Introduction
In an attempt to make the work of many pilots and to make aviation safer, various technologies have been introduced in the past 50 years. One of the major advancements in flying aides has been Synthetic Aperture Radar (SAR).
SAR involves the use of more than one radar signal so as to develop images of high resolution. A radar transmitter such as antenna is attached to a moving aircraft or airborne body and the different radar echoes at each positions are assessed so as to come up with a target image. The transmitter is attached to the body of an aircraft and produces a pulse that is broad and has an orientation towards the vertical. The transmitter should have a clear and open illumination of the below terrain and objects; that the aircraft is flying above. The SAR antenna emits intermittent radar signals on the aircraft’s path of flight and the reflected echoes- vary due to distance and the nature of the reflecting surface- are recorded and then stored by the aircraft’s onboard computer. Readings are taken at each point and are later combined to form a ‘synthetic aperture’ that resembles a huge and extended antenna.
Some aircraft store the transmitter readings in an onboard chip while some make real time relays to control stations at the ground. The data collected from the transmitters is used to create aviation maps based on radar reflectivity. In the recent years the accuracy of radar maps has been refined to a range of plus or minus 10 cm. SAR makes use of the collected amplitude data of the waves and makes minimal use of the phase data in coming up with radar reflectivity maps.
The raw SAR data is transformed to processed data by the use of Fourier techniques. This is done using special computers that aid in processing the data. An advantage of SAR has been its ability to transmit signals at very long distances and function effectively at conditions that limit other forms of imaging devices such as clouds and extreme atmospheric conditions. Unlike devices that make use of optical images SAR signals do not grow weak as the transmission range is increased.
Background
The development of SAR has been fueled and driven by the efforts of aeronautical engineers. This is despite the fact that SAR is more closely related to mathematics than it is to engineering (Cheney & Nolan, 2002). This is because SAR involves the use of geometry, seismic inversions and advanced math. SAR has a wide range of uses; it is used in medicine, engineering, military and aviation.
SAR was developed by Wiley Carl who worked for the Goodyear Aircraft Corporation (GAC) in the 1950s. SAR was accidentally discovered as the researcher was working on a ‘correlation guidance system’. GAC later sponsored developments in the 1950 – 1970. SAR has evolved gradually over the years to become what it is today.
In aviation SAR involves the use of an antenna that releases electro-magnetic pulses which land on the terrain, are scattered, reflected and then detected by the antenna. Mathematical calculations based in integral geometry are used to come up with an image of the terrain (Cheney & Nolan, 2002).
In aviation there are two types of antennas. There are synthetic array antennas and real array antennas. In synthetic array antennas; for each transmitted pulse there exists an individual element to receive the pulse. Synthetic arrays have a much narrower width of the beams as compared to real arrays due to a higher phase shift. Real array antennas on the other hand involve the transmission and reception of pulses by all antennas and elements of the transmission system. Real arrays have two common types of radiation patterns; one way and two way radiation patterns (Wirth, 2001). Two way results from the merging of the one way pattern with the same phase shift and has a much narrower shape, while one way results from the addition of a changing phase shift of the antenna elements to the field.
The range of transmission of a SAR should always be more than the length of the transmitting antenna. If this is not the case then the distances to the respective elements is usually not the same, this will result in an increase in the sidelobe levels and a sequential decrease of gain; with an increase in antenna length. Unfocused arrays are a result of such a setting (Kovaly, 2007).
SAR operates based on the Doppler Effect/ principle. The Doppler Effect explains the change of frequency of waves emitted from a moving object relative to a stationary observer or object. Frequency variation is at it’s highest to the observer when the emitted wave travels parallel to the direction of travel of the emitting body. The Doppler Effect is created by coherent pulsed radar, continuous wave radar and frequency modulated radar. Pulse Doppler radar systems embrace the use of the Doppler effects in creating images of specific bodies and objects. Bodies that have little or no motion such as houses, hills and trees will have relatively low Doppler frequencies while bodies that move such as trucks, trains and vehicles will generally have a higher Doppler frequency (Miekle, 2008).
SARs work using the production of two dimensional images; namely range and azimuth dimensions. Range is the computation of the physical distance of an object from the source of a signal. This is measured using a comparison of the relative amount of time taken for the echo to be reflected back to the aircraft. It has been found that signals of short width produce finer resolution of the range. Azimuth is perpendicular in direction to the range and requires a huge antenna to focus the transmitted signals and received signals into a sharp beam. The Azimuth resolution is determined by the degree of sharpness of the beam (Franceschetti & Lanari, 1999)
Design
Analysis of the Problem
‘You need to design a SAR system for an aircraft operating at X band. The plane can fly to a maximum altitude of 10 km. The aircraft should be able to identify the highways. Assume the system can detect signals for 1 – 10 km range.’
SAR type = X band
Altitude of flight = 10 km
Highways should be identified therefore cell size = 30 m
Range of signals along flight path = 10 m
Assume speed of flight is = 500 m / s
Assume speed of light is = = 299 792 458 m / s
Bandwidth
Bandwidth refers to the measurement ‘span’ of frequencies that a SAR signal emits or that are passed by the ‘band limiting stages’ of a SAR system. The resolution abilities of a system are determined by the system’s bandwidth. The resolution of a SAR system can be improved by increasing the bandwidth and vice versa. To achieve a higher bandwidth the wavelength of the signal can be increased; reduced to achieve a shorter bandwidth.
Bandwidth is a function of the pulse width/ length. It is derived from the formula:
B = 1 / Tt
Where;
B = Bandwidth
Tt= Pulse duration
The pulse duration Tt is = 1µs
Therefore the bandwidth =
B = 1 / 0. 000001
B = 1 000 000 Hz
Bandwidth = 1 000 MHz
The pulse physical length can be calculated as =
L = c * Tt
Where:
C = speed of light
Tt = pulse duration
L = 299 792 458 m / s * 0.000001s
L = 299. 792 458 m
Physical length of the pulse = 0. 299 792 5 km
Frequency
In the working of SAR systems there is an alternating switching on and off of the sending and receiving signals of the aircraft antenna. This is done so as to avoid interference of the sent and reflected waves from the transmitter. The frequency at which pulses are emitted is called Pulse Repetition Frequency (PRF).
In the design of a SAR system the PRF is not made very large because it may cause an interference ‘overlap’ of signals from the near and the distant ends of the transmission ranges.
PRF refers to the number of pulses emitted by a transmitter divided by the time taken to emit each pulse. PRF is used in SAR to determine the ‘maximum target range’ and the ‘maximum Doppler velocity’. The reciprocal of PRF is PRT which stands for ‘Pulse Repetition Time’ (Kingsley & Quegan, 1999).
1 km ↔ 10km
Near range is = 1 km
Far range is = 10 km
PRF = 1 / (t2 – t1)
Where =
t2 = 2 * H / ( C * CosØ2)
t1 = 2 * H / ( C * CosØ1)
Where =
H = 10 km
C = 299 792 458 m / s
CosØ1 = 10 / hypotenuse1
Hypotenuse1 = 10. 049 km
CosØ1 = 10 km / 10. 049 km = 0. 9951
CosØ2 = 10 / hypotenuse2
Hypotenuse 2 = 14. 142 km
CosØ2 = 10 / 14.142 = 0. 7071
t2 = 2 * 10 000 / (299 792 458 m / s * 0. 7071)
t2 = 0. 000094
t2 = 94 µs
t1 = 2 * 10 0000 / (299 792 458 m / s * 0. 9951)
t1 = 0. 000067
t1 = 67 µs
PRF = 1 / (t2 – t1)
PRF = 1 / (27 µs)
PRF < 37 037 Hz
The maximum allowable PRF is 37. 037 MHz
PRFmax = 37. 037
The SAR is of X band type and the average frequency of an X band radar is usually 8 GHz to 12 GHz. For basic calculations it is assumed that the frequency is 10 GHz.
Processing Method
There are two types of processing methods namely, parallel and series. A parallel method of processing the data will be used in the design. This is because when the data is processed in parallel it results in a much shorter processing time. For parallel processing to work, Doppler filters must be used to filter feedback recorded from different azimuth angles. Parallel processing conforms to the Doppler Effect and works in accordance to Doppler frequency. Each reflected signal has a distinct frequency that is not similar to the source frequency; this difference between these two frequencies is similar to the azimuth separation. Parallel processing enables the SAR users to achieve a higher precision and ‘real time rates’ (Raney, 1994)
Number of Elements
For us to be able to determine the number of antenna elements needed we will have to assume the speed of the aircraft to be 500 m / s. An understanding of the number of pulses per second is also needed so as to identify the distance between the pulses. PRF will be used so as to acquire the number of antenna elements needed.
The PRF is 37 037 pulses per second. This translates to:
Distance between the pulses = 500 m/ 37 037 Hz
Distance between the antenna elements = 0. 0135 m
Number of elements = 10 m/ 0. 0135 m
Number of elements = 740 antenna elements
Type of Antenna
There are two types of antennas, ‘real array’ and ‘synthetic array’ antennas. Real array antenna signals are sent and received by all the constituent elements of the system while in synthetic arrays signals are sent and received by each respective element only.
In this design synthetic array antennas will be used as they have a higher resolution and accuracy compared to real array antennas. SAR also has the advantage of having a smaller beamwidth as compared to real array radars.
SAR produces finer resolutions as compared to real array radars due to its characteristic of having narrower beamwidths. The antenna should be large as larger antennas have a higher resolution as compared to smaller ones (Balanis, 2005). An aperture that is bigger also has a smaller beamwidth and a higher gain compared to smaller apertures. In the design we will use an antenna of 3.5 m.
Cell Resolution
Cell Size
A cell is rectangular in shape and has two dimensions namely Da and Dr. Da represents the resolution along the path of flight of the aircraft; azimuth and Dr represents the resolution across the path of flight; range resolution.
Since in our case the aircraft should be able to detect highways the cell size will be 30 m.
To find Dr we will use =
Dr = L / 2
Dr = 299. 792 458 m / 2
Dr = 149. 896 m
Da = λ * R / 2 * La
Da = 0. 03 * 1 000 / 2 * 3. 5
Da = 4. 2857 m
Da = λ * R / La
Da = 0. 03 * 10 000 /2 * 3. 5
Da = 4. 2857 m
Minimum azimuth resolution = 0. 4 * Leff
Leff = 1. 2 * sqrt(λ * R)
Leff = 1.2 * sqrt(0. 03 * 1 000)
Leff = 6.5726 m
Array Type
This design will involve the use of synthetic arrays. Synthetic arrays will be used as the signals are transmitted and received by each individual element. A focused array will be used in the design since the length of the aircraft antenna is smaller compared to the antenna range. Due to this, ‘phase shifters’ will be implemented so as to compensate for the antenna limitation.
In our design we have an array of 740 elements.
This translates to 740 * 740 = 547 600
The number of phase corrections will be 547 600 phase corrections.
To reduce this problem of huge computing times, the Doppler frequency is introduced.
Limitations
This design has a major limitation when it comes to cell size. Once the cell size is minimized the target object can be viewed more clearly and vividly however, this increases the computation time. This is particularly true in high detailed targets and those of large coverage. This limitation can be neutralized by the use of high level computers and those with large capacities so as to compensate for the high levels of processing needed.
This design cannot operate at extremely high frequencies and thus the resolution of a SAR system cannot be increased by adjusting the operating frequency of the system. If the frequency of SAR could be adjusted then the resolution of the system could be adjusted by simply manipulating the frequencies. This is a limitation of SAR as it’s resolution can only be affected by changing the beamwidth and gain.
As the width/ length of an array is increased the gain and the bandwidth drops. This forces the designers of this SAR system to put in place measures to ensure that the array length maintains an optimum value for proper functioning of the system. The beamwidth and gain also change as the range of the SAR system changes. Wavelength also affects the later properties and has to be kept at an optimum value. This relationship does not remain linear and it changes as the source of the signal approaches the target; the range becomes smaller and the beamwidth starts decreasing (Petersen, 2007).
