## 4 Near-Space High-Resolution and Wide-Swath Imaging  
### System Configuration  
Future SAR will be required to produce high resolution imagery over a wide surveillance area. However, it is a contradiction to obtain both unambiguous high azimuth and wide swath. The actual achievable resolution and swath width is subject to a number of restrictions imposed by various operating factors. The details can be found in [70]. A basic limitation is the minimum antenna area constraint, which can be represented by [71]  
\[A_{r}=W_{a}L_{a}\geq\frac{4v_{a}\lambda R_{c}\tan(\theta)}{c_{o}} \tag{9}\]  
where \(W_{a}\) and \(L_{a}\) are the antenna width and length respectively, \(v_{a}\) is velocity of the SAR platform, \(R_{c}\) is the slant range from radar to the midswath, \(\theta\) is the incidence angle, and \(c_{o}\) is the speed of light. This requirement arises because the illuminated ground area must be restricted, so that the radar does not receive ambiguous echoes in range or/and azimuth (Doppler). In this respect, a high operating operational PRF is desirable to suppress azimuth ambiguity. But the magnitude of the operating PRF is limited by range ambiguity. By rearranging the terms in Equation (9) with the expression of SAR azimuth resolution, the ratio of swath width (\(W_{s}\)) to azimuth resolution (\(\rho_{a}\)) is found to be  
\[\frac{W_{s}}{\rho_{a}}<\frac{c_{o}}{2v_{a}\sin(\theta)} \tag{10}\]  
Figure 8: The azimuth-variable characteristics of Doppler chirp rate for near-space passive bistatic SAR. From Equation (10) we see that the ratio between azimuth resolution and swath width depends on platform velocity and incidence angle. Generally, \(c_{o}/v_{a}\) is nearly constant at 20,000 for LEO satellites and typically in the range of 300,000-750,000 for airborne systems. As near-space SAR can fly at a velocity from 0 m/s to 1,500 m/s, the \(c_{o}/v_{a}\) will be greater than 100,000. Therefore, compared to spaceborne SAR and airborne SAR, near-space provides an optimal solution to simultaneous high-resolution and wide-swath SAR imaging. Nevertheless, to further alleviate the requirements on the minimum antenna area, applying some additional techniques is necessary. Several techniques have been suggested [72, 73], but the use of a quad-element array will become difficult for high-resolution applications because synthesizing a number of apertures is required. If multiple sub-apertures (e.g., \(N\)) in azimuth (see Figure 9) is employed, the area of each sub-aperture antenna is then restricted by  
\[A_{rs}\geq\frac{4v_{s}\lambda R_{c}\tan\left(\theta\right)}{c_{0}}\cdot\frac{1} {N}. \tag{11}\]  
Clearly the minimum area for each sub-aperture antenna can be \(N\)-times smaller than that of a monostatic SAR. In this case, the displaced phase centre technique [73] can then be used to gain additional samples, which enables an efficient suppression of azimuth ambiguities, _i.e._, the multiple sub-apertures in azimuth allows for the division of a broad Doppler spectrum into multiple narrow-band subspectra with different Doppler centroids. A coherent combination of the subspectra will then yield a broad Doppler spectrum for high azimuth resolution. A distinct channel is associated with each sub-aperture signal which is separately amplified, down-converted and digitized. In this way, the acquired data are split according to the azimuth angular position, _i.e._, the instantaneous Doppler centre frequency. As a result, while given knowledge of the relative squint angles of each sub-aperture (and hence the Doppler centre frequency for each sub-aperture) and assuming suitable isolation between the beams, each channel can be sampled at the Nyquist rate appropriate to the bandwidth covered by each narrow sub-aperture, instead of that covered by the full aperture. The conclusion is unambiguous range and swath width can be further increased by using a near-space SAR with multiple antennas in azimuth.