1. Radar Performance Factors

2. Objectives
Define the following radar terms and interpret/apply their relationships that effect radar performance.
- Duty Cycle (DC) - Directional Gain (Gdir)
- Pulse Width (PW) - Power Gain (G)
- Pulse Repetition Time (PRT) - Peak Power (Ppk)
- Average Power (Pave) - Minimum Range (Rmin)
- Bandwidth (BW)
- Maximum Unambiguous Range (Runamb)
Angular resolution (cross range resolution) (Rcross)
- Number of returns per sweep (circular scan)
- Pulse Compression Ratio (PCR)
- Threshold level (TL)
- Receiver sensitivity
- Transmitted power
Calculate Power Gain and Effective Antenna Aperture.
List the factors that determine radar cross section.

3. AN/SPS-55
Type I-band (8 to 10 GHz) surface search and navigation radar.
Specifications Antenna Rotation rate: 16 rpm Polarization: circular or linear Horizontal beamwidth (3 dB): 1.5º Vertical beamwidth (3 dB): 20º Gain: 31 dB
Transmitter Frequency: I-band ( GHz). A G-band ( GHz) version is also available Peak power: 130 kW PRF/pulse-width: 750 pps/1 µs; 2,250 pps/0.12 µs
Receiver Type: low noise
Bandwidth: 1.2 MHz (long pulse); 10 MHz (short pulse) Receiver processors: linear logarithmic, FTC, variable sensitivity time control

4. Carrier Frequency Frequency emitted by the antenna
Determines antenna size and directivity of beam.
Lower Frequency
longer range
bigger antenna required (L≈λ/2)
more power required (same E field over longer distance)
Higher Frequency
Support high resolution features
better ability to resolve targets
smaller antenna (L ≈ λ /2)
greater attenuation losses. (scattering & absorption)
Carrier Frequency
a. Determines antenna size and directivity of beam.
b. Lower Frequency the longer the distance can travel, the bigger the
antenna required, and the more power required.
c. The higher the frequency the better the resolution and the ability to
detect smaller targets. Also the small the antenna size and the greater
the attenuation losses.
     
  RADAR (CARRIER) FREQUENCY - Higher frequency = shorter l, smaller antenna size, higher antenna directivity and improved detection of small targets. Since the radar beam travels in a straight line, it also means shorter range. At lower freqs, radar beams refract more in the atmosphere causing longer ranges. Low frequency = larger beam width.

5. Pulse Shape Determines range accuracy and min/max range.
Desire pulse with vertical leading and trailing edge.
Crisp leading edge – improves range accuracy
Crisp trailing edge – improves min range
Crisp edges – improve range resolution
But perfect square wave requires infinite bandwidth
Min Range
Range Accuracy
Pulse Shape
a. A pulse is made by summing several sinusoid waves of various
frequencies.
- A perfect pulse (vertical leading and trailing edges) requires the receiver
to process an infinite number of sine wave freq.
- Internal circuit noise will also distort a pulse.
b. Determines the range accuracy. (closer to vertical the better)
Use graphic pulse to show rise time can confuse timing to get range.
c. Pulse shape can also effect minimum detection range.
- Already discussed that. Pulse must be off before echo returns.
a)       PULSE SHAPE - determines range accuracy, minimum range (Rmin) and range resolution. An ideal pulse would be perfectly square which is not possible. Desire steep leading edge - better for timer (less rise time gives better “start” point for timer) and more accurate range; Also, a sloped trailing edge = receiver blanked longer - therefore minimum range would increase and target resolution would decrease (both detrimental).
Trailing edge
Leading edge
time
Xmit off
Xmit on
 Range Accuracy Rmin (decreases) Range Resolution (smaller)

