The radar and its ground environment
1.3 MAIN MONOSTATIC RADAR COMPONENTS
1.3.12 Determination of position
Once the decision is made as to whether something is there, the best estimation must be made for its location. Methods and the accuracy obtained are described in Chapter 13.
1.3.13 Common components and timing
The components in a radar must operate together and in proper time, so every radar needs a number of control pulses or triggers. Typical trigger timings are shown in Figure 1.9, where the time is divided into receiving or listening time (when the echoes return) and the dead time in between. Activity starts long before the transmitter pulse with the basic pulse repetition frequency or system trigger. This is delayed to generate the other triggers. The names and numbers of triggers vary from radar to radar. Typical triggers are listed in Table 1.5.
SSR pretrigger
Modulator trigger
Modulation trigger
Zero range trigger
Sensitivity time control
trigger End of
range trigger Beam end
of range triggers
Dead time
Dead Listening or receiving time time
Transmitter pulse Basic pulse
repetition frequency or system trigger
Figure 1.9 The principal triggers in a low pulse repetition frequency radar.
Table 1.5 Typical radar triggers
Time Trigger Purpose
End of dead time Secondary surveillance radar Sent to the SSR so that it has time to choose and code its (SSR) pretrigger interrogation pulses
Modulator trigger Sent to the modulator in the transmitter to start the modulator pulse which is sent to the output stage Modulation trigger Sent to the stage which modulates the radio frequency input
for the output stage
Receiving or Zero range trigger Starts the sweeps on the displays, and so on.
listening time Sensitivity time control (STC) Switches off the sensitivity time control trigger
End of beam triggers Switch off the video outputs from the receivers to reduce collapsing loss
End of range trigger Switches off all the video outputs and starts the dead time Start of dead time This gives a pause until the end of dead time during which:
• Echoes beyond maximum range return
• The receiver is gated off to allow the use of test and calibration pulses in the system
Medium and high pulse repetition frequency radars send pulses during the listening times for longer ranges. During transmission the receivers are blanked or eclipsed, giving holes in the coverage. This reduces the probability of detection for the radar and the increase of the signal-to-noise ratio necessary to bring back the probability of detection to the specified value is called the eclipsing loss.
Early and present day magnetron radars use a relatively simple trigger generation and distribution as is shown in Figure 1.10.
Secondary surveillance radar (SSR)
Primary radar transmitter
Trigger generator
Primary radar receiver
Signal processor SSR
pretrigger
Range and STC triggers
Display Range
triggers
Range triggers
Total jitter ' E
n k'1
J2
j, k
Figure 1.10 Trigger generation for a basic magnetron radar.
(1.2) Modern radars with higher performance operate coherently. A central coherent oscillator (COHO), often 30 MHz or 60 MHz, provides a reference phase for the transmitted and received signals. The oscillator frequency is divided down to provide clocks to delay and synchronize all the triggers, the digital signal processors, and computers. This provides a much tighter control of the timing to reduce jitter losses for greater signal processing performance. Figure 1.11 shows the coherent oscillator and trigger generator block for the main block diagram for a coherent radar in Figure 1.8.
The timing accuracy of the triggers is critical for the performance of coherent signal processing (Chapter 11). The primary frequency reference is the coherent oscillator and as the sine wave from it is counted and the triggers are distributed there is a propagation of timing jitter. Each logical circuit has its jitter random component (standard deviation) and, if the jitter for the kth stage is Jj,k, then the standard deviation of the jitter from n stages will be
The same applies for the jitter at the output of a counter which counts up to n except that the values of Jj are equal so that the jitter is Jj/n. An example is given in Section 3.6.4.
Secondary surveillance radar (SSR)
Primary radar transmitter
Frequency divider
Trigger generator
Primary radar receiver
Analogue to digital converter
Signal processor Detector Clocks
Coherent oscillator
SSR pretrigger
Range and STC triggers
Range triggers Range triggers
Range triggers
Triggers:
Modulator Modulation
Power density at distant object ' PtGt 4BR2
W/m²
Power density returning to radar ' PtGt 4BR2
F
4BR2 W/m²
Antenna gain, G ' 4B Antenna area 82 Figure 1.11 Timing, trigger generation, and distribution.
(1.3)
(1.4)
(1.5) 1.4 BASIC QUANTITIES, MAXIMUM RANGE
The power relationships used in the initial models are based on a single pulse and do not include any losses. The losses are considered in each chapter. Integration of a number of these pulses is considered in the signal processing and threshold chapters (Chapters 11 and 12).
The transmitter transmits a large pulse with a peak power of P watts, a width of J seconds, and a wavelength of 8
t
meters. The pulse is radiated by the antenna and the pulse travels to the object at a range, R meters. The power density reaching the object is (compare with (6.2))
The object has a scattering area (often called the reflecting area) of F square meters. The power is scattered equally in all directions so that the power density returning to the radar is
The antenna gain is proportional to its area measured in wavelengths. This is from (5.13):
Effective antenna area ' G82 4B m2
Power intercepted by the antenna ' PtGt 4BR2
F 4BR2
Gr82 4B W
Receiver noise power ' kTB W
Signal&to&noise ratio ' PtGt 4BR2
F 4BR2
Gr82 4B
J kT ' PtJGtGr82F
(4B)3R4kT
Signal&to&noise ratio ' PtGt 4BR2
F 4BR2
Gr82 4B
J kT
1 L ' PtJGtGr82F
(4B)3R4kTL
(1.6)
(1.7)
(1.8)
(1.9)
(1.10) Thus, the effective antenna area is
The echo signal power intercepted by the antenna is from (6.4):
The critical power ratio is the signal-to-noise ratio. Most of the noise is generated by the first stage of the receiver and depends on the equivalent receiver noise temperature T K.
where k is Boltzmann’s constant 1.38 × 10 J/K;-23 T is the noise temperature K;
B is the receiver bandwidth Hz.
