Radar was invented in the early 1900s and applied during World War II to detect aircraft. The basic principles of radar involve transmitting electromagnetic signals that are reflected off targets and detected. A typical radar system includes a transmitter, antenna, receiver, and display. The radar range equation relates key variables such as transmitted power, wavelength, target radar cross-section, and system losses to the maximum detectable range. Integration of multiple radar returns can improve the signal-to-noise ratio and increase detection 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.

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

36. RAMP Radar

37. RAMP Radar

39. RAMP Radar

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

79. Radar Cross Section Examples: Corner reflector Transparent Absorber

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

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

107. Transmitter Power For radars which do not use pulse waveforms the average energy per repetition is used:

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.

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

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

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: