Spacecraft RF Communications Course Sampler
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Transcript of Spacecraft RF Communications Course Sampler
Spacecraft RF Communication Day 1:
10/30/2013 John Reyland, PhD
• Spacecraft communications introduction • RF signal transmission • RF carrier modulation • Noise and link budgets
Day 2:
Day 3:
• Error control coding • Telemetry systems • Analog Signal Processing • Digital Signal Processing
• Kalman filters • Satellite systems • Special topics
Stop me and ask!!!!
RF Signal Transmission
10/30/2013
.( )tθ
( )v t
( )( ) ( ) co s ( )rv t v t tθ=
Fixed inertial reference frame
Doppler frequency shift and time dilation affect RF channels where receiver and/or transmitter are moving relative to each other
RF Signal Transmission
Some Definitions:
10/30/2013
c = Speed of light, 3e8 meters/second
cf = Carrier frequency (Hz) ( )tθ = Angle between receiver’s forward velocity and
line of sight between transmitter and receiver
( )( ) ( ) co s ( )rv t v t tθ= = Velocity of receiver relative to transmitter
( )df t = Doppler carrier frequency shift at receiver
( )tT t = Transmit symbol time
( )rT t = Receive symbol time
RF Signal Transmission
Example 1:
10/30/2013
cf = 1 GHz = 1e+9 Hz
( )v t v= = 350 meters/second (constant, approx. Mach 1)
( )tθ = 0 (constant, worst case for Doppler shift)
rv v= = Velocity of receiver relative to transmitter
( ) 350 10(350)( ) 1 9 11673 8 3d d c
vf t f f e Hzc e
= = = = = =
Doppler carrier frequency shift at receiver
1( ) 1 61 6t tT t T ee
= = = − =+
Transmit symbol time
350( ) (1 6) 1 (1 6)(1.000001167)3 8
tr r t
vTT t T T e ec e
= = + = − + = − =
Receive symbol time
This means receive symbol time increases by 0.0001167%. - called time dilation
RF Signal Transmission
10/30/2013
d = distance between transmitter and receiver at leading edge of transmit pulsed+vTt = distance between transmitter and receiver at trailing edge of transmit pulse
Transmit Pulse, duration = Tt
Received Pulse, duration = Tr
dc=
td vTc+ =
Propagation time at leading edge of transmit pulse
Propagation time at trailing edge of transmit pulse
t td vT vTdc c c+ − = =
Additional time duration of pulse at the receiver
1tt t
vT vT Tc c
+ = + =
Dilated time duration of pulse at the receiver
RF Carrier Modulation
10/30/2013 John Reyland, PhD
Binary Phase Shift Keying (BPSK)
( )b n ( )x k( )a n
Antipodal Mapping
PulseForming
cos 2 RlL
π
Modulator
( )y l( )p k1 10 1⇒ +⇒ −
k = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 n = 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4
( )x k
( )y l
0 L 2L 3L 4L 5L
-Fb 0 Fb 2Fb-2Fb
0 Fc = RFb Fc = -RFb
R=1 implies one modulating cycle per symbol. R=2.5 in this example
RF Carrier Modulation
10/30/2013 John Reyland, PhD
Quadrature Phase Shift Keying (QPSK)
( )e eb n
( )a n
Serial 2 Parallel
PulseForming
1 10 1⇒ +⇒ −
( )o ob n
( )p k
( )p k ( )Qx l
( )Ix l
cos 2 RlL
π
Modulator
( )y l
sin 2 RlL
π
( )Iy l
( )Qy l
0 L 2L 3L 4L 5L 6L 7L 8L 9L
( )Ix k k = 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 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8
k = 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 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 ( )Qx k
( )a n 10
( )Iy l
( )Qy l
RF Carrier Modulation
10/30/2013 © John Reyland, PhD
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 In this example, M=4
0 1 2 3 4 5 6 7 8 9 10 11 120 0 0 0 1 1 1 1 2 2 2 2 3
nk==
Channel 0 SymbolsChannel 1 Symbols
Channel 2 SymbolsChannel 3 Symbols
Each channel now transmits QPSK symbols at block rate Fs/M
( ) ( )i qb n jb n+
IDFT
(4 3)b k +(4 2)b k +(4 1)b k +
(4 )b k
(4 3)s k +(4 2)s k +(4 1)s k +(4 )s k
RF Carrier Modulation
10/30/2013 © John Reyland, PhD
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 phase memory, i.e. current phase transition only depends on previous phase.
