the Fourier transformaNon • There are no more than N/2 unique Euler coefficients, this sets the highest frequency of a series of N samples. This is what we call the Nyquist limit • MulNplicaNon of coefficients in the frequency domain is convoluNon of two funcNon in the Nme domain. • Parseval’s idenNfy says that the sum of the squares in the frequency domain is equal to the sum of the squares in the Nme domain. (proof via auto convoluNon) 06/10/17 TU Del3 class ae3-535 32
- 33. • It means that you shi3 two funcNons along one another while you mulNply the result, input are f and g, the output is h • With the convoluNon theorem we can build/design/analyze filters • Most of the filtering in digital radios is implemented by convoluNon 06/10/17 TU Del3 class ae3-535 33 h(t) = f (τ)g(t −τ)d −∞ ∞ ∫ τ F(ω) = FFT( f (t)) G(ω) = FFT(g(t)) H(ω) = F(ω)⊗ G(ω) fast slow
- 34. • Whenever we discreNze a signal we sample it at a certain interval Δx (or Δt) • Undersampling results in aliasing with the consequence that the spectrum is deformed • Here is a video on aliasing, study it yourself • Oversampling is never a problem, the more the beSer, oversampling counteracts aliasing • Frequency resoluNon is determined by the record length, records that are too short cause a poorly resolved frequencies 06/10/17 TU Del3 class ae3-535 34
- 37. • Bandwidth: the signal spectrum is limited to a spectral range (a more formal definiNon comes later) • Topic is related to filters: most electronic circuits behave like filters • A filter is nothing more than a convoluNon of the signal Nmes a weight (or filter) funcNon. • Low-pass, high-pass, band-pass, notch filters 06/10/17 TU Del3 class ae3-535 37
- 42. • All informaNon that we send or receive is affected by bandwidth limitaNons, various reasons why this is the case • The frequencies that we chose in the EM spectrum are modulated on top of a carrier frequency, needs explanaNon, what is modulaNon? • The use of carrier frequencies, (or more general, the use of bandwidth and the power density in the spectrum) is restricted by regulaNons • There are internaNonal/federal/naNonal agreements on the use of frequencies and permiSed power levels. • Commercial aspects with regard to obtaining bandwidth (purchase UTMS frequencies, any idea of the price?) 06/10/17 TU Del3 class ae3-535 42
- 43. A F A F O antenna informaNon A: amplifiers, F: band pass filters, O: local oscillator “InformaNon” changes either the frequency, the phase or the amplitude of the oscillator The band pass filters are required to eliminate, unwanted, parasiNc frequencies such as overtones which are taboo on the output Never operate a transmiSer without an antenna, because it is likely to kill the output amplifier The use of transmiSers is bound to regula2ons, only certain frequencies, power, and bandwidth can be used for designated applicaNons. 06/10/17 TU Del3 class ae3-535 43 Transmission line
- 44. antenna L L C A A SPKR D A: amplifier D: demodulator C D Input Output The voltage level a3er demodulaNon proporNonal to amplitude input signal 06/10/17 TU Del3 class ae3-535 44
- 45. • Receiver design assumes that there is a circuit (a filter) with a bandwidth sufficiently narrow to isolate a radio signal from neighboring frequencies. • Receiver design assumes that the first amplifier has a sufficient bandwidth • Receiver design assumes that the amplifier gain is sufficient, nothing is said yet about the signal to noise raNo • Receiver Design assumes that we are able to receive amplitude modulated signals. In reality this design works to maybe a few megahertz (MHz). For our applicaNons we go much further in frequency space, also, other modulaNon techniques are used • TransmiSer design assumes supressed distorNons 06/10/17 TU Del3 class ae3-535 45
- 46. • All amplifiers are somewhat non-linear, this means that the input does not linearly translate to the output. • Output ≠ Gain × Input • The consequence of non-linearity is that intermodulaNon products will occur • You can demonstrate intermodulaNon by inserNng two signals with different frequenNes into an amplifier.
- 51. • Quality amplifiers (receivers etc) is specified as the level of the 3rd order intermodulaNon • You can not assume that amplificaNon is the answer to building the most sensiNve receiver or most powerful transmiSer ever • The reality is that you need to do something against intermodulaNon • Usually you combine amplifiers with filters to design a system that works for a selected frequency range.
