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Components of a Pulse Radar SystemPresentation Transcript
1. Radar OUTLINE History Applications Basic Principles of Radar
Components of a Pulse Radar System The Radar equation Moving Target
Indicator (MTI) radar
2. Radar History Invented in 1900s (patented in 1904) and reinvented in the
1920s and 1930s Applied to help defend England at the beginning of World
War II (Battle of Britain) Provided advance warning of air raids Allowed
fighters to stay on ground until needed Adapted for airborne use in night
fighters Installed on ships for detecting enemy in bad weather (Bismarck)
3. Radar-Applications Air Traffic Control Air Navigation Remote Sensing
Marine Law Enforcement and highway safety Space Military
4. Radar-Applications Air Traffic Control Monitor the location of aircraft in
flight Monitor the location of aircraft/vehicles on surface of airports PAR
(precision approach radar) Guidance for landing in poor weather
5. Radar-Applications Air Navigation Weather radar Terrain avoidance and
terrain following Radar altimeter Doppler Navigator
6. Radar-Applications Remote Sensing Weather observation Planetary
observation (Venus probe) Mapping Ground Penetration radar
7. Radar-Applications Marine Detecting other ships, buoys, land Shore-based
radar for harbour surveillance and traffic control Law Enforcement and
highway safety Traffic speed radar Collision warning Blind area surveillance
for cars and school buses Intrusion alarms
8. Radar-Applications Space Rendezvous and docking Moon landing Remote
Sensing (RADARSAT)
9. Radar Basic Principles Transmits an electromagnetic signal modulated with
particular type of waveform. (modulation depends on requirements of
application) Signal is reflected from target Reflected signal is detected by radar
receiver and analyzed to extract desired information
10. Radar Modulation Types Simple Pulse; one or more repetition frequencies
Frequency Modulation FM (radar altimeters) Pulse with Chirp (pulse
compression) CW (continuous wave) - police radar (Doppler) Pseudorandom
code
11. Radar Basic Principles Distance can be determined by measuring the time
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difference between transmission and reception Angle (or relative bearing) can
be determined by measuring the angle of arrival (AOA) of the signal (usually
by highly directive antenna) If there is a radial component of relative velocity
between radar and target it can be determined from the Doppler shift of the
carrier
12. Radar Basic Principles Two types of radar: Monostatic - transmitter and
receiver use same antenna Bistatic - transmitter and receiver antennas are
separated, sometimes by large distances
13. Radar Generic Radar System Local Oscillator
14. Radar - Generic System Transmitter Magnetron, Klystron, or a solid state
oscillator followed by power amplifiers Power levels: Megawatts peak, several
kW average Duplexer or Isolator To keep the power from the transmitter from
entering the receiver. E.g. 2MW output, .1 pW input Ratio: 10 19 or 190 dB IF
Amplifier/Matched Filter
15. Radar - Generic System Detector: Extracts the modulation pulses which are
amplified by the video amplifier Threshold Decision: Determines whether or
not a return has been detected
16. Radar - Generic System Display: Usual display is a plan position indicator
(PPI)
17. Radar The Influence of LNA (low noise amplifier) an LNA is not always
beneficial since it decreases the dynamic range (DR) of the receiver DR is the
difference between the maximum signal which can be processed (usually
determined by the compression level of the mixer) The minimum detectable
level determined by the noise power The tradeoff is between sensitivity and
dynamic range
18. Radar (LNA) Input to Mixer
19. Radar Antennas Radars which are required to determine the directions as
well as the distances of targets require antenna patterns which have narrow
beamwidths e.g. The narrower the beamwidth, the more precise the angle
Fortunately, a narrow beamwidth also gives a high Gain which is desirable as
we shall see.
