1. Radar <ul><li>OUTLINE </li></ul><ul><li>History </li></ul><ul><li>Applications </li></ul><ul><li>Basic Principles of Radar </li></ul><ul><li>Components of a Pulse Radar System </li></ul><ul><li>The Radar equation </li></ul><ul><li>Moving Target Indicator (MTI) radar </li></ul>
2. Radar <ul><li>History </li></ul><ul><ul><li>Invented in 1900s (patented in 1904) and reinvented in the 1920s and 1930s </li></ul></ul><ul><ul><li>Applied to help defend England at the beginning of World War II (Battle of Britain) </li></ul></ul><ul><ul><ul><li>Provided advance warning of air raids </li></ul></ul></ul><ul><ul><ul><li>Allowed fighters to stay on ground until needed </li></ul></ul></ul><ul><ul><li>Adapted for airborne use in night fighters </li></ul></ul><ul><ul><li>Installed on ships for detecting enemy in bad weather (Bismarck) </li></ul></ul>
3. Radar-Applications <ul><li>Air Traffic Control </li></ul><ul><li>Air Navigation </li></ul><ul><li>Remote Sensing </li></ul><ul><li>Marine </li></ul><ul><li>Law Enforcement and highway safety </li></ul><ul><li>Space </li></ul><ul><li>Military </li></ul>
4. Radar-Applications <ul><li>Air Traffic Control </li></ul><ul><ul><li>Monitor the location of aircraft in flight </li></ul></ul><ul><ul><li>Monitor the location of aircraft/vehicles on surface of airports </li></ul></ul><ul><ul><li>PAR (precision approach radar) </li></ul></ul><ul><ul><ul><li>Guidance for landing in poor weather </li></ul></ul></ul>
5. Radar-Applications <ul><li>Air Navigation </li></ul><ul><ul><li>Weather radar </li></ul></ul><ul><ul><li>Terrain avoidance and terrain following </li></ul></ul><ul><ul><li>Radar altimeter </li></ul></ul><ul><ul><li>Doppler Navigator </li></ul></ul>
7. Radar-Applications <ul><li>Marine </li></ul><ul><ul><li>Detecting other ships, buoys, land </li></ul></ul><ul><ul><li>Shore-based radar for harbour surveillance and traffic control </li></ul></ul><ul><li>Law Enforcement and highway safety </li></ul><ul><ul><li>Traffic speed radar </li></ul></ul><ul><ul><li>Collision warning </li></ul></ul><ul><ul><li>Blind area surveillance for cars and school buses </li></ul></ul><ul><ul><li>Intrusion alarms </li></ul></ul>
9. Radar <ul><li>Basic Principles </li></ul><ul><ul><li>Transmits an electromagnetic signal modulated with particular type of waveform. (modulation depends on requirements of application) </li></ul></ul><ul><ul><li>Signal is reflected from target </li></ul></ul><ul><ul><li>Reflected signal is detected by radar receiver and analyzed to extract desired information </li></ul></ul>
10. Radar <ul><li>Modulation Types </li></ul><ul><ul><li>Simple Pulse; one or more repetition frequencies </li></ul></ul><ul><ul><li>Frequency Modulation FM (radar altimeters) </li></ul></ul><ul><ul><li>Pulse with Chirp (pulse compression) </li></ul></ul><ul><ul><li>CW (continuous wave) - police radar (Doppler) </li></ul></ul><ul><ul><li>Pseudorandom code </li></ul></ul>
11. Radar <ul><li>Basic Principles </li></ul><ul><ul><li>Distance can be determined by measuring the time difference between transmission and reception </li></ul></ul><ul><ul><li>Angle (or relative bearing) can be determined by measuring the angle of arrival (AOA) of the signal </li></ul></ul><ul><ul><li>(usually by highly directive antenna) </li></ul></ul><ul><ul><li>If there is a radial component of relative velocity between radar and target it can be determined from the Doppler shift of the carrier </li></ul></ul>
12. Radar <ul><li>Basic Principles </li></ul><ul><ul><li>Two types of radar: Monostatic - transmitter and receiver use same antenna </li></ul></ul><ul><ul><li>Bistatic - transmitter and receiver antennas are separated, sometimes by large distances </li></ul></ul>
13. Radar <ul><li>Generic Radar System </li></ul>Local Oscillator
