Synthetic Aperture Radar

One of the important requirements of a modern airborne radar is that of providing high-quality radar mapping such that topographical features and potential targets may be identified and classified. The quality of the radar map depends upon its ability to resolve very closely spaced objects on the ground – in the most demanding case down to within a few feet.

The problem surrounding the need to resolve to such high resolution may be understood by reviewing the ground footprint of a radar beam radiated directly abeam the aircraft as shown in Figure 4.30. The oval footprint may be resolved into smaller cells or pixels. Along the radar boresight (perpendicular to the aircraft track) the range swath may be resolved into finer range resolution cells. Across the radar beam (along the aircraft track) the increments are azimuth increments as far as the radar is concerned.

The range resolution of a pulsed radar was described in Chapter 3. It will be recalled that, for a pulse of width
, the range resolution increases as the pulse width becomes smaller. For a 1 ms pulse, the range may be resolved to 500 ft ( 150 m); for a 0.1 ms pulse this would be reduced to 50 ft ( 15 m); for a 0.01 ms pulse the resolution would reduce to 5 ft ( 1.5 m) and so on. The major limitation to this approach to increasing range resolution relates to the frequency spectrum associated with a very short pulse. In Chapter 3 the receiver bandwidth required to pass all the frequency components is determined by the 3 dB bandwidth which in

aircraft-rear.vsd 270604

Range Swath

Resolution Cell Along Track

Increments

Pulse 1 Pulse 2 Pulse 3 Pulse 4 Pulse n

Along Track Increments

Figure 4.30 Principle of synthetic aperture radar.

164 ADVANCED RADAR SYSTEMS

turn is related to the pulse width, where B¼ 1=
. For the 0.01 ms pulse the bandwidth is 100 MHz. The impact of bandwidth depends upon the value of the carrier frequency; for an AI radar operating at 10 GHz, a 100 MHz bandwidth is not excessive, but, as frequency decreases, it may become more of a problem. Pulse compression techniques as described earlier in the chapter can achieve significant improvements in range resolution by a factor in the hundreds. This does not improve the bandwidth, however, as the bandwidth must still be sufficient to accommodate the compressed pulse.

Azimuth resolution is more problematical. The along-track resolution is determined by the azimuth bandwidth using the following formula:

3 dB¼ =L ðradÞ

wherev  is the wavelength and L is the antenna length. The range resolution cell is R 3 dB, where R is the range at which the resolution cell is being considered.

For a for sideways looking airborne radar (SLAR) with a 5 m (16.5 ft) long antenna operating at 3 GHzð ¼ 10 cmÞ and at a range of 50 nautical miles (90.9 km) the azimuth range resolution cell is 60 ft (18.2 m), still at least an order of magnitude away from the desired performance.

The answer to this problem is to use a technique called synthetic aperture radar (SAR). In this solution the aircraft forward movement is used to create a large synthetic or artificial aperture, as can be seen in Figure 4.30. The aircraft shown on the left of the diagram is transmitting a series of pulses at constant intervals, which equates in turn to constant along-track increments. A series of patches of ground will be illuminated abeam the aircraft and the return from pulses 1; 2; 3; 4; . . . ; n may each be detected and collected in a series of range bins. The principle of this technique, easily implemented in a digital computer, is shown in Figure 4.31.

Pulse 1 Pulse 2 Pulse 3 Pulse 4 Pulse n Range Bins

Memory

Unfocused Array

Memory scanned rapidly to refresh

display

Discard

Figure 4.31 Collection and storage of successive pulse returns.

After a series of pulse returns has been stored, the oldest are eventually discarded; the number of pulse returns retained before discarding is a function of the algorithm being used. This memory bank of the returns of the previous n pulses may be rapidly scanned to present a strip-line picture of the area of the terrain being mapped. For reasons that will be described shortly, this fairly crude SAR processing technique is referred to as an unfocused array.

The key point about the forward movement of the aircraft is that it allows the signal processing to synthesise an aperture much larger than the real aperture (5 m or 16.5 ft) in the previous example. In a typical SAR application, an array length equivalent to 50 m or more may be synthesised, and in this case the azimuth resolution may be determined by the following approximate formula:

SAR azimuth resolution R 2 L

where  is the wavelength (m), R is the range (m) and L is the synthetic array aperture (m).

Using the figures in the former illustration, and using the synthetic array aperture figure, a SAR azimuth resolution of 3 ft or about 0.9 m may be achieved at 50 nm (90.9 km). This is an order of resolution that allows roads and, in some cases, road vehicles to be discriminated.

Also, for range resolution – receiver bandwidth considerations apart – it was shown earlier that similar resolutions may be achieved by using pulse compression techniques. In this case, using a pulse width of 1 ms and pulse compression ratios of 100 or more, 3 ft range resolution may also be achieved. A combination of pulse compression to improve range resolution (across track) and synthetic aperture techniques to improve azimuth resolution (along track) means that very high resolutions in both directions may be achieved at long range.

As an aside, working numbers to determine the minimum resolution requirements for ground features are:

Roads and map details : 30--50 ftð10--15 mÞ

Shapes=objects : 1

5-- 1

20of the major dimension

Therefore, an SAR radar providing 3 ft resolution at 50 nm would be able to distinguish freeways and trucks with ease, although compact cars may escape resolution.

The point was made earlier that the array configuration described in Figures 4.30 and 4.28 represented an unfocused array; the term ‘unfocused array’ will now be explained, with reference to Figure 4.32. The figure shows an unfocused array at the top of the diagram. If a linear array of length L is radiating abeam the aircraft, all the successive pulses will be radiated at right angles to the array and the pulse paths will effectively be in parallel. Another way of viewing this, considering an optical simile, is that the array will be focused at infinity.

Therefore, point P will not be at the focus of the array; this effect is accentuated the closer P is to the array, or the shorter the range. These effects become more pronounced the larger the array and limit the effectiveness of an unfocused array. As a rule of thumb, the most effective azimuth resolution yielded is approximately equal to 0.4 times the array length.

The focused array is depicted in the lower part of the diagram – this has a slightly curved configuration to emulate a parabolic reflector. In this situation all the successive pulses are effectively focused at point P and the unfocusing errors will be negated. To achieve this effect, two adjustments need to be made. Allowance has to be made for the fact that pulses at

166 ADVANCED RADAR SYSTEMS

the extremity of the array have to travel a small but finite distance,
R, further to reach point P than pulses originating from the centre of the array. Also, pulses originating from the leading edge of the array have to be biased by a minute angular increment to the rear (clockwise), while those from the trailing edge have to be biased by a similar angular increment forwards (counterclockwise). If these adjustments can be made during the digital processing operation by taking account of the motion of the aircraft, the SAR array can be focused at point P.

The computations undertaken to formulate the focused array are outlined in Figure 4.33. The top matrix comprises range bins that are populated during each successive range sweep. The contents are incremented until eventually the oldest return is discarded. The data in each column are read every time the array advances by the minimum azimuth resolution distance. Each array is focused by applying the necessary corrections and summed individually for each bin. The magnitude of each range bin is fed into the display memory. Once the last memory location has been filled, the display memory is decremented and the oldest data discarded. The display memory contents are fed to a display or recording media device.

In effect, this process is similar to the unfocused array data manipulation, except the focused array is continually updated. The process of summing the columns in the range bin array is called azimuth compression and the effect is to synthesise a new array every time the radar advances by the incremental along-track distance.

As for all these transformations, a number of trade-offs need to be made. However, after taking into account a range of factors, the ultimate azimuth resolution achieved by using a focused array is given by the following formula:

Minimum azimuth resolution distance¼length of the real antenna 2

R

P

P

Unfocused Array

Focused Array L

L

R + ∆R R + ∆R

Focused at Infinity

Focused at Point P

Figure 4.32 Unfocused versus Focused SAR Array.