- 52. antenna L L C A A SPKR D A: amplifier D: demodulator F: a filter HF: high frequency IF: intermediate frequency O: local oscillator X: mixer A X F O C L Variable tuning capacitor, dual secNons IF HF Armstrong 1918 06/10/17 TU Del3 class ae3-535 52
- 53. • Local oscillator: runs in parallel with the LC tuning circuit coupled to the antenna • Mixer: circuit that mulNplies two signals • Low-pass: filter to isolate the intermediate frequencies (IF) a3er filtering • A high gain amplifier for the intermediate frequencies (early days: 455 kHz) • For an IF > 0 we call this a superheterodyne receiver, when the IF=0 it is called a zero-IF receiver. • Most receiver designs are based on the superhetrodyne concept. 06/10/17 TU Del3 class ae3-535 53
- 54. • It is easier to build a high-gain amplifier within a specified frequency range than to build a wideband, high-gain amplifier. • As a result superheterodyne receivers are more sensiNve, because of the IF amp and Osc/Mixer setup • Superheterodyne receivers can go up to higher frequencies since mixers and oscillators and band-limited LNAs can be built up to several GHz. • However, the receiving range is limited because of the set- up of the local oscillator and the choice of an IF • The price to pay is more complexity, but sNll this is worth the effort because of the increased sensiNvity • Superheterodyne receivers are preferred because of their ability to reject intermodulaNon products. 06/10/17 TU Del3 class ae3-535 54
- 55. • Modify the design a3er the mixer • Use an Analog to Digital Converter (ADC) with a sufficient sampling rate, bandwidth and digital resoluNon (10 bit to 31 bit range) • ADC output routed into FFT / iFFT processors • So3ware takes care of the demodulaNon • DVB TV dongles: $30, tunable range to 1GHz • Dedicated SDR’s: $500, tunable range to 10 GHz • SDR used in the satellite tracking (Q2: Nov-Jan) 06/10/17 TU Del3 class ae3-535 55
- 58. f(x) g(x) 06/10/17 58 h(x) = f (x)⊗ g(x) Show that this happens with MATLAB when you mulNply two block funcNons
- 60. • Amplifiers can not provide output outside a specified voltage range, otherwise voltage clipping occurs • The output of the amplifier is restricted to 20 Volt peak to peak, the amplifier gain is 14 decibel (dB), it can operate between 0 and 100 MHz • dB = 10 log10( signal/reference ) • Two signals with an equal amplitude are injected at 10 and 10.1 MHz, what is the maximal amplitude to avoid intermodulaNon products on the output
- 65. • Analog circuits – Kirchhof and Ohm’s law – AdmiSance of inductors and capacitors – RC LC and RLC networks – Q factor • Transmission lines – Telegraphers equaNon – Coax, twin-lead and other transmission lines – Quarter-lambda impedance transformer • Antenna’s – Half and quarter lambda dipoles, Yagi’s and paraboles – Balanced to unbalanced transformaNon, baluns
- 66. • The sum of all incoming and outgoing currents at a node in a network of components is zero. • Voltage = Current x Resistance • Power = Voltage x Current • Now we add inductors, capacitors and resistors to build a network. 06/10/17 TU Del3 class ae3-535 66
- 68. • There are differenNal equaNons for current and voltage through capacitors and inductors. They result in a so- called replacement resistance for the component • The replacement resistance of a capacitor is called ZC • The replacement resistance of an inductor is called ZL • Both replacement resistances are from now on called impedances of the C and the L component ZC = 1 jωC and ZL = jωL with j = −1 ω = 2π f where f is the frequency in Hz 06/10/17 TU Del3 class ae3-535 68
- 71. • Impedance is the electrical resistance of a component of a circuit of components to an alternaNng current • AdmiSance is the reciprocal of impedance (Impedance ≈ Ohm, AdmiSance ≈ Siemens) • Reactance is the opposiNon of a change in electrical current to voltage or vise versa like capacitors and indictors show
- 72. R C SPST VC +VR = 0 with C = Q V and I = dQ dt Q(t) C + I(t)R = 0 ⇒ Q(t) C + dQ(t) dt R = 0 Q(t) = −RC dQ dt ⇒ Q(t) = Q(t0 )e−t/τ with τ=RC so that V(t) =V(t0 )e−t/τ When a complex notation is used R.ejωt + ejωt jωC = 0 ⇒ ω = j RC 06/10/17 TU Del3 class ae3-535 72
- 73. ZC = 1 jωC and ZL = jωL ZLC = ( 1 ZL + 1 ZC )−1 = ∞ ⇒ ω = 1 LC C L I known parallel resistance consequence The only thing you need to know is the impedance of inductors and capacitors, The parallel resistance should be infinite for a LC circuit without dissipaNon In that case ω should be as given, it is maintained when there are no losses 06/10/17 TU Del3 class ae3-535 73
