The radar and its ground environment
1.7 PERFORMANCE
approached with similar range s and signal-to-n oise ratios in directions along and across the base line. Below this value, the coverage elongates and finally splits into two, giving only local coverage arou nd the two sites. Notice that this also applies to the elevation coverage. This has the effect of changing the traditional coordinates as shown in Table 1.7.
Table 1 .7
Comparison of monostatic and bistatic radar characteristics
Monostatic radar Bistatic radar
Measured Coverage
Range Slant range, R Slant range, RT + RR
Elliptical coordinates Cassinian coordinates Ranges to transmitter or receiver must be calculated Radial velo city Doppler frequency Hyperbolic Doppler frequency contours Azimuth and elevation Radar antenna Usually measured by the receiving antenna
The choice of ra dar freque ncy is limited, for civil rad ars, to the bands allocated to radars. The gain available from a given size of antenna depends on its dimensions in wavelengths; hence, portable radars and small radars tend to use higher frequencies. Radars mounted on vehicles and ships can support larger antennas and the largest are used by fixed ground installations. Radars mounted on vehicles or ships generally must operate in all types of weather, and the higher frequency radars, abo ve S-band , are particular ly susceptible to rain clutter. Examples are en route radars for a ir traffic control (range 150 nautical miles, or 278 km) which tend to use L-band; airfield approach radars S-band (range 60 nautical miles or 111 km); and those that cover the runways out to 10 km use X or a higher band , as do small ships’
radars.
The accuracy o f radar mea surement d epends o n the signal-to-no ise ratio (see C hapter 13 ). The signa l-to-noise ratio for accurate m easureme nt is normally greater than that necessary for detection so that the range or sign al-to-noise ratio for measuring the radar acc uracy must be defined sep arately. The following are exam ples:
• Range accuracy, standard deviation 10 m;
(All at a range of 30 km.)
• Azimuth accuracy, standard deviation 0.1 degree;
• Elevation accuracy, standard deviation 0.1 degree;
• Doppler frequency accuracy, standard deviation 10 Hz.
A knowledge of the radar site supported by map studies allows the amplitude and extent of the radar clutter to be estimated to find how great the dynamic range or the receiving system must be (including sensitivity time control) and how much clutter cancellation is required. Coherent signal processing allows precise sorting or suppression of signals according to their Dop pler freque ncy. In additio n to not allow ing large clutter sign als to swamp wanted ech o signals using tapering, the radar itself must not generate any interfering signal components that may be mistaken for wanted echo signals. This gives rise to the concept of stability, namely that interfering signals and noise caused by spurious instabilities in gain an d timing must b e a small fractio n, often 60 d B to 80 dB, of the u seful echo sign al.
These figures give bases for the range, resolution, accuracy, and stability budge ts. The range budget determines the sizes of the transmitter, a ntenna, and receiver sen sitivity. Perform ance marg ins must be estim ated to co mpensate for the losses in the system, and most of the factors listed under performance reduce the signal-to-noise ratio, thus reducing maximum range and accuracy. D uring the dev elopmen t of a radar, the goals for the characteristics o f some com ponents may not be met while others may be exceeded. The most convenient way of managing the daily state of the performance budgets is to u se a comp uter spread sheet.
The remaining chapters in this book end with the effects of the stages in the chapter on radar performance, for Chapter 1 these are the effects of the common components. These figures are gathered in Chapter 14 (Performance).
Four me asures of pe rformance are treated: the effects on rang e, resolution, a ccuracy, and stability.
1.7.1 Effects on range
The choice of pulse repetition frequencies determines the maximum instrumented range and the maximum unambiguous Doppler frequency. The probability of having an echo to measure is reduced in medium and hig h pulse repetition frequency radars that have parts of the listening time blanked for transmitter pulses. To cover the gaps, such radars often operate over a number o f pulse repetitio n frequenc ies, and to hav e the same se nsitivity as a radar without such holes, or eclipses, the signal-to-noise ratio has to be increased. T his increase is called eclipsing loss.
