principles of space communication systems · principles of space communication systems space for...

Principles of space communication systems Space for Education, Education for Space

Space for Education, Education for Space ESA Contract No. 4000117400/16NL/NDe

Specialized lectures

Principles of space communication systems

Peter Farkaš


• Connection with previous lectures • Link Budget • Muscles • Essence

– AWGN channel alias DSC channel model – modulation – discrete AWGN channel – why BPSK? – why channel coding?

• Channel Codes • Hard versus soft decoding • Concluding remarks

Layout

2


• Prof. Hubinský

Described very well difficulties and problems with Deep Space Communication (DSC)

• Assoc. Prof. Valko

Mentioned that the bottleneck is channel throughput Often there is lot data and it is impossible (difficult or time consuming) to bring them to Earth

Connection

3


What we will imagine if we hear DSC?

4


5

Image: ESA


ESA's tracking station network Estrack

6

Image: ESA


Spectra for Deep Space Communication Present & Future

7

Visible light 430–770 THz 4.3x1012 to 7.7x1012 Hz

X Ray spectrum 30 petaHz – 30 exaHz (3×1016 Hz to 3×1019

Credit: Augmented snapshot from ESA video

Image: ESA


ESA's tracking station Antenna

8

Image: ESA


ESA's tracking station Demux

9

Image: ESA


ESA's tracking station Demux

10

Image: ESA


11

Image: ESA

This are just a muscles & resource 4 DSC


Are the muscles strong enough?

12

Image: ESA


Are the muscles strong enough?

13

If not can it help to built a bigger HW and use more power ?

Image: ESA


Range equation

14

224)(

m

W

d

Pdp t

Isotropic radiator


Range equation

15

224)(

m

W

d

Pdp t

tP

d

Isotropic radiator


Range equation

16

224)(

m

W

d

Pdp t

tP

d

err AdpP )(

Isotropic radiator


Range equation

17

224)(

m

W

d

Pdp t

tP

d

24 d

APP ert

r

Isotropic radiator


Range equation

18

dB3

dB3

peak


Range equation

19

dB3

dB3

peak

steradians4πoveraverage

intensitypowermaxG


Range equation

20

dB3

dB3

peak

steradians4πoveraverage

intensitypowermaxG

24 d

APGP ertt

r


Range equation

21

2

2;

4

er

err A

AG

24 d

AGPP ertt

r

4

2

rer GA

S

rttrttr

L

GGP

d

GGPP

24


Range equation ->Link Budget

22

S

rttr

L

GGPP

Srtt

S

rttr LGGP

L

GGPP 101010101010 log10log10log10log10log10log10


Link Budget Example: Voyager I

23

WPt 18

MHzfc 8415

md 50002060258167

dBiGt 48

dBiGr 85



24

f

c m03565,0

108415

1036

8

Hzfc 8415

md 50002060258167

48283202377047816580955274046428

03565,0

5000206025816742

SL



25

f

c m03565,0

108415

1036

8

Hzfc 8415

md 50002060258167

48283202377047816580955274046428

03565,0

5000206025816742

SL

dBLS 317



26

mWPt 18000

dB317

dBmPt 5,82

dBiGt 48

dBiGr 8,73

dBmPt 7.112



27

mWPt 18000

dB317

dBmPt 5,82

dBiGt 48

dBiGr 8,73

dBmPt 7.112 Is this enough? (for reliable transmission)


Reliability BER

28

rationoisetosignalfBER

At the receiving end !


Signal to noise ratio

29

N

S

In analog systems In digital systems



30

N

S


dBN

S10log10



31

N

S


dBN

S10log10

0N

Eb



32

N

S


dBN

S10log10

0N

Eb

dBN

Eb

0

10log10


Energy per bit has to be computed!

33

TR

STE

p

b


Can we also use some brain products?