- 74. : used for low-pass filtering Power supply TransmiSer end stage L C C R A B Zb = 1 1 Zc + 1 R = R jωRC +1 Za = Zl + Zb = − ω2 RCL − jωL − R jωRC +1 Zb Za = −R ω2 RCL − jωL − R output filter Zt = 1 1 Zc + 1 Za impedance at A 06/10/17 TU Del3 class ae3-535 74 0
- 76. C L R Energy loss in a LCR circuit Z−1 = ZL −1 + ZC −1 + R−1 To obtain the dissipation P: V = Hejωt so that T = 2π ω P = 1 T V2 Z0 T ∫ dt = H2 R 1+ (ω2 LC −1)2 R2 ω2 L2 P0 = P(ω0 ) = H2 R and ω0 = 1 LC Search now the ω where P(ω0 ) = 1 2 2 P(ω) since this results in the bandwidth (ω2 LC −1)2 R2 =ω2 L2 ⇔ (ω −ω0 )(ω +ω0 ) = ω RC ≈ ω0Δω By definition Q = ω Δω =ω0RC = RC LC = R C L (Quality factor) 06/10/17 TU Del3 class ae3-535 76
- 77. • For a parallel LCR circuit it is Q=R.sqrt(C/L) • For a series LCR circuit it is Q=(1/R).sqrt(L/C) • Q says of a something about the bandwidth of the analog LCR circuit • Q says also something about the bandwidth of an antenna • Tuning LC circuit : parallel LCR • Antenna replacement circuit : series LCR
- 80. • The larger the Q factor the more the parallel LC circuit resembles that of a perfect resonator at ω0 that is free of dissipaNon • In reality there is always some dissipaNon, even a high impedance amplifier does show energy loss. • As a result of Q<∞ all filters in radio receivers come with a finite bandwidth. • Fundamentally; any receiver has a bandwidth larger then zero 06/10/17 TU Del3 class ae3-535 80
- 83. 06/10/17 TU Del3 class ae3-535 83 In a transmission line signal propagation is described by the so-called telegraphers equations (Oliver Heaviside, 1880) ∂V(x,t) ∂x = −L ∂I(x,t) ∂t − R.I(x,t) ∂I(x,t) ∂x = −C ∂V(x,t) ∂t −G.V(x,t) For an ideal line we can set R = 0 and G = 0, we find: ∂V(x,t) ∂x = −L ∂I(x,t) ∂t and ∂I(x,t) ∂x = −C ∂V(x,t) ∂t so that ∂2 V(x,t) ∂t2 −u2 ∂2 V(x,t) ∂x2 = 0 and ∂2 I(x,t) ∂t2 −u2 ∂2 I(x,t) ∂x2 = 0 where u =1 LC is the propagation speed in the transmission line
- 84. What do we get? • Both V(x,t) and I(x,t) are soluNons of wave equaNons • The transmission speed in the line is not always equal to the speed of light, this is only true for certain ideal loss-less transmission lines • Transmission lines therefore have a characterisNc impedance depending on how they are designed. 06/10/17 TU Del3 class ae3-535 84
- 85. Standing wave soluNon Let us try separation of variables V(x,t) =V(x)exp( jωt) and I(x,t) = I(x)exp( jωt) in this case one case show that: d2 V(x) dx2 + ω2 LC.V(x) = 0 and d2 I(x) dx2 + ω2 LC.I(x) = 0 we define wave number k =ω LC = ω u d2 V(x) dx2 + k2 V(x) = 0 and d2 I(x) dx2 + k2 I(x) = 0 Result: one dimensional Helmholtz wave equation
- 86. General soluNon standing waves 06/10/17 TU Del3 class ae3-535 86 V(x) =V1 e− j.k.x +V2 ej.k.x I(x) = V1 z0 e− j.k.x − V2 z0 ej.k.x z0 = L C V x (characterisNc impedance) Coaxial cables usually come with an impedance between 50Ω and 100Ω, twin lines 300 to 450Ω. Coax: asymmetric, Twin: symmetric
- 91. • ProperNes: – Impedance – Gain – Sense of direcNon – PolarizaNon – Bandwidth (replacement is series LCR) • Let’s start with a half wavelength dipole 06/10/17 TU Del3 class ae3-535 91
- 92. Current Voltage Current Voltage t=0 t=½T 06/10/17 TU Del3 class ae3-535 92 Impedance: Zdipole = 73Ω, Gain: Gdipole = 2.14 dBi DefiniNon of the decibel
- 93. • The decibel is defined as: • Normally Pref = 1 – dBW is used for power relaNve to 1 WaS – dBm is used for power relaNve to 10-3 WaS – dBi is the gain relaNve to an isotropic antenna – dBd is the gain relaNve to a dipole – dBc is takes relaNve to a carrier • MathemaNcs: – Adding dB’s is the same as mulNplicaNon – SubtracNng dB’s : divide values dB=10log10 P Pref ! " # $ % &
- 96. • The dipole is symmetric, thus posiNve on one side and negaNve on the other. • Our modern transmission lines are asymmetric in parNcular because we desire the mantle of the coaxial cable to be neutral (thus grounded) • The remedy is to use a balun (balanced to unbalanced transformer) • Some balun designs are also impedance transformers (discussed later)
- 107. • Dipole • Half dipole, quarter dipole, etc • MulN-element yagi antennas • Helical antenna’s • Patch antenna’s • Parabolic antenna’s • AcNve antenna’s (means that a remote receiving antenna in a noise free environment comes with an LNA to counteract transmission line losses) 06/10/17 TU Del3 class ae3-535 107
- 108. • Antenna gain reveals that the antenna is somehow direcNonal. • Your ears and your voice are direcNonal antennas • Rather than that all radiated power goes out in every direcNon, a direcNonal antenna takes care of radiaNng the transmiSed power along a paSern. • Antenna gains are expressed as dBi and these are relaNve to a theoreNcal isotropic antenna that has unit gain. • DirecNonal antennas has a front-back raNo in dB • When you receive a signal a similar thing happens, the incoming energy is focused onto one point 06/10/17 TU Del3 class ae3-535 108