14. Radar - Generic System <ul><li>Transmitter </li></ul><ul><ul><li>Magnetron, Klystron, or a solid state oscillator followed by power amplifiers </li></ul></ul><ul><ul><li>Power levels: Megawatts peak, several kW average </li></ul></ul><ul><li>Duplexer or Isolator </li></ul><ul><ul><li>To keep the power from the transmitter from entering the receiver. E.g. 2MW output, .1 pW input </li></ul></ul><ul><ul><li>Ratio: 10 19 or 190 dB </li></ul></ul><ul><li>IF Amplifier/Matched Filter </li></ul>
15. Radar - Generic System <ul><li>Detector: </li></ul><ul><ul><li>Extracts the modulation pulses which are amplified by the video amplifier </li></ul></ul><ul><li>Threshold Decision: </li></ul><ul><ul><li>Determines whether or not a return has been detected </li></ul></ul>
16. Radar - Generic System <ul><li>Display: </li></ul><ul><li>Usual display is a plan position indicator (PPI) </li></ul>
17. Radar <ul><li>The Influence of LNA (low noise amplifier) </li></ul><ul><ul><li>an LNA is not always beneficial since it decreases the dynamic range (DR) of the receiver </li></ul></ul><ul><ul><li>DR is the difference between </li></ul></ul><ul><ul><ul><li>the maximum signal which can be processed (usually determined by the compression level of the mixer) </li></ul></ul></ul><ul><ul><ul><li>The minimum detectable level determined by the noise power </li></ul></ul></ul><ul><li>The tradeoff is between sensitivity and dynamic range </li></ul>
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 <ul><li>Narrow beamwidth implies large physical size </li></ul><ul><ul><li>Antennas are usually parabolic reflectors fed by a waveguide horn antenna at the focus of the parabola </li></ul></ul>
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
24. Radar <ul><li>Basic Radar Range Equation </li></ul><ul><ul><li>RF energy transmitted with power P t </li></ul></ul><ul><ul><li>If transmitted equally in all directions (isotropically) the power density of the signal at distance R will be P t /4 π R 2 </li></ul></ul><ul><ul><li>If the antenna is directional it will have “GAIN” (G) in any particular direction. </li></ul></ul><ul><ul><li>Gain is simply the power density produced in a particular direction RELATIVE to the power density produced by an isotropic antenna </li></ul></ul>
25. Radar <ul><li>Basic Radar Range Equation - Gain </li></ul><ul><ul><li>The gain of an antenna usually refers to the maximum gain </li></ul></ul><ul><ul><li>Thus, if the radar antenna has gain the power density at distance R becomes </li></ul></ul><ul><ul><li>P t G /4 π R 2 </li></ul></ul>
26. Radar <ul><li>Basic Radar Range Equation - Cross Section </li></ul><ul><ul><li>When the signal reaches a target some of the energy is reflected back towards the transmitter. </li></ul></ul><ul><ul><li>Assume for now that the target has an area ρ and that it reflects the intercepted energy equally in all directions. </li></ul></ul><ul><ul><li>NOTE: This is obviously not true and we shall have to make allowances for this later on </li></ul></ul>
27. Radar <ul><li>Basic Radar Range Equation - Cross Section </li></ul><ul><ul><li>Thus the power radiated from the target is (P t G /4 π R 2 ) ρ </li></ul></ul><ul><ul><li>And the power density back at the radar is (P t G /4 π R 2 )( ρ /4 π R 2 ) </li></ul></ul>
28. Radar <ul><li>Basic Radar Range Equation - Maximum Range </li></ul><ul><ul><li>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 </li></ul></ul><ul><ul><li>The minimum signal detectable by the receiver is S min and this occurs at the maximum range R MAX </li></ul></ul><ul><ul><li>Thus S min = (P t G /4 π R MAX 2 )( ρ /4 π R MAX 2 ) A e </li></ul></ul><ul><ul><li>or R MAX =[P t G A e /(4 π) 2 S min ] ¼ </li></ul></ul>
