TCOM 707 Advanced Link Design

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TCOM 707Advanced Link Design

• FALL 2004
• Innovation Hall 135 Thursdays 430 710 p.m.
• Dr. Jeremy Allnutt
  jallnutt_at_gmu.edu

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General Information - 1

• Contact Information
• Room Science Technology II, Room 269
• Telephone [phone]
• Email jallnutt_at_gmu.edu
• Office Manager lfortney_at_gmu.edu
• Office Hours
• Mondays and Tuesdays 300 600 p.m.Please, by
  appointment only

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General Information - 2

• Course Outline
• Go to http//ece.gmu.edu/coursepages.htmor
  http//telecom.gmu.edu and click on Course
  Schedule
• Scroll down to TCOM 707
• Snow days call [phone]
• You MUST have a Mathematical Calculator
  please, simple ones only

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General Information - 3
As a general rule, no more than 40 of any paper
should be drawn directly from another source

• Homework Assignments
• Feel free to work together on these, BUT
• All submitted work must be your own work
• Web and other sources of information
• You may use any and all resources, BUT
• You must acknowledge all sources
• You must enclose in quotation marks all parts
  copied directly and you must give the full
  source information

5
General Information - 4

• Exam and Homework Answers
• For problems set, most marks will be given for
  the solution procedure used, not the answer
• So please give as much information as you can
  when answering questions partial credit cannot
  be given if there is nothing to go on
• If something appears to be missing from the
  question set, make and give assumptions used
  to find the solution

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General Information - 7

• Class Grades
• Emphasis on overall effort and results
• Balance between HW, tests, and class project
• Homework - 10
• Tests - 30 30
• Project Presentation - 30

This is the final exam
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TCOM 707 Course Plan

• Go to http//ece.gmu.edu/coursepages.htm or
  http//telecom.gmu.edu and click on Course
  Schedule scroll down to TCOM 707
• In-Class Tests scheduled for - October 7th,
  2004 Radar systems - November 4th, 2004
  Satellite Systems
• In-Class Final exam (Project presentation) -
  December 16th, 2004

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TCOM 707 Lecture 1 Outline

• Introduction to Radar Systems
• Background
• Time, frequency, and spectrum considerations
• Range calculations
• Pulse repetition frequency issues
• Derivation of radar equation
• Radar applications

Check out Introduction to Radar Systems, 2nd
ed., Merrill I. Skolnik, McGraw-Hill, 2001, ISBN
0-07-290980-3
And special thanks to Dr. Tim Pratt of VT,
primary author of ECE 5635
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TCOM 707 Lecture 1 Outline

• Introduction to Radar Systems
• Background
• Time, frequency, and spectrum considerations
• Range calculations
• Pulse repetition frequency issues
• Derivation of radar equation
• Radar applications

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Background 1

• RADAR Radio Detection And Ranging
• Detection of targets (primary skin reflection)
• Range (time delay)
• Velocity (differential time delay or Doppler)
• Angle (azimuth)
• Target Characteristics (echo properties)
• Ground mapping (under, above, space)

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Background 2

• Radar principles
• Transmit a very short ( 1?s) burst of radio
  waves (usually at microwave frequencies)
• Wait for reflected radiowaves (the echo) to
  come back to the radar
• Process the returned signal (the echo) using
  radar parameters

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Background 3

• Echo Strength
• This is proportional to the Radar Cross Section
  (RCS) of the target, and it tells us about the
  SIZE of the target in radar terms
• Delay Time
• This is proportional to the range from the radar
  to the target (and back!)

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Background 4
scatterer
Short RF pulse (kW)
t1
Received pulse (pW)
Time delay t2 t1 td
t2
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Background 5
Necessitated by imminence of WW II

• First radar was Chain Home
• Primitive COTS approach
• HF (four spot frequencies, 20 to 55 MHz)
• Tall transmit towers
• Dipole detectors
• A-Scan display

Well take a brief look at CH
For more details, please visit http//www.radarpag
es.co.uk/mob/ch/chainhome.htm
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Chain Home 1
Curtain Array
Receive crossed dipoles
240
360
Transmit
Receive
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Chain Home 2
Transmit towers
The radar did not track it merely floodlit
the area to be investigated. Receive lobes were
similar
Backlobe
Forwardlobe
Plan view of transmit facility with a schematic
of the antenna pattern
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Chain Home 3
Here, five CH radars cover a large section of the
coast
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Chain Home 4
Possible targets
Movement of radar trace
Amplitude
Possible targets
Clutter
?
Clutter
Distance
A-Scan display
PPI display
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Background 6