- 109. • Dipole: 2.14dBi for a λ/2 dipole, 1.76dBi for dipoles shorter than λ/4: link • Helical: for example 11.8dBi for 5 turns at 5.8GHz with λ/4 spacing: link • Patch: e.g. 9dBi or up: link • Parabolic: e.g. 30 to 40 dBi: link • Yagi (VHF): e.g. 10-20 dBi: link 06/10/17 TU Del3 class ae3-535 109
- 110. • hSps://en.wikipedia.org/wiki/Dipole_antenna • hSp://www.daycounter.com/Calculators/Helical- Antenna-Design-Calculator.phtml • hSps://en.wikipedia.org/wiki/Patch_antenna • hSp://www.qsl.net/pa2ohh/jsparabolic.htm • hSp://www.k7mem.com/Electronic_Notebook/ antennas/yagi_vhf.htm
- 113. Ohm Kirchhof and Power • What is the dissipated power P for a voltage V or a constant current “I” across resistor R? • Is the previous statement also true when V and “I” show a phase difference? • Assume a sine signal with amplitude of Vpeak volt over resistor R • What is the average power P over a cycle? 06/10/17 TU Del3 class ae3-535 113
- 116. Q factor parallel LCR circuit • In a parallel LCR circuit we have: L=10μH C=5pF R=106Ω • Plot the impedance against frequency so that the bandwidth of the filter becomes visible • What is the bandwidth, is there an agreement between the formula and the plot • Is this filter acceptable for a shortwave (SW) receiver circuit, ie. the tuning filter of the receiver? • Use the websdr from lecture 1 as an example. 06/10/17 TU Del3 class ae3-535 116
- 117. Q factor in series LCR circuit • The derivaNon on Q for a series LCR circuit can be found in a manual • In a series LCR circuit we have: L=10μH C=5pF R=50Ω • What is impedance of this circuit in the frequency domain • Scale the plot of the impedance against frequency such that we can see the bandwidth of this filter. • The series LCR circuit is a replacement model for antennas.
- 119. This lecture • Impedance matching • IntroducNon to modulaNon • Signal propagaNon • Signal and noise • Link margin calculaNon • Reference material: – Electronics, A system approach, 6th ediNon Neil Storey – Week 1.3: Chapters 1-9 – Week 1.4 and 1.5: Chapter 29
- 120. Op2mal power transfer problem 06/10/17 TU Del3 class ae3-535 120 R1 R2 V • Compute the dissipaNon over R2 while V and R1 are fixed. • For what R2 is there an opNmal power from the generator to R2 R1 : line R2 : load
- 121. Impedance matching • Impedances: – Transceiver : design of power amplifier (50 Ω) – Transmission line : type of line that is used (50 Ω) – Antenna : type of antenna that is used (we hope it is 50 Ω) – In the ideal case all impedances should be the same • The reality is: – The antenna does not match to the transmission line – TransmiSed signal is reflected back to the transmiSer, – Reflected signal could damage the transmiSer • For RF circuits we measure a standing wave raNo (SWR) – We opNmize the SWR and it should become 1 – There are various ways to accomplish an impedance match 06/10/17 TU Del3 class ae3-535 121
- 122. Standing wave ra2o • The SWR is formally defined as: • R is the impedance of the antenna and Z0 the characterisNc impedance of the transmission line • The SWR is always greater or equal to 1 • A Vector Network Analyzer (VNA) measures the admiSances as a funcNon of frequency SWR = R Z0 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ±1
- 126. Antenna tuner (1)
- 127. Antenna tuner (2) • The following ciruit is an T-shaped antenna tuner • Purpose of this circuit is to transform impedances – Between transmiSer and transmission line – Between transmission line and antenna 50 Ohm Large impedance range
- 128. • The T-shaped tuner transforms impedances • The le3 tuner is made of a roller inductor and variable capacitors, it can handle signals up to a few hundred WaSs • The right tuner is made of relays that switch between fixed inductors and fixed capacitors • One can show that the T-shaped tuner behaves like an ideal transformer as long as there are no Ohm like losses in the components • The quality of the components in antenna tuner become a significant concern, especially for high power transfer
- 129. • Quarter wavelength transmission line: this is a tuner for specific frequencies (see lecture 1.3) • Other configuraNons of L and C components, are also tuners. • Transformers can behave like tuners (this is an exercise for this week) • Antenna tuners should not be confused with the LC resonant tuning circuit of a receiver.