20. Radar Antennas Narrow beamwidth implies large physical size Antennas
are usually parabolic reflectors fed by a waveguide horn antenna at the focus
of the parabola
21. Radar Antennas Phased Arrays One of the big disadvantages of the
parabolic antennas is that they have to be physically rotated in order to cover
their area of responsibility. Also, military uses sometimes require the beam to
be moved quickly from one direction to another. For these applications Phased
Array antennas are used
22. Radar Antennas Phased Arrays Physical Electronic Phase Shift
23. Radar Antennas Phased Arrays
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24. Radar Basic Radar Range Equation RF energy transmitted with power P t If
transmitted equally in all directions (isotropically) the power density of the
signal at distance R will be P t /4 π R 2 If the antenna is directional it will have
“GAIN” (G) in any particular direction. Gain is simply the power density
produced in a particular direction RELATIVE to the power density produced
by an isotropic antenna
25. Radar Basic Radar Range Equation - Gain The gain of an antenna usually
refers to the maximum gain Thus, if the radar antenna has gain the power
density at distance R becomes P t G /4 π R 2
26. Radar Basic Radar Range Equation - Cross Section When the signal
reaches a target some of the energy is reflected back towards the transmitter.
Assume for now that the target has an area ρ and that it reflects the
intercepted energy equally in all directions. NOTE: This is obviously not true
and we shall have to make allowances for this later on
27. Radar Basic Radar Range Equation - Cross Section Thus the power
radiated from the target is (P t G /4 π R 2 ) ρ And the power density back at the
radar is (P t G /4 π R 2 )( ρ /4 π R 2 )
28. Radar Basic Radar Range Equation - Maximum Range The radar antenna
has a effective are A e and thus the power passed on to the receiver is P r = (P
t G /4 π R 2 )( ρ /4 π R 2 ) A e The minimum signal detectable by the receiver is
S min and this occurs at the maximum range R MAX Thus S min = (P t G /4 π R
MAX 2 )( ρ /4 π R MAX 2 ) A e or R MAX =[P t G A e /(4 π) 2 S min ] ¼
29. Radar Basic Radar Range Equation - Monostatic Usually the same antenna
is used for transmission and reception and we have the relationship between
Gain and effective area: Thus
30. Radar Pulse Repetition Frequency (PRF) One of the more common radar
signal is pulsed RF in which the two variables are the pulse width and the
repetition rate. To avoid ambiguity it is necessary to ensure that echoes from
targets at the maximum range have been received before transmitting another
pulse i.e. The round trip time to maximum range is: 2R MAX / c . So this is the
minimum repetition period so the maximum PRF is c / 2R MAX
31. Radar Peak Power/Average Power/Duty Cycle τ T τ = pulse width T= pulse
repetition period (1/PRF) P ave = P peak ·( τ /T) P peak
32. Radar Pulse width determines range resolution ΔR=cτ/2 Narrow pulse
width High Peak Power For solid state transmitters we would like low peak
power
33. Radar Example TRACS (Terminal Radar and Control System): Min signal:
-130dBW (10 -13 Watts) G: 2000 λ: 0.23 m (f=1.44GHz) PRF: 524 Hz σ : 2m 2
What power output is required?
34. Radar Radar Frequencies Most operate between 200MHz and 35 GHz
Exceptions: HF-OTH (High frequency over the horizon) ~ 4 MHz Millimetre
radars ( to 95 GHz) Laser radar (or Lidar)
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35. Radar Simple Radar Range Equation Final Radar Range Equation
36. RAMP Radar
37. RAMP Radar
38. RAMP Radar Final Radar Range Equation
39. RAMP Radar
40. Radar Radar Range Equation: This equation is not very accurate due to
several uncertainties in the variables used: 1. S min is influenced by noise and
is determined statistically 2. The radar cross section fluctuates randomly 3.