• CH and all subsequent surveillance radars are
  Primary Radars
• Primary Radars use skin echo to detect targets
• Most airports and controlled airspaces use both
  Primary and Secondary Radars
• Secondary radars relies on a cooperative target
  to relay information from a transponder

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Background 7
1see http/virtualskies.arc.nasa.gov/communication
/youDecide/Transponder and http//www.trvacc.org/w
eb/training/ref/squak.asp

• Secondary radars transmit an encoded signal to
  the targets transponder
• The transponder replies with an encoded message
  with information about the airplane
• A typical transponder can be set to any of 4096
  identifying codes1
• Military transponders are called IFF
  (Identification, Friend or Foe)

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TCOM 707 Lecture 1 Outline

• Introduction to Radar Systems
• Background
• Time, frequency, and spectrum considerations
• Range calculations
• Pulse repetition frequency issues
• Derivation of radar equation
• Radar applications

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Time, frequency, and spectrum considerations 1
c f ? ?, where c velocity of light in vacuo
3 ? 108 m/s, f
frequency, in Hz and ?
wavelength, in metersExampleWhat is the
wavelength for a frequency of 3
GHz?AnswerWavelength ? c/f (3 ? 108)/(3
? 109) 10-1
0.1m 10 cm
Important note on units
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Time, frequency, and spectrum considerations 2

• Radar engineers use a wide mix of units
• Miles, yards, meters, nautical miles, knots,
  hours, etc.
• Calculations are easier if a standard set of
  units are used
• The international standards for electrical
  engineers is the MKS system
• meters, kilograms, seconds

Do NOT mix units!
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Time, frequency, and spectrum considerations 3
Scaling in MKS units ? 1,000 or
103 kilo k ? 1,000,000 or 106 Mega M ?
1,000,000,000 or 109 Giga G ?
1,000,000,000,000 or 1012 Tera T ? 1,000 (or
? 10-3) milli m ? 1,000,000 (or ?
10-6) micro ? ? 1,000,000,000 (or ?
10-9) nano n ? 1,000,000,000,000 (or ?
10-12) pico p ? 1,000,000,000,000,000 (or ?
10-15) femto f
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Time, frequency, and spectrum considerations 4A

• All radio waves are polarized
• The direction of the E field defines the
  polarization sense

Direction of travel (z-axis)
E Electric fieldH Magnetic field
This is a linearly polarized wave
E
E, H, and z-axes are mutually orthogonal
H
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Time, frequency, and spectrum considerations 4B

• The E vector may rotate leading to another
  special case Circular Polarization

E Electric field
This is a right hand circularly polarized wave
Direction of travel (z-axis)
E
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Time, frequency, and spectrum considerations 5
The E and H fields vary sinusoidally at the
frequency of the wave and with distance from the
source (and reflector)
Direction of travel (z-axis)
This is a linearly polarized wave
E
H
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Time, frequency, and spectrum considerations 6

• Radio waves are reflected by smooth conducting
  surfaces e.g. a metal sheet, water
• Treat reflection using ray theory, as in optics.

Normal to surface
Incident ray
Reflected ray
?
?
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Time, frequency, and spectrum considerations 7A

• Non-conductive materials allow radio waves to
  pass through, but .
• If dielectric constant ? 1.0 (air), partial
  reflection will occur

Medium 1
Medium 2
Incident ray
Partially reflected ray
Partially transmitted ray
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Time, frequency, and spectrum considerations 7B

• Can take the real part of the dielectric constant
  refractive index n
• reflection coefficient, ?,can be found from the
  two refractive indices of media 1 and 2

? 1 -
(n1 - n2)2
(n1 n2)2
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Time, frequency, and spectrum considerations 8

• How to measure the energy of a radio wave?
• Difficult to measure volts and amps above about
  100 MHz
• Can measure power (watts)
• All radar calculations are carried out in Watts
• but more likely in ?W, nW, pW, etc.
• or in dBW, dBm, etc.

