Mae 342 Lecture 16

Copyright 2008 by Robert Stengel. All rights reserved. For educational use only.http://www.princeton.edu/~stengel/MAE342.html

Communications Space System Design, MAE 342, Princeton University

Robert Stengel

• Antenna characteristics

• Power transmission andreception

• Signals, information, andnoise

• Analog and digital modulation

• Communication link budgets

!

C bits /s( ) =W log2S

N+1

"

# $

%

& '

Antenna Gain• Isotropic (uniform) radiation of power, P, from the center of a sphere of radius, r

• Power per unit area (power density) of the sphere!s surface

!

p = P 4"r2

• Power received from isotropic radiatorover area, S

!

PS = Sp

• Power received over area, S, if all poweris focused uniformly on that area byantenna with gain, G

!

PS =GSpS = P

• Power density in S with idealized focused antenna

!

pS = P GS

• Idealized antenna gain

!

G =P

SpS=4"r2

S!

" = beamwidth half # angle

Typical Antenna Pattern

• Gain vs. angle from boresight axis (2-D)

• Geff is average gain over beamwidth

• Beamwidth variously defined as –3 dB cone angle or half-angle

Communications Geometry

• Ground station communication and tracking limited by its minimumelevation angle, !

• Fixed (non-steerable) antenna must have sufficient beamwidth to transmitor receive

• Antenna gains and radiated power must be adequate, given slant rangeand noise environment

Beamwidth Coverage

• Broad or narrowcoverage may bedesired

!

"(cone) #21

fd,deg

f = carrier signal frequency,GHz

d = reflector diameter,m

Beamwidth of reflector antenna

Relationship of Antenna Area and

Signal Wavelength to Antenna Gain

• Power received from the transmitter

!

Geff =4"Aeff

#2

!

Aeff = effective antenna area,m2

" = carrier signal wavelength,m

= c / f

c = speed of light # 3$108m /s

f = carrier signal frequency,Hz

!

Pr = prAr =GtPtAr

4"r2

!

pr = power density at receiving antenna

Ar = effective area of receiving antenna

Gt = gain of transmitting antenna

Pt = transmitted power

r = distance between transmitting antenna and receiving antenna

• Power ratio

!

Pr(watts)

Pt(watts)

=G

tAr

4"r2

• Effective antenna gain (transmitting or receiving)

Antenna Characteristics Characteristics of Typical

Spacecraft Antennas

Conical logspiral antenna

!

Gain(dBi) =10logAntenna Gain

Isotropic Antenna Gain

Communications

Carrier FrequenciesDSCS-3

Alternative Expressions

for Power Ratio

!

Pr(watts)

Pt (watts)=GtAr

4"r2=AtAr

#r( )2

=AtAr f

2

cr( )2

=GtGr#

2

4"r2=GrAt

4"r2

• Power ratio in decibels

!

10log10Pr

Pt

"

# $

%

& ' (dB) =G

t(dB) +10log10 Ar

(dB) (10log10 4) (dB) ( 20log10 r(dB)

Atmospheric Attenuation, Multipath, and

Ionospheric Effects on Space-Earth

Communication

!

Pr

Pt(dB) =

Pr

Pt

"

# $

%

& ' ideal

(dB) ( Absorbtion(dB) ( Rainfall(dB)

± Multipath(dB) (CrossPolarization(dB)

Linear and Circular

Polarization of Waves

• Transmit andreceive antennasmust be alignedfor bestcommunication

• Left or righthelical rotationof signal

Detected Power and Noise

!

Pr

Pt(dB) =

Pr

Pt

"

# $

%

& ' ideal

(dB) ( Absorbtion(dB) ( Rainfall(dB)

± Multipath(dB) (CrossPolarization(dB)

!

Pr = Pcarrier + Pinformation " Pcarrier

Pd = Pr + Pn

• Receiver!s detected power includes components from

– transmitter!s carrier signal

– information signal

– noise

• Noise sources

– Receiver thermal and “front end” noise

– Atmospheric, cosmic, solar, and man-made noise

!

Pn = Pnreceiver + Pnatmosphere + Pnsolar + Pncosmic + Pnman"made

Receiver Noise

!

Pn

= kTW (watts)

T = 290 10NF(dB ) /10 "1( )= 290 F "1( )

!

k = Boltzmann' s constant =1.38 "10#23w # s /°K

T = effective receiver temperature,°K

W = bandwidth,Hz

NF = receiver noise figure

F = receiver noise factor

• Noise power and temperature

• Noise power density

!

No

= Pn/W = kT(watts /Hz)

Other Noise Sources

!

Pn "#n

or 1 fn

Solar NoiseCosmic and

Atmospheric Noise

Signal-to-Noise Ratio and

Information Content

!