6. Pulse Width
Interval of time between leading edge of pulse and trailing edge of pulse.
Usually measured in microseconds (m).
Usually measured at half-power points.
Determines Rmin and range resolution.
Short pulse width
Long pulse width
Reduces max radar range
Better range resolution
Shorter Min detectable range
Increases max radar range
Degrades range resolution
Longer min detection range
. Pulse Width.
a. Determines range resolution and minimum detection range for same
reasons as pulse shape. Can’t have pulse on when the echo returns.
b. To lesser extent, pulse width can determine maximum range.
- Pulse has to be big enough to hold enough energy to travel to the
target and return.
- The bigger the pulse the more energy it can hold and the further
away the target can be an still get a measurable return.
- [Power in wave is product of peak power and pulse width]
c. The narrower the pulse the better the range resolution
- This is a trade off with amount of power in the pulse and effective the
maximum range of the radar. LIMITS the range.
a)       PULSE WIDTH - determines radar range resolution, max detection range and min range (Rmin). The outgoing pulse must physically clear the antenna before the return can be processed. For good resolution and min range, desire narrow PW. But in order to be detected, a target must return an echo strong enough to be identified by the receiver as a valid contact. The energy in the returned signal may be increased by increasing Ppeak (limited by size and quality of power supply) or by increasing PW.

7. Pulse Compression Signal processing technique.
allows use of wide pulses to increase range while maintaining the higher resolution of short pulses.
Increases frequency of the wave within the pulse.
Allows for good range resolution while packing enough power to provide a large maximum range.
Pulse Compression. Technique that allows use of wide pulses to enhance detection capability while maintaining the range solution of short pulsed transmissions.
a. Technique of modify the pulse so that the frequency in the pulse
continually is increased.
b. This allow more energy to be put in a pulse increasing range.
How’s it work:
a. When pulse echo returns it passes through filters which
- slows down passing lower frequencies so faster end frequencies
pile up on top of lower frequencies
b. This results in a higher return pulse output and a narrower pulse width.
a)       PULSE COMPRESSION - signal processing technique that allows use of wide pulses to enhance detection capability while maintaining resolution of short pulses; Transmitted pulse is increased in frequency over the duration of pulse. When received, it passes through pulse compression filter which allows the trailing edge of the transmission to move through faster which electronically compresses the transmission.

8. Pulse Compression

9. Typical Pulse Widths Radar PW (msec) AN/SPS-10 1.3 – 0.25 AN/SPS-55
AN/SPS-40
60 / 3
AN/SPS-49
125 / 2
AN/SPS-48
9 / 3
AN/SPY-1
51 / 6.4

10. Pulse Repetition Frequency (PRF)
Number of pulses transmitted per second
Expressed in Hz or PPS
Higher PRF
More hits per sweep
Higher probability of detection
Max theoretical range decreases
Unambiguous range decreases
Fire Control Radars
Use high PRF for high update rate
Search Radars
Use low PRF
Compensate thru slower scan or wider beam
 PRF
Scan Rate
a)       PULSE REPETION FREQUENCY (PRF) - high PRF will improve resolution; Trade
off is that it decreases maximum unambiguous range.
Runambig

11. Runambig
Unambiguous Return – Return of echo prior to transmittal of next pulse (within unambiguous range).
Ambiguous Return –
Eclipsed Return – echo from first pulse appears as second pulse is transmitted.
Second Time Around Return – echo from first pulse arrives after second pulse sent.

12. Typical PRFs

13. Beamwidth (BW)
Measure of angular extent of the most powerful portion (main lobe)
½ power points (-3dB)
q = kl/L
k= 0.88 linear
1.02 circular
a)       Beam Width (BW) - a measure of the angular extent of the most powerful portion (main lobe) of radiated energy (review Lesson 2 handout); drawn through ½ power points (-3dB points).
Frequency increases
Wavelength decreases
Beamwidth decreases
Length of antenna increases
Beamwidth decreases

14. Beamwidth Vs. Accuracy
1. The size of the width of the beam (beam-width) determines the angular accuracy of the radar. From drawing we see that the target could be any where in the beam to produce a return. Ship B can more accurately determine where the target really is.
2. The function of the radar determines how narrow the beam-width is needed.
a Search radars sacrifice accuracy for range. (wide beam-widths at high
power)
b. Tracking or targeting radars require more accuracy (narrow beam-
widths)
3. If the target is located on the center line of the beam lobe, the return will be the strongest.
Key Point:. Beam-widths determine the angular accuracy of the radar.
Lead in: Angular accuracy can be use to measure azimuth and elevation depending on which way the antenna is oriented.

