### Written By:

Preeti Jain

If you have sometimes experienced the reflection of a sound due to the presence of a sound reflecting object like a canyon/ cave, etc. you have in a way experienced how radar functions. When you shout near towards a valley or a mountain, the reflection of a sound, i.e., the echo comes back. The time an echo requires to come back can be used to estimate the distance of the reflecting object, provided the speed of sound in air is known. Radar functions in a similar manner to find out the location of the reflection object using RF waves.

So, What is RADAR? Radar is an acronym for RAdio Detecting And Ranging. The name itself suggests that the radars are used to detect the presence of object and determine its range, i.e.,
Fig. 1: A Representational Image of RADAR or Radio Detecting and Ranging used to Detect Presence and Range of an Object

distance and bearing, using radio frequency waves.

Radars are being used to measure different parameters
1.      Range                    Using Pulse Delay
2.      Velocity                  From Doppler Frequency Shift
3.      Angular Direction     Using Antenna Pointing
4.      Target Size              From magnitude of reflected energy
5.      Target Shape           Analyzing reflected signal as a function of direction
6.      Moving Parts            Analyzing modulation of the reflected signal

Cost and complexity of radar is dependent upon the number of functions it performs. Radars are used for various applications like Surveillance, imaging, remote sensing, altitude measurement, etc.

Basic principle governing the functionality of radar is due to the properties of radiated electromagnetic energy.
·         The electromagnetic energy travels through space in a straight line, at a constant speed (approximately the speed of light). The propagation of these waves differs slightly because of atmospheric effects.
·         When the electromagnetic waves strike an electrically conductive surface, a part the energy is reflected back towards the source, rest of the reflected energy gets radiated in different directions.
·         Receipt of reflected energy towards the source is an indication of the obstacle in the direction of propagation.
These basic principles are utilised in Radar to determine distance, and bearings of the target, i.e., a reflecting object.

The block diagram of a primary Radar is shown below:
Fig. 2:  A Block Diagram Representing the basic Principle of RADAR

·         Transmitter
The radar transmitter produces microwave signal, which is typically short duration high-power RF- pulses of energy for a pulsed radar.
·         Duplexer
Duplexer acts as a switch; it switches the antenna between the transmitter and receiver. This obviates the need for separate transmitting and receiving antennas. Duplexer prevents high power energy to go into receiver (high power pulses can damage the receiver) while transmission and prevents reflected signal to be fed to the transmitter during reception.
·         Antenna
The transmitting antenna radiates the transmitting energy to signals in space, in desired directions.

The radiated energy propagates with constant velocity. When it finds the target, the energy is scattered, a part of which is reflected towards the transmitting antenna. The antenna receives the reflected energy and feed it to the duplexer. The duplexer directs this energy towards the receiver.
The receiver demodulates the received reflected energy and analyzes the signal to find target parameters.
·         Display
The receiver sends the output to display, which shows the analyzed signal in an easily understandable user friendly manner.

## Basic Concepts

1.      Time Delay Ranging
Target Range is the fundamental parameter measured by Radars. It is computed using calculation of round trip time of the pulse and velocity of light.
For Bistatic radars (transmitting and receiving antenna are at different locations),

Rt + Rr = c Tr

For Monostatic radars (transmitting and receiving antenna are collocated, Rt = Rr),
R = c Tr /2,

where,

Rt is distanceof target from transmitter,
Rr is distanceof target from receiver,
C is velocity of light,
Tr is round trip time.
Fig. 3: A Diagram Illustrating the Computation of Slant Range

Range R, thus computed is called slant range.

Two aircrafts at same distance but flying at different altitudes are reported to be at different distance on a radar display. This is because radars report slant range, not a horizontal distance.
Fig. 4:  A Diagram Demonstrating Different Distances of two Airplanes on a Radar Display

2.      Pulse Repetition Frequency
Radar systems radiate pulse during transmission time (pulse width t), wait for the echo to come back during listening period and then again transmit the pulse. Synchroniser maintains timing synchronization between associated circuits.
Time between the beginning of one pulse to the start of next pulse is called Pulse Repetition Time (PRT) and reciprocal of PRT is called pulse repetition frequency (PRF); PRF of radar system is the number of pulses transmitted per second. Choice of PRF is quite crucial as it affect the maximum range of the radar.
Fig. 5: A Figure Representing Pulse Repetition Time

3.      Maximum Unambiguous Range
Due to the presence of strong targets, echo of the first radiated pulse is received after transmission of the pulse. Radar treats it as the echo from the second pulse and hence reports wrong range. This is called range ambiguity.
Maximum unambiguous range is given by
As said earlier, choice of PRT decides maximum unambiguous range.
Fig. 6:  A Figure Representing the Equation of Maximum Unambiguous Range

4.      Minimum Detection Range
When the leading edge of an echo pulse falls inside the transmitting pulse, computation of round trip time and hence the range calculation is not possible. During transmission of a pulse, reception is OFF as duplexer is connected to the transmitter only. Hence, the minimum detectable range Rmin is given by
Fig. 7: A Figure Representing the Equation of Maximum Unambiguous Range

where, trec is recovery time of a duplexer.
Rmin defines the blind range; targets in close vicinity are not detected.

