EXHIBIT A

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From Wikipedia, the free encyclopedia

Continuous-wave radar is a type of radar system where a known stable frequency continuous wave radio

energy is transmitted and then received from any reflecting objects.[1]Continuous wave (CW) radar uses

Doppler, which renders the radar immune to interference from large stationary objects and slow moving clutter.

[2]

CW radar systems are used at both ends of the range spectrum.

Inexpensive radio-altimeters, proximity sensors and sport accessories that operate from a few dozen feet

to several kilometers

Costly early warning CW angle track (CWAT) radar operating beyond 100km for use with surface to air

missile systems

1 Operation

1.1 Unmodulated Continuous Wave

1.2 Modulated Continuous Wave

1.3 Monostatic Radar

1.4 Bistatic Radar

2 Advantage

3 Limitations

4 See also

5 References

There are two types of continuous wave radar.

Unmodulated continuous wave

Modulated continuous wave

There are two different antenna configurations used with continuous wave radar.

Monostatic radar

Bistatic radar

The main advantage of CW radar is that energy is not pulsed so these are much simpler to manufacture and

operate. They have no minimum or maximum range, although the broadcast power level imposes a practical

limit on range. Continuous wave radar maximize total power on a target because the transmitter is broadcasting

continuously.

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The military uses continuous-wave radar to guide semi-active radar homing (SARH) air-to-air missiles, such as

the U.S. AIM-7 Sparrow and standard missile. The launch aircraft illuminates the target with a CW radar signal,

and the missile homes in on the reflected radar waves. Since the missile is moving at high velocities relative to

the aircraft, there is a strong Doppler shift. Most modern air combat radars, even pulse Doppler sets, have a CW

function for missile guidance purposes.

Maximum distance in a continuous wave radar is determined by the overall bandwidth and transmitter power.

This bandwidth is determined by two factors.

Transmit energy density (watts per Hertz)

Receiver filter size (bandwidth divided by the total number of filters)

Doubling transmit power increases distance performance by about 20%. Reducing the total FM transmit noise

by half has the same effect.

Frequency domain receivers used for continuous wave Doppler radar receivers are very different from

conventional radar receivers. The receiver consists of a bank of filters, usually more than 100. The number of

filters determines the maximum distance performance.

Doubling the number of receiver filters increases distance performance by about 20%. Maximum distance

performance is achieved when receiver filter size is equal to the maximum FM noise riding on the transmit

signal. Reducing receiver filter size below average amount of FM transmit noise will not improve range

performance.

A CW radar is said to be matched when the receiver filter size matches the RMS bandwidth of the FM noise on

the transmit signal.

Unmodulated Continuous Wave

This kind of radar can cost less than $100. Return frequencies are shifted away from the transmitted frequency

based on the Doppler effect when objects are moving. There is no way to evaluate distance. This type of radar is

typically used with competition sports, like golf, tennis, baseball, and NASCAR.

The transmitter is the strongest source of RF energy in the vicinity of the receiver unless there is a large

physical barrier along the line of sight, such as a mountain. There must be a strong Doppler shift between the

receiver and the reflector, otherwise the bleed-through signal reaching the receive antenna from the transmit

antenna will overwhelm the reflected signal arriving at the receiver.

Continuous wave radar with no FM modulation only detects moving targets, as stationary targets (along the line

of sight) will not cause a Doppler shift. Reflected signals from stationary and slow-moving objects are masked

by the transmit signal, which overwhelms reflections from slow-moving objects during normal operation.

Modulated Continuous Wave

Frequency-modulated (FM) continuous wave radar are capable of determining distance. This increases

reliability by providing distance measurement along with speed measurement, which is essential when there is

more than one source of reflection arriving at the radar antenna.

Distance measurement is implemented using a technique known as frequency modulated continuous-wave

radar. In this system the signal is not a continuous fixed frequency, but varies up and down over a fixed period

of time. Range is determined by evaluating the frequency-spread of the received signal.

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FM modulation is used with CW radar altimeters used with aircraft, CW early warning radar, and proximity

sensors. Doppler shift is not always required for detection when FM modulation is used.

The transmitter frequency can slew up and down as follows.

Sine wave, like air raid siren

Sawtooth wave, like the chirp from a bird

Triangle wave, like police siren in the US

Square wave, like police siren in the UK

FM modulation on the receive signal increases with distance. This smears out, or blurs, the Doppler signal. CW

radar range detection involves FM demodulation to sharpen the Doppler signal by reducing the blurring like

auto-focus on a camera.

The transmit frequency is used to down-convert the receive signal to baseband, and the amount of frequency

shift between the transmit signal and the reflected signal increases with time delay (distance). FM Modulation

index riding on the receive signal corresponds with range. Small frequency-spread is produced by nearby

reflections. A larger frequency-spread corresponds with more time delay and a longer range. The amount of

demodulation required to sharpen up the signal corresponds with distance.

Range demodulation is usually limited to 1/6 wavelength of the transmit modulation. Instrumented range for

100Hz FM modulation would be 250km. The radar is not guaranteed to report the correct distance for

reflections from distances beyond the instrumented range.

Monostatic Radar

The radar receive antenna is located nearby the radar transmit antenna in monostatic radar.

Feed-through_null is typically required to eliminate bleed-through between the transmitter and receiver to

increase sensitivity in practical systems. This is typically used with continuous wave angle tracking (CWAT)

radar receivers that are interoperable with surface to air missile systems.

