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- 1. Spacecraft RF Communication Day 1: • • • • Spacecraft communications introduction RF signal transmission RF carrier modulation Noise and link budgets Day 2: • • • • Error control coding Telemetry systems Analog Signal Processing Digital Signal Processing Day 3: • Kalman filters • Satellite systems • Special topics 10/30/2013 John Reyland, PhD Stop me and ask!!!!
- 2. RF Signal Transmission Doppler frequency shift and time dilation affect RF channels where receiver and/or transmitter are moving relative to each other v(t ) θ (t ) vr (t ) = v(t ) co s(θ (t ) ) Fixed inertial reference frame 10/30/2013 .
- 3. RF Signal Transmission Some Definitions: c = Speed of light, 3e8 meters/second f c = Carrier frequency (Hz) θ (t ) = Angle between receiver’s forward velocity and line of sight between transmitter and receiver (t ) co s θ (t ) ) vr (t ) v= ( Velocity of receiver relative to transmitter f d (t ) = Doppler carrier frequency shift at receiver Tt (t ) = Transmit symbol time Tr (t ) = Receive symbol time 10/30/2013
- 4. RF Signal Transmission Example 1: f c = 1 GHz = 1e+9 Hz v(t )= v= 350 meters/second (constant, approx. Mach 1) θ (t ) = 0 (constant, worst case for Doppler shift) vr= v= Velocity of receiver relative to transmitter v = d f d (t ) f= f c = c Tt (t ) = Tt = (1e9 ) 350 10(350) = = 1167 Hz Doppler carrier frequency shift at receiver = 3e8 3 1 = 1e − 6 = Transmit symbol time 1e + 6 Tr (t ) =Tr =Tt + vTt 350 =(1e − 6) 1 + =(1e − 6)(1.000001167) = Receive symbol time c 3e8 This means receive symbol time increases by 0.0001167%. - called time dilation 10/30/2013
- 5. RF Signal Transmission d = distance between transmitter and receiver at leading edge of transmit pulse d+vTt = distance between transmitter and receiver at trailing edge of transmit pulse d = Propagation time at leading edge of transmit pulse c Received Pulse, duration = Tr d + vTt c = Propagation time at trailing edge of transmit pulse Transmit Pulse, duration = Tt d + vTt c Tt + d vTt Additional time duration of pulse at the receiver − c = c = vTt v = Tt 1 + = Dilated time duration of pulse at the receiver c c 10/30/2013
- 6. RF Carrier Modulation Binary Phase Shift Keying (BPSK) a ( n) b( n) 1 ⇒ +1 0 ⇒ −1 R=1 implies one modulating cycle per symbol. R=2.5 in this example R cos 2π l L p(k ) Antipodal Mapping Pulse Forming x(k ) y (l ) Modulator x(k ) n = 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 k = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 -2Fb -Fb 0 Fb 2Fb y (l ) Fc = -RFb 0 10/30/2013 L 2L 3L 4L 5L John Reyland, PhD 0 Fc = RFb
- 7. RF Carrier Modulation R cos 2π l L Quadrature Phase Shift Keying (QPSK) be (ne ) a ( n) p(k ) R sin 2π l L 1 ⇒ +1 0 ⇒ −1 bo (no ) Serial 2 Parallel p(k ) y (l ) yI (l ) xI (l ) yQ (l ) xQ (l ) Modulator Pulse Forming 1 0 a ( n) n = 0 0 0 0 1 1 1 1 2 2 2 = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 n = 0 0 0 0 1 1 1 1 2 2 2 = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 xI ( k ) k xQ ( k ) k 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 y I (l ) yQ (l ) 0 10/30/2013 L 2L 3L 4L 5L John Reyland, PhD 6L 7L 8L 9L
- 8. RF Carrier Modulation OFDM starts by converting high speed symbols indexed by n at rate 1/Ts Into parallel blocks indexed by k at rate 1/T = M/Ts bi ( n ) + jbq ( n ) b(4k ) b(4k + 1) Each channel now transmits QPSK symbols at block rate Fs/M s(4k ) s(4k + 1) b(4k + 2) IDFT In this example, M=4 s(4k + 2) s(4k + 3) b(4k + 3) Channel 3 Symbols Channel 2 Symbols Channel 1 Symbols Channel 0 Symbols n = 0 1 2 3 4 5 6 7 8 9 10 11 12 k= 0 0 0 0 1 1 1 1 2 2 10/30/2013 2 2 3 © John Reyland, PhD
