# Design of Tracking, Telemetry, Command (TT&C) and Data Transmission Integrated Signal in TDD Mode
## 2 The Modulation System for the BOCcos and APSK Integrated Signal
### Signal Mode  
Based on the slit-spectrum characteristics, BOC and APSK signals are proposed to be used in the design of the TT&C and data transmission integrated signal. Mathematically, the BOC signal can be expressed as (1):  
\[s_{tt\&c}(t)=d(t)\cdot g(t)\cdot c(t) \tag{1}\]  
where \(d(t)\) is navigation data, \(g(t)\) represents the PN sequence and \(c(t)\) is the subcarrier sequence. For the BOC signal subcarrier, which can be chosen as sine phase, cosine phase, or non-zero dual polarity codes. Different subcarrier will influence the characteristics of the BOC signal. The BOCcos signal has the deepest null-forming in the center frequency than the other BOC signals. This property makes it easier to extract the 16 APSK signal at the receiving end. Thus, we adopt BOCcos signal to transmit TT&C services. In a BOCcos signal, \(g(t)\) and \(c(t)\) can be expressed as (2) and (3):  
\[g(t)=\sum_{k=-\infty}^{\infty}\alpha_{k}p_{T_{c}}(t-kT_{c}) \tag{2}\]  
\[c(t)=sign[\cos(2\pi f_{s}t)]\quad 0\leq t\leq T_{c} \tag{3}\]  
Here, \(\alpha_{k}=\pm 1\). \(T_{c}\) is the width of the PN code. \(p_{T_{c}}\) is the PN sequence.  
To express the split spectrum characteristics of the BOC signal more intuitively [25], the power spectrum of the BOCcos signal is shown in (6):  
\[P_{BOC\cos}(f)=f_{c}\Bigg{[}\frac{\cos(\frac{\pi f}{f_{c}})\sin^{2}\!\left( \frac{\pi f}{4f_{c}}\right)}{\pi f\cos\!\left(\frac{\pi f}{2f_{c}}\right)} \Bigg{]}^{2} \tag{4}\]This paper uses APSK to achieve data transmission services [24]. The baseband signal of APSK is expressed as (4):  
\[s_{dt}(t)=D(t)R(t)\exp\left[j*\left(\frac{2\pi}{n_{d}}i+\theta\right)\right]\ \ \ \ i=0,1, \cdots,n_{d}-1 \tag{5}\]  
where \(D(t)\) is the data and \(R(t)\) is the radius of the constellation diagram. \(n_{d}\) is the signal points of a concentric circle. \(\theta\) represents the initial phase.  
The signal model of the integrated signal at baseband is shown as (5):  
\[s_{t}(t)=s_{tt\&rc}(t)+s_{dt}(t)=d(t)g(t)sign[\cos(2\pi f_{s}t)]+s_{dt}(t) \tag{6}\]  
For a BOCcos signal, the parameters (\(m\),\(n\)) of a BOCcos(\(m\),\(n\)) signal are determined by the spectrum shape, the signal bandwidth and the bandwidth of the APSK signal. \(m\) is the multiple of the subcarrier frequency \(f_{s}\) relative to the reference frequency \(f_{base}\), which means \(f_{s}=m\times f_{base}\). \(n\) is the multiple of the spread spectrum code frequency \(f_{c}\) relative to the reference frequency \(f_{base}\), and thus \(f_{c}=n\times f_{base}\). Here, \(f_{base}=1.023\) MHz [26].  
To transmit voice, image and video, high-speed data transmission service often needs several Mbps or even hundreds of Mbps. Therefore, we set the bandwidth of data transmission as 10 MHz. Using 16 APSK can achieve the transmission rate of hundreds of Mbps.  
The BOCcos(15,2.5) signal is used to modulate the TT&C data in Galileo systems [25]. Besides, the bandwidth of the 16 APSK signal should be less than the bandwidth of BOCcos's null-forming. Thus, we use BOCcos(30,5) signal with the same properties as BOCcos(15,2.5) to transmit TT&C signal. The spread spectrum code frequency \(f_{c}\) is 5.115 MHz, and the subcarrier frequency \(f_{s}\) is 30.69 MHz. The 16 APSK signal is 10 MHz, which is used for data transmission services. The constellation diagram of 16 APSK is shown in Figure 1a. It has two concentric circles. The inner circle has four points, and the outer circle has twelve points [27; 28].  
The spectrum of the integrated signal at the intermediate frequency (IF) end is shown in Figure 1c.  
Figure 1: _Cont._