Therefore, in real practical terms, even with a focused array, the minimum azimuth resolution distance is limited; in the example previously quoted with a 5 m (16.5 ft) real array, the azimuth resolution is limited to 2.5 m or 8 ft.

The key to azimuth resolution is the Doppler processing and signal integration process.

Figure 4.34 shows the Doppler shift history as a radar approaches, passes abeam and then recedes from the target.

As the aircraft flies by the target, the Doppler shift starts atþ2  Vr=, reduces through zero as the aircraft passes abeam and then decreases to 2  Vr=. As the target passes abeam, the rate of change in frequency is maximum, and immediately adjacent to zero frequency the lines are virtually straight. Also, for a number of evenly spaced points positioned near to each other the frequency difference between them,
f , will be constant.

Therefore, each of the returns will have a different frequency, determined by its azimuth position, and by using Doppler filtering techniques that azimuth position may be measured.

The way in which this processing is achieved is shown in Figure 4.35.

The incoming video returns are modified by applying the necessary phase corrections as described above to focus the array. Then each point has a constant Doppler frequency which can be discriminated from the others and which relates to its azimuth position. Each time the radar travels a distance equal to the array length to be synthesised, the phase-corrected signals that have been gathered in the range bin row are fed to the array of Doppler filters in the columns. The integration time for the filters is the same time it takes the radar to transit the array length, and the number of Doppler filters in each column thus depends upon the length of the array. The greater the array length, the longer is the integration time and the

Range Bins

Figure 4.33 Computation associated with formulating a focused array.

168 ADVANCED RADAR SYSTEMS

greater the number of Doppler filters formed for a given frequency coverage. Therefore, as the array length increases, the filters become narrower and azimuth resolution becomes finer.

As in this region abeam the target the points on the ground are evenly spaced, and the frequencies are evenly spaced, a fast Fourier transform (FFT) may be used to form the filters which minimises the amount of computing required.

Doppler Filters

Figure 4.34 Doppler history of radar passing a target.

Focussing

Figure 4.35 Example of Doppler processing.

The use of synthetic aperture imaging is an important asset in today’s airborne platforms.

Figure 4.36 is an example of an SAR picture that shows two rows of tanks with a resolution equivalent to 1 ft. The picture shows one of the curious features of SAR images: each tank has a large shadow in the six o’clock area, showing that the targets were illuminated from the twelve o’clock position. Therefore, although sophisticated data processing enables the target to be viewed in high resolution at long range, it cannot negate the fact that the target was illuminated at a low grazing angle.

The SAR principles have been described for a fixed antenna scanning terrain abeam of the aircraft. There are other modes that are commonly used:

1. Spotlight mode. In the spotlight mode the look angle of the real antenna is altered so that it always illuminates the target. This has a number of advantages. Since the real antenna is always trained on the target, the length of the synthetic array is not limited by the beamwidth of the real antenna. Also, the fact that the target is viewed from different aspects helps to reduce the graininess of the response.

2. Doppler beam sharpening. Doppler beam sharpening (DBS) is a subset of SAR operation, lacking several signal processing refinements, and as a result it lacks the performance of the more sophisticated SAR mode. Nevertheless it provides a significant improvement in performance over the real-beam mapping that is the baseline mapping mode in many radars.

3. Inverse SAR. Inverse SAR (ISAR) is a variant of SAR that is used against moving targets that have a rotational component; normally, SAR is used against fixed ground targets.

ISAR effectively uses the minor Doppler shifts caused as a result of target movement.

ISAR may be used against aircraft or moving ground targets such as ships.

The difference between the main modes of ground mapping, including real beam, DBS, SAR and ISAR, are difficult to envisage without a direct comparison. For an air-to-ground radar with the basic parameters listed in Table 4.2, a top-level comparison is given in Table 4.3.