- 9. RF Carrier Modulation Advantage: Bit polarity can match alternating I,Q polarity Disadvantages: To detect bits, have to know where two bit pattern boundaries are. Even/Odd bits cannot interchange Important: This signal has only one bit of modulo 2π phase memory, i.e. current phase transition only depends on previous phase. 10/30/2013 © John Reyland, PhD
- 10. Noise and Link Budgets Important antenna specifications: • Beamwidth: Angular field of view • Gain: Increase in power due to directionality • Sidelobe rejection: Attenuation of signals outside beamwidth 10/30/2013 © John Reyland, PhD
- 11. Error Control and Channel Coding Time Diversity: After receiver reassembles, all errors can be corrected See [R5] and [R6] 10/30/2013 © John Reyland, PhD
- 12. Error Control and Channel Coding Maximum Likelihood (ML) detector: Detection mechanism uses the log-likelihood ratio, for detection filter output rrec: p ( r | S1 ) p1 = log LML = log p (r | S ) 0 p0 Log-likelihood ratio sign is most probable hard decision 10/30/2013 © John Reyland, PhD
- 13. Error Control and Channel Coding ML decisions in a general N dimensional signal space: 1 p ( r | Sm ) = π N0 N ∏e −( rk − Smk ) 2 N0 k =1 − N0 1 ln p ( r | S= ln (π N 0 ) − m) 2 N0 N ∑(r k =1 k − S mk ) The most likely transmitted signal Sm minimizes the Euclidian distance: D ( r= , Sm ) 10/30/2013 N ∑ ( rk − Smk ) 2 k =1 © John Reyland, PhD 2
- 14. Error Control and Channel Coding Maximum a posteriori (MAP) detector: Start with Bayes rule: p(S | r) = p (r | S ) p (S ) p (r ) p ( S1 | r ) = p ( S0 | r ) p ( r | S1 ) p ( S1 ) p (r ) p ( r | S1 ) p ( S1 ) = p ( r | S0 ) p ( S0 ) p ( r | S0 ) p ( S0 ) p (r ) MAP Log-likelihood ratio = likelihood ratio based on observation + a priori information ratio LMAP p ( S1 | r ) p ( r | S1 ) p ( S1 ) log = log p(S | r) p ( r | S ) + log p ( S ) 0 0 0 A priori: Information knowable independent of experience A posteriori: Information knowable on the basis of experience 10/30/2013 © John Reyland, PhD LMAP = LML if p ( S1 ) = p ( S0 )
- 15. Error Control and Channel Coding Concatenated coding for Voyager mission to Saturn and Uranus Power efficiency is extremely important: Coding gain of 6dB can double the communications range between spacecraft and earth ([C8], page 172) Voyager telecommunications achieved 10-6 BER at EbN0 = 2.53dB, 2Mbits/sec. What system considerations are not very important? Bandwidth efficiency, not many other users out there. Delay, waiting time for image reconstructions is OK 10/30/2013 © John Reyland, PhD
- 16. Error Control and Channel Coding Turbo coding basic concept explained by an example 10/30/2013 © John Reyland, PhD
- 17. Error Control and Channel Coding Turbo Decoder diagram for this example: The maximum a posteriori (MAP) log likelihood ratio: col MAP L p ( S1 | r ) p ( r | S1 ) p ( S1 ) col row = log = log + log = LML + LAP = LML + LEXT p(S | r) p (r | S ) p(S ) 0 0 0 10/30/2013 © John Reyland, PhD
- 18. Error Control and Channel Coding Log likelihood ratio of modulo two addition of two soft decisions (see []): ( L ( r0 ⊕ r1 ) L ( r0= sig nL ( r0 ) ) sig nL ( r1 ) ) min L ( r0 ) , L ( r1 ) = ) L ( r1 ) ( ( ) This addition rule is used to combine data and parity into extrinsic information Extrinsic means extra, or indirect, information derived from the decoding process 10/30/2013 © John Reyland, PhD
- 19. Error Control and Channel Coding 10/30/2013 © John Reyland, PhD
- 20. Error Control and Channel Coding Column decode generates new extrinsic information 10/30/2013 © John Reyland, PhD
- 21. Error Control and Channel Coding Column extrinsic information can be feedback to row decoder for a new iteration 10/30/2013 © John Reyland, PhD