5.      Theoretical Maximum Range Equation
Range equation express the relation between various parameters of a radar system affecting the received signal power and thereby the range.
Reflected received power is given by
Fig. 8: A Figure Illustrating the Equation of Theoretical Maximum Range

Where,             Pr =     Power returned to the target. This power should be greater than the minimum detectable signal of the receiver.
Pt =     Transmitted Power. Power returned is directly related to this power.
G =      Antenna Gain; it is a measure of the ability of focussing energy into a directed beam.
l =      Signal Wavelength. It affects antenna aperture; antenna aperture can be visualised as a circle normal to incident radiation such all incoming radiations pass through it. Higher is the operating frequency, smaller is the antenna.
st =     Radar Cross Section (RCS). Ability of the target to reflect radiated energy is given by the term radar cross section area. It depends on number of parameters like size and shape of the target, operating frequency, material of the reflecting surface, etc.
R =      Slant Range. Range obtained is affected by free space path loss. Free space path loss is the attenuation of radiated electromagnetic energy in the free space with no obstacles between the source and receiver. Power loss is purely a function of the square of the distance.
L =      Loss factor. Apart from free space path loss, various other phenomena (multipath effects, attenuation by precipitation, atmospheric gases, etc.) affect the received power at the receiver. All these need to be taken into account while calculated range of the radar.

From this equation, maximum radar range can be expressed as
Fig. 9: A Figure Illustrating the Equation of Maximum Radar Range

Note that to increase the range by double, transmitter power has to be quadrupled.
Pr (min.) is called minimum discernable signal (MDS) and its typical value is somewhere near -110 dBm for good receivers.

## Concepts Contd..

6.      Bearing Measurements.
The direction (azimuth and elevation angles) to the target is determined by measuring the direction in which the antenna is pointing when the echo is received.  The azimuth angle is an angle between the vertical plane containing the target and the reference direction, measured in a horizontal plane. The elevation angle is an angle between the horizontal plane and the line of sight, measured in the vertical plane.
Fig. 10: A Figure Demonstrating the Accuracy of Azimuth Angle and Elevation angle Measured in a Horizontal Plane

The accuracy of angular measurement is determined by the directivity of the antenna.

Ability to distinguish between close targets is called target resolution of the radar. It is defined in both, range and bearing.
Range resolution is the ability to distinguish between two targets on the same bearing but at different ranges. It depends on the transmitted pulse width, target parameters, etc; pulse width being the major factor. Theoretical range resolution of radar is given by
Fig. 11: A Diagram Representing Equation of Theoretical Range Resolution

Angular (Bearing) resolution is the minimum angular separation at which two similar targets at the same range can be separated. It is determined by the -3 dB beam width of an antenna. Two identical targets are resolved in angle if they are separated by more than the beam width of an antenna.
The angular resolution is given by the following formula:
Fig. 12: A Diagram Representing Equation of Angular Resolution

Where, q is antenna beamwidth and R is the slant range.

8.      Threshold Detection
Received signal is demodulated and is processed by threshold logic. If the received signal is greater than the set threshold, presence of the target is declared. As received signal is affected by thermal noise, clutter, various interferences, the probability of detection is affected.
Typical received signal is shown in the following graph.
Fig. 13: A Figure Illustrating Demodulation and Processing of Signal Received by Threshold Logic

Since the received signal strength is increased due to thermal noise at ‘A’, it causes false alarm (declaration of a target which is not present). On the other end, the received signal strength has decreased at ‘B’ leading a miss (target is not declared even when it is present).

9.      Doppler Shift
Echo of a radar signal sent toward a moving target will have its frequency shifted and the shift in the frequency is related to the velocity of the moving target. This occurs due to Doppler Effect. Doppler shift will occur only when the relative velocity vector has a radial component.
Fig. 14: An Image Representing Equation of Doppler Shift

When slant range R is reducing, i.e., the target is approaching, the Doppler shift will increase and when R is increasing, Doppler shift decreases. The phenomena are used to measure the velocity of the target. For this purpose, Doppler filter bank is used, i.e., radar operating band is divided into very narrow non overlapping sub-bands and power out of each filter is used to estimate velocity.

10. Clutter & Interference
A nuisance factor that can degrade performance of search radar is clutter. Clutter is nothing, but echoes from stationary or slow moving targets. Clutter makes detection more difficult. An aircraft flying at low altitudes is hard to see against echoes returned from the terrain. Detection of a small target on the surface of land or sea is severely affected by unwanted clutter echoes.
Fig. 15: An Image Representing Clutter and Interference Effect in RADAR

Other factor which contributes to interference is the multipath effect.