There are losses in the system 4. Propagation effects caused by the earth’
surface and atmosphere
41. Radar Probabilities Due to the statistical nature of the variables in the radar
equation we define performance based on two main factors Probability of
Detection (P d ) The probability that a target will be detected when one is
present Probability of False Alarm (P fa ) The probability that a target will be
detected when one is not present
42. Minimum Signal Detection of Signals in Noise Typical output from
receiver’s video amplifier, We have to determine how to decide whether a
signal is present or not
43. Minimum Signal Threshold Detection Set a threshold level and decide that
any signal above it is a valid reply from a target. Two problems: 1. If the
threshold is set too high Probability of Detection is low 2. If the threshold is
set too low Probability of False Alarm is high
44. Receiver Noise and Signal/Noise Ratio Source of Noise is primarily thermal
or Johnson Noise in the receiver itself Thermal noise Power = kTB n Where k
is Boltzmann’s Constant (1.38 x 10 -23 J/K) T is the temperature in Kelvins
(~Celsius +273) B is the Noise Bandwidth of the receiver
45. Receiver Noise and Signal/Noise Ratio Noise Bandwidth B n H(f 0 )
46. Receiver Noise and Signal/Noise Ratio Noise Bandwidth In practice, the
3dB bandwidth is used. B n H(f 0 )
47. Receiver Noise and Signal/Noise Ratio Noise Figure Amplifiers and other
circuits always add some noise to a signal and so the Signal to Noise Ratio is
higher at the output than at the input This is expressed as the Noise Figure of
the Amplifier (or Receiver) F n = (noise out of a practical reciver) (noise out of
an ideal (noiseless) receiver at T 0 ) G a is the receiver gain
48. Receiver Noise and Signal/Noise Ratio Since G a = S o / S i (Output/Input)
and kT 0 B is the input noise N i then finally
49. Receiver Noise and Signal/Noise Ratio Since G a = S o / S i (Output/Input)
and kT 0 B is the input noise N i then finally
50. Receiver Noise and Signal/Noise Ratio Modified Range Equation
51. Probability Density Functions Noise is a random phenomenon e.g. a noise
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voltage can take on any value at any time Probability is a measure of the
likelihood of discrete event Continuous random functions such as noise
voltage are described by probability density functions (pdf)
52. Probability Density Functions e.g.
53. Probability Density Functions e.g. for a continuous function
54. Probability Density Functions Definitions Mean Mean Square Variance
55. Common PDFs Uniform This is the pdf for random phase
56. Common PDFs Gaussian or Normal Very common distribution Uniquely
defined by just the first and second moments Central Limit Theorem
57. Common PDFs Rayleigh Detected envelope of filter output if input is
Gaussian Uniquely defined by either the first or second moment Variance
58. Common PDFs Exponential Note: Probable Error in Notes
59. Calculation of Minimum Signal to Noise Ratio First we will determine the
threshold level required to give the specified average time to false alarm (T fa ).
This is done assuming no signal input. We shall also get a relationship
between T fa and P fa . Then we add the signal and determine what signal to
noise ratio we need to give us the specified probability of detection (P d )
60. Calculation of Minimum Signal to Noise Ratio B V B IF /2 Gauss in
Rayleigh out P fa =
61. Calculation of Minimum Signal to Noise Ratio assuming t k =1/B IF
62. Calculation of Minimum Signal to Noise Ratio Now we have a relationship
between False alarm time and the threshold to noise ratio This can be used to
set the Threshold level
63. Calculation of Minimum Signal to Noise Ratio Now we add a signal of
amplitude A and the pdf becomes Ricean. i.e. a Rice distribution This is
actually a Rayleigh distribution distorted by the presence of a sine wave
Where I 0 is a modified Bessel function of zero order
64. Calculation of Minimum Signal to Noise Ratio This is plotted in the
following graph
65. Calculation of Minimum Signal to Noise Ratio From this graph, the
minimum signal to noise ratio can be derived from: a. the probability of
detection b. the probability of false alarm
66. Integration of Radar Pulses Note that the previous calculation for signal to
noise ratio is based on the detection of a single pulse In practice a target
produces several pulses each time the antenna beam sweeps through its
position Thus it is possible to enhance the signal to noise ratio by integrating
(summing ) the pulse outputs. Note that integration is equivalent to low pass
filtering. The more samples integrated, the narrower the bandwidth and the
lower the noise power
67. Integration of Radar Pulses Note: The antenna beam width n b is arbitrarily
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defined as the angle between the points at which the pattern is 3dB less than
the maximum 3dB Beam Width θ B If the antenna is rotating at a speed of θ S