15. Radiation Pattern Square Antenna

16. Radiation Pattern Circular Antenna

17. Scan Rate Scan rate (Ω) How fast antenna is rotated (user controlled)
Too fast…miss min number of returns
Too slow…incomplete radar coverage
Scan Rate & Beam Width & PRF together affect number of returns processed by the receiver
Too fast: insufficient hits for pulse integration
The antenna is out of position before pulse returns.
Too slow: Not covering enough area quick enough to pick up a fast moving target.

18. Scan Rate & Beam Width
SCAN RATE AND BEAM WIDTH - Scan rate is a function of how fast antenna is rotated - too fast could miss minimum required number of returns to indicate a valid target; if too slow, difficult to determine false targets. Beam width = sharpness of antenna beam; a sharp beam must be pulsed more often to get the minimum # of signal returns necessary for target detection. Radar antennas have ½ the BW of communication antennas since radar antennas are used to both transmit & receive the signal. Scan rate & beam width affect radar probability of detection.

19. Transmitter Power
High peak power is desirable to achieve maximum ranges.
But low power supports being covert.
Sometimes power is a design parameter
Sometimes power is a design constraint
TRANSMITTER POWER - the more power out of the transmitter (Ppeak increased), the longer the maximum detection range and the larger the size of the radar. Note: For many systems, it is desirable to keep average power (Pavg) fixed, therefore, the Duty Cycle must also remain fixed. We do this by adjusting PW or PRF since DC = PW x PRF.

20. Radar Cross Section Major factors which determine RCS
Target’s size
Shape
Material
Aspect angle (relative to radar)
radar frequency
polarization
RCS () measured in m2

21. RCS WW-II B-26

22. Signal Reception
Explain why only portion of the signal gets to the target and only a fraction of that signal gets back to the receiver.
SIGNAL RECEPTION - only small portion of transmitted energy actually strikes target and reflects back to receiver, plus spreading losses in both directions; Mega Watts transmitted, peco Watts received. Note: the smaller the received signal, the longer the range capabilities
The weaker the signal the receiver can process (Smin), the greater the effective range.

23. Receiver Bandwidth The frequency range the receiver can process.
Receiver must process many frequencies.
Pulse train is series of sine waves that approximate a square wave shape.
Frequency shifts occur from Doppler Effects.
Reduce bandwidth?
Increases the Signal-to-Noise ratio (good).
Returned signal frequency may be outside of bandwidth. (bad).
Receiver Bandwidth:
a. To create a pulse many different frequency sine waves are summed so a
radar must combine RF energy of different frequencies.
b. Doppler effects also shift the frequencies so the radar must be capable of
receiving and processing many frequencies.
c. The range of frequencies is the bandwidth of the receiver.
d. Reduce the bandwidth increases the signal-to-noise & distorts the pulse.
RECEIVER BANDWIDTH - Affects pulse shape. The transmitted radar pulse train is actually a series of sine waves that approximate a square wave and the preponderance of energy transmitted by the radar is at the intended (carrier) frequency. The receiver must be designed to detect and amplify a band or range of frequencies above and below the transmitted frequency. BW must be wide enough to accommodate all frequencies included in the transmitted pulse or the receiver will distort the pulse shape and degradation of performance will result.