- 131. • Consider a carrier which is nothing more than a signal with a constant frequency and amplitude • To transfer informaNon (data, music, spoken word, TV signals etc etc) you must do something with the carrier (like vary the amplitude of frequency or phase) • InformaNon (signal) is now modulated on the carrier μ μ μ+ν μ-ν 06/10/17 TU Del3 class ae3-535 131 ejµt e± jνt = ej(µ±ν )t
- 133. 06/10/17 TU Del3 class ae3-535 133 Signal Modulated On carrier Spectrum Frequency modulaNon Amplitude modulaNon
- 134. FM beRer than AM? • Yes: – FM less suscepNble to variaNons in recepNon strength – FM is therefore more resilient to noise – FM does not require highly linear amplifiers • No: – Requires more bandwidth, FM is typically used at frequencies >100 MHz where there is enough bandwidth – DemodulaNon circuits are more difficult (PLL’s etc) (is not a real issue nowadays) 06/10/17 TU Del3 class ae3-535 134
- 136. There are many modula2on schemes • Analog modula2on AM FM PM SM SSB (LSB,USB) • Digital modula2on ASK APSK CPM FSK MFSK MSK OOK PPM PSK QAM SC- FDE TCM • Spread spectrum CSS DSSS FHSS THSS MulNple access: CDMA FDMA TDMA • Should you know them by heart? No, just read the documentaNon. 06/10/17 TU Del3 class ae3-535 136
- 137. Some examples • Instrument landing systems (ILS) depend on space modulaNon (SM) • Dialpad of a telephone, FSK/DTMF, each number or symbol has one or more unique frequencies • Global posiNoning system: spread spectrum based on BPSK PRN code modulaNon • GSM 3G : WCDMA, wideband code division mulNple access 06/10/17 TU Del3 class ae3-535 137
- 138. Signal propaga2on • A3er the signal leaves the antenna it propagates through space. • PropagaNon is controlled by refracNve properNes of the medium. • At the receiver we assume the incoming signal to be near or above the noise floor of the receiver, o3enNmes this aspect depends on the propagaNon of the signal
- 139. What is refrac2on? • An electromagneNc wave normally travels at the speed of light c • This is only true in vacuum where the refracNve index n = 1 • In a medium like glass (water, air etc) we get n>1, the propagaNon speed becomes v = c/n • Where n depends on the frequency of the EM wave we say the medium is dispersive • The Earth ionosphere is dispersive for radio waves • Air is slightly dispersive for light
- 142. Characteris2cs HF propaga2on • There is a so-called criNcal frequency, this is where we get the verNcal transmiSed signal back to the ground • Above the criNcal frequency signals ONLY reflect under an certain angle, this explains the so-called skip zone • There is a maximum usuable frequency, above this signals go out to space. • The maximum usuable frequency (the MUF) may go up to 50 MHz, o3en it is less • Sporadic E-layer reflecNons occur up to 150 MHz.
- 143. • Phase speed relates to the carrier • Group speed relates to modulated signal • Informa2on content is by definiNon transported with the group speed • The phase speed may be faster than light • The laSer is not a contradicNon with the theory of relaNvity 06/10/17 TU Del3 class ae3-535 143
- 144. • Rayleigh 1881 found the following relaNon: • Velocity dispersion • There is a similar relaNon for the refracNon index λ λ d dv vv p pg −= df dn fnn pg += 06/10/17 TU Del3 class ae3-535 144
- 147. Physics of noise at the receiver 06/10/17 TU Del3 class ae3-535 147 In reality we deal with electronic components which have a certain temperature T, all components emit electromagnetic radiation: P = kT B with k =1.38064854×10−23 J K−1 and B bandwidth The Bolzmann constant comes from k = R N where R is a gas constant and N Avogadro's number For semiconductors etc the thermal voltage is: VT = kT q where q is the charge of an electron P is the Power contained in the noise
- 148. Physics of noise: spectral density 06/10/17 TU Del3 class ae3-535 148 Spectral density is specified in dBm/Hz, but how? For T=290K (room temperature) we find Pdbm =10log10 ( kT 10−3 ) = −174 dBm/Hz for a bandwidth of 1 MHz we get -114dBm, note that the dBm calculation refers to 1mW and that we can add to multiply or subtract to divide due to the definition of the decibel.
- 149. Physics of noise: How low can you go? • For a low noise amplifier (LNA) near the boiling point of Helium we get -192 dBm/Hz. • This level could be obtained in the cold end of a radio telescope for which a coolant is used (o3en Nitrogen, someNmes Helium) • Deep space measures 2.7K which is remnant of the big bang and this is 2dBm/Hz under the cold end of a radio telescope. 06/10/17 TU Del3 class ae3-535 149
- 150. Measure signal and noise • For this we use a spectrum analyzer • When we measure signal and noise at room temperatures we have to deal with the Excess Noise RaNo (ENR) which is -174 dBm/Hz, • ENR = 10log10(kTB/10-3)) where T=290K and B=1 Hz • Noise generators (e.g. noise diodes) exist to test the behavior of electronic circuits, that is, put noise into a circuit and see what comes out at all frequencies. • AlternaNve: use a signal generator • Carrier to noise raNo (CNR): essenNally the CNR is used to compute the error to bit raNo (Eb/N0 raNo) 06/10/17 TU Del3 class ae3-535 150