Preferred units for link budget calculations
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Time, frequency, and spectrum considerations 9

• All radio signals have a defined bandwidth
• Many definitions of bandwidth
• null-to-null, 3 dB, absolute, noise, etc.
• In general, bandwidth amount of frequency space
  occupied by the signal
• Some examples are
• FM radio (200 kHz)
• Analog TV (video sound 6 MHz)

Otherwise known as spectrum occupancy
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Time, frequency, and spectrum considerations 10A

• Bandwidth (spectrum) is related to the time
  waveform through the Fourier transform, V(f)
• Rectangular pulse ? (sin x)/(x) spectrum

V(f)
This is a Two-sided spectrum
V(t)
t (s)
f (Hz)
0
T
-2/T
-1/T
1/T
2/T
0
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Time, frequency, and spectrum considerations 10B
V(t)
t (s)
0
T
V(f)
This is a One-sided spectrum
Radar pulse at a carrier frequency of fc
f (Hz)
fc -2/T
fc 2/T
fc -1/T
fc 1/T
fc
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Time, frequency, and spectrum considerations 11

• Radio receiver bandwidth is defined by filters
  (usually at IF)
• Noise bandwidth B Hz

Baseband
Passband
Ideal
V(f)
V(f)
Real
f
f
0
B
fc
fc - B/2
fc B/2
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TCOM 707 Lecture 1 Outline

• Introduction to Radar Systems
• Background
• Time, frequency, and spectrum considerations
• Range calculations
• Pulse repetition frequency issues
• Derivation of radar equation
• Radar applications

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Range Calculation - 1

• Velocity, v, distance/time
• Can assume v 3 ? 108 m/s 300 m/?s
• Round trip distance 150 m/?s Example if the
  delay is 1,500 ?s, the range to the target is
  225 km
• Some useful numbers Time delay 1 ?s per 150 m
  of target range Time delay for a target at 1 km
  6.67 ?s

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Range Calculation - 2

• Range, R (c TR)/2 (eqn. 1.1 in
  Skolnik)where TR is the time taken for the round
  trip of the pulse from the radar to the target
  and back again, in seconds. The factor 2 appears
  in the denominator because of the two-way (round-
  trip) propagation.With the range in kilometers
  (km) or nautical miles (nmi), and TR in
  microseconds (?s), eqn. (1.1) becomes
• R(km) 0.15TR(?s) or R(nmi) 0.081 TR (?s)

Example
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Range Calculation - 3
What is the range in kilometers and nautical
miles to a target with a time delay of 27 ?s?
R(km) 0.15TR(?s) or R(nmi) 0.081 TR
(?s) 0.15 ? 27 or
0.081 ? 27 4.05 km or
2.187 nmi
This calculation is for a single pulse. Most
radars send more than one pulse to provide for
sample averaging and updates on target position
in the required time interval for tracking
resolution. Echo from a distant target can
arrive after the second pulse in the pulse train,
leading to range ambiguities
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Range Calculation 4A
Target 2, range 18 km
Target 1, range 6 km
Primary radar prf 10 kHz
Time, seconds
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Range Calculation 4B
Target 2, range 18 km
A prf of 10 kHz gives one pulse every 0.0001 s
0.1 ms
Target 1, range 6 km
Primary radar prf 10 kHz
Remembering Range in km 0.15TR(?s), lets look
at the A-scan
Time, seconds
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Range Calculation 5
A range of 6 km gives a delay time of 40 ?s and a
range of 18 km gives a delay time of 120 ?sNote
that target 2 is so far away that the echo does
not reach the radar until after the next pulse,
giving an incorrect range of 3 km
Amplitude
Transmit pulse
Transmit pulse
Target 1
Target 1
Target 2
Time, t, in ms
0 0.04
0.1 0.12 0.14
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TCOM 707 Lecture 1 Outline

• Introduction to Radar Systems
• Background
• Time, frequency, and spectrum considerations
• Range calculations
• Pulse repetition frequency issues
• Derivation of radar equation
• Radar applications

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Pulse Repetition Frequency Issues 1
Equation 1.2 in Skolnik

• Unambiguous range Runambc/(2fp) where fp
  the pulse repetition frequency (prf)
• NOTEKeep the units the same! If the velocity
  of light is in m/s, the range will be in meters
• Examplefp 1 kHz 1,000 HzRunamb c/(2fp)
  (3 ? 108)/(2 ? 1,000) 1.5 ? 105 150 km

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Pulse Repetition Frequency Issues 2
Example We require an unambiguous range of at
least 200 km. What is the maximum prf to meet
this requirement?Round trip time tp (2 ?
range)/c seconds
(2 ? 2 ? 105)/(3 ? 108) seconds
1.33 ? 10-3 seconds
1.33 msThus max. prf fp 1/tp
1/(1.33 ? 10-3) 751.8797 ? 750 Hz
Alternatively, since Runamb c/(2fp), fp c/(2
? 200 ?103)
(3 ? 108)/(2 ? 200 ?103) 750 Hz
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Pulse Repetition Frequency Issues 3