## Performance

Performance of a Radar system is governed by various factors
·         Receiver Sensitivity & Signal to noise ratio:
Signal to noise ratio determines the ability to recognize targets in presence of random noise (which is always present). Noise sets the lower limit of receiver sensitivity. Smaller the signal receiver can process, better the measurement range of the radar. Good signal to noise ratio reduces false alarms and target miss and enhances probability of detection.
Receiver bandwidth is basically the frequencies, receiver can process. Reducing the bandwidth increases S/N ratio but distorts transmitted pulse & reduces probability of detection.
·         Scan Rate
Scan rate is the speed of rotation of the antenna (or the beam). It determines the dwell time on the target. High PRF radars scan more quickly; low PRF radars scan relatively slowly.
·         Power
Ratio of Radiated power to PRT is the average power. More the radiated power more is the range, but smaller average power enables use of smaller radar components.
·         Operating frequency
Choice of frequency is determined by atmospheric transmission windows and the function of radar. Frequency determines optimum antenna size, receiver input stages, power levels, etc.

Other parameters effecting radar performance are pulse repetition frequency, radar cross section of target, antenna gain, operating frequency and antenna aperture, which have already been discussed earlier.

## Displays

Current radar displays uses digital processing techniques to display the information in a TV-like format using a raster scan. Using these techniques, multifunctional displays are created and used in modern radar systems.

Earlier radars used different kinds of displays, primarily based on CRT.
1.      A- Display
A- Display displays received power vs. range on an oscilloscope.
A sawtooth voltage generator is used on X-axis and it moves the oscilloscope spot across the screen at a defined rate. Start of ‘Sweep’ coincides with start of ‘transmitted pulse’ and speed of movement of the oscilloscope spot is set based on maximum return time of the echo. Reflected echo is plotted on a Y-axis.
Fig. 16: A Figure Displaying 'A' Display and its Range on an Oscilloscope

Since X-axis reflects time, range of the target can be determined using time of flight principle.

2.      B- Display
B- Display displays Range (on Y-axis) vs. Azimuth angle (on X-axis) on an oscilloscope.
A saw tooth voltage generator is used on Y-axis and it moves the oscilloscope spot across the screen at a defined rate. Depending upon the azimuth angle of the antenna, a proportional voltage signal is fed on X-axis.

H-scope is a variant of B-scope; it plots Range Vs elevation angle.
Fig. 17: A Figure Displaying 'B' Display vs. Azimuth angle on an Oscilloscope

3.      C-Display
C-Display displays Elevation Angle (on Y-axis) vs. Azimuth angle (on X-axis) on an oscilloscope.
Fig. 18:  A Figure Illustrating 'C' display Elevation Angle vs. Azimuth Angle on an Oscilloscope

4.      Plan Position Indicator
It is one of the widely used displays. Distance from the centre indicates range, angle around the display represents azimuth angle to the target.
Fig. 19: A Representational Diagram of Plan Position Indicator

## Frequency Bands

Radars operating frequency is governed by the applications and therefore different types of radars operate in different frequency bands.

 Frequency Band (IEEE) Primary Application HF, VHF Primarily used for early warning and over-the-horizon radars UHF(300 M -1 G) Used for Early warning radars, Wind profilers L-band(1G -2G) Used for Air Route Surveillance Radars.Used by first civilian remote sensing American satellite carrying SAR (SEASAT) and Japanese JERS-1 satellites (L band SAR) and NASA airborne system. S-band Used on board the Russian ALMAZ satellite, Magellan mapped Venus C-band Commonly used on airborne (CCRS Convair-580 and NASA AirSAR) and spaceborne systems (including ERS-1 and 2(SAR & radar altimeter) and RADARSAT. X-Band Used on airborne systems for military reconnaissance and terrain mapping Ka, K, and Kubands Used in early airborne radar systems but uncommon today.

Fig. 20: A Representational image of Radar Jamming

High amount of RF energy is flooded in the Radar operating band. This causes signal to noise ratio of the radar to go down.

2.      Using Repeater Jammers
Radars operate on the time-of-flight principle of the received echo. Repeaters, for each received pulse, sends back more than one pulse to cause the radar computer to calculate the incorrect range. However, radars also use counter-measures like staggered PRF, Jitter PRI, Stagger-Jitter patterns, etc.

3.      Reducing RCS.
The magnitude of the reflected signal depends upon the RCS of the target. Hence, to escape from enemy radar, the aircrafts use mechanisms to reduce the RCS. Some of the methods are
(a)    Shaping , i.e., no tilt angles, no sharp corners
(b)   Use of radar absorbing materials
(c)    Use of secondary scatterers for the purpose of cancellation.

### In the expression included in

In the expression included in point #7.      Radar Resolutions

Where, q is antenna beamwidth and R is the slant range.

there is no 'q' given.

is it q*R*sin(?/2)?

Otherwise, the article is flawless and very useful...

Regards

a

hi