- 152. Link margin calcula2on 06/10/17 TU Del3 class ae3-535 152 TransmiSer Receiver PT PR Free space loss PR = PT − L +GT +G R with L = 4πd λ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 or in dB L = −20log10 (λ)+ 20log10 (d)+ 21.98 where 21.98 =10log10 ((4π)2 ) M = PR − Nr is the so called link margin, preferable it is > 0 Nr = kT B + Nd Nd : You got it from the noise floor measurement
- 153. Example link margin calcula2on • Transmit power : 10mW which is 10dBm • Receiver noise: -100dBm (noise floor measurement) • Distance = 1000m, Frequency=5.8GHz, FSL = 107.7dB • Gains transmiSer: 0dB, receiver: 0dB (ant./line etc) • Margin: 10-107.7-(-100) = 2.3dB > 0 dB (ok); – Obstacles (wet leaves, etc) would aSentuate the signal – They introduce noise or even completely block the signal – Any reflector in the Fressnel ellipse affects the quality • Various opNons to improve the situaNon: – Increase the antenna gain – Choose beSer antenna posiNons (no trees, hills, buildings) 06/10/17 TU Del3 class ae3-535 153
- 154. RSSI calculaNon • RSSI stands for Received Signal Strength Indicator and it is expressed in dB • There is no standard for the definiNon of RSSI • SomeNmes it is, the higher the RSSI, the beSer recepNon, so 90db is closest possible to the transmiSer • SomeNmes it is 0dB when (theoreNcally) all the transmiSer output is fed back into the receiver • In the laSer case RSSI’s at close range are not 0, and you have to measure the RSSI offset 06/10/17 TU Del3 class ae3-535 154
- 155. Signal, noise, bandwidth 06/10/17 TU Del3 class ae3-535 155 dB f Signal 1 Signal 2 noise Clearly signal 1 is below the noise level, and signal 2 is above it, and intuiNvely you would think that signal 1 could not be received while signal 2 could, however, this is not per se true. In week 1.5 we will conNnue with this topic SNR
- 159. Efficiency frequency shi3 keying (FSK) • WSPR is a 4 tone FSK modulaNon with a bandwidth of 6 Hz. • The efficiency of a 200mW WSPR beacon is the same as a … WaS SSB transmiSer. • SSB modulaNon for 3kHz audio signal • Hint: what maSers is the spectral density
- 160. Exercise: LC tuner with given Q • Signal and noise arrive at an antenna, • Bandwidth of the antenna is 2MHz • Noise density : -125dB/Hz, • Signal density: -120db/Hz, width 10 kHz • Bandpass filter: throughput behaves like a parallel LCR circuit, Q=1000 L=5μH C=30pF • What is the SNR before the filter? • What is the SNR a3er the filter 06/10/17 TU Del3 class ae3-535 160
- 163. Digital modula2on • Examples – Morse codes (CW) – 4 tone fsk: WSPR already menNond – BPSK (PSK-31 etc) • Shannon Hartley theorem • Bit to error rate • Symbol to error rate Army poster for learning CW
- 170. Discussion points • The earliest radio communicaNon was digital • Most satellite communicaNon is digital • Advanced digital communicaNon is able to break the 0dB signal to noise raNo that we menNoned • New topics: – Shannon-theorem – Energy efficiency and reliability
- 171. Shannon-Hartley theorem C = Blog2 (1+ S N ) C: channel capacity in bits/second B: bandwidth in Hz S: signal level N: power level Examples: SNR= 10dB → C/B = 3.5 SNR= 0dB → C/B = 1 SNR=-10dB → C/B = 0.135 (explain this!)
- 173. Consequence Shannon-Hartley • The channel capacity C (expressed in bits per second) is in reality less compared to what Shannon Hartley predicts • Efficiency depends on the modulaNon scheme, only certain opNmized digital modulaNon techniques get close to what Shannon-Hartley predicts • Related : – Energy to bit raNo relaNve to thermal noise level (Eb/No), this is the efficiency of a modulaNon technique – Bit Error RaNo BER, tells something about the reliability of a modulaNon technique depending on Eb/No
- 176. Spectral efficiency • Spectral efficiency η is the amount of bits/sec that can be transmiSed per Hz, units: bit/s/Hz • Next we look at the “energy per bit” with respect to “thermal noise level” (Eb/No) and the spectral efficiency parameter η. • We will show that Eb/No=(2η-1)/η • As a result there is a lower bound for Eb/No • Shannon-limit: min(Eb/No) = min((2η-1)/η) hSp://www.ingenu.com/2016/07/back-to-basics-the-shannon-hartley-theorem/
- 177. We start with S N =100.1×SNRdb C ≤ Blog2 1+ S N ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ and S N B = Eb No C C B = log2 1+ Eb No C B ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⇒ 2C B −1= Eb No C B η = C B ⇒ 2η −1 η = Eb No ⇒ η→0 lim 2η −1 η ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = ln(2) = 0.693... As a result we find that min Eb No ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ dB = -1.592... dB
- 179. Digital receiver sensi2vity model The relation between carrier (signal) to noise ratio and the spectral density of energy is B C N = Eb N0 fb where fB is the bit rate and B the bandwidth, EB N0 is the energy per symbol to noise ratio spectral density. As a result the receiver sensitivity sensitivity σ becomes: σ =10log10 (B)+10log10 C N ⎛ ⎝ ⎜ ⎞ ⎠ ⎟−174dBm + NF which is equivalent to: σ =−174dBm + NF + Eb N0 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ dB +10log10 ( fB ) Where NF is the noise floor of the receiver, it says something about the quality of the receiver.