• Typical prf values
• 300 Hz long range radar 500 km max.
  range(strategic defense and airport facilities)
• 8,000 Hz very short range radar 18.75 km max.
  range(local defense against missiles)
• 300 1,700 Hz are widely used values of prf

C- and S-band radars
Ku- and Ka-band radars
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Radar Frequencies 1
Specific radiolocationBand Nominal (radar)
bands based on ITUdesignation frequency
range assignments for Region 2HF 3 30
MHzVHF 30 300 MHz 138 144 216 225
MHzUHF 300 1000 MHz 420 450 890 942
MHzL 1000 2000 MHz 1215 1400 MHz S 2000
4000 MHz 2300 2500 2700 3700 MHzC 4000
8000 MHz 5250 5925 MHzX 8000 12,000
MHz 8500 10680 MHzKu 12 18 GHz 13.4
14.0 15.7 17.7 GHz K 18 27 GHz 24.05
24.25 GHzKa 27 40 GHz 33.4 36.0 GHzmm 40
300 GHz
Table 1.1 in Skolnik
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Radar Frequencies 2

• Low frequencies (lt6 GHz)
• Little rain attenuation, hence
• Long(er) range, which requires
• High(er) power and
• Low prf
• Large dead zone possible
• Simpler T/R cell design
• Best for large area defense

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Radar Frequencies 3

• High frequencies (gt8 GHz)
• Rain attenuation becoming significant, hence
• Short(er) range, which can use
• Low(er) power and
• High prf
• Large dead zone NOT possible
• More complicated T/R cell design
• Best for local defense

Eased by low power needs
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Radar Frequencies 4
High frequencies and elevation angles, very
directive
Plane wavefront launched by radar
As frequencies/ elevation angles reduce, energy
forms strong ground wave and can also produce
some scattered energy over the horizon (OTH)
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TCOM 551 Lecture 1 Outline

• Introduction to Radar Systems
• Background
• Time, frequency, and spectrum considerations
• Range calculations
• Pulse repetition frequency issues
• Derivation of radar equation
• Radar applications

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Radar Equation 1
Isotropic antenna radiating equally in every
direction
Ever expanding spheres of flux
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Radar Equation 2

• If the isotropic antenna has a transmit power of
  Pt watts, what is the flux density at any given
  distance, R (range), from the isotropic antenna?
• Since the isotropic antenna radiates equally in
  every direction, we need to find the surface area
  of the sphere at distance, R
• Surface area of the sphere 4?R2

Hence we can find the power flux density
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Radar Equation 3

• The power flux density (pfd) at a distance R from
  the isotropic antenna is given by pfd Pt /
  4?R2 W/m2

Example
Skolnik equation 1.3
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Radar Equation 4

• If an isotropic antenna radiates 10 watts of
  power, what is the power flux density at a
  distance of 1 km?
• pfd Pt / 4?R2 10 / 4?(1,000)2 10 /
  12,566,370.62 0.7957747 ? 10-6W/m2
  0.7957747 ?W/m2 795.8 nW/m2

Note 1 keep the units correct
Note 2 this value is very small
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Radar Equation 5

• The power flux density (pfd) at a distance R from
  the isotropic antenna is given by pfd Pt /
  4?R2 W/m2
• But what if the antenna is NOT isotropic?
• A non-isotropic antenna will have a preferred
  direction in which more energy is transmitted

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Radar Equation 6

• Most radar antennas are not isotropic
• Additional power in the required direction is the
  gain of the antenna over that of an isotropic
  antenna
• Define antenna gain, G, asG

Flux density with Test Antenna at range RFlux
density with Isotropic Antenna at range R
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Radar Equation 7
Maximum power in this direction
360o Contour, referred to as an antenna pattern,
showing the power radiated in the given directions
0o
90o
270o
The difference in power can be described by the
gain in these directions
Minimum power in this direction
180o
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Radar Equation 8

• Antennas that radiate in a preferred direction
  are called directional antennas
• The Gain, G(?) over the preferred angular range
  ?, is given byG(?) (P(?)) / (Po / 4?)