29. Radar <ul><li>Basic Radar Range Equation - Monostatic </li></ul><ul><ul><li>Usually the same antenna is used for transmission and reception and we have the relationship between Gain and effective area: </li></ul></ul>Thus
30. Radar <ul><li>Pulse Repetition Frequency (PRF) </li></ul><ul><ul><li>One of the more common radar signal is pulsed RF in which the two variables are the pulse width and the repetition rate. </li></ul></ul><ul><ul><li>To avoid ambiguity it is necessary to ensure that echoes from targets at the maximum range have been received before transmitting another pulse </li></ul></ul><ul><ul><li>i.e. The round trip time to maximum range is: </li></ul></ul><ul><ul><li>2R MAX / c . So this is the minimum repetition period so the </li></ul></ul><ul><ul><li>maximum PRF is c / 2R MAX </li></ul></ul>
31. Radar <ul><li>Peak Power/Average Power/Duty Cycle </li></ul>τ T τ = pulse width T= pulse repetition period (1/PRF) P ave = P peak ·( τ /T) P peak
32. Radar <ul><li>Pulse width determines range resolution </li></ul><ul><li>ΔR=cτ/2 </li></ul><ul><li>Narrow pulse width High Peak Power </li></ul><ul><li>For solid state transmitters we would like low peak power </li></ul>
33. Radar <ul><li>Example </li></ul><ul><li>TRACS (Terminal Radar and Control System): </li></ul><ul><ul><li>Min signal: -130dBW (10 -13 Watts) </li></ul></ul><ul><ul><li>G: 2000 </li></ul></ul><ul><ul><li>λ: 0.23 m (f=1.44GHz) </li></ul></ul><ul><ul><li>PRF: 524 Hz </li></ul></ul><ul><ul><li>σ : 2m 2 </li></ul></ul><ul><li>What power output is required? </li></ul>
34. Radar <ul><li>Radar Frequencies </li></ul><ul><ul><li>Most operate between 200MHz and 35 GHz </li></ul></ul><ul><li>Exceptions: HF-OTH (High frequency over the horizon) ~ 4 MHz </li></ul><ul><li>Millimetre radars ( to 95 GHz) </li></ul><ul><li>Laser radar (or Lidar) </li></ul>
35. Radar <ul><li>Simple Radar Range Equation </li></ul><ul><li>Final Radar Range Equation </li></ul>
36. RAMP Radar
37. RAMP Radar
38. RAMP Radar <ul><li>Final Radar Range Equation </li></ul>
39. RAMP Radar
40. Radar <ul><li>Radar Range Equation: </li></ul>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 <ul><li>Probabilities </li></ul><ul><ul><li>Due to the statistical nature of the variables in the radar equation we define performance based on two main factors </li></ul></ul><ul><li>Probability of Detection (P d ) </li></ul><ul><ul><li>The probability that a target will be detected when one is present </li></ul></ul><ul><li>Probability of False Alarm (P fa ) </li></ul><ul><ul><li>The probability that a target will be detected when one is not present </li></ul></ul>
42. Minimum Signal <ul><li>Detection of Signals in Noise </li></ul><ul><li>Typical output from receiver’s video amplifier, </li></ul><ul><li>We have to determine how to decide whether a signal is present or not </li></ul>
43. Minimum Signal <ul><li>Threshold Detection </li></ul><ul><li>Set a threshold level and decide that any signal above it is a valid reply from a target. </li></ul><ul><li>Two problems: </li></ul><ul><ul><li>1. If the threshold is set too high Probability of Detection is low </li></ul></ul><ul><ul><li>2. If the threshold is set too low Probability of False Alarm is high </li></ul></ul>
44. Receiver Noise and Signal/Noise Ratio <ul><li>Source of Noise is primarily thermal or Johnson Noise in the receiver itself </li></ul><ul><li>Thermal noise Power = kTB n </li></ul><ul><ul><li>Where k is Boltzmann’s Constant (1.38 x 10 -23 J/K) </li></ul></ul><ul><ul><li>T is the temperature in Kelvins (~Celsius +273) </li></ul></ul><ul><ul><li>B is the Noise Bandwidth of the receiver </li></ul></ul>
45. Receiver Noise and Signal/Noise Ratio <ul><li>Noise Bandwidth </li></ul>B n H(f 0 )