º/s and the Pulse repetition frequency is f p the number of pulses on target is n
B = θ B f p / θ S or if rotation rate is given in rpm (ω m ) n B = θ B f p / 6 ω m
68. Integration of Radar Pulses integration before detection is called
predetection or coherent detection integration after detection is called post
detection or noncoherent detection If predetection is used SNR integrated = n
SNR 1 If postdetection is used, SNR integrated n SNR 1 due to losses in the
detector
69. Integration of Radar Pulses Predetection integration is difficult because it
requires maintaining the phase of the pulse returns Postdetection is relatively
easy especially using digital processing techniques by which digitized
versions of all returns can be recorded and manipulated
70. Integration of Radar Pulses The reduction in required Signal to Noise Ratio
achieved by integration can be expressed in several ways: Integration
Efficiency: Note that E i (n) is less than 1 (except for predetection) Where (S/N)
1 is the signal to noise ratio required to produce the required P d for one pulse
and And (S/N) n is the signal to noise ratio required to produce the required P
d for n pulses
71. Integration of Radar Pulses The improvement in SNR where n pulses are
integrated is called the integration improvement factor I i (n) Note that I i (n) is
less than n Another expression is the equivalent number of pulses n eq
72. Integration of Radar Pulses Integration Improvement Factor
73. Integration of Radar Pulses False Alarm Number Note the parameter n f in
the graph This is called the false alarm number and is the average number of
“decisions” between false alarms Decisions are considered as the discrete
points at which a target may be detected unambiguously Recall that the
resolution of a radar is half the pulse width multiplied by the speed of light τ τ
τ
74. Integration of Radar Pulses False Alarm Number Thus the total number of
unambiguous targets for each transmitted pulse is T/ τ where T is the pulse
repetition period (1/f P ) We multiply this by the number of pulses per second
(f P ) to get the number of decisions per second Finally we multiply by the
False alarm rate (T fa ) to get the number of decisions per false alarm. n f = [ T/
τ][f P ][T fa ]
75. Integration of Radar Pulses False Alarm Number But T x f P =1 and τ 1/B
where B is the IF bandwidth so n f T fa B 1/P fa n f = [ T/ τ][f P ][T fa ]
76. Integration of Radar Pulses Effect on Radar Range Equation Range
Equation with integration Expressed in terms of SNR for 1 pulse
77. Integration of Radar Pulses Example: Radar: PRF: 500Hz Bandwidth :1MHz
Antenna Beamwidth: 1.5 degrees Gain: 24dB Transmitter Power 2 MW Noise
Figure: 2dB P d : 80% P FA : 10 -5 σ: 2m 2 Freq: 1GHz Antenna Rotation speed:
30 degrees/s What is maximum range?
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78. Radar Cross Section To simplify things the radar range equation assumes
that a target with cross sectional area σ absorbs all of the incident power and
reradiates it uniformly in all directions. This, of course, is not true When the
radar pulse hits a target the energy is reflected and refracted in many ways
depending on the material it is made of Its shape Its orientation with respect to
the radar Radar Cross Section (RCS)
79. Radar Cross Section Examples: Corner reflector Transparent Absorber
80. Radar Cross Section Simple Shapes: The sphere is the simplest shape to
analyze: It is the only shape for which the radar cross section approximates the
physical cross section
81. Radar Cross Section Simple Shapes: The sphere is the simplest shape to
analyze: But even a sphere gives some surprises!
82. Radar Cross Section Simple Shapes: The word “aspect” is used to refer to
the angle from which the object is being viewed. Obviously the RCS of a
sphere is independent of the aspect angle but that is not true in general The
metallic rod for example:
83. Radar Cross Section Simple Shapes: Another relatively simple shape is the
Cone Sphere
84. Radar Cross Section Real life targets are much more complicated: a large
number of independent objects scattering energy in all directions scattered
energy may combine in-phase or out of phase depending on the aspect angle
(scintillation) All techniques for determining RCS have severe limitations;
Calculation: GTD (geometric theory of diffraction) Experimental: Full scale:
very expensive Scale models: lose detail
85. Radar Cross Section Experimental RCS
86. Radar Cross Section Experimental RCS
87. Radar Cross Section RCS Examples
88. Stealth Fighter F117 Radar Cross Section 0.003m 2
89. Radar Cross Section Cross Section Fluctuations Cross sections fluctuate
for several reasons meteorological conditions lobe structure of antenna
varying aspect angle of target How do we select the cross section to use in
the Radar Range Equation? choose a lower bound that is exceeded 90-95% of
time? conservative - possibly excessive power