Interrupted continuous wave can be used to eliminate bleed-through between the transmit and receive antenna.

This kind of system typically takes one sample between each pair of transmit pulses, and the sample rate is

typically 30kHz or more. This technique is used with the least inexpensive kinds of radar, such as those used for

traffic monitoring and sports.

Bistatic Radar

The radar receive antenna is located far from the radar transmit antenna in bistatic radar. The transmitter is

fairly expensive, while the receiver is fairly inexpensive and disposable.

This is typically used with semi-active radar homing including most surface to air missile systems. The transmit

radar is typically located near the missile launcher. The receiver is located in the missile.

The transmit antenna illuminates the target in much the same way as a search light. The transmit antenna also

issues an omnidirectional sample.

The receiver uses two antennas - one antenna aimed at the target and one antenna aimed at the transmit antenna.

The receive antenna that is aimed at the transmit antenna is used to develop the feed-through null, which allows

the target receiver to operate reliably in or near the main beam of the antenna.

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Continuous wave radar are cheap enough for the average home budget. Some are small enough to carry in your

pocket.

Because of their simplicity, CW radar are inexpensive to manufacture relatively free from failure, and cheap to

maintain.

CW radars, such as Trackman[3] and Personal Pitcher[4], are inexpensive and are being used in sports to track

ball and equipment parameters.

More sophisticated CW radar systems can reliably achieve accurate detections exceeding 100km distance while

providing missile illumination.

Unmodulated continuous wave radar cannot measure distance, and the beam is usually broad with side-lobes

that extend to the side and behind the radar antenna . There is no way to determine which object corresponds

with which speed measurement when there is more than one moving object near the receiver. Moving objects

include birds flying near objects in front of the antenna. Reflections from small objects directly in front of the

receiver can be overwhelmed by reflections entering antenna side-lobes from large object located to the side,

above, or behind the radar, such as trees with wind blowing through the leaves, tall grass, sea surface, freight

trains, busses, trucks, and aircraft.

Cheap unmodulated radar systems are only reliable when used with one object in a sterile environment free

from vegetation, aircraft, birds, weather phenomenon, and other nearby vehicles.

With 20dB antenna side-lobes, a truck or tree with 1,000 square feet of reflecting surface behind the antenna

can produce a signal as strong as a car with 10 square feet of reflecting in front of a small antenna that lacks

directionality.

This is a typical problem with radar speed guns used by law enforcement officers, NASCAR events, and sports,

like baseball, golf, and tennis. Interference from a second radar, automobile ignition, other moving objects,

moving fan blades on the intended target, and other radio frequency sources will corrupt measurements. These

systems are limited by wavelength, which is 0.3 meter at Ku band, so the beam spread exceeds 45 degrees if the

antenna is smaller than 12 inches (0.3 meter). Significant antenna side-lobes extend in all directions unless the

antenna is larger than the vehicle on which the radar is mounted.[5]

side-lobe suppression and FM range modulation are required for reliable operation. There is no way to know the

direction of the arriving signal without side-lobe suppression, which requires two or more antenna, each with its

own individual receiver. There is no way to know distance without FM range modulation.

Speed, direction, and distance are all required to pick out an individual object.

This limitations is well known among radar engineers.

Law enforcement agencies include hand held laser in the mix of tools needed for law enforcement to confirm

reliable speed and position of an individual vehicle in traffic after radar detects excessive speed.[6] [7][8]

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Doppler radar

Fm-cw radar

Pulse-Doppler radar

1. ^ "Continuous-wave Radar" (https://web.archive.org/web/20120418124039/http://www.fas.org/man/dod-101/navy

/docs/es310/cwradar/cwradar.htm) . Federation of American Scientists. http://www.fas.org/man/dod-101/navy

/docs/es310/cwradar/cwradar.htm.

2. ^ "Continuous-wave Radar" (https://web.archive.org/web/20120418124039/http://www.radartutorial.eu/02.basics

/rp06.en.html) . Radartutorial.eu. http://www.radartutorial.eu/02.basics/rp06.en.html.

3. ^ "Trackman" (https://web.archive.org/web/20120418124039/http://trackman.dk/) . trackman. http://trackman.dk/.

4. ^ "Personal Pitchter" (https://web.archive.org/web/20120418124039/http://www.personalpitcher.com/) . Personal

Pitcher. http://www.personalpitcher.com/.

5. ^ "Ranger EZ" (https://web.archive.org/web/20120418124039/http://www.mphindustries.com

/radar_lidar.php?product=ranger) . MPH Industries. http://www.mphindustries.com/radar_lidar.php?product=ranger.

6. ^ "Stalker Hand Held Police Laser" (https://web.archive.org/web/20120418124039/http://www.stalkerradar.com

/lidar_lr.shtml) . Stalker Radar. http://www.stalkerradar.com/lidar_lr.shtml.

7. ^ "Laser Speed Detector" (https://web.archive.org/web/20120418124039/http://www.digitalallyinc.com/speedguns.html) . Digital Ally. http://www.digitalallyinc.com/speed-guns.html.

8. ^ "Speed Laser" (https://web.archive.org/web/20120418124039/http://www.mphindustries.com

/radar_lidar.php?product=speedlasers) . MPH Industries. http://www.mphindustries.com

/radar_lidar.php?product=speedlasers.

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Categories: Radar

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