A set of five articles published by Michael Parker, Altera Corporation
(only the first part shown on these pages) 

Original Links  

Part 2

Part 3

Part 4

Part 5

This Part 1 reproduced from : http://www.eetimes.com/document.asp?doc_id=1278779 

First, some wavelengths collected from another source : http://www.alternatewars.com/BBOW/Radar/Radar_Bands_Wavelengths.htm

World War II Bands





214 – 236 MHz

1.4 - 1.27 m


300 MHz

1 m


425-610 MhZ

70.6 - 49.18 cm


1250-1380 MhZ

24 - 21.74 cm


2700-3900 MHz

11.11 - 7.69 cm


5300-5520 MHZ

5.66 - 5.43 cm


9230 – 9404 MHz

3.25 - 3.19 cm


16000 MHz

1.88 cm


>20000 MHz

1.5 cm


40000 MHz

7.5 mm






0 - 200 MHz

Up - 1.5 meters


200 - 250 MHz

1.5 - 1.2 meters


250 - 500 MHz

1.2 m - 0.60 m


500 - 1500 MHz

60 - 20 cm


2000 - 4000 MHz

15 - 7.5 cm


4000 - 8000 MHz

7.5 - 3.75 cm


8000 - 12000 MHz

3.75 - 2.5 cm


12000 - 18000 MHz

2.5 - 1.67 cm


18000 - 26000 MHz

1.67 - 1.15 cm


26000 - 40000 MHz

11.54 - 7.5 mm


40000 - 75000 MHz

7.5mm - 4 mm


75000 - 111000 MHz

4mm - 2.7 mm

NATO (modern)





0 - 250 MHz

Up - 1.2 m


250 - 500 MHz

1.2 - 0.6 m


500 - 1000 MHz

60 - 30 cm


1000 - 2000 MHz

30 - 15 cm


2000 - 3000 MHz

15 - 10 cm


3000 - 4000 MHz

10 - 7.5 cm


4000 - 6000 MHz

7.5 - 5 cm


6000 - 8000 MHz

5 - 3.75 cm


8000 - 10000 MHz

3.75 - 3 cm


10000 - 20000 MH

3 - 1.5 cm


20000 - 40000 MHz

15 - 7.5 mm


40000 - 60000 MHz

7.5 - 5 mm


60000 - 100000 MHz

5 - 3 mm



Radar (RAdio Detection And Ranging) is widely used in both commercial and military applications. Air traffic control, mapping of ground contours and automotive traffic enforcement are just a couple civilian applications. Radar is ubiquitous in military applications being used in aircraft, missiles, ships, tanks, helicopters, ground stations, and more.
Radar frequency bands
Radar systems transmit electromagnetic, or radio waves. The reflected radio waves can be detected by the radar system receiver. The frequency of the radio waves used depends upon the radar application and are commonly classified according to Table 1.


Radar Band Frequency (GHz) Wavelength (cm)
Millimeter (EHF) 40.0 to 100  0.75 to 0.30
Ka 26.5 to 40.0 1.10 to 0.75
K 18.0 to 26.5 1.70 to 1.10
Ku 12.5 to 18.0 2.40 to 1.70
X 8.00 to 12.5 3.75 to 2.40
C 4.00 to 8.00 7.50 to 3.75
S 2.00 to 4.00 15.0 to 7.50
L 1.00 to 2.00 30.0 to 15.0
UHF 0.30 to 1.00 100  to 30.0


The required antenna size is proportional to wavelength and therefore inversely proportional to frequency. The ability of the radar to focus the radiated and received energy in a narrow region is also dependent upon both antenna size and frequency choice.
A larger antenna allows the beam to be more tightly focused at a given frequency. The "focusing" ability of the antenna is often described using an antenna lobe diagram (see Figure 1), which plots the directional gain of an antenna over the azimuth (side to side) and elevation (up and down). 
Most airborne radars operate between the L and Ka bands, also known as the microware region. Many short range targeting radars, such as on a tank or helicopter, operate in the millimeter band. Many long range ground based operate at UHF or lower frequencies, due to the ability to use large antennas and minimal atmospheric attenuation and ambient noise.

Radar Range Equation


Detection of objects using radar involves sophisticated signal processing.
For a single pulse the following signal to noise ratio is :



Figure 1. Antenna gain plot.

Observe that the received power drops with the fourth power of the range, so radar systems must cope with very large dynamic ranges in the receive signal processing. The radar energy seen by the target drops proportional to the range squared. The reflected energy seen by the radar receiver further drops by a factor of the range squared. The ability to detect very small signals in the presence of large interfering signals is crucial to operate at longer ranges.