- 180. Summary • A digital receiver model differs from an analog modulaNon receiver model • The -174 dBm is because we assume that the receiver operates at room temperature • The noise floor (NF) of the receiver comes from the noise floor experiment, typically it is 2 to 5dB for the receiver • The Eb/N0 raNo is the energy we put in each bit relaNve to the noise floor, it say something about the effort we put in the process • fb term, this is the data rate that we design for • Spectral efficiency Eb/No and the BER/SER say something about the modulaNon technique
- 182. Radio astronomy • In Radio Interferometry astronomers listen to natural radio sources in the universe • Radio astronomers also help to track deep-space planetary probes. • Radio source Cygnus A on the right seen with the VLA interferometer • Angular resoluNon is defined by aperture and wavelength (α=λ/D) • Detectability is angular resoluNon and sensiNvity (square root bandwidth Nmes integraNon Nme) 06/10/17 TU Del3 class ae3-535 182 Lobes only seen by VLA
- 185. Very long baseline interferometry • By using two or more radio telescopes the aperture increases, we call this syntheNc aperture because VLBI emulates a very large telescope • CorrelaNon analysis between signals received at both radio telescopes increases the signal to noise raNo of the galacNc radio signal • CorrelaNon of signal between the telescopes enables the observaNon of very weak signals • The clocks are independent, you need the best clocks in the world to run the interferometer observaNon program. Hydrogen masers are therefore used. 06/10/17 TU Del3 class ae3-535 185
- 186. Sensi2vity (σ) of the radio interferometer • Number of baselines (N) • Bandwidth of the signal (Δν) • IntegraNon Nme (tint) • Efficiency of the antenna (ρ) • System temperature (Tsys) • Correlator efficiency (ηc) σ = ρ Tsys ηc N (N −1) Δν tint hSps://science.nrao.edu/faciliNes/alma/CDE_V2.0_INTERFEROMETRY.pdf
- 188. GPS signal structure • Spread spectum modulaNon is used • L1 frequency (1575.42MHz = 154×10.23MHz) • L2 frequency (1227.60MHz = 120×10.23MHz) • Two frequencies help to model the ionospheric range delay effect (refracNon) • The modulaNon scheme used is bi-phase shi3 keying (BPSK) using a unique Gold code by satellite. (S/V) • For GPS the max number of codes is 37 06/10/17 TU Del3 class ae3-535 188
- 189. GPS signal structure • What informaNon is relevant for the user? – L1 : contains C/A codes and the P (or Y) codes – L2 : contains P (or Y) codes – C/A codes bandwidth is 1.023 MHz, data rate = 50 bps – P(Y) code bandwidth is 10.23 MHz, data rate = 50 bps • Codes are unique for each GPS space vehicle (S/V) – Code repeNNon length C/A = 1023, or 1 milliseconds at 1.023 mbps – Code length P(Y) = 6.19 x 1012, or 7 days at 10.23 mbps, – The full P(Y)-code cycle is length is however much longer • New GPS signals are planned in the near future, the above overview is not meant to represent the new situaNon • Also: GNSS = GPS + Galileo + Glonass + Beidou 06/10/17 TU Del3 class ae3-535 189
- 190. PRN or Gold code XOR 0 1 0 0 1 1 1 0 D Ck Q Flip Flop FF1 FF4 FF5 FF6 FF7 FF8 FF2 FF3 preset clock PRN code XOR A B C 01001110101… XOR truth table Q=D a3er acNve flank of Ck hSps://www.maximintegrated.com/en/app-notes/index.mvp/id/1890
- 191. Proper2es PRN code • The PRN codes are pseudo random, the codes are unique, this is how you find a satellite • The C/A code generator is known, we know the presets and the XOR logic • PRN codes repeat a3er a certain Nme interval • C/A clear access repeNNon: 1 msec • Align PRN codes by a digital code correlator • The last step results in a code phase measurement within the GPS receiver
- 193. GPS Receiver • EssenNally it is a superheterodyne receiver except that you would not be able to hear anything because: – All S/V PRN signals are on top of one another – The signals are below the noise level of the receiver • So how would this work? SNR < 1 seems a bit strange. • Digital code correlaNon solves this problem: – Generate PRN code replica’s (C/A and NAV are always accessible, P-codes were open, Y-codes are classified) – Degrees of freedom during correlaNon are the code phase offset and the frequency of the signal. – Conclusion, there are at least two tracking loops in a GPS receiver, one aligns the codes, the other aligns the frequency 06/10/17 TU Del3 class ae3-535 193
- 196. 06/10/17 TU Del3 class ae3-535 196 By correlating the received signal with a replica code you introduce a so-called processing gain: db(Gain) = 10 log10 bandwidth of the PRN code bandwidth of the data rate ! " # $ % & db(Gain) =10 log10 2MHz 100Hz ! " # $ % & = 43db which lifts the signal above the noise level Processing gain due to correla2on For more details: D. Doberstein, Fundamentals of GPS receivers, appendix A, Springer Verlag 2012
- 197. GPS naviga2on • Transmit Nme of GPS signal is known (atom clock) • Received from the GPS S/V’s are (X,Y,Z,T)satellite • Observed: Code-phase difference between the local oscillator (iniNally not synchronized) and the transmiSed code • This informaNon is called pseudo-range informaNon (comes with a 1msec ambiguity) • Pseudo range = c . (Treceived – Tsend) + Biasreceiverclock • Phase range à integrate the Doppler effect (This is what scienNsts/engineers call the carrier phase) 06/10/17 TU Del3 class ae3-535 197
- 200. Exercise on digital modula2on • Problem descripNon – Assume a 2.4 GHz QPSK signal, – Channel spacing is 40 MHz for 802.11n wifi – Assume SNRs between -15 and +15dB – BER = 1/2*erfc(sqrt(2*Eb/No)*sin(pi/4)) • Exercise: – The channel capacity is a funcNon of the SNR, How is the BER is affected by the SNR? Make a graph. – At what SNR is your wifi connecNon sNll comfortable? – EsNmate the spectral efficiency parameter, and the minimum Eb/No that is possible. 06/10/17 TU Del3 class ae3-535 200
- 202. Exercise on Global Posi2oning System • Describe how a GPS receiver obtains a standalone navigaNon soluNon • How many satellite do you need? • What are the main error sources • How can you improve a standalone GPS soluNon?
