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RADAR               RAdio Detection And Ranging Part 2 of 2

Radar equation

                          Area Aeff                                                                             PT .GT
                                                                                              Power Density =
                                                                                                                4π .R 2

                   Tx                     PT                                                                              Sphere x gain

                                                                                                    Radar cross-section δ
                                                                                                    Fraction of incident power
                                                                                                    of source
                   PT .G T        1
 Power Density =           . δ.
                   4π .R 2      4π .R 2


                                                                         PT G T σ
        Output power from the receive antenna                     PR =
                                                                         (4πR )  2 2

        General antenna relationship                 G=           Aeff

                                                                         PT G T λ σ
                                                                             2    2
        Output power from receive antenna                         PR =
                                                                         ( 4 π ) R4

        Maximum range                 Rmax occurs when PR = S min (minimum detectable signal)

                            ⎡ PT GT λ2 σ ⎤ 4
                     Rmax = ⎢             ⎥
                            ⎣ (4π ) S min ⎦

                           Rmax proportional to (PT ) 4 - to double Rmax need 16 x PT
        Note:       i)

                    ii) apparent dependence on            λ2      can be misleading. For a fixed antenna

                    G∝                         ∴ G 2 λ 2 ∝ 1 λ2
                              λ   2

                    suggests short wavelengths for maximum range
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The radar equation above over-estimates the maximum range because it does not include

•        effects of the propagating medium and multipath effects eg atmospheric absorption, ducting
•        atmospheric noise
•        system losses - in antenna feeds, etc
•        signal processing noise
•        target fluctuations
•        clutter - radar scattering from the region around the target which is illuminated by the radar

Statistical nature of radar detection

The received radar signal is superimposed on a 'noise' signal. The noise can arise from

•        receiver noise - generated internally in the radar receiver
•        atmospheric noise - fluctuations in the meteorological conditions
•        target fluctuations - as the target orientation with respect to the radar beam changes its radar
         cross-section (RCS) changes
•        clutter - reflections from areas of the ground or sea surface around the target which are
         illuminated by the radar beam

The word noise was put in inverted commas above because noise is strictly a random and
spontaneous process whereas the target fluctuations and clutter may be systematic to some extent,
though as far as the qualitative radar return signal is concerned their effects appear to be quite
An additional effect that can degrade the radar performance is multipath - there may be several
return signals to the radar that may combine with different phases to increase or decrease the direct-
path echo.

A typical echo + noise radar receiver output is shown below. (Note that the signal shown is the
envelope of the microwave signal - the GHz frequency microwave signal is fed through an envelope
detector). It is clear that the correct setting of a threshold is vital if targets are to be correctly identified
without false alarms. If the thresh-hold is set too high genuine targets will be missed, if it is too low a
peak in the noise signal can give a false alarm.
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       Noise In
                                      Rx                                      (Si/Ni )
                                                        Noise Figure (F) =                F. ≥ 1 F ≥ 0dB
                                                 So                          (So/No )
        Signal In
                                 Adds noise NA

Fig 15 Signal + noise at receiver output, showing the importance of setting the thresh-
       hold to avoid missing targets or false alarms.

Effect of receiver noise

The noise added by the radar receiver is specified by the receiver noise figure F which is defined by

                    Si     So
                    Ni     No

        Here             N i = kTo B is the available noise power at the input

                                                                                                                      ⎛ So   ⎞
        If the minimum acceptable signal to noise ratio at the radar receiver output is ⎜
                                                                                        ⎜                                    ⎟
                                                                                                                      ⎝ No   ⎠ min

        this requires a minimum signal at the receiver input of S min which is given by

                        ⎛S           ⎞        ⎛S      ⎞
        S i = S min = F ⎜ o
                        ⎜N           ⎟N i = F ⎜ o
                                     ⎟        ⎜N      ⎟kTo B
                        ⎝ o          ⎠        ⎝ o     ⎠