2π
Noise and Link Budgets
10/30/2013 © John Reyland, PhD
Important antenna specifications:
• Beamwidth: Angular field of view • Gain: Increase in power due to directionality • Sidelobe rejection: Attenuation of signals outside beamwidth
Error Control and Channel Coding
10/30/2013 © John Reyland, PhD
Time Diversity:
After receiver reassembles, all errors can be corrected See [R5] and [R6]
Error Control and Channel Coding Maximum Likelihood (ML) detector:
10/30/2013 © John Reyland, PhD
Detection mechanism uses the log-likelihood ratio, for detection filter output rrec:
( )( )
1 1
0 0
|log log
|ML
p r S pLp r S p
= =
Log-likelihood ratio sign is most probable hard decision
Error Control and Channel Coding ML decisions in a general N dimensional signal space:
10/30/2013 © John Reyland, PhD
( )( )
( ) ( ) ( )
2
0
10
200
10
1|
1ln | ln2
k mkr SNN
mk
N
m k mkk
p r S eN
Np r S N r SN
π
π
− −
=
=
=
−= − −
∏
∑
The most likely transmitted signal Sm minimizes the Euclidian distance:
( ) ( )2
1,
N
m k mkk
D r S r S=
= −∑
Error Control and Channel Coding Maximum a posteriori (MAP) detector:
10/30/2013 © John Reyland, PhD
Start with Bayes rule:
( )( )
( )( )
( )( )
1 1 1
0 0 0
| |log log log
| |MAP
p S r p r S p SL
p S r p r S p S
= = +
MAP Log-likelihood ratio = likelihood ratio based on observation + a priori information ratio
( ) ( ) ( )( )
||
p r S p Sp S r
p r=
( )( )
( ) ( )( )
( ) ( )( )
( ) ( )( ) ( )
1 1
1 1 1
0 00 0 0
|| |
|| |
p r S p Sp S r p r p r S p S
p r S p Sp S r p r S p Sp r
= =
A priori: Information knowable independent of experience A posteriori: Information knowable on the basis of experience
( ) ( )1 0if MAP MLL L
p S p S=
=
Error Control and Channel Coding Concatenated coding for Voyager mission to Saturn and Uranus
10/30/2013 © John Reyland, PhD
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
Error Control and Channel Coding Turbo coding basic concept explained by an example
10/30/2013 © John Reyland, PhD
Error Control and Channel Coding
The maximum a posteriori (MAP) log likelihood ratio:
10/30/2013 © John Reyland, PhD
( )( )
( )( )
( )( )
1 1 1
0 0 0
| |log log log
| |col col rowMAP ML AP ML EXT
p S r p r S p SL L L L L
p S r p r S p S
= = + = + = +
Turbo Decoder diagram for this example:
Error Control and Channel Coding Log likelihood ratio of modulo two addition of two soft decisions (see []):
10/30/2013 © John Reyland, PhD
( ) ( ) ( ) ( )( ) ( )( ) ( ) ( )( )0 1 0 1 0 1 0 1min ,L r r L r L r sig nL r sig nL r L r L r⊕ = =
This addition rule is used to combine data and parity into extrinsic information Extrinsic means extra, or indirect, information derived from the decoding process
Error Control and Channel Coding
10/30/2013 © John Reyland, PhD
Error Control and Channel Coding
10/30/2013 © John Reyland, PhD
Column decode generates new extrinsic information
Error Control and Channel Coding
10/30/2013 © John Reyland, PhD
Column extrinsic information can be feedback to row decoder for a new iteration
Error Control and Channel Coding
10/30/2013 © John Reyland, PhD
Final turbo decode output is derived from all available statistically independent information:
Note how confidence levels are improved
Channel Equalization Techniques
10/30/2013 John Reyland, PhD
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: ( ) ( )received transmits t s t δ= −
Channel Equalization Techniques
10/30/2013 © John Reyland, PhD
See [E1] and [E2]
A decision feedback nonlinear adaptive equalizer:
Analog Signal Processing
10/30/2013 © John Reyland, PhD
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
1010
10 3 13
10log 0.001 100.001
100 10 10 10 0.10 1
dBmPwatts
dBm wattsPP P
dBm picowattdBm milliwatt
− − −
= = − ⇒ = =
⇒
Analog Signal Processing
10/30/2013 © John Reyland, PhD
A complex representation is required at baseband because the modulation will cause the instantaneous phase to go positive or negation:
( ) ( )( ) co s ( ) sin ( )BBj tBB BBe t j tθ θ θ= +
Because the phase is now always positive, complex exponential terms are redundant ( ) ( ) ( )( ) co s ( ) sin ( )RF BBj t t
RF BB RF BBe t t j t tω θ ω θ ω θ+ = + + +
( ) ( ) ( )( ) ( )cos ( ) RF BB RF BBj t t j t tRF BBt t e eω θ ω θω θ + − ++ = +Signal now can be real:
This forces the existence of a negative image (ignored for most analog processing):
Analog Signal Processing
10/30/2013 © John Reyland, PhD
Voltage Sampling: Undesired signals are all aliased at full power:
Current Sampling: Images at multiples of sampling rate are attenuated:
Analog Signal Processing
Compete Transmitter
10/30/2013 © John Reyland, PhD
Let’s discuss the function of the reconstruction filter and the bandpass filter…
Digital Signal Processing
We will organize our DSP discussion around the digital receiver architecture below:
10/30/2013 John Reyland, PhD
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.