24. Receiver Sensitivity  Sensitivity  Smin  MDS  Rmax
Smallest return signal discernible against noise background.
An important factor for determination of maximum radar range.
Smin = Minimum Signal for Detection (W)
MDS = Minimum Discernable Signal (dBm)
 Sensitivity  Smin  MDS  Rmax
Receiver Sensitivity:
a. Defined as the smallest return signal that can produce an electrical signal
to the indicator that is discernible against the noise background.
b. Sensitivity is an important factor in determining the maximum radar
range.
c. Smallest discernible signal is measured in milliwatts and is referred to
Smin, Minimum Signal for Dection.
a)       RECEIVER SENSITIVTY - desire high receiver sensitivity; the more sensitive, the smaller the MDS (like hearing test) and the better the radar range. A large Smin or MDS is NOT desirable since sensitivity would decrease and ability to detect would also decrease.
Large Smin / MDS NOT desirable.
Sensitivity would decrease.
Detection ability would decrease.
Max Range would decrease

25. Signal-to-Noise Ratio
Ability to recognize target in background noise.
Noise is always present - external and internal.
At some range, noise will be greater than target return.
Noise or Smin sets lowest limit of the radar sensitivity.
Whichever (Noise or Smin) has the higher value.
Threshold Level used to suppress noise.
The higher SNR - the better!
Signal-to-Noise Ratio:
a. Noise (always present) sets the absolute lower limit of the sensitivity of
the radar sets. (At some range the noise will be greater than the echo)
Example: Look at a walkie talkie. If you turn down the gain control eventual you will not
hear the voice only the static. The static is noise.
b. Noise includes atmospheric disturbances, Jamming, stray signals.
Noise is inherent in electronic circuits as random electron
motion through a resister causes stray noise.
c. To cope with this problem, the operator can set a threshold level. If
signals are below this threshold level, they will not be displayed.
* If threshold level is set too low - you get many false detentions.
* If set to high - could mask out the real contact. Must compromise.
SIGNAL TO NOISE RATIO (SNR) - Ratio of the return radar signal to the noise voltage. Noise is generated by electronic components of radar system itself as well as externally; Limits sensitivity. The higher the SNR the better.

26. Radar Range Equation s PtGAes R = (4p)2Smin 4pR2 1 4pR2 1 Pt G Ae Smin
a)       Threshold Level - signal level above which receiver recognizes return as valid target.
* If set too low - false targets * If set too high - missed targets
s – Radar Cross Section
1/4
PtGAes
R =
(4p)2Smin

27. Radar Range Equation s PtGAes R = (4p)2Smin 4pR2 1 4pR2 1 Pt G Ae Smin
Pt – Power at the transmitter
Large EM Field
Corona Effect
Ionizes air
Arcing
Ionized air conducts
1/4
PtGAes
R =
(4p)2Smin

28. Radar Range Equation s PtGAes R = (4p)2Smin 4pR2 1 4pR2 1 Pt G Ae Smin
G – Antenna Power Gain
Product of
r – Antenna Efficiency
Gdir – Directive Gain
1/4
PtGAes
R =
(4p)2Smin

29. Radar Range Equation s PtGAes R = (4p)2Smin 4pR2 1 4pR2 1 Pt G Ae Smin
Ae – Effective Antenna
Product of
r – Antenna Efficiency
A – Antenna Area
1/4
PtGAes
R =
(4p)2Smin

30. Radar Range Equation s PtGAes R = (4p)2 Smin 4pR2 1 4pR2 1 Pt G Ae
Spherical Spreading
To and From Target
Represents spreading of omni-directional antenna
1/4
PtGAes
R =
(4p)2 Smin

31. Radar Range Equation s PtGAes R = (4p)2 Smin 4pR2 1 4pR2 1 Pt G Ae
Smin – Minimum Sensitivity
Lowest energy level receiver is capable of detecting
Lower Smin – Better the range capability
1/4
PtGAes
R =
(4p)2 Smin