Bringing a radar into operation from development that does not have expensive excess performance is a constant struggle to limit the losses to a minimum. Examples of losses are:
• Radio frequency losses:
Waveguide or transmission loss from the transmitter to the duplexer;
Duplexer losses from input port to the port to the antenna;
Waveguide or transmission loss from the duplexer to the antenna;
For frequency diversity radars, the dip lexer losses;
Internal losses in the antenna;
Atmosp heric loss be tween the ante nna and the scatterer of intere st;
Losses caused by the sca tterer not being at an optimum a spect, fluctuation losses;
Atmospheric loss between the scatterer and the antenna;
Losses in the receiving antenna, in stacked beam radars there is a different radio frequency path for transmission and reception;
Losses in the waveguide or transmission line between the antenna and the duplexer;
For frequency diversity radars, the dip lexer losses;
Losses in the receiver protector and sensitivity time control (STC) attenuator;
(1.17)
• Receiver and signal proc essor losses:
Loss caused mismatch in the matching filter or tapering losses in the pulse compression stage;
Quantization loss in the analogue-to-digital converter;
Losses in signal processing caused by logarithmic video, moving target indicator or detector processing;
Losses during the recogn ition (extraction) of valid echo signals.
1.7.2 Resolution
T he resolutions in range, angle, and Doppler frequency are part of the basic design of the radar and depend on the effective transm itter pulse width, a ntenna bea mwidth, and signal proce ssor, respec tively.
During the path of the sig nals from the tra nsmitter back to the point where signals are extracted or displayed, the pulse becomes stretched in range and angle (azimuth and elevation), and the principal stages are shown in Table 1.8.
Table 1 .8
Places where waveforms are stretched
Cause Range Angle
Large scatterers Over on e pulse length radially Over on e beamw idth Limited rec eiver band width Stretches echo pulse
Matching or pulse compression stage
Stretched in range
Moving target indicator or detector
Shifted and stretched in an gle
1.7.3 Accuracy
The accuracy of measuremen t is based on the Wo odward equation [6 , p. 105 (2 7)] which is ge neral and a pplies to measurem ents in range, an gle, and D oppler fre quency. T he standard deviation o f the error, F, is given by
where F is the standard deviation o f the error for the dimension of ., namely:
for range, the range resolution cell width (time or distance);
for angle, the an gular resolutio n;
for Doppler frequency, the frequency resolution (frequency or radial velocity);
k is a constant;
R is the signal-to-noise ratio.
The point of measurement for J and R is where the information is used in either the extrac tor or the disp lay. Table 1.8 shows where J is stretched in time and Sectio n 1.7.1 sho ws where the s ignal to noise ra tio, R, is reduced.
An equation similar to (1.17) is used for angle accuracy in azimuth and elevation with similar dilutions of accuracy for signal-to-noise ratio and antenna beamwidth. Moving target indicators and the tapering used to increase the suppression of clutter in mov ing target dete ctors widen the effective anten na beam width at the extra ctor. The estimation of Doppler frequency depends on the effective bandwidth and signal to noise ratio at the point of estimation.
Most of the statistical distributions describing accuracy are Gaussian a lthough angles derived from monopulse radars should have, theoretically, a Cauchy distribution. In trials of three-dimen sional stacked beam rad ars with an aircra ft flying at a constant height, the resulting distribution was found experimentally to be Gaussian.
The timing error (jitte r) is normally small, comp ared with oth er factors whe n all pulses are derived from the same, stable frequency source, generally the stable oscillator (STALO).
1.7.4 Stability
The trigger generation and distribution system is the start of the propagation of synchronization jitter (see Section 3.6.4), which is critical so that radar instability does not limit the quality of the signal processing.
Modern moving target detector signal processors demand a rock stable clock and stable trigger system.
REFERENCES
1. Stevens, M . C., Secondary Surveillance Radar, Norwood, Massachusetts: Artech House, 1988.
1. Daniels, D ., ed., Ground Penetrating Radar, 2nd ed., Stevenage: I.E.E., 2005.
2. Skolnik, M . I., Rada r Hand book, New York: McGraw-Hill, 1970.
4. Skolnik, M . I., Rada r Hand book, 2nd ed., New York: McGraw-Hill, 1990.
5. Weisstein , E. W., ed ., CRC C oncise E ncyclop aedia o f Mathem atics, Boca Raton, Florida: CRC Press, 1999.
6. Woodward, P. M., Proba bility and Information Theory with Applications to Radar, 2nd ed., Oxford: Pergamon Press, 1964 and reprinted by Artech House in 1980.
R
C
Lamp to stabilize the gain at 3
Output
R C
A + -
Working point ' R
(j2BfCR % 1) R % 1
j2BfC % R
j2BfCR%1
&1 3
25
Figure 2.1 Block diagram of a Wien bridge oscillator.
(2.1)