# A GNSS/5G Integrated Three-Dimensional Positioning Scheme Based on D2D Communication
## 2 Methods  
### System Model  
We consider a GNSS/5G integrated three-dimensional positioning system, as depicted in Figure 1, consisting of some GNSS satellites, \(M\) BSs and \(N\) MUs. The latter are denoted as \(\mathcal{M}=\{1,2,\cdots,M\}\) and \(\mathcal{N}=\{1,2,\cdots,N\}\), respectively. For convenience, Table 1 lists some important notations in this paper. We assume that the positions of the BSs are accurate. The MUs contain the requesting nodes that need positioning and the cooperative nodes with inaccurate known positions. Actually, the requesting nodes belong to cooperative nodes in cooperative positioning, while here we only name the MUs who serve as the reference nodes as the cooperative nodes, just to distinguish them. The requesting nodes and the cooperative nodes are denoted as \(\mathcal{N}\mathcal{R}=\{1,2,\cdots,NR\}\) and \(\mathcal{N}\mathcal{C}=\{1,2,\cdots,NC\}\)respectively. To be specific, each MU not only receives the positioning signals from the GNSS satellites, but is also capable of communicating with other MUs besides the BSs, known as D2D communication. The signals from the BSs and other MUs can also be used for positioning purpose. We assume that each D2D pair occupies one of the orthogonal frequency bands, and thus, there is no interference between these signals.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Description** \\ \hline \(\mathcal{M}=\{1,2,\cdots,M\}\) & Set of \(M\) BSs \\ \(\mathcal{N}=\{1,2,\cdots,N\}\) & Set of \(N\) MUs \\ \(\mathcal{NR}=\{1,2,\cdots,NR\}\) & Set of \(NR\) requesting nodes \\ \(\mathcal{NC}=\{1,2,\cdots,NC\}\) & Set of \(NC\) cooperative nodes \\ \(p_{i}=(x_{i},y_{i},z_{i})\) & The position of node \(i\) \\ \(d_{ij}\) & The distance between node \(i\) and \(j\) \\ \(d_{ij}\) & The estimated distance between node \(i\) and \(j\) \\ \(t_{0j_{i}},t_{ij}\) & The departure and arrival time of the signal from node \(j\) to \(i\), respectively \\ \(\Delta t_{ij}\) & The traveling time of the signal from node \(j\) to \(i\) \\ \(c\) & Speed of light \\ \(PL_{ij_{i}}^{b},PL_{ij_{j}}^{m}\) & The path loss of the signal between the BS and the MU and MUs, respectively \\ \(f_{c}\) & The carrier frequency of the transmitted signal \\ \(SF_{ij}^{b}\) & Shadow fading of the signal between the BS and the MU \\ \(a_{ij^{\prime}}^{b}\) & Flat fading coefficient of the signal between the BS and the MU and MUs, respectively \\ \(st_{ji},\,sr_{ij}\) & The transmitted and received signal from node \(j\) to \(i\), respectively \\ \((\varepsilon,Min\)\(\!\!  
D2D communication enables two MUs in proximity to communicate directly without being relayed by a BS, which provides additional signal observations besides those from the BSs, and a meshed network structure rather than the traditional star shaped one can be obtained [18; 19]. In this case, the requesting nodes can set up plenty of D2D links with other MUs, including the cooperative nodes and the other requesting nodes, to obtain pseudo ranges and share the position information and measurements. Actually, D2D positioning requires multi and frequent connection and a small amount of data, which is contrary to D2D communication. Meanwhile, a control link consuming much fewer resource is implemented for D2D discovery, link evaluation and resource allocation. Thus, to save link and time resource, an MU only exchanges the necessary data with other MUs via the D2D control links for positioning purposes [28].  
As shown in Figure 1, each MU is connected to the BSs and some other MUs in proximity. If an MU is far from a BS, it may not be able to receive the signal from the BS. For example, the distance between BS 2 and MU 4 is too far to receive a qualified signal for MU 4 to position. Generally speaking, each MU needs four BSs for three-dimensional positioning without considering time synchronization in the wireless network. Here, the signals from the BSs and other close MUs can all be used for positioning.