# Integration of LTE 230 and LTE 1800 in Power Wireless Private Networks
## 4 Integration of the Access Network  
### Synchronization Signal of TD-LTE 1800  
In the LTE 1800 system, \(T_{s}\)\(=1/\left(15000\times 2048\right)\) s is defined as the basic unit of time. One radio frame occupies \(T_{f}=307200\cdot T_{s}=10\) ms in the time domain, which is divided into two half-frames of length 5 ms. One half-frame consists of five subframes. Each subframe is divided into two slots of length 0.5 ms. For normal cyclic prefix (CP), one slot consists of seven OFDM symbols. Figure 5 shows the frame structure of LTE 1800 [18]. Figure 4: Schematic diagram of the core network integration controller. Figure 5: The frame structure of the LTE 1800 system. Since the frequency allocation for the power industry is a nonpairing spectrum in China, the TDD mode is used in PWPNs. The uplink-downlink configuration can be adjusted flexibly according to Table 2, where D and U represent downlink and uplink subframes, respectively. S denotes a special subframe with the three fields DwPTS, GP, and UpPTS, which are used for downlink transmission, protection between D and U, and uplink transmission, respectively. In the frequency domain, 12 subcarriers form a unit resource taking up 180 kHz bandwidth in total. A primary synchronization signal (PSS) is generated by the Zadoff-Chu (ZC) sequence in the frequency domain, which can be written as follows [19]:  
\[v_{u}(n)=\left\{ \begin{array}{ll}e^{-j\frac{\mathrm{max}(n+1)}{63}}&n=0,1, \ldots,30\\ e^{-j\frac{\mathrm{max}(n+2)(n+1)}{63}}&n=31,32,\ldots 61\end{array} \right., \tag{1}\]  
where \(u\) is the root of the ZC sequence corresponding to \(N_{\mathrm{ID}}^{(2)}\). In the frequency domain, the sequence \(v_{u}(n)\) is mapped to the resource elements according to  
\[ \begin{array}{ll}a_{k,l}=v(n),&n=0,\ldots,61,\\ k=n-31+\frac{N_{\mathrm{RB}}^{DL}N_{SC}^{RB}}{2}.\end{array}  \tag{2}\]  
A secondary synchronization signal (SSS) is generated by an interleaved concatenation of two length-31 binary sequences. The two concatenated sequences can be written as  
\[ \begin{array}{ll}d(2n)=\left\{\begin{array}{ll}s_{0}^{(m_{0})}(n)c_{0}(n )&\quad\text{in $subframes$ 0$}\\ s_{1}^{(m_{1})}(n)c_{0}(n)&\quad\text{in $subframes$ 5$}\end{array}\right.\\ d(2n+1)=\left\{\begin{array}{ll}s_{0}^{(m_{0})}(n)c_{1}(n)z_{1}^{(m_{0})}& \quad\text{in $subframes$ 0$}\\ s_{1}^{(m_{1})}(n)c_{1}(n)z_{1}^{(m_{1})}&\quad\text{in $subframes$ 5$}\end{array}\right.\end{array}  \tag{3}\]  
where \(0\leq n\leq 30\). Terms \(m_{0}\) and \(m_{1}\) are decided by cell-identity group \(N_{ID}^{(1)}\) according to  
\[ \begin{array}{ll}m_{0}=m^{\prime}\text{mod}31\\ m_{1}=(m_{0}+\lfloor m^{\prime}/31\rfloor+1)\text{mod}31\\ m^{\prime}=N_{ID}^{(1)}+q(q+1)/2,q=\left\lfloor\frac{N_{ID}^{(1)}+q^{\prime}( q^{\prime}+1)/2}{30}\right\rfloor,q^{\prime}=\left\lfloor N_{ID}^{(1)}/30\right\rfloor \end{array}  \tag{4}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Uplink–Downlink** \\ **Configuration** \\ \end{tabular}  } & \multicolumn{3}{c}{**Downlink-to-Uplink**} & \multicolumn{6}{c}{**Subframe Number**} \\ \cline{2-11}  & **0** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline
**0** & 5 ms & D & S & U & U & U & D & S & U & U & U \\ \hline
1 & 5 ms & D & S & U & U & D & S & U & U & D \\ \hline
2 & 5 ms & D & S & U & D & D & S & U & D & D \\ \hline
3 & 10 ms & D & S & U & U & U & D & D & D & D \\ \hline
4 & 10 ms & D & S & U & U & D & D & D & D & D \\ \hline
5 & 10 ms & D & S & U & D where \(s_{0}^{(m_{0})}(n)\) and \(s_{1}^{(m_{1})}(n)\) are defined as  
\[ \begin{array}{l}s_{0}^{(m_{0})}(n)=\widetilde{s}((n+m_{0})\text{mod}31)\\ s_{1}^{(m_{1})}(n)=\widetilde{s}((n+m_{1})\text{mod}31)\end{array}  \tag{5}\]  
and where \(\widetilde{s}(i)=1-2x(i),0\leq i\leq 30\), is defined by  
\[x(\tilde{i}+5)=\Big{(}x(\tilde{i}+2)+x(\tilde{i})\Big{)}\text{mod}2\ 0\leq \tilde{i}\leq 25, \tag{6}\]  
with initial conditions \(x(0)=0,x(1)=0,x(2)=0,x(3)=0,x(4)=1\).