# Design of Tracking, Telemetry, Command (TT&C) and Data Transmission Integrated Signal in TDD Mode
## 3 The Receiving Method of the Integrated Signal in the TDD Mode
### Motion Compensation Method in TDD Mode  
For multi-node spacecraft/aircraft networks, it is necessary to synchronize the time and eliminate the clock difference between different nodes. After that, the unified time standard can be adopted in the whole network [35]. In addition, the network does not need all nodes to use the global navigation satellite system (GNSS) or a ground station for timing and positioning, which greatly saves resources. In the ground system, clock synchronization technology mainly includes average time and double-difference or triple difference observation [36; 37; 38]. For intersatellite/aircraft links, the time synchronization and true distance can be measured via dual one-way ranging (DOWR) [36; 39; 40]. However, the DOWR method needs to measure the pseudo-range and velocity at the same time. In the TDD mode, the pseudo-range and velocity results obtained by the local measurements between different nodes are not obtained simultaneously. Here, we take nodes A and B as an example. The pseudo-ranging and velocity results of node A can be expressed as \(\rho_{A}(t_{1})\) and \(v_{A}(t_{1})\), and the results of node B can be expressed as \(\rho_{B}(t_{2})\) and \(v_{B}(t_{2})\). \(t_{1}\) and \(t_{2}\) are the times when the results are obtained by local satellites or aircraft, respectively. Because the TDD mode cannot receive and transmit signals at the same time, the relation between \(t_{1}\) and \(t_{2}\) can be expressed as (7):  
\[t_{1}=t_{2}+T_{sp}+\Delta t \tag{7}\]  
where \(T_{sp}\) is the switching period between the receiving and transmitting processes. \(\Delta t\) denotes the error in the measurement process. Via the following steps, the time of A and B measuring the pseudo-range and velocity can be corrected to the same time. Step 1. Calculate the radial acceleration value \(a_{A}(t)\) between the spacecraft using the spacecraft orbit elements or the inertial navigation system (INS). Step 2. According to (15), we can calculate the correct velocity \(v\prime_{B}(t_{2})\) using the radial acceleration value \(a(t)\):  
\[v\prime_{B}(t_{2})=v_{A}(t_{1})+\int_{t_{1}}^{t_{2}}a_{A}(t)dt \tag{8}\]  
Figure 3: Design of TT&C signal processing. (**a**) Signal acquisition (**b**) Normalized power spectrum of the IF signal (**c**) Normalized power spectrum of the signal after the desubcarrier (**d**) Normalized power spectrum of the signal after the low-pass filter. Step 3. The Doppler frequency \(f_{d}\) can be calculated by (9). \[f_{d}(t_{2})=\
u_{B}(t_{2}).\frac{f_{RF}}{c} \tag{9}\]  
Here, \(c\) is the speed of light. \(f_{RF}\) is the radio frequency. Step 4. \(\
u_{B}(t_{2})\) is used to modify the pseudo-range value \(\rho\prime_{B}(t_{2})\) of the spacecraft via (10):  
\[\rho\prime_{B}(t_{2})=\rho_{A}(t_{1})+\int_{t_{1}}^{t_{2}}\biggl{[}\
u_{A}(t_{ 1})+\int_{t_{1}}^{t_{2}}a_{A}(t)dt\biggr{]}dt \tag{10}\]  
The second term on the right side of (11) is the pseudo-distance modifier. Step 5. \(\
u_{B}(t_{2})\) and \(\rho\prime_{B}(t_{2})\) are used to conduct DOWR. \(f_{d}\) and \(\rho\prime_{B}(t_{2})\) are sent to the carrier tracking loop and code tracking loop to guarantee the stable tracking of the loop without receiving a signal. The acceleration value \(a(t)\) of spacecraft can be obtained by spacecraft orbit elements or the INS. The former should consider oblate earth model, atmospheric resistance, lunar gravitation and sun gravitation perturbations, etc. And it uses J4 orbit propagator or high precision orbit perturbations (HPOP) to calculate the acceleration value. In [41], the error of orbit propagator is less than \(10^{-3}\) m/s\({}^{2}\). These elements can be uploaded in each satellite through the ground station at regular intervals. The latter method uses INS to obtain the acceleration value of the spacecraft. The messages are obtained autonomously by INS. The [42] shows the measurement value of INS is less than \(10^{4}\) m/s\({}^{2}\).