- 22. Error Control and Channel Coding Final turbo decode output is derived from all available statistically independent information: Note how confidence levels are improved 10/30/2013 © John Reyland, PhD
- 23. Channel Equalization Techniques Raised cosine pulses have an extremely important attribute: at the ideal sampling points, they don’t interfere with each other Over an ideal channel, delayed transmit signal will be observed at the receiver. Ideal channel: 10/30/2013 sreceived (t ) stransmit (t − δ ) = John Reyland, PhD
- 24. Channel Equalization Techniques A decision feedback nonlinear adaptive equalizer: See [E1] and [E2] 10/30/2013 © John Reyland, PhD
- 25. Analog Signal Processing For gain planning, receiver has to cope with contradicting requirements ADC Input: Only one optimum power level for best performance = Max ADC input – received signal peak to average power ratio (PAPPR) Antenna Input: Needs to handle wide range of inputs from -100 dBm or less to 0dBm or more dBm P10 Pwatts PdBm 10log10 Pwatts = 0.001 10 0.001 10 0.1 −100dBm ⇒ 10−1010−3 =−13 = picowatt 0dBm ⇒ 1milliwatt 10/30/2013 © John Reyland, PhD
- 26. Analog Signal Processing A complex representation is required at baseband because the modulation will cause the instantaneous phase to go positive or negation: = co s θ BB (t ) ) + j sin (θ BB (t ) ) e jθ BB (t ) ( Because the phase is now always positive, complex exponential terms are redundant e = co s ωRF t + θ BB (t ) ) + j sin (ωRF t + θ BB (t ) ) ( j (ωRF t +θ BB ( t ) ) Signal now can be real: cos (ωRF t + θ BB (t= e )) j (ωRF t +θ BB ( t ) ) +e − j (ωRF t +θ BB ( t ) ) This forces the existence of a negative image (ignored for most analog processing): 10/30/2013 © John Reyland, PhD
- 27. Analog Signal Processing Voltage Sampling: Undesired signals are all aliased at full power: Current Sampling: Images at multiples of sampling rate are attenuated: 10/30/2013 © John Reyland, PhD
- 28. Analog Signal Processing Compete Transmitter Let’s discuss the function of the reconstruction filter and the bandpass filter… 10/30/2013 © John Reyland, PhD
- 29. Digital Signal Processing We will organize our DSP discussion around the digital receiver architecture below: This setup is suitable for many linear modulations. Nonlinear demodulation would replace the equalizer with a phase discriminator and also probably not have carrier tracking. 10/30/2013 John Reyland, PhD
- 30. Digital Signal Processing Intermediate center frequency Fif = 44.2368 MHz. Does this mean sampling frequency Fs > 88.4736 MHz ? No, we can bandpass sample, by making Fs = (4/3) Fif = 58.9824 MHz. This has advantages: • Lower sample rate => smaller sample buffers and fewer FPGA timing problems • Fif can be higher for the same sample rate, this may make frequency planning easier Disadvantage is that noise in the range [Fs/2 Fs] is folded back into [0 Fs/2] 10/30/2013 John Reyland, PhD
- 31. Digital Signal Processing Complex basebanding process in the frequency domain, ends with subsampled Fs = 29.491 MHz 10/30/2013 John Reyland, PhD
- 32. Digital Signal Processing Halfband Filter response HalfBand filter Impulse Response, Order=11 0.6 0.4 Typical Matlab code: 0.2 0 -0.2 Fss = 58.9824e6; 1 2 3 4 5 6 7 8 9 10 11 Resp, dB 0 -10 -20 -30 -40 0 3.6864 7.3728 11.0592 14.7456 18.432 Frequency (MHz) 22.1184 25.8048 29.4912 0 3.6864 7.3728 11.0592 14.7456 18.432 Frequency (MHz) 22.1184 25.8048 29.4912 Resp, linear 1 0.5 0 10/30/2013 John Reyland, PhD % Setup halfband filter for input subsampling PassBandEdge = 1/2-1/8; StopBandRipple = 0.1; b=firhalfband('minorder', … PassBandEdge, … StopBandRipple, … 'kaiser'); % Check frequency response [hb,wb] = freqz(b,1,2048); plot(wb,10*log10(abs(hb))); set(gca,'XLim',[0 pi]); set(gca,'XTick',0:pi/8:pi); set(gca,'XTickLabel',(0:(Fss/16):(Fss/2))/1e6);