- 204. Learning goals • Get hands on experience with radio hardware • Moteino boards, arduino + radio modem 06/10/17 TU Del3 class ae3-535 204
- 205. Set-up prac2cal • Prepare – Form groups of max 4 students – Study the manual in the pracNcal directory – Install so3ware as is explained in the manual • AcNvity: – Each groups gets two moteino boards – Verify the installaNon procedure – Get it to work in the classroom. • Start with the group assignment 06/10/17 TU Del3 class ae3-535 205
- 206. Hardware available • Moteino board, much like an Arduino Uno except that it comes with a radio modem, a RFM69W • You can transceive at 433MHz or 866 MHz in Europe under the condiNons that apply to ISM frequency regulaNons • We will only use the 866 MHz, reason: the antenna length • Moteino boards are connected via an USB connector to any Windows, Mac or Linux system • InstallaNon: – Arduino IDE environment – FTDI drivers, – Libraries for the RFM69W, SPIFlash – Moteino hardware model • 30 boards available for ae3-535 communicaNons pracNca; • You may want to consider to use the boards for the space project 06/10/17 TU Del3 class ae3-535 206
- 208. What do you get? • Moteino board, plugged onto a breadboard • Jumper wires and USB cables • Sign-up with name and student ID and return the hardware a3er period Q2 • You can leave your experiment on the 9th floor, e.g. in my office, • You can take the boards with you as long as safe transportaNon is demonstrated • Preferred way of transportaNon: a carton box • Any boards that leaves the faculty needs to be registered 06/10/17 TU Del3 class ae3-535 208
- 215. Installa2on for the Windows/MAC • Get IDE version 1.6.1 from arduino.cc or blackboard (IDE: integrated development environment) • Get the required FTDI drivers (only required when there is a need to update them) • Get the required hardware model from www.lowpowerlab.com, select MoNno (not MEGA) as hardware model in the IDE • Get the RFM69 library from www.lowpowerlab.com • Get the SPFlash library from www.lowpowerlab.com • Ignore library updates by the IDE, only rely on the libraries from lowpowerlab.com • Do not reinvent the wheel, but make use C/C++ code from the example directory, blackboard or the internet. 06/10/17 TU Del3 class ae3-535 215
- 216. Classroom exercise • PracNce run with the moteino boards – Beacon is in the classroom – Nodes are with the student groups • Purpose – Install and verify the so3ware – Establish communicaNon – Once this works you can start with the group assignment 06/10/17 TU Del3 class ae3-535 216
- 218. • Groups are defined in week 1.6 • Work on the 4 problems in the assignment • Submit the group assignment report to turniNn on brightspace. We only need 1 PDF file.
- 219. • Experiment – Find an area that is mostly free of obstrucNon – Measure the RSSI offset close to the beacon. – Measure the RSSI values at a distance up to 100 meter from the beacon – Evaluate the free space loss term in the link budget. • ReporNng – Answer all quesNons related to the FSL experiment – Include a plot the measured free space loss – Match the plot with a FSL equaNon • Maximum: 3 points out of 10 06/10/17 TU Del3 class ae3-535 219
- 220. • You solve 5 exercise problems in the group • One non-trivial exercise per week from w1.1 to w1.5 • Maximum: 3 points out of 10
- 221. • Experiment: – Collect staNsNcs on the number of packets that arrived without an error and with an error (a retry in the so3ware) – Modify the so3ware and derive the BER as a funcNon of the SNR • ReporNng – Plot the bit error rate of the experiment over a sufficient wide range of SNRs – Is there an analyNcal funcNon that gets close to the measured BER – Plot the spectral efficiency as a funcNon of the Eb/No raNo, for details see week 1.5 lecture • Maximum: 2 points out of 10
- 222. Experiment to simulate a satellite to groundstaNon link • Experiment – You need two set-ups of the Arduino IDE – No baSery powered experiments are allowed, only laptop and USB – One moteino is the satellite, the other moteino is the ground staNon – The satellite performs measurements of the NTC and/or LDRs. – Ground staNon collects the measurements – LEDs are the actuators on the satellite – Make a funcNonal diagram first, consult a supervisor to check the design – Get it to work and demonstrate the end-result to the TA • ReporNng – Include the schemaNc, calculate the current by pin in the moteino board – The full experiment should be described in the report. • Maximum: 2 points out of 10
- 223. • What we always expect – A group report should be submiSed as one unsigned PDF file – No separate MATLAB or Python code files or plots – Clearly state which problem (1 to 4) you are reporNng – All names and study numbers should be included – DistribuNon of tasks should be included in the report – Deadline: November the 14th 2017. • Mandatory – Free space loss experiment: 3 points – Exercises previous weeks: 3 points • OpNonal – ModulaNon performance : 2 points – SimulaNon ground staNon satellite: 2 points