34


Information Theory

35

Claude Elwood Shannon 1916-2001

„Encoder“ „Decoder“

Noise

][bpsCR

0BER...01100010

Image: MFO

Photo: By Jacobs, Konrad – http://owpdb.mfo.de/detail?photo_id=3807, CC BY-SA 2.0 de https://commons.wikimedia.org/w/index.php?curid=45380422


Coding

36

Source coding

Source decoding

Channel Coding

Channel decoding)

Modulator

Demodulator

Channel

Separation principle of IT


Source coding example

37

Source coding

2

11 P

4

12 P

4

13 P

source



38

Source coding

2

11 P

4

12 P

4

12 P

source

00 2

01 2

11 2

Codewords length



39

Source coding

2

11 P

4

12 P

4

12 P

i

J

i

i PPH

1

2log

source

00 2

01 2

11 2

Codewords length



40

Source coding

2

11 P

4

12 P

4

12 P

message

bit

PPH i

i

i

5.1

log3

1

2

source

00 2

01 2

11 2

Codewords length



41

Source coding

2

11 P

4

12 P

4

12 P

binit

bit75.0

2

5.1

source

00 2

01 2

11 2

Codewords length



42

Source coding

2

11 P

4

12 P

4

12 P

0 1

10 2

11 2

source

Codewords



43

Source coding

2

11 P

4

12 P

4

12 P

0 1

10 2

11 2

source

Codewords

message

binitn 5.12.2.

4

11.

2

1}{



44

Source coding

2

11 P

4

12 P

4

12 P

binit

bit1

5.1

5.1

0 1

10 2

11 2

source

Codewords

message

binitn 5.12.2.

4

11.

2

1}{


Coding

45

Source coding

Source decoding

Channel Coding

Channel decoding)

Modulator

Demodulator

Channel

Here is also redundancy: coding, protocols, synchronization …


Energy per bit has to be computed!

46

TR

STE

p

b


DSC Channel ?

47


AWGN

• Johnson Thermal Noise

48

Hz

WkT 0

0

)(tn

t


AWGN

• Distribution of samples Thermal noise

49

n

2

2

1)(

n

enp


AWGN

Two sided “frequency world” Model

50

n

)(np

0

f

Hz

WN

20

0


AWGN

One- sided “frequency world” Model

51

n

)(np

0

f

Hz

WN0

0


AWGN

One- sided “frequency world” Model

52

n

)(np

0

f

Hz

WN0

0 W

0.NWN


AWGN channel

• Model, which is too idealistic for terrestrial channels, but is quite accurate for deep space channel.

Model

53

)(ts )()()( tntstr i

)(tn


Formula for AWGN channel capacity

54

sbitWN

SWCW /1log

0

2



55

sbitWN

SWCW /1log

0

2



56

sbitWN

SWCW /1log

0

2

xy log

1 x

y



57

sbitWN

SWCW /1log

0

2

ex xx

1

01lim



58

sbitWN

SWCW /1log

0

2

ex xx

1

01lim

sbitWN

S

S

WN

S

NCW /1log

0

200



59

sbitWN

SWCW /1log

0

2

ex xx

1

01lim

sbitWN

S

S

WN

S

NCW /1log

0

200

sbitWN

S

WS

NC

S

WN

/1loglim

0

0

20



60

sbitWN

SWCW /1log

0

2

ex xx

1

01lim

sbitWN

S

S

WN

S

NCW /1log

0

200

sbitWN

S

WS

NC

S

WN

/1loglim

0

0

20

sbitxxS

NC x /1log

0

lim 1

20



61

sbitWN

SWCW /1log

0

2

ex xx

1

01lim

sbitxxS

NC x /1log

0

lim 1

20

sbiteS

NC /log2

0



62

sbitWN

SWCW /1log

0

2

ex xx

1

01lim

sbitxxS

NC x /1log

0

lim 1

20

sbiteS

NC /log2

0

sbitN

Se

N

SC /44.1log

0

2

0


Digital modulation

63


Digital modulation

64

)(,),(),(1 tststs Mi

Modulation alphabet (channel symbols)

time T

)(tsi)(ts j


Modulation rate

65



time T

)(tsi)(ts j

s

symbolch

TRM

.1


How is conected with transmission rate?

66



s

symbolch

TRM

.1

s

bitRp


Digital modulation

67

)(tsi )()()( tntstr i

)(tn



Matched Filter

)(ˆ tsi

decision (MAP )


Digital modulation BPSK

68



TttfAts c 0)2cos()(1




69






Signal space - geometrical representation

70

“… every waveform of finite length and with a finite frequency spectrum can be represented as a point or radius vector in N-space.” “Thus, each of the m signals considered … can be represented by its own point or radius vector.”