        Using this value of S min in the equation derived earlier for Rmax we obtain


                                ⎡        PT GT λ2 σ
                                               2              ⎤4
                         Rmax = ⎢                             ⎥
                                ⎢ (4π ) kT0 B F (S 0 N 0 )min ⎥
                                ⎣                             ⎦

B is the IF bandwidth of the receiver. Usually we make B ≈ 1/ τ where                                 τ    is the width of the radar
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From the above formula it would appear that we can increase the maximum range by decreasing the
radar receiver bandwidth, but the effect is to distort and diminish the echo pulse, thereby reducing the
sensitivity of the radar. If the pulse width (ie duration) is increased to accommodate a decrease in the
bandwidth B this reduces the radar resolution.

The most effective way of increasing the maximum range is to decrease the receiver noise figure F by
using low noise devices in the front end of the receiver - eg a HEMT.

Target fluctuations

•       radar targets are complex shapes with dimensions which are usually large compared with the
        radar wavelength so that there is considerable scope for constructive and destructive
        interference between the waves reflected from different parts of the target
•       the target may change its orientation with respect to the incident radar beam during the time it
        is being observed
•       the reflectivity of a target is specified by its RCS (radar cross-section) s which is a measure
        of the fraction of the incident energy that is scattered in the direction of the receiving antenna
•       it is difficult to calculate the RCS of real targets. RCS values are usually determined by
        measurement as a statistical average of the signal reflected by the target. RCS values
        depend upon the radar wavelength and the orientation of the target. The figure below shows
        the variation of RCS with the direction of illumination for an aircraft. The RCS can vary by
        20dB or more. These variations are superimposed on variations due to atmospheric
        fluctuations, receiver noise etc.

           RCS target fluctuations – an         Typical vertical coverage pattern for a
           aircraft illuminated                 surveillance radar, showing the lobes and
           from different directions.           nulls caused by ground reflections.
           Ci l            i      l
       Fig.16 Radar cross-section of an aircraft illuminated from different directions (from P
A Lynn)
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•         a range of models - Swerling models - are used to describe the statistical variations in the
          RCS s in terms of probability distributions p (σ )dσ which gives the probability that the
          cross-section lies between σ and σ + dσ . The modells are summarised below.

          Case1. Echoes have a constant amplitude for all hits on one scan but there is no correlation
                 between the echoes from one scan to the next.
                 This form of distribution applies to complex shapes with many similar reflecting
                 surfaces eg aircraft
          Case2. Echoes vary from pulse to pulse as well as scan to scan - this may arise with a
                 rapidly fluctuating target

                                                                                ⎛ −σ ⎞
          The PDF for both cases 1 and 2 is p (σ ) =
                                                                             exp⎜       ⎟ with σ ≥ 0
                                                                      σ (av ) ⎜ σ (av ) ⎟
                                                                                ⎝       ⎠
          s(av) is the long-term average RCS.

          Cases 3 and 4. These are the same as cases 1 and 2, respectively, but they apply to
                         targets which have one dominant reflecting surface. Then

                                          4σ          ⎛ − 2σ ⎞
                        p(σ ) =                       ⎜ σ (av ) ⎟ with σ ≥ 0
                                                   exp⎜         ⎟
                                    σ (av )    2
                                                      ⎝         ⎠
Multipath effects

Multipath arises when the signal reflected by the target is returned to the receive antenna by more
than one path. Then the total received signal depends upon the phase relationships between the
signals which travel by the different paths. Usually the most important paths are the direct signal and
the ground reflected signal - particularly if the 'ground' is a water surface because at microwave
frequencies water has a reflection coefficient which is close to unity and so the amplitudes of the
direct and the ground waves will be almost equal. Their sum can vary between almost zero
(antiphase) and twice each amplitude.

         ‘in phase’ or
         180 degrees out of
                                                                               Ground reflected



Fig 17     Multipath
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           Multipath depends upon the environment of the receive antenna - ie adjacent scatterers - and
           the polar pattern of the antenna. It may be possible to point nulls of the antenna radiation
           pattern in the direction of strong multipath scatterers.