46. Receiver Noise and Signal/Noise Ratio <ul><li>Noise Bandwidth </li></ul>In practice, the 3dB bandwidth is used. B n H(f 0 )
47. Receiver Noise and Signal/Noise Ratio <ul><li>Noise Figure </li></ul><ul><ul><li>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 </li></ul></ul><ul><ul><li>This is expressed as the Noise Figure of the Amplifier (or Receiver) </li></ul></ul><ul><ul><li>F n = (noise out of a practical reciver) (noise out of an ideal (noiseless) receiver at T 0 ) </li></ul></ul>G a is the receiver gain
48. Receiver Noise and Signal/Noise Ratio <ul><li>Since G a = S o / S i (Output/Input) </li></ul><ul><li>and kT 0 B is the input noise N i </li></ul>then finally
49. Receiver Noise and Signal/Noise Ratio <ul><li>Since G a = S o / S i (Output/Input) </li></ul><ul><li>and kT 0 B is the input noise N i </li></ul>then finally
50. Receiver Noise and Signal/Noise Ratio <ul><li>Modified Range Equation </li></ul>
51. Probability Density Functions <ul><li>Noise is a random phenomenon </li></ul><ul><li>e.g. a noise voltage can take on any value at any time </li></ul><ul><li>Probability is a measure of the likelihood of discrete event </li></ul><ul><li>Continuous random functions such as noise voltage are described by probability density functions (pdf) </li></ul>
52. Probability Density Functions <ul><li>e.g. </li></ul>
53. Probability Density Functions <ul><li>e.g. for a continuous function </li></ul>
54. Probability Density Functions <ul><li>Definitions </li></ul><ul><ul><li>Mean </li></ul></ul><ul><ul><li>Mean Square </li></ul></ul><ul><ul><li>Variance </li></ul></ul>
55. Common PDFs <ul><li>Uniform </li></ul>This is the pdf for random phase
56. Common PDFs <ul><li>Gaussian or Normal </li></ul>Very common distribution Uniquely defined by just the first and second moments Central Limit Theorem
57. Common PDFs <ul><li>Rayleigh </li></ul>Detected envelope of filter output if input is Gaussian Uniquely defined by either the first or second moment Variance
58. Common PDFs <ul><li>Exponential </li></ul>Note: Probable Error in Notes
59. Calculation of Minimum Signal to Noise Ratio <ul><li>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 . </li></ul><ul><li>Then we add the signal and determine what signal to noise ratio we need to give us the specified probability of detection (P d ) </li></ul>
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 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 <ul><li>Example: </li></ul><ul><ul><li>Radar: </li></ul></ul><ul><ul><ul><li>PRF: 500Hz Bandwidth :1MHz </li></ul></ul></ul><ul><ul><ul><li>Antenna Beamwidth: 1.5 degrees Gain: 24dB </li></ul></ul></ul><ul><ul><ul><li>Transmitter Power 2 MW Noise Figure: 2dB </li></ul></ul></ul><ul><ul><ul><li>P d : 80% P FA : 10 -5 </li></ul></ul></ul><ul><ul><ul><li>σ: 2m 2 Freq: 1GHz </li></ul></ul></ul><ul><ul><ul><li>Antenna Rotation speed: 30 degrees/s </li></ul></ul></ul><ul><ul><ul><li>What is maximum range? </li></ul></ul></ul>
78. Radar Cross Section <ul><li>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. </li></ul><ul><li>This, of course, is not true </li></ul><ul><li>When the radar pulse hits a target the energy is reflected and refracted in many ways depending on </li></ul><ul><li>the material it is made of </li></ul><ul><li>Its shape </li></ul><ul><li>Its orientation with respect to the radar </li></ul>Radar Cross Section (RCS)
80. Radar Cross Section <ul><li>Simple Shapes: </li></ul><ul><ul><li>The sphere is the simplest shape to analyze: </li></ul></ul>It is the only shape for which the radar cross section approximates the physical cross section
81. Radar Cross Section <ul><li>Simple Shapes: </li></ul><ul><ul><li>The sphere is the simplest shape to analyze: </li></ul></ul>But even a sphere gives some surprises!