V. A. Kotelnikov, Theory of Potential Noise Immunity, DrSc. Thesis 1946

Image: By Kremlin.ru, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=18257931


Signal space (GFT)

71



ji

jiEdttt i

ji;0

;)()(

)(...)()()( 121211111 tatatats NN

)(...)()()( 22221212 tatatats NN

)(...)()()( 2211 tatatats NMNMMM

Kotelnikov, Theory of Potential Noise Immunity, DrSc. Thesis 1946


Signal space

72



ji

jiEdttt i

ji;0

;)()(

),...,,()( 112111 Naaats

),...,,()( 222212 Naaats

),...,,()( 21 MNMMM aaats


Signal space

73



ji

jiEdttt i

ji;0

;)()(

),...,,( 112111 Naaas

),...,,( 222212 Naaas

),...,,( 21 MNMMM aaas



74

)(1 t

)(2 t

1a

2a

s


signal as a point in signal space

75

)(1 t

)(2 t

1a

2a

s



76

If to the transmitted signal is added a noise waveform with a vector which can have an arbitrary direction and arbitrary length, then the resulting received waveform will also be characterized by a point in N-space, which most often will not coincide with any of the points corresponding to signals. Depending on the position of this point, the receiver will reproduce some message or other …

V. A. Kotelnikov : Theory of Potential Noise Immunity, DrSc. Thesis, 1946



77

)(1 t

)(2 t

1a

2a

s

r

n



78







79





bEbE


Digital modulation 64-QAM

80




Optimal receiver (without tr. code)

81


)(tn



Matched Filter

)(ˆ tsi

decision (MAP )


Error rates depend on Euclidian distance

82




Transmission rate ? Modulation Rate

83





84


Modulation alphabet (channel symbols) symbolbinitMK /log2



85

Mp RKR .




86



Mp RR

Mp RR 6


Back to IT

87


Dig. Modul. -> discrete AWGN channel

88


Dig. Modul.> discrete (d.)AWGN channel

89

bpM ERERS


1D signal set AWGN channel capacity?

90

R. M. Fano, „Transmission of Information“, MIT Press 1961

symbolbitN

EC /

21log

2

1

0

2

E0s E1s


When we get energy efficient DSC?

91

symbolbitN

EC /

21log

2

1

0

2

J

symbolbit

E

N

E

E

C /

21log

2

1

0

2


C/E [bit per symbol/J] (N0 =1)

92

C/E

[b

it p

er

sym

bo

l/J]

(N

0 =

1)

10log 10 E/ N0


C/E [bit per symbol/J] (N0 =1)

93

C/E

[b

it p

er

sym

bo

l/J]

(N

0 =

1)

10log 10 E/ N0

44.1



94

J

symbolbit

N

E

E

C /21log

2

1

0

2



95

ENERGY EFFICIENT RANGE

J

symbolbit

N

E

E

C /21log

2

1

0

2

2

10

0

N

E

0 1/2 dB35.0log10 10


bps ? in energy efficient range

96

symbolbitN

EC /44.1

0

2

10

0

N

E

How much bps we can get in this range ?

sbitN

ERCRCR M

Mp /44.10



97

symbolbitN

EC /44.1

0

2

10

0

N

E


sbitN

S

N

ERCRCR M

Mp /44.144.100



98

symbolbitN

EC /44.1

0

2

10

0

N

E


sbitCN

S

N

ERCRCR M

Mp /44.144.100


Bit Error Rate (BER)?

99


Bit Error Rate (BER)?

100

“energy of a pulse for a given noise power density is the effective determinant of error probability.”

V. A. Kotelnikov, Theory of Potential Noise Immunity, DrSc. Thesis 1946


AWGN channel optimal detection?

• Without coding only hard decision (detection is possible “old fashion”)

Hard detection

101


)(tn



Matched Filter

)(ˆ tsi

decision (MAP )


AWGN channel optimal detection?

• Without coding only hard decision (detection is possible “old fashion”)

Hard detection

102


)(tn



Matched Filter

)(ˆ tsi

decision (MAP )

Rz


Hard decision (detection)

103

z

2

0

1

2

1

0

12

1)/(

ay

eszp

2

0

2

2

1

0

22

1)/(

ay

eszp


BPSK BER

104

0

2

N

EQBER


Uncoded BPSK BER? in energy ef. range

105

1104.2


LESSON LEARNED

106

“If one wants to signal both Energy-efficient and reliably with

binary modulation on deep space channel than one must use channel coding”

J. Massey, DSC & Coding: A Marriage Made in Heaven, Reprint Springer 1992


Channel Coding

• Coding gain up to date codes more than 9 dB at BER =10-5

Coding gain

107

0

log10N

Eb

BER 110

210

310

410

510

5 6 7 8 9 10 [dB]