Total power transmitted by the antenna in all
directions
Power transmitted per unit solid angle by the
antenna
4? is the total solid angle from the center of a
sphere
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Radar Equation 9

• There are two different measures for describing
  the power distribution around an antenna
• The directivity of the antenna and
• The gain of the antenna (sometimes more correctly
  called the power gain)
• Directivity is referenced to the mean power
  radiated
• Gain is referenced to an isotropic antenna

This is the more important descriptor.We will
look at how it increase the flux density
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Radar Equation 10
Antenna Gain GPower Pt watts
1 m2 surface
R
Power flux density, F, for a directive antenna
with gain, G, isF
G Pt
Equation 1.4 in Skolnik
4 ? R2
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Radar Equation 11

• When the gain, G, of an antenna is referred to,
  it is usually the maximum gain that is being
  spoken of
• The Maximum Gain, G, is usually achieved on Bore
  Sight, i.e. on the principal axis of the antenna
• Antenna patterns are reference to 0 dB (the gain
  of an isotropic antenna) most calculations are
  carried out in dB

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Radar Equation 12
Main lobe
Second side lobe
Third side lobe
First side lobe
Boresight direction
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Radar Equation 13
Gain (dB)
0
-3
-10
3 dB down from peak gain
3 dB beamwidth
-20
Main lobe
Side lobes
-30
-40
?
Rectangular (or Cartesian) plot of the angle off
bore sight
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Radar Equation 14

• Parabolic antennas are the most common form of
  directive antennas in microwave communications
• The gain of a parabolic antenna is given
  by gain 4?A/?2 (?D/?)2

A Aperture area ?(radius)2
?(diameter/2)2Therefore, 4?A/?2 4
?(?(diameter/2)2)/?2 4 ?2D2/4?2 (?D/?)2
Example
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Radar Equation 15

• A parabolic antenna has an aperture diameter, D,
  of 2m. It will operate at 12 GHz. What is the
  gain, both as a ratio and dB value?Answer
  First find the wavelengthVelocity of radio wave
  frequency ? wavelength,
  i.e. c f? Thus 3 ? 108
  12 ? 109 ? ?, and so
  ? 3 ? 108 / 12 ? 109 m
  0.025 m

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Radar Equation 16

• Now we can find the gain from gain 4?A/?2
  (?D/?)2 and so the gain, G, of the parabolic
  antenna isG (? ? 2 / 0.025)2 63,165.46817
  63,165 or, in dB, G 10 log (63,165.46817) 48
  dB

But this is only the theoretical answer!
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Radar Equation 17

• Antennas are never perfect
• The actual gain achieved is therefore less than
  the theoretical gain calculated
• The difference can be thought of as the
  efficiency of the antenna, ?
• Actual gain Theoretical gain ? ?
• ? value is between 1 (perfect) and 0

Example
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Radar Equation 18

• ExampleThe calculated gain of an antenna is 50
  dB. The efficiency of the antenna is 75. What
  is the real gain of the antenna?AnswerFirst
  change 50 dB to a ratio ? 100,000Second
  Multiply by 0.75 ? gain of 75,000Third convert
  back to dB ? 48.8 dBThe real gain of the antenna
  is 48.8 dB

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Radar Equation 19

• Sometimes, the real gain is calculated from a
  knowledge of the effective aperture
• The effective aperture of an antenna is the
  physical aperture ? ?, that isAe A ? ?
• This ? is the same efficiency used earlier

Example
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Radar Equation 20

• A 2m diameter antenna has an efficiency of 75.
  What are the real and effective apertures?
• Real aperture, A ? (radius)2 ? (1)2 ?
  3.14 m2
• Effective aperture Ae ?A ? ? 3.14
  0.75 ? 3.14
  2.36 m2

Derivation of Radar Equation will be in lecture 2
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TCOM 707 Lecture 1 Outline

• Introduction to Radar Systems
• Background
• Time, frequency, and spectrum considerations
• Range calculations
• Pulse repetition frequency issues
• Derivation of radar equation
• Radar applications

73
Basic Pulse Radar
Switch
Antenna
Transmitter
TX
RX
Receiver
Controller
C
Display unit
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Basic Pulse Radar
This is the T/R cell
Switch
Antenna
Transmitter
TX
RX
Receiver
Controller
C
Display unit
75
Types of Radar 1
Type ApplicationPulse (incoherent) Target
detection Range Measurement SurveillanceDo
ppler (coherent) Velocity measurements MTI Sepa
rates moving targets from clutter Pulse
Doppler Range and Velocity
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Types of Radar 2
Type ApplicationTracking Range and Angle
measurement Fire control, Guidance Synthetic
Aperture High spatial resolution Very rapid
tracking AEW (AWACS) Airborne pulse
Doppler separates moving targets from clutter
using a moving radar (Highly complicated
space-time adaptive processing)