Clutter refers to the scattering of a radar beam by the ground, sea etc around the target. Because the
target may occupy only a small fraction of the total area illuminated by the radar beam its echo may
be lost in the clutter. In some cases the clutter signal may be random and noise-like in nature, but it
may also have systematic features - for example, scattering from the sea may be particularly strong at
frequencies where there is some sort of match between the radar wavelength and the wavelength of
the water waves - either the main waves which are immediately apparent, or the 'fine-structure' waves
that are superimposed on the main waves. These in turn will depend upon the wind strength and
direction and the depth of the water, so that there will be correlations between the clutter
characteristics and the meteorological conditions.
On land, similarly, clutter depends upon the nature and topology of the surface, the moisture content
of the ground, the siting of the radar antenna etc.
Various steps can be taken to diminish the effects of clutter on the echo signal, such as
     (i) filter out echo signals that are do not have a Doppler frequency shift - this permits the
     removal of the clutter component from echoes from moving targets
     (ii) de-sensitise the receiver for a short time after the transmission of a radar pulse, so that
     you will reduce the signal from the receiver due to clutter from the close environment,
     which is likely to be dominant. This is done to avoid saturating the receiver. It does           not
improve the signal to clutter ratio for the receiver

                        Tx                                                     saturation



Fig 18 Receiver sensitivity (gain) reduction for short ranges to reduce clutter signal

    (iii) shape the antenna beam to reduce clutter

   Sea surface                                  Sea surface

           Fig 19 Narrowing of radar beam to reduce clutter
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    (iv) if the statistical distribution of the clutter (its PDF) is known it may be possible to
    reduce its effect by appropriate signal processing.

Pulse compression
• the sensitivity of a radar - ie its ability to detect weak echo signals - depends upon the energy
   which is contained in the transmitted pulse, not the power transmitted. Thus, long medium power
   level pulses are as effective as short high power pulses if they contain the same amount of
   energy. Lower power pulses avoid electrical breakdown in waveguide etc and are more suitable
   for semiconductor sources.
• the disadvantage of using long pulses is that they degrade the radar range resolution
• a solution is to use pulse compression in which the short radar pulse is lengthened before
   transmission to reduce its avarage power level, but coded so that its frequency changes linearly
   during the duration of the pulse (a chirp pulse). The echo chirp pulse is compressed (pulse
   compression) as soon as it is received so that the range resolution of the original short pulse is
   restored. Pulse expansion and compression can be achieved using matching pairs of SAW
   (surface acoustic wave).



        Fig. 20 A chirp pulse (linear FM pulse)
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Synthetic aperture radar
• a large effective antenna aperture is obtained by using an antenna on a moving platform (an
   aircraft or an orbiting satellite) and combining the returned signals from radar pulses transmitted
   at many successive positions. The antenna may be considered as a large linear array

•   the large effective aperture gives a very large improvement in the angular resolution of the radar

•   SARs are usually sideways-looking radars that illuminate a swathe of the earth's surface. The
    resolution is often specified in terms of the along-track or azimuthal resolution and the range
    resolution perpendicular to the swathe. The along track resolution is improved by the application
    of the SAR technique, but the range resolution is determined by the pulse duration in the same
    way as for a conventional radar. Range resolution can be improved by standard pulse
    comprression techniques

•   SARs have many applications in remote sensing The advantage of microwave remote sensing
    is that it can be carried out at night and through rain and fog ie under conditions where optical
    methods cannot be used. Polar regions which have continuous cloud cover for long periods can
    always be monitored. This information is invaluable for the understanding and prediction of a
    range of environmental coditions - weather forecasting, global warming and sea level changes.

Remote sensing applications of SAR include

•   measurement of ocean currents
•   measurements of ocean temperatures
•   monitoring of vegetation, use of pesticides, fertilizers etc
•   surveys of natural resources - minerals etc
•   imaging of the earth's surface
•   monitoring of the atmosphere - CFCs, temperature distributions etc

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