The receiver bandwidth is taken to be the reciprocal of the transmitter pulse width, J seconds. Thus, the signal-to-noise ratio at the receiver is taken to be (no losses)
Losses in signal-to-noise ratio are caused by resistive losses in the system and by design. Sometimes it is better to sacrifice gain in the system to obtain better side lobes or better clutter suppression, so (1.9) is extremely dangerous. If the product of the losses is L, then (1.9) becomes
To illustrate the calculation, a hypothetical radar is assumed that has the characteristics shown in Table 1.6.
Signal&to&noise ratio ' C F
R4 (1.11)
Table 1.6
Characteristics of a hypothetical radar with an assumed receiver noise figure of 2 dB
Characteristic Original units MKS units Value for calculation dB
Transmitter peak power, P t 1 MW 1 000 000 W 1 000 000 60
Transmitter pulse width, J 1 µs 10 s 10 -60
t
-6 -6
Wavelength, 8 10 cm 0.1 m 0.01 -20
Antenna gain, transmitting, Gt 35 dB 3 162.278 3 162.278 35
Antenna gain, receiving, Gr 35 dB 3 162.278 3 162.278 35
Subtotal numerator in (1.10) 1 000 000 100 000 50
(4 a)³ 1 984.402 1 984.402 32.976
Boltzmann's constant, k 1.381.10 J/K-23 1.381.10-23 -228.599
Receiver temperature, a noise 460 K 460 26.628
Product of the losses 10 dB 10 10 10
Subtotal denominator in (1.10) 1.260 10 -178.995-18
Constant, C 7.935 10+20 208.995
Table 1.6 allows the fixed radar parameters to be combined into a constant, C. These calculations have a wide arithmetic range, so that in the past decibels had to be used which is also shown in Table 1.6. The signal-to-noise equation reduces to
where C is the constant from Table 1.6.
An example of the signal-to-noise ratio for a one square meter area scatterer is shown in Figure 1.12. If the signal-to- noise ratio for the given probability of detection for a given false alarm rate in Chapter 12 is 10 dB, then the radar will have a range of 94.4 km. The dynamic range of the signal above the noise level is 100 dB here; for longer range radars, the dynamic range is greater. The dynamic range for signal processing can be reduced using sensitivity time control (STC) (see Chapter 7, Receivers) and, as in the past, limiting.
For normal air surveillance radars, Figure 1.12 shows in addition the mean clutter expected if the radar is situated near the ground (clutter models are discussed in Section 6.6). Whereas the aircraft cross-section does not vary with range, the clutter cross-section is proportional to range up to the radar horizon (assumed to be at 30 km) and decreases beyond the horizon. Clutter is rarely solid, and the log-normal model is used (see Section 6.6.2). A typical simulated clutter scenario is added in Figure 1.13.
0 20 40 60 80 100
20 40 60 80 100 120 140
Range km Signal-to-noise ratio
and Clutter-to-noise ratio
dB
Signal-to- noise ratio
Mean clutter- to-noise ratio
10 dB threshold
0 20 40 60 80 100
20 40 60 80 100 120 140
dB
20 25 30 35 40 45 50 55
26 28 30 32 34
Range km
10 dB above noise threshold Median
clutter to noise level dB
Signal to noise level dB Mean clutter to
noise level dB
Symbols showing points where the wanted echo is 10
dB greater than the clutter in the range 25 to35 km
Figure 1.12 Typical signal-to-noise and clutter-to-noise ratios for the radar in Table 1.6.
Figure 1.13 Signal-to-noise ratio with simulated log-normal clutter signals.
With a mean-to-median ratio of 20 dB, the mean level of the clutter is determined by the clutter spikes. The enlargement shows the situation between 25 km and 35 km and that there is a possibility of detection with a signal-to- clutter level of 10 dB between the spikes as shown by the dots in the enlargement circle in Figure 1.13. Figure 1.14 shows the density of these dots over the full range, and Figure 1.15 shows the probability of detection per kilometer within the radar’s range.
Figure 1.14 Signal-to-n oise ratio of a standard scatterer when the signal-to-clutter ratio exceeds 10 dB.
Figure 1.15 The probabilities of seeing a standard scatterer between clutter.
will be groups of cells with bad probabilities of detection. Either the radar must be used only for larger scatterers, for example for airliners, the clutter level may be reduced by reducing the resolution cell in range using a shorter transmitter pulse width or antenna beamwidth, or the clutter level reduced by signal processing (Chapter 11, Signal processing). In practice, it is difficult to see between bright clutter points on a cathode ray tube, and the radar picture requires a large amount o f memory to reduce the amount o f clutter displayed .