Pulsed Radar Operation


Most radar systems are pulsed, meaning that the radar will transmit a pulse and then listen for receive signals, or echoes. This avoids the problem of a sensitive receiver trying to operate simultaneously with a high power transmitter.
The pulse width or duration is an important factor. The radars operate by "binning" the receive signals. The receive signal returns are sorted into a set of bins by time of arrival relative to the transmit pulse. The time interval is in proportion to the round-trip distance to the object(s) reflecting the radar waves. By checking the receive signal strength in the bins, the radar can sort the returns across the different bins, which correspond to different ranges. This can be performed while scanning across desired azimuths and elevations.



Figure 2.  A representation of basic radar operation

Having many range bins allows more precise range determinations. A short duration pulse is likely to be detected and mapped into only one or two range bins, rather than being spread over many bins. However, a longer pulse duration or width allows for a greater amount of signal energy to be transmitted and a longer time for the receiver to integrate the energy. This means longer detection range. In order to optimize for both fine range resolution and long range detection, radars use a technique called pulse compression.
Pulse compression
The goal of pulse compression is to transmit a long duration pulse of high energy, but to detect a short duration pulse in order to localize the receive filter output response to one or at most two radar range bins. Early radars accomplished this by transmitting a signal with linear frequency modulation. The pulse would start at a low frequency sinusoid and increase the frequency over the duration of the radar pulse. This is referred to a "chirp". A special analog filter is used at the receive end, with non-linear phase response. This filter has a time lag that decreases with frequency. When this rate of time lag decrease is matched to the rate of increase in the chirp, the result is a very short, high amplitude output from the filter. The response of the pulse detection has been "compressed".
Digital radars also perform pulse compression, but using matched filter. The transmitted radar pulse uses a pseudo random sequence of phase modulations and is detected using a filter matched to that same sequence, then the resulting output will match only when the stored sequence matches the received sequence. The timing resolution of the receive signal is equal to the transition time of the phase changes, which can be very rapid. This detection method can also filter out undesired signals that do not match the stored sequence. 

Pulse repetition frequency
The pulse repetition frequency (PRF) is the rate of transmitting pulses, on which receive processing is then performaed. The higher the PRF, the greater the average power the radar is transmitting (assuming the peak power of each pulse is limited by the transmit circuitry) and the greater the detection range. A high or fast PRF also allows for more rapid detection and tracking of objects, as range measurements at a given azimuth and elevation can be performed during each PRF interval. A high PRF is also a disadvantage, which means it has a limited distance to perform unambiguous determination of range.
Range to target is measured by round trip delay in the received echo. It is the speed of light multiplied by the time delay and divided by two to account for the round trip.

Rmeasured = vlight tdelay / 2

The maximum range that can be unambiguously detected is limited by the PRF. This is more easily seen by example. If the PRF is 10 kHz, then there is 100 µ seconds between pulses. Therefore, all return echoes should ideally be received before the next transmit pulse. This range is simply found by multiplying the echo delay time by the speed of light and dividing by two to account for the roundtrip. 

Rmaximum = (3x108 m/s) (100x10-6 sec) / 2 = 15 km

Suppose the radar system sorts the returns into 100 range bins, based upon the time delay of reception. The range resolution of this radar system is then 0.15 km, or 150 meters. However, there may be returns from distances beyond 15 km. Suppose that a target aircraft #1 is five km in the distance and target aircraft #2 is twenty-one km in the distance. Target aircraft #1 will have a delay of:

tdelay = 2 Rmeasured / vlight = 2 (5x103 ) / 3x108 = 33 us

Target aircraft #2 will have a delay of: 


tdelay = 2 Rmeasured / vlight = 2 (21x103 ) / 3x108 = 140 us
The first target return will be mapped into the 33rd out of 100 range bin and the second target to 40th range bin. This is called a range ambiguity.
The target(s) which are within the 15 km range are said to be in the unambiguous range. This is analogous to the sampling rate. The range ambiguity is analogous to aliasing during the sampling process (see Figure 3).



The obvious solution is to use a lower PRF. This approach works, but the benefits of the high PRF are lost. Another solution to this problem is to transmit different pulses at each PRF interval. However, this has the downside of complicating the receiver, as it must now use multiple matched filters at each range bin and at each azimuth and elevation. This will effectively double the rate of digital signal processing required for each separate transmit pulse and matched filter pair used.

Typically, most radar systems will vary the PRF, depending on the operational mode of the radar. This will be discussed further when Doppler radar processing is covered in a future installment in this series.


About the author



As senior DSP technical marketing manager, Michael Parker is responsible for Altera’s DSP-related IP, and is also involved in optimizing FPGA architecture planning for DSP applications.

Mr. Parker joined Altera in January 2007, and has over 20 years of DSP wireless engineering design experience with Alvarion, Soma Networks, TCSI, Stanford Telecom and several startup companies. 


Original links  

Part 2

Part 3

Part 4

Part 5