# Ocean Surface Topography Altimetry by Large Baseline Cross-Interferometry from Satellite Formation
## 4 CFS for Baseline Decorrelation Compensation
### Principle of Baseline Decorrelation  
The interferometry of microwave also follows the optical diffraction grating principle from physical optics, therefore, the essential reason for baseline decorrelation is the radar look angle difference, which introduces a relative shift between the target spectrum received by two antennas [18; 29]. The dual antennas in normal interferometry mode transmit pulses of the same carrier frequency and bandwidth, or, in other words, the transmitted spectrum window for target observing is identical, as shown in the upper left corner of Figure 7. The transmitted pulse eventually measures the target in space domain, and the spatial frequency of the target is usually defined as wavenumber, i.e., the reciprocal of the wavelength. Due to the tiny difference of look angle, the transmitted spectrum window will be shifted and stretched after being projected to the wavenumber domain (the stretching effect can be omitted since radar carrier frequency is much higher than signal bandwidth), as shown in the bottom of Figure 7. Only the overlapped region of wavenumber can be used for interferometry, leaving the non-overlapped part to decay to phase noise.  
Figure 6: Real-time distance and baseline variation versus latitude during half an orbit cycle. (**a**) Real-time distance, (**b**) cross-track baseline length, (**c**) along-track baseline length, and (**d**) baseline inclination angle.  
Since wavenumber and frequency are basically the same physical quantity in space and time domain, therefore, the wavenumber shift can be equally expressed by frequency shift [18]:  
\[\Delta f\approx f_{0}\frac{B_{\perp}\cos\theta}{H\tan(\theta-\beta)} \tag{12}\]  
where \(f_{0}\) is the radar carrier frequency, \(B_{\perp}=B\cos(\theta-\alpha)\) is the vertical component of cross-track baseline, and \(\beta\) is the average slope of ocean surface which changes the local incidence angle of microwave. According to Equation (12), longer vertical baseline and smaller look angle result in a bigger non-overlapped part of the received target spectrum, and since the envelope of the target spectrum is relatively flat, the baseline decorrelation can be expressed as [18]:  
\[\gamma_{B}=1-\frac{\Delta f}{W_{b}}=1-\frac{f_{0}B_{\perp}\cos\theta}{W_{b}\tan (\theta-\beta)H} \tag{13}\]  
From Equation (13), we learn that enlarging the bandwidth can relatively restrain baseline decorrelation. However, a larger bandwidth leads to lower signal-to-noise ratio (SNR), as well as heavier data transmitting volume, which should be avoided to facilitate extensive OST altimetry. Besides, the cross-track baseline of LB-IRA can extend to 1000 m or even longer and enlarging the signal bandwidth cannot be of much help since the frequency shift is far larger than the signal bandwidth. Figure 8 shows the frequency shift versus radar look angle: the cross-track baseline length is 1000 m in this case. The frequency shift can reach to 180-760 MHz among the angle range of 0.7-4\({}^{\circ}\), which is far bigger than the bandwidth of most of the spaceborne SAR/InSAR. It appears that larger look angle can alleviate the demand for wider bandwidth, however, even if the look angle increases to 20\({}^{\circ}\), the maximum coherence is only 0.69, affected by baseline decorrelation alone, under the 100 MHz of bandwidth setting.