82. Radar Cross Section <ul><li>Simple Shapes: </li></ul><ul><ul><li>The word “aspect” is used to refer to the angle from which the object is being viewed. </li></ul></ul><ul><ul><li>Obviously the RCS of a sphere is independent of the aspect angle but that is not true in general </li></ul></ul><ul><ul><li>The metallic rod for example: </li></ul></ul>
83. Radar Cross Section <ul><li>Simple Shapes: </li></ul><ul><ul><li>Another relatively simple shape is the Cone Sphere </li></ul></ul>
84. Radar Cross Section <ul><li>Real life targets are much more complicated: </li></ul><ul><ul><li>a large number of independent objects scattering energy in all directions </li></ul></ul><ul><ul><li>scattered energy may combine in-phase or out of phase depending on the aspect angle (scintillation) </li></ul></ul><ul><li>All techniques for determining RCS have severe limitations; </li></ul><ul><li>Calculation: </li></ul><ul><ul><li>GTD (geometric theory of diffraction) </li></ul></ul><ul><li>Experimental: </li></ul><ul><ul><li>Full scale: very expensive </li></ul></ul><ul><ul><li>Scale models: lose detail </li></ul></ul>
89. Radar Cross Section <ul><li>Cross Section Fluctuations </li></ul><ul><ul><li>Cross sections fluctuate for several reasons </li></ul></ul><ul><ul><ul><li>meteorological conditions </li></ul></ul></ul><ul><ul><ul><li>lobe structure of antenna </li></ul></ul></ul><ul><ul><ul><li>varying aspect angle of target </li></ul></ul></ul><ul><ul><li>How do we select the cross section to use in the Radar Range Equation? </li></ul></ul><ul><ul><ul><li>choose a lower bound that is exceeded 90-95% of time? </li></ul></ul></ul><ul><ul><ul><li>conservative - possibly excessive power </li></ul></ul></ul>
90. Radar Cross Section <ul><li>Cross Section Fluctuations </li></ul><ul><ul><li>How do we select the cross section to use in the Radar Range Equation? </li></ul></ul><ul><ul><ul><li>use an assumed (or measured) pdf along with correlation properties (rate of change) </li></ul></ul></ul><ul><ul><li>This was done by Swerling (Rand Corp, 1954) </li></ul></ul><ul><ul><li>He assumed two types of targets: </li></ul></ul><ul><ul><ul><li>one with many, similar sized scatterers </li></ul></ul></ul><ul><ul><ul><li>one with one prominent scatterer and many smaller ones </li></ul></ul></ul>
91. Radar Cross Section <ul><li>Cross Section Fluctuations </li></ul><ul><ul><li>How do we select the cross section to use in the Radar Range Equation? </li></ul></ul><ul><ul><li>Swerling also considered the cases where </li></ul></ul><ul><ul><ul><li>the cross section did not change significantly while the radar beam was illuminating the target </li></ul></ul></ul><ul><ul><ul><li>the cross section changed from pulse to pulse within the beam </li></ul></ul></ul><ul><ul><li>So we ended up with 4 Swerling target classifications </li></ul></ul>
92. Radar Cross Section <ul><li>Cross Section Fluctuations </li></ul><ul><ul><li>Swerling Case 1 </li></ul></ul><ul><ul><ul><li>constant during scan </li></ul></ul></ul><ul><ul><ul><li>PDF </li></ul></ul></ul><ul><ul><li>Swerling Case 2 </li></ul></ul><ul><ul><ul><li>changing from pulse to pulse </li></ul></ul></ul><ul><ul><ul><li>PDF </li></ul></ul></ul>Note that this is an Exponential distribution