Mariner 69 2.2 dB Pioneer 9 3 dB . . . Turbo Code 9 dB


Channel Coding hard

• Linear Block Code is a k-dimensional subspace of an n-dimensional vector space over GF(q)

Introduction

108


Channel Coding hard

Clasification

109

Linear Nonlinear

Block

Tree

Linear Block Codes

Nonlinear Block Codes

Linear Tree Codes

Nonlinear Tree Codes

Polar Codes


Channel Coding hard

• Linear Block Code is a k-dimensional subspace of an n-dimensional vector space over GF(q)

Introduction

110

Évariste Galois (25 October 1811 – 31 May 1832)

GF(2)

}1,0{

+ 0 1

0 0 1

1 1 0

x 0 1

0 0 0

1 0 1


Repetition Code

111

(111)

(000)


Repetition Code

112

(111)

(000)


Repetition Code

113

(111)

(000)

[3, 1, 3] code

[n, k, dm] code


Repetition Code

114

(000)

[3, 1, 3] code

[n, k, dm] code (111)


Channel Coding hard

• [7,4,3] Hamming Code Introduction

115

1i

2i3i

4i

Hamming 1915 - 1998

Photo: By Source (WP:NFCC#4), Fair use, https://en.wikipedia.org/w/index.php?curid=40177109


Channel Coding hard

• Hamming Code Introduction

116

1i

2i3i

4i

6c

5c 4c

3c 1c0c

2c


Channel Coding hard

• Hamming Code Introduction

117

1i

2i3i

4i

6c

5c 4c

3c 1c0c

2c16 ic

25 ic

34 ic

43 ic

4210 iiic

3212 iiic

4321 iiic


Channel Coding hard

• Hamming Code Generator Matrix Introduction

118

6c

5c 4c

3c 1c0c

2c16 ic

25 ic

34 ic

43 ic

4210 iiic

3212 iiic

4321 iiic

PIG

1101000

0110100

1110010

1010001

G


Channel Coding hard

Introduction

119

16 ic 25 ic 34 ic 43 ic 4210 iiic

3212 iiic

4321 iiic

1101000

0110100

1110010

1010001

G

1i

2i

3i

4i


Channel Coding hard

• Generator Matrix Introduction

120

16 ic

25 ic

34 ic

43 ic

4210 iiic

3212 iiic

4321 iiic

Gic

1101000

0110100

1110010

1010001

G

4321 ,,, iiiii

0123456 ,,,,,, cccccccc


Channel Coding hard

• Control equations Introduction

121

6c

5c 4c

3c 1c0c

2c

02456 cccc

01345 cccc

00356 cccc


Channel Coding hard

• Control Matrix Introduction

122

1001011

0101110

0010111

H

0.1.0.0.1.0.1.1 0123456 ccccccc

0.0.0.1.0.1.1.1 0123456 ccccccc

0.0.1.0.1.1.1.0 0123456 ccccccc

IPHT

0

TcH

0

TcH


1001011

0101110

0010111

H

Tanner Graph

123


Reed Solomon Codes

124

121 ..)( tjjj xxxxg

Reed, I. S. and Solomon, G., “Polynomial Codes Over Certain Finite Fields,” SIAM Journal of Applied Math., vol. 8, 1960, pp. 300-304.

MDS non-binary block codes 1 kndm


Reed Solomon Codes

125

121 ..)( tjjj xxxxg

17,188,204

)())()(()(15210

xxxxxg

DVB-T


CCSDS Codes

126

Consultative Committee for Space Data Systems (CCSDS) concatenated coding system that uses RS as the outer code, and a convolutional inner code.

RS encoder

RS decoder

Convolutional Code encoder

Convolutional Code decoder (Viterbi)

Modulator

Demodulator

Channel


Deep Space LDPC- Comand Codes Control matrix A

127

[128, 64, ]


Deep Space LDPC- Comand Codes Generator matrix G

128

[128, 64, ]


Convolutional Codes

129

data

„Logic“

Tree Code Encoder

codeword

...01d

...01c


Convolutional Codes

130

data

„Logic“

Tree Code Encoder

codeword

...01d

...01c

...01c

...01d


Convolutional Code

131

...01d


Convolutional Codes

132

S0= 00

S1= 10

S2= 01

S3= 11

00/0

11/1

01/1

10/1

10/0

01/000/1

11/0


Convolutional Codes

133

S0

S1

S2

S3

0/00 0/00 0/00

1/01

0/00

1/01

0/00

1/01

0/00

1/01


Convolutional Codes

134


AWGN Channel Capacity BPSK + Coding in AWGN channel

135

54321 60 98712 10 11 12

1

5.0

4105 BER

Mariner 69 un-coded

Mariner 69 RM

Pioneer 9 Convol.code

Turbo-code LDPC

rN

E r

dB

B 12log10

0


MAP & ML

136

)/1(

.