S

N=Pr(watts)

Pn(watts)

!

S

NdB( ) = P

r(dB) " P

n(dB)

!

Pr(dB) "10log

Pr(watts)

1watt

#

$ %

&

' (

• Channel capacity

!

C bits /s( ) =W log2S + N

N

"

# $

%

& '

=W log2S

N+1

"

# $

%

& '

!

W = bandwidth,Hz

Information Bandwidth

!

fc = carrier frequency,Hz

W = "f = f2# f

1= information signal bandwidth,Hz

• Low-frequency information signal superimposed on(i.e., modulates) high-frequency carrier radio signalfor transmission

• Information signalformats– Analog (continuous)

– Digital (discrete)

– Digitized analog (i.e., A/Dconversion)

Power spectral density oftransmitted signal

Analog Amplitude, Frequency, and

Phase Modulation of Carrier Signal

Digital Amplitude-, Frequency-, and Phase-

Shift Modulation of Carrier Signal Digital Modulation vs.

Analog Modulation

PCM: pulse-code modulationFM: frequency modulationAM: amplitude modulation

• Analog

– Amplitude modulationconserves bandwidth

– Frequency modulationspreads informationbandwidth over larger RFbandwidth

• Digital

– Pulse-code modulation(particularly phase-shiftkeying) uses RF powermost efficiently

Signal-to-Noise Ratio

per Bit, Eb/No

!

S = received signal power

N = received noise power

W = bandwidth of receiver

R = data bit rate

!

Eb : energy per bit

No : noise power spectral density

!

Eb

No

=S

N

W

R

Link Budget for a

Digital Data Link

!

Eb

No

=PtLlG

tLsLaG

r

kTsR

!

Pt = transmitter power

Ll = transmitter " to" antenna line loss

Gt = transmit antenna gain

Ls = space loss

La = transmission path loss

Gr = receive antenna gain

k = Boltzmann' s constant

Ts = system noise temperature

!

Eb

No

=S

N

W

R

• Link budget design goal is to achievesatisfactory Eb/No by choice of link parameters

Typical Spacecraft System

Noise Temperature

Bit Error Rate vs. Eb/No• Goal is to achieve

lowest bit error rate(BER) with lowest Eb/No

• Implementation lossesincrease required Eb/No

• Link margin is thedifference between theminimum and actualEb/No

• BER can be reduced byerror-correcting codes

– Number of bitstransmitted isincreased

– Additional check bitsallow errors to bedetected andcorrected

Some Natural Numbering Systems

• Natural numbers: non-negative, whole numbers

• Other numbersystems– Octal (Base 8)

– Hexadecimal(Base 16)

– DNA (Base 4)[ATCG]

Denary (Base 10) Binary (Base 2) Unary (Base 1)

0 0 ?

1 1 1

2 10 11

3 11 111

4 100 1111

5 101 11111

6 110 111111

7 111 1111111

8 1000 11111111

9 1001 111111111

10 1010 1111111111

11 1011 11111111111

Digits Binary Digits Marks

"Bits" (John Tukey)

Two 5-finger hands True-False Chalk and a rock

One 10-finger hand Yes-No Abacus

Present-Absent "Chisenbop"

American Standard Code for

Information Interchange (ASCII) Code

http://en.wikipedia.org/wiki/Ascii

Binary Oct Dec Hex Glyph100 0000 100 64 40 @100 0001 101 65 41 A100 0010 102 66 42 B100 0011 103 67 43 C100 0100 104 68 44 D100 0101 105 69 45 E100 0110 106 70 46 F100 0111 107 71 47 G100 1000 110 72 48 H100 1001 111 73 49 I100 1010 112 74 4A J100 1011 113 75 4B K100 1100 114 76 4C L100 1101 115 77 4D M100 1110 116 78 4E N100 1111 117 79 4F O

• 7 data bits plus parity bit

• Widely used in computers

• 94 printable characters

Manchester Code for

Telecommunication

• Each data bit has one transition and occupies the same amount of time

• Self-clocking

• Widely used on Ethernet

http://en.wikipedia.org/wiki/Manchester_code

Error Detection

and Correction• Parity check (simple)

– Transmitter

• n Data bits added up

• Parity bit added to make sumeven

• n+1 bits transmitted

– Receiver

• Check to determine if word isodd or even

• If odd, odd number of errors hasbeen detected (but not corrected)

– Column-wise parity check of mwords determines where bits arecorrupted

• Additional bits must betransmitted

• Turbo code (complex): see

http://en.wikipedia.org/wiki/Turbo_code

Typical Command and

Telemetry Characteristics

TDRS

Typical Communication

Satellite Transponder

Characteristics

Next Time:Flight Computers and Computing

Mae 342 Lecture 16

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