Sheet 1 of 8

RADAR

RAdio Detection And Ranging Part 2 of 2

Radar equation
Effective receiving Area Aeff

Power Density =

PT .GT 4 .R 2

Tx

PT

Sphere x gain of antenna

Radar cross-section

GT
PT .G T 1 . . 4 .R 2 4 .R 2

Fraction of incident power density of source

Power Density =

Output power from the receive antenna

PR =

(4R )
2 2

PT G T
2 2

Aeff

General antenna relationship

G=

Aeff
PR = PT G T 3 ( 4 ) R4

Output power from receive antenna

Maximum range

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

4 2 2 PT GT Rmax = 3 (4 ) S min

Note:

i)

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

ii) apparent dependence on aperture

can be misleading. For a fixed antenna

2 2 G2 T 1

suggests short wavelengths for maximum range

Sheet 2 of 8

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 etc 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 beam

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 random. 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 directpath 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.

Sheet 3 of 8

Threshold

Radar Output Voltage

Time No Noise In

Rx
Noise Figure (F) =
Signal In powers

G
Adds noise NA

So

(Si/Ni ) (So/No )

F. 1 F 0dB

Fig 15 Signal + noise at receiver output, showing the importance of setting the threshhold 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

F=
Here

Si Ni

So No N i = kTo B is the available noise power at the input

If the minimum acceptable signal to noise ratio at the radar receiver output is this requires a minimum signal at the receiver input of S min which is given by

So No

min

So S i = S min = F N o

So N N i = F o

kTo B

Using this value of S min in the equation derived earlier for Rmax we obtain
2 2 4 PT GT Rmax = 3 (4 ) kT0 B F (S 0 N 0 )min
1

B is the IF bandwidth of the receiver. Usually we make B 1/ where pulse.

is the width of the radar

Sheet 4 of 8

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 aircraft illuminated from different directions. Ci l i l

Typical vertical coverage pattern for a surveillance radar, showing the lobes and nulls caused by ground reflections.

Fig.16 Radar cross-section of an aircraft illuminated from different directions (from P A Lynn)

Sheet 5 of 8

a range of models - Swerling models - are used to describe the statistical variations in the RCS s in terms of probability distributions p ( )d which gives the probability that the cross-section lies between and + d . 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 The PDF for both cases 1 and 2 is p ( ) = 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

1 exp with 0 (av ) (av )

p( ) =
Multipath effects

(av )

2 exp with 0 (av )

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 phase

Ground reflected

Receiving signal

range

Fig 17

Multipath

Sheet 6 of 8

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 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
Avoids receiver saturation

Tx Receiver sensitivity

time

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

Sheet 7 of 8

(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).

P(out)

Fig. 20 A chirp pulse (linear FM pulse)

Sheet 8 of 8

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