93. Radar Cross Section <ul><li>Cross Section Fluctuations </li></ul><ul><ul><li>Swerling Case 3 </li></ul></ul><ul><ul><ul><li>constant during scan </li></ul></ul></ul><ul><ul><ul><li>PDF </li></ul></ul></ul><ul><ul><li>Swerling Case 4 </li></ul></ul><ul><ul><ul><li>changing from pulse to pulse </li></ul></ul></ul><ul><ul><ul><li>PDF </li></ul></ul></ul>Note that this is a Rayleigh distribution
94. Radar Cross Section <ul><li>Cross Section Fluctuations </li></ul><ul><li>In practice we classify targets as follows: </li></ul><ul><li>Swerling 1; small, slow target, e.g. Navy destroyer </li></ul><ul><li>Swerling 2: small, fast target, e.g. F-18 fighter </li></ul><ul><li>Swerling 3: large, slow target e.g. Aircraft Carrier </li></ul><ul><li>Swerling 4: large, fast target e.g. Boeing 747 </li></ul>
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 the expected targets
104. Transmitter Power <ul><li>The P t in the radar range equation is the peak RMS power of the carrier </li></ul><ul><li>Sometimes the average power P ave is given </li></ul><ul><li>Rearranging gives the duty cycle </li></ul>
105. Transmitter Power <ul><li>The P t in the radar range equation is the peak RMS power of the carrier </li></ul><ul><li>Sometimes the average power P ave is given </li></ul><ul><li>Rearranging gives the duty cycle </li></ul>
106. Transmitter Power <ul><li>With P ave in the radar range equation the form is as follows: </li></ul><ul><li>Note that the bandwidth and pulse width are grouped together. Since they are almost always reciprocals of one another, their product is 1. </li></ul>
107. Transmitter Power For radars which do not use pulse waveforms the average energy per repetition is used:
108. Range Ambiguity <ul><li>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 </li></ul>
109. Range Ambiguity <ul><li>Range ambiguity may be resolved by using more than one prf. </li></ul><ul><li>In this case the ambiguous returns show up at a different range for each prf </li></ul>
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 <ul><li>There are two main types: </li></ul><ul><ul><ul><li>pencil beam and fan beam </li></ul></ul></ul><ul><li>The pencil beam is narrow in both axes and is usually symmetrical </li></ul><ul><ul><li>it is usually used in tracking radars. </li></ul></ul>
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
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 <ul><li>Plumbing Loss </li></ul><ul><li>Any discontinuity in the waveguide will cause losses, </li></ul><ul><li>Primarily because discontinuities cause reflections. </li></ul><ul><li>Examples of plumbing Loss: </li></ul><ul><ul><li>Connectors </li></ul></ul><ul><ul><li>Rotary Joints </li></ul></ul><ul><ul><li>Bends in Transmission Line </li></ul></ul>
126. Losses <ul><li>Plumbing Loss </li></ul><ul><li>Connectors: </li></ul><ul><ul><li>0.5dB </li></ul></ul><ul><li>Bends: </li></ul><ul><ul><li>0.1dB </li></ul></ul>
127. Losses <ul><li>Plumbing Loss </li></ul><ul><li>Rotary Joint: </li></ul><ul><ul><li>0.4dB </li></ul></ul>
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
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: