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


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


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


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


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



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

Presenter

Presentation Notes

L = samples/symbol, R=1 implies one modulating cycle per symbol. R=2.5 in this example


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



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


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


Time Diversity:

After receiver reassembles, all errors can be corrected See [R5] and [R6]

Error Control and Channel Coding Maximum Likelihood (ML) detector:


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

Presenter

Presentation Notes

SD=0 means receiver has no confidence in bit decision, obliviously true

Error Control and Channel Coding ML decisions in a general N dimensional signal space:


( )( )

( ) ( ) ( )

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=

= −∑

Presenter

Presentation Notes

SD=0 means receiver has no confidence in bit decision, obliviously true

Error Control and Channel Coding Maximum a posteriori (MAP) detector:


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=

=

Presenter

Presentation Notes

SD=0 means receiver has no confidence in bit deci sion , obliviously true ML = MAP is symbols are equiprobable

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

Presenter

Presentation Notes

Used to protect data on CDs, the outer coder is a Reed Solomon block coder k = number of payload bits in block, n = number of coded bits in block, n-k = number of parity bits in block rows with >nb elements interlaces code word bits

Error Control and Channel Coding Turbo coding basic concept explained by an example


Presenter

Presentation Notes

Even if there is a terminating input bit sequence (i.e. returns coders to all zero state) because of the interleaver it is nearly impossible to return both coders to all zero state.


The maximum a posteriori (MAP) log likelihood ratio:


( )( )

( )( )

( )( )

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:

Presenter

Presentation Notes


Error Control and Channel Coding Log likelihood ratio of modulo two addition of two soft decisions (see []):


( ) ( ) ( ) ( )( ) ( )( ) ( ) ( )( )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

Presenter

Presentation Notes

Circle with plus sign means modulo 2 addition



Presenter

Presentation Notes




Column decode generates new extrinsic information



Column extrinsic information can be feedback to row decoder for a new iteration



Final turbo decode output is derived from all available statistically independent information:

Note how confidence levels are improved

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: ( ) ( )received transmits t s t δ= −

Presenter

Presentation Notes

Example pulse has 0 excess BW

Channel Equalization Techniques


See [E1] and [E2]

A decision feedback nonlinear adaptive equalizer:

Presenter

Presentation Notes

Linear and nonlinear part adaptation can be separate There is an error propagation problem with the nonlinear part

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

1010

10 3 13

10log 0.001 100.001

100 10 10 10 0.10 1

dBmPwatts

dBm wattsPP P

dBm picowattdBm milliwatt

− − −

= = − ⇒ = =

⇒

Presenter

Presentation Notes

CDMA base station mitigates power variation problem by closed loop power control of handsets



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):

Presenter

Presentation Notes

Note: the conjugate would be a single complex tone on the negative frequency axis Note that has exponential spins faster, it moves further out on the axis Centered at 0 Hz, an arbitrary signal must have arbitrary positive and negative spectral components The only way to represent that is with a complex exponential



Voltage Sampling: Undesired signals are all aliased at full power:

Current Sampling: Images at multiples of sampling rate are attenuated:


Compete Transmitter


Let’s discuss the function of the reconstruction filter and the bandpass filter…

Presenter

Presentation Notes

LTC5588 is Quad Mod example, TI DAC 5681 is DAC example

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.

Presenter

Presentation Notes

We will go over each block but maybe not in that order



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]



Complex basebanding process in the frequency domain, ends with subsampled Fs = 29.491 MHz



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


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)



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


Kalman Filters A Kalman filter estimates the state of an ‘n’ dimensional discrete time process governed by the linear stochastic difference equation:


( ) ( 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:


Special Topics

NASA Space Telecommunications Radio System (STRS)


Presenter

Presentation Notes

Each “radio supplier can encapsulate company proprietary circuit or software designs, provided the modules meet the specific architecture rules and expose the interfaces defined for each module.”

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.

Spacecraft RF Communications Course Sampler

Technology

p r s p s p r p s1 r

p r sm

log p r s

log ps r p r s

p r s1 p1

ln p r s

log p s

lmlif p s1