- 33. Digital Signal Processing DSP Circuits for IF to Complex BB process Fs/4 Local Oscillator Inphase Halfband Filter I(n) + jQ(n) = [1+j0,0+j1,-1+j0,0-j1,1+j0, ...] HI(z) = h0 + z-2h2 + z-3h3 + z-4h4 + z-6h6 Ib(n) x(n) Z-1 h0 Z-1 Z-1 Z-1 Z-1 Z-1 0 h2 h3 h4 0 h6 Ihb(n) 2 Qb(n) Z-1 h0 Z-1 Z-1 Z-1 Z-1 Z-1 0 h2 h3 h4 0 h6 Qhb(n) 2 Quadrature Halfband Filter HQ(z) = h0 + z-2h2 + z-3h3 + z-4h4 + z-6h6 10/30/2013 John Reyland, PhD
- 34. Digital Signal Processing Input Samp. Index @ Fs Local Oscillator: I(n) + jQ(n) = Mixer Output Quadrature Halfband Filter Tap Signals x(n) x(0) x(1) x(2) x(3) x(4) x(5) x(6) x(7) I(n) 1 0 -1 0 1 0 -1 0 Q(n) 0 1 0 -1 0 1 0 -1 Ib(n) x(0) 0 -x(2) 0 x(4) 0 -x(6) 0 Qb(n) 0 x(1) 0 -x(3) 0 x(5) 0 -x(7) h0 0 x(1) 0 -x(3) 0 x(5) 0 -x(7) 0 0 0 x(1) 0 -x(3) 0 x(5) 0 h2 0 0 0 x(1) 0 -x(3) 0 x(5) h3 0 0 0 0 x(1) 0 -x(3) 0 h4 0 0 0 0 0 x(1) 0 -x(3) 0 0 0 0 0 0 0 x(1) 0 h6 0 0 0 0 0 0 0 x(1) x(8) x(9) 1 0 0 1 x(8) 0 0 x(9) 0 x(9) -x(7) 0 0 -x(7) x(5) 0 0 x(5) -x(3) 0 0 -x(3) x(10) x(11) -1 0 0 -1 -x(10) 0 0 -x(11) 0 -x(11) x(9) 0 0 x(9) -x(7) 0 0 -x(7) x(5) 0 0 x(5) x(12) x(13) 1 0 0 1 x(12) 0 0 x(13) 0 x(13) -x(11) 0 0 -x(11) x(9) 0 0 x(9) -x(7) 0 0 -x(7) x(14) x(15) -1 0 0 -1 -x(14) 0 0 -x(15) 0 -x(15) x(13) 0 0 x(13) -x(11) 0 0 -x(11) x(9) 0 0 x(9) 10/30/2013 John Reyland, PhD Quadrature Half Band Output @ sample rate = Fs/2 0 x(1)*h0 0 -x(3)*h0 + x(1)*h2 x(1)*h3 x(5)*h0 - x(3)*h2 + x(1)*h4 -x(3)*h3 -x(7)*h0 + x(5)*h2 - x(3)*h4 + x(1)*h6 x(5)*h3 x(9)*h0 - x(7)*h2 + x(5)*h4 x(3)*h6 -x(7)*h3 -x(11)*h0 + x(9)*h2 - x(7)*h4 + x(5)*h6 x(9)*h3 x(13)*h0 - x(11)*h2 + x(9)*h4 x(7)*h6 -x(11)*h3 -x(15)*h0 + x(13)*h2 - x(11)*h4 + x(9)*h6
- 35. Spacecraft Downlink Tracking Downlink Doppler measurements: Range rate and uplink pre-compensation 10/30/2013 John Reyland, PhD
- 36. Kalman Filters A Kalman filter estimates the state of an ‘n’ dimensional discrete time process governed by the linear stochastic difference equation: x(k ) Ax(k − 1) + Bu (k − 1) + w(k − 1) = A = (n by n) Represents the system dynamics of the system whose state we are trying to estimate. Control input matrix B = (n by l) is optional Discrete time state vector x(k ) is not directly observable, however we can measure: = Hx(k ) + v(k ) z (k ) H = (m by n) v(k ) is a random variable representing the normally distributed measurement noise p (v) ~ N ( 0, Q ) w(k ) is a random variable representing the normally distributed process noise p ( w) ~ N ( 0, Q ) 10/30/2013 John Reyland, PhD
- 37. Kalman Filters Kalman filter prediction/correction loop: Inputs current time flight dynamics, outputs prediction of t seconds ahead position: 10/30/2013 John Reyland, PhD
- 38. Special Topics NASA Space Telecommunications Radio System (STRS) 10/30/2013 John Reyland, PhD
- 39. NASA STRS General-purpose Processing Module (GPM): Supports radio reconfiguration, performance monitoring, ground testing and other supervisory functions Signal Processing Module (SPM): Implements digital signal processing modem functions such as carrier estimation, equalization, symbol tracking and estimation. Components include ASICs, FPGAs, DSPs, memory, and interconnection bus. Radio Frequency Module (RFM): Provides radio frequency (RF) passband filter and tuning functions as well as intermediate frequency (IF) sampling. Also includes transmit RF functions. Components include filters, RF switches, diplexer, LNAs, power amplifiers, ADCs and DACs. 10/30/2013 John Reyland, PhD

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