## 5 Motion Compensation  
Strict relative position or altitude is essential for the near-space radars described above. As a matter of fact, problems arise due to the presence of atmospheric turbulence, which introduce platform trajectory deviations from normal position or altitude (roll, pitch, and yaw angles) [82, 83]. Hence, motion compensation is required. In current radar systems, GPS and inertial navigation system (INS) are usually deployed for this task. However, for near-space radars, motion measurement facilities may not be reachable because of their limited load capabilities, so some new efficient motion compensation techniques should be developed.  
Active transponder, which was used for calibrating high-resolution imaging radars [84, 85], can be used for motion compensation. This transponder retransmits the received signal with artificial Doppler frequencies to the receiver. If the artificial Doppler drift is chosen to be larger than the Doppler bandwidth of the raw data, the transponder signals can be separated during subsequent signal processing, allowing to extract the platform's motion information without clutter interference. In this way, successful motion compensation may be achieved.  
As shown in Figure 11, the active transponder consists of a low-noise amplifier followed by a bandpass filter. A voltage controlled attenuator (VCA) is used to modulate the received signal in a manner that the retransmitted signal will show two additional Doppler frequencies. Afterwards the signal will be amplified to an appropriate level and retransmitted towards the receiver. Hence this transponder can be seen as an amplitude modulator  
\[S_{c}(t)=[\gamma+\beta\cos(2\pi f_{m}t+\varphi_{m})]\cdot s_{0}(t)=\frac{\beta }{2}e^{j(-2\pi f_{m})t-j\varphi_{m}}\cdot s_{0}(t)+\gamma\cdot s_{0}(t)+\frac{ \beta}{2}e^{j(2\pi f_{m})t+j\varphi_{m}}\cdot s_{0}(t) \tag{17}\]  
where \(f_{m}\) is the transponder modulation frequency, \(\varphi_{m}\) is the starting phase and \(s_{0}(t)\) is the transmitted  
Figure 10: Azimuthal spectra synthesis for multichannel subsampling in case of three channels.  
signal. We can notice that, the retransmitted signal will show the original signal and two additional Doppler frequencies, one positively and one negatively shifted. Assuming the transmitted signal is one chirp signal, the spectrum of retransmitted radar signal modulated by the transponder is shown in Figure 12. This allows to extract the motion compensation information without clutter interferences.  
The corresponding near-space sensor received signal can be represented by  
\[S_{R}(t)=S_{s}(t)+[\gamma+\beta\cos(2\pi f_{m}t+\varphi_{m})]\cdot S_{m}(t) \tag{18}\]  
where \(S_{s}(t)\) and \(S_{m}(t)\) denote the unmodulated part and the echo of the transponder without the amplitude modulation, respectively. Afterwards, \(S_{m}(f)\) can be transformed back into its time-domain representation \(s_{m}(t)\) using an inverse Fourier transform. Evaluating the phase of \(s_{m}(t)\) leads to a motion compensation solution [86]. In this way, placement of several transponders in a planned imaging region can help to get motion information about the near-space platform and enable subsequent motion compensation. Note that the range histories to the visible transponders can be determined very accurately, particularly because of the high SNR performance. Additionally, we think raw data-based autofocus algorithm may be a good a choice for near-space radar motion compensation [83, 87], but further investigations are required.  
Figure 11: Transponder based motion compensation.  
Figure 12: Spectrum of retransmitted signal modulated by the transponder.