.

)/1( iiii zsP

II

I

zsP

izz

2

0

1

2

1

0

12

1)/(

ay

eszp

2

0

2

2

1

0

22

1)/(

ay

eszp


MAP & ML

137

)1(

)1(

.

.

)1/(

)1/(

i

i

ii

ii

sP

sP

II

I

szp

szp)/1(

.

.

)/1( iiii zsP

II

I

zsP

izz

2

0

1

2

1

0

12

1)/(

ay

eszp

2

0

2

2

1

0

22

1)/(

ay

eszp


MAP & ML

138

)1/(

)1/(

2

1

ii

ii

szp

szp

l

lLR (def.):


Without coding

139

MAP 1)1(

)1(

)1/(

)1/(

i

i

ii

ii

vP

vP

vzp

vzp

0

)()()ˆ( vLyLvL c Without C

1ln)1(

)1(ln

)1/(

)1/(ln

i

i

ii

ii

vP

vP

vzp

vzp


With coding

140

)()()ˆ( vLzLvL c )ˆ()()()ˆ( vLvLzLvL ec

Without C With C

Ext.

A’priory

channel

)ˆ(vLeReal number: (signature – Hard absolute value- reliability


Turbocode

141

Interl.

4iS 3iS1

1

1

1

1

1

1

1

2iS 1iS1

1

1

1

1

1

1

1

iS1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1iS1

1

1

1

1

1

1

1

4iS 3iS1

1

1

1

1

1

1

1

2iS 1iS1

1

1

1

1

1

1

1

iS1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1iS1

1

1

1

1

1

1

1

...011100d

...011100)1( dc

...01)2( c

...01)3( c

12)(

ii xs

12)1( ii xs

}1,1{ is}1,0{ic}1,0{id


Turbo - decoding

142

)(vLApriory

SISO I )(vLIe

)ˆ()()()ˆ( vLvLyLvL ec

)()()ˆ( vLyLvL c )(yLc

SISO II

)(vLIIe

iii nvy


LDPC code decoding

143

0111001011

1010111010

1101011100

0110110101

1001100111

H

c1 c2 c3 c4 c5 c6 c7 c8 c9 c10

z1

z2 z3 z4

z5


Tanner Graph & Belief Propagation

144

c1 c2 c3 c4 c5 c6 c7 c8 c9 c10

z1 z2 z3 z4 z5

+ + + + +


Penalty binary code & BPSK

145

binit

bit

n

kRC



146

binit

bit

n

kRC

bitRRR CMp



147

binit

bit

n

kRC

bitRRR CMp

Fourier bandwidth W is proportional to C

p

MR

RR



148

binit

bit

n

kRC

bitRRR CMp


p

MR

RR



149

binit

bit

n

kRC

bitRRR CMp


p

MR

RR

Shannon Bandwidth for dimensional signal set MRB



150

s

bit

NB

SBCB

2

1log2

1

02

1MRB



151

s

bit

NB

SBCB

2

1log2

1

02

1MRB

s

bit

NR

SRC

M

MRM

2

1log2

1

02



152

bCMM ERRERS

s

bit

NR

SRC

M

MRM

2

1log2

1

02



153

bCMM ERRERS

s

bit

NR

SRC

M

MRM

2

1log2

1

02

s

bit

N

ER

ER

SC bC

bC

RM

2

1log2

1

02



154

s

bit

N

ER

ER

SC bC

bC

RM

2

1log2

1

02

C

CMR

2

2

1ln

0

0

N

ER

N

ER

bC

bC



155

2

1CR 76.0 dB2.1

bC ERE


CONCLUSION

156

In future we will need efficient reliable codes with not too complex decoding and as short codewords as possible Visible light and X ray spectrum can offer more Hz And so higher throughput


Thank you for you attention

157

principles of space communication systems · principles of space communication systems space for...

Documents