Digital Signal Processing
10/30/2013 John Reyland, PhD
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]
Digital Signal Processing
10/30/2013 John Reyland, PhD
Complex basebanding process in the frequency domain, ends with subsampled Fs = 29.491 MHz
Digital Signal Processing
10/30/2013 John Reyland, PhD
Halfband Filter response Typical Matlab code:
1 2 3 4 5 6 7 8 9 10 11-0.2
0
0.2
0.4
0.6HalfBand filter Impulse Response, Order=11
0 3.6864 7.3728 11.0592 14.7456 18.432 22.1184 25.8048 29.4912-40
-30
-20
-10
0
Frequency (MHz)
Resp
, dB
0 3.6864 7.3728 11.0592 14.7456 18.432 22.1184 25.8048 29.49120
0.5
1
Frequency (MHz)
Resp
, line
ar
Fss = 58.9824e6; % 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);
Digital Signal Processing DSP Circuits for IF to Complex BB process
10/30/2013 John Reyland, PhD
Inphase Halfband Filter
HI(z) = h0 + z-2h2 + z-3h3 + z-4h4 + z-6h6
Quadrature Halfband Filter
HQ(z) = h0 + z-2h2 + z-3h3 + z-4h4 + z-6h6
Fs/4 Local Oscillator
I(n) + jQ(n) = [1+j0,0+j1,-1+j0,0-j1,1+j0, ...]
x(n)
Ib(n)
Qb(n)
Z-1
0h0
Z-1
h6
Z-1
0
Z-1
h4
Z-1
h3
Z-1
h2
2
Z-1
0h0
Z-1
h6
Z-1
0
Z-1
h4
Z-1
h3
Z-1
h2
2
Ihb(n)
Qhb(n)
Digital Signal Processing
10/30/2013 John Reyland, PhD
Input Samp. Index @ Fs
Local Oscillator: I(n) + jQ(n) =
Mixer Output Quadrature Halfband Filter Tap Signals Quadrature Half Band Output @ sample rate = Fs/2
x(n) I(n) Q(n) Ib(n) Qb(n) h0 0 h2 h3 h4 0 h6 x(0) 1 0 x(0) 0 0 0 0 0 0 0 0 0 x(1) 0 1 0 x(1) x(1) 0 0 0 0 0 0 x(1)*h0 x(2) -1 0 -x(2) 0 0 x(1) 0 0 0 0 0 0 x(3) 0 -1 0 -x(3) -x(3) 0 x(1) 0 0 0 0 -x(3)*h0 + x(1)*h2 x(4) 1 0 x(4) 0 0 -x(3) 0 x(1) 0 0 0 x(1)*h3 x(5) 0 1 0 x(5) x(5) 0 -x(3) 0 x(1) 0 0 x(5)*h0 - x(3)*h2 + x(1)*h4 x(6) -1 0 -x(6) 0 0 x(5) 0 -x(3) 0 x(1) 0 -x(3)*h3 x(7) 0 -1 0 -x(7) -x(7) 0 x(5) 0 -x(3) 0 x(1) -x(7)*h0 + x(5)*h2 - x(3)*h4 +
x(1)*h6 x(8) 1 0 x(8) 0 0 -x(7) 0 x(5) 0 -x(3) 0 x(5)*h3 x(9) 0 1 0 x(9) x(9) 0 -x(7) 0 x(5) 0 -x(3) x(9)*h0 - x(7)*h2 + x(5)*h4 -
x(3)*h6 x(10) -1 0 -x(10) 0 0 x(9) 0 -x(7) 0 x(5) 0 -x(7)*h3 x(11) 0 -1 0 -x(11) -x(11) 0 x(9) 0 -x(7) 0 x(5) -x(11)*h0 + x(9)*h2 - x(7)*h4 +
x(5)*h6 x(12) 1 0 x(12) 0 0 -x(11) 0 x(9) 0 -x(7) 0 x(9)*h3 x(13) 0 1 0 x(13) x(13) 0 -x(11) 0 x(9) 0 -x(7) x(13)*h0 - x(11)*h2 + x(9)*h4 -
x(7)*h6 x(14) -1 0 -x(14) 0 0 x(13) 0 -x(11) 0 x(9) 0 -x(11)*h3 x(15) 0 -1 0 -x(15) -x(15) 0 x(13) 0 -x(11) 0 x(9) -x(15)*h0 + x(13)*h2 - x(11)*h4
+ x(9)*h6
Spacecraft Downlink Tracking Downlink Doppler measurements: Range rate and uplink pre-compensation
10/30/2013 John Reyland, PhD
Kalman Filters A Kalman filter estimates the state of an ‘n’ dimensional discrete time process governed by the linear stochastic difference equation:
10/30/2013 John Reyland, PhD
( ) ( 1) ( 1) ( 1)x k Ax k Bu k w k= − + − + −
Discrete time state vector is not directly observable, however we can measure: ( )x k
( ) ( ) ( )z k Hx k v k= +
( )v k
( )w k
is a random variable representing the normally distributed measurement noise
is a random variable representing the normally distributed process noise
( )( ) ~ 0,p v N Q
( )( ) ~ 0,p w N Q
(n by n)A = Represents the system dynamics of the system whose state we are trying to estimate. Control input matrix is optional (n by l)B =
(m by n)H =
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
Special Topics
NASA Space Telecommunications Radio System (STRS)
10/30/2013 John Reyland, PhD
NASA STRS
10/30/2013 John Reyland, PhD
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.