90. Radar Cross Section Cross Section Fluctuations How do we select the
cross section to use in the Radar Range Equation? use an assumed (or
measured) pdf along with correlation properties (rate of change) This was
done by Swerling (Rand Corp, 1954) He assumed two types of targets: one
with many, similar sized scatterers one with one prominent scatterer and many
smaller ones
91. Radar Cross Section Cross Section Fluctuations How do we select the
cross section to use in the Radar Range Equation? Swerling also considered
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the cases where the cross section did not change significantly while the radar
beam was illuminating the target the cross section changed from pulse to
pulse within the beam So we ended up with 4 Swerling target classifications
92. Radar Cross Section Cross Section Fluctuations Swerling Case 1 constant
during scan PDF Swerling Case 2 changing from pulse to pulse PDF Note that
this is an Exponential distribution
93. Radar Cross Section Cross Section Fluctuations Swerling Case 3 constant
during scan PDF Swerling Case 4 changing from pulse to pulse PDF Note that
this is a Rayleigh distribution
94. Radar Cross Section Cross Section Fluctuations In practice we classify
targets as follows: Swerling 1; small, slow target, e.g. Navy destroyer Swerling
2: small, fast target, e.g. F-18 fighter Swerling 3: large, slow target e.g. Aircraft
Carrier Swerling 4: large, fast target e.g. Boeing 747
95. Radar Cross Section The effect of Cross section fluctuation on required
Signal to Noise
96. Radar Cross Section Calculating the Effect of fluctuating cross section on
Radar Range Additional SNR
97. Radar Cross Section Calculating the Effect of fluctuating cross section on
Radar Range Modified Integration Efficiency
98. Radar Cross Section Calculating the Effect of fluctuating cross section on
Radar Range To incorporate the varying radar cross section into the Radar
Range Equation: 1. Find S/N from Fig 2.7 using required P d and P fa 2. From
Fig 2.23, find the correction factor for the Swerling number given, calculate
(S/N) 1 3. If n pulses are integrated, use Fig 2.24 to find the appropriate I i (n) 4.
Substitute the (S/N) 1 and I i (n) into the equation
99. Radar Cross Section Calculating the Effect of fluctuating cross section on
Radar Range Example: P d = 90% P fa = 10 -4 Antenna beam width: 2 º Antenna
rotation rate: 6 rpm f p =400Hz Target: Swerling II
100. Radar Cross Section Calculating the Effect of fluctuating cross section on
Radar Range (S/N) 1 =12dB additional (S/N) =8dB new (S/N) 1 =20dB
101. Radar Cross Section Calculating the Effect of fluctuating cross section on
Radar Range number of pulses integrated n= θ x f p /6xω = 2x400/36 = 22.2 I n
(n)= 18 dB
102. Radar Cross Section Calculating the Effect of fluctuating cross section on
Radar Range Note that the Swerling Cases are only very crude approximations
Swerling himself has since modified his ideas on this and has extended his
models to include a range of distributions based on the Chi-square (or Gamma)
distribution
103. Radar Cross Section Radar Cross Section The objective is to obtain the
specified probability of detection with the minimum Transmitter power This is
because the size, cost and development time for a radar are a function of the
maximum transmitter power Thus it is important to develop a correct model for
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the expected targets
104. Transmitter Power The P t in the radar range equation is the peak RMS
power of the carrier Sometimes the average power P ave is given Rearranging
gives the duty cycle
105. Transmitter Power The P t in the radar range equation is the peak RMS
power of the carrier Sometimes the average power P ave is given Rearranging
gives the duty cycle
106. Transmitter Power With P ave in the radar range equation the form is as
follows: Note that the bandwidth and pulse width are grouped together. Since
they are almost always reciprocals of one another, their product is 1.
107. Transmitter Power For radars which do not use pulse waveforms the
average energy per repetition is used:
108. Range Ambiguity As was mentioned earlier, the reply for a given pulse
may arrive after the next pulse has been transmitted. This gives rise to RANGE
AMBIGUITY since the radar assumes that each reply results from the
preceding pulse
109. Range Ambiguity Range ambiguity may be resolved by using more than
one prf. In this case the ambiguous returns show up at a different range for
each prf
110. Antenna Parameters Gain Definition: Note that since the total power
radiated can not be more than the power received from the transmitter, G(
θ,φ)d θ d φ < 1 Therefore, if the gain is greater than 1 in one direction it is less
than one in others.
111. Antennas Types There are two main types: pencil beam and fan beam The
pencil beam is narrow in both axes and is usually symmetrical it is usually used
in tracking radars.
