# A Fine Fast Acquisition Scheme for a Communication and Navigation Fusion System
## 3 Fast Acquisition Method
### Search Space Reduction Method  
The location of FSBSs are fixed, which gives CNFS positioning receiver the opportunity to obtain the prior information to reduce the size and the number of search space. Based on the characteristic of PRN code, network topology, and the requirement of area division, the number of total PRN code IDs used in the current positioning system is 64. It takes a long time to iterate through all possibilities of code ID. When the positioning receiver receives signal from a certain FSBS, the code IDs belong to adjacent FSBSs can be confirmed. In this case, the adjacent transmitter information (ATI) is provided by navigation message or server. The second frame of navigation message, where the assistant information including ATI is provided, is shown as Figure 6 below:  
Several factors need to be considered such as the limitation of navigation message length, LDPC encoding requirements and the characteristic of topology. Therefore, ATI in navigation message only contains 6 code ID of adjacent FSBSs. Take a typical cellular network shown in Figure 7 as an example, receiver (red spot A) in the FSBS1 hexagon area can receive positioning signals transmitted from at least four FSBSs (FSBS1 to FSBS4). After the decoding of these navigation messages, the code IDs of FSBS5 to FSBS14 can be obtained by the positioning receiver. Assuming that receiver moves from position A to position B, signals transmitted from FSBS10 and FSBS11 should be received and processed by the receiver. Because of the ATI obtained before, the code ID search range is reduced from 64 to 10. On the other hand, all the FSBS information is stored on a server. Therefore, the ATI can also be obtained by accessing server database using mobile communication system. Besides the topology in Figure 7, specific network topology changes according to environments. CNFS also needs an indoor distribution system to realize coverage supplement in indoor environments, the network of which has no fixed topology. However, no matter how the topology changes, adjacent transmitters always exist. Figure 6: Second frame of navigation message. Fixed location of signal transmitters in CNFS also means that the relative location between transmitters is fixed. Meanwhile, the distance between two adjacent transmitters is pretty small compared with the distance between two satellites in GNSS system. Assuming that the maximum distance between two transmitters is \(\mathrm{d_{BS}}\). Considering the limitation of the acquisition sensitivity, the positioning receiver cannot receive signals transmitted from two transmitters that the distance between both is more than \(\mathrm{3d_{BS}}\). For a DSSS-CDMA system, the delay estimation is equivalent to the code phase estimation. Therefore, the maximum code phase difference \(\mathrm{c_{dmax}}\) of received signal can be expressed as  
\[\mathrm{c_{dmax}}=\frac{\mathrm{3d_{BS}}}{\mathrm{cT_{c}}} \tag{17}\]  
where \(\mathrm{c}\) is the light speed. After the receiver realizes successful acquisition of the first signal. The code phase search range \(\mathrm{S_{c}}\) of the following signal can be reduced based on the code phase estimation of the acquired signal  
\[\mathrm{c_{iR}}\in\left\{ \begin{array}{cc}(\mathrm{c_{0}}-\mathrm{c_{dmax}},\ \mathrm{c_{0}}+\mathrm{c_{dmax}}),&\mathrm{c_{0}}\geq\mathrm{c_{dmax}}\\ \left(\mathrm{c_{0}}-\mathrm{c_{dmax}}+\frac{\mathrm{N_{p}}}{\tau},\ \frac{\mathrm{N_{p}}}{\tau}\right)\cup(0,\ \mathrm{c_{0}}+\mathrm{c_{dmax}}),&\mathrm{c_{0}}<\mathrm{c_{dmax}}\end{array} \right. \tag{18}\]  
where \(\mathrm{c_{iR}}\) is the code phase search range of \(i\)-th signal, \(\mathrm{c_{0}}\) is the code phase estimation result of the firstly acquired signal, which is also called CPPI, \(\mathrm{N_{p}}\) is the chip number of one period code.