Every SAR system has a limit of the finest possible azimuth resolution that it can attain. The finest attainable azimuth resolution is a function of the effective length. It is expressed as
Dam = 0. 4 * Leff
Where:
Dam = minimum azimuth resolution
Leff = effective length
Array antennas usually have phase errors and to correct this error a phase shifting mechanism is effected onto each element of the system. A mathematical formula is derived for the phase error and is applied onto each antenna element. Phase shifters allow for the use of any array length.
This system will also have a problem of computing overloads. This is due to the high amount of data that is computed and the large number of corrections to be processed. Computing problems are minimized by the manipulation of the data in parallel as it saves on time compared to series computation. Doppler filters are used in this kind of processing (Petersen, 2007).
A huge limitation of high performance SAR systems is the presence of phase errors; both high and low frequency. Phase errors limit the quality of resolution that can be achieved. This is a major setback for all aircraft using SAR especially satellite
Summary
SAR is very useful in today’s world. It has gained reputation and uses in various applications. It is used in the military for spying using unmanned aircraft, targeting in weapons and warheads for military aircraft, and for surveillance. SAR is now widely used in politics than ever before; where nations set treaties such as nuclear treaties and use SAR technology to spy and ensure these treaties are adhered to. Another advantage of SAR is its ability to penetrate opaque bodies that were initially impenetrable and offer guidance to pilots and aviation crew. SAR can be able to penetrate foliage materials and thus provide proper information to the pilot on the suitability of a landing ground.
Latest developments in SAR have unveiled improvements such as change detection characteristics that enable an aircraft’s onboard system to store data at one point and compare the data to that collected at a different point in time and inform the pilot of any changes. This is important as the plane’s onboard computer can store data that pertains to the landing grounds and alert the pilot of any changes. This will allow the pilot to detect features in the landing ground that he / she may not recognize visually. Another development is the use of 3- D SAR. ‘3- D SAR involves the use of more than one SAR antenna on a single aircraft, this results in an interferometric SAR that is much more accurate in generating surface profile maps’ (Miekle, 2008).
SAR has numerous advantages such as its ability to function in all weather patterns. SAR systems store the navigation data in the onboard computers and this data is then used to fly unmanned aircraft and manned aircraft on autopilot. These systems also have an advantage of high accuracy and detail compared to other imaging systems.
The benefits of SAR cannot be underscored and every pilot or potential pilot understands the importance of having a functioning SAR system. If properly maintained and fitted SAR aviation equipment are fairly cheap to install and maintain, furthermore they have a long service life. The future is sure to unveil more advanced and useful forms of SAR.
Below are summarized specifications for the design
- Bandwidth = 1 000 MHz
- Physical length of the pulse = 0. 299 792 5 km
- PRFmax = 37. 037
- Number of elements = 740 antenna elements
- Da min = 4. 2857 m
- Da max= 4. 2857 m
- Leff = 6.5726 m
- The number of phase corrections will be 547 600 phase corrections.
References
Balanis, A. (2005). Antenna theory: analysis and design. San Francisco, CA: John Wiley.
Cheney, M., & Nolan, J. (2002). Synthetic Aperture Inversion. New York, NY: SIAM press.
Franceshetti, G., & Lanari, R. (1999). Synthetic aperture radar processing. Florida: CRC Press.
Kingsley, S., & Quegan, S. (1999). Understanding radar systems. London: SciTech Publishing.
Kovaly, J. (2007). Synthetic aperture radar. Michigan: Artech House publishers.
Miekle, H. (2008). Modern radar systems. Texas: Artech House publishers.
Petersen, J. (2007). Understanding Surveillance Technologies Spy Devices, Privacy, History & Applications. New York: CRC Press.
Raney, K. (1994). Precision SAR processing using Chirp scaling. Wales: IEEE.
Wirth, W. (2001). Radar techniques using array antennas. Wales: IET publications.