112. Antennas Nike-Hercules Missile Tracking Antenna
113. Antennas Nike-Hercules Missile Tracking Antenna Beamwidth: 1 º
114. Antennas Pencil beams are not good for searching large areas of sky.
Search radars usually use fan beams which are narrow in azimuth and wide in
elevation The elevation pattern is normally designed to be of “cosecant
squared” pattern which gives the characteristic that a target at constant
altitude will give a constant signal level.
115. Antennas φ 0 <φ<φ m substituting in radar range equation Note: There is
an error in the notes
116. Antennas since
117. Antennas Beamwidth vs Scan Rate This tradeoff in the radar design is
between a. being able to track the target which implies looking at it often and
b. detecting the target which implies integrating a lot of pulses at each look
Note: increasing the PRF decreases the unambiguous range
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118. Radar Cross Section Questions: 1. Design a test to measure the Radar
Cross Section of an object 2. A corner cube reflector reflects all of the energy
that hits it back towards the radar. Assuming a physical area of 1 m 2 and a
“beam width” of the reflected energy to be equal to the beam width of the
radar antenna, What is the RCS of the reflector?
119. Losses Controllable losses fall into three categories: a. Antenna Beam
shape b. Plumbing Loss b. Collapsing Loss
120. Losses Beam Shape Loss During the previous discussions it was
assumed that the signal strength was the same for all pulses while the antenna
beam was on the target. This, of course is no true. The beamwidth is defined
as being between the 3 dB points and so the signal strength varies by 3 dB as
it passes the target
121. Losses Beam Shape Loss The shape of the beam between the 3 dB points
is assumed to be Gaussian i.e. where θ B is the half power beam width and the
amplitude of the maximum pulse is 1.
122. Losses Beam Shape Loss θ =k θ B /(n B -1) Two way beam shape: S 4
=exp(-5.55( θ 2 /θ B 2 )) S 4 =exp(-5.55( k/(n B -1)) 2 ) 1 The sum of the power of
the four RH pulses is θ B θ B /(n B -1) 1 2 3 4 k
123. Losses Beam Shape Loss 1 The sum of the power of the ALL pulses is
The ratio of the power in n equal to the power in the actual pulses is NOTE:
Error in Notes θ B θ B /(n B -1) 1 2 3 4 k
124. Losses Plumbing Loss Almost all of the signal path in a radar is
implemented by waveguide Exception: UHF frequencies where waveguide size
becomes unwieldy. This is because a. waveguide can sustain much higher
power levels than coaxial cable. (and can be pressurized) b. Losses in
waveguide are much lower than in coaxial cable
125. Losses Plumbing Loss Any discontinuity in the waveguide will cause
losses, Primarily because discontinuities cause reflections. Examples of
plumbing Loss: Connectors Rotary Joints Bends in Transmission Line
126. Losses Plumbing Loss Connectors: 0.5dB Bends: 0.1dB
127. Losses Plumbing Loss Rotary Joint: 0.4dB
128. Losses Plumbing Loss Note that losses in common transmit/receive path
must be doubled
129. Losses Collapsing Loss If a radar collects data in more dimensions than
can be used, it is possible for noise to be included in the measurement in the
dimension “collapsed” or discarded. n n n n e.g. if a radar measures elevation
as well as range and azimuth, it will store target elevation information in an
vector for each range/azimuth point. If only range and azimuth are to be
displayed, the elevation cells are “collapsed” and thus many noise
measurements are added with the actual target information n s+n n n n n n n n
n n n n s+n s+n s+n n n n n n n
130. Losses Collapsing Loss n n n n
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131. Losses Collapsing Loss n n n n Example: 10 cells with signal+noise, 30
cells with noise P d =0.9 n fa =10 -8 3 4 2.1 1.4 L i (30)=3.5dB L i (10)=1.7dB L C
(30,10)=1.8dB
132. Surveillance Radar n n n n Radar discussed so far is called a searchlight
radar which dwells on a target for n pulses. With the additional constraint of
searching a specified volume of space in a specified time the radar is called a
search or surveillance radar. Ω is the (solid) angular region to be searched in
scan time t s then where t 0 is the time on target n/f p Ω 0 = the solid angle
beamwidth of the antenna θ A θ E
133. Surveillance Radar n n n n Note: Thus the search radar equation becomes:
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12/14/13 Components of a Pulse Radar System
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