## 2 System Structure
### Rx/Tx  
The Rx/Tx is the crucial part in the system. It receives the real GPS Radio Frequency (\(RF^{GPS}\)) signal using an outdoor Receiving Antenna (RA), estimates the pseudoranges \(\rho_{1,2,..,N}^{GPS}\) from the RA to each satellite and sends them to the server. Meanwhile, the Rx/Tx separates each satellite's signal and transmits the separated signal to the user terminal via several (at least three for 2-D positioning) indoor Transmitting Antennas (TA\({}_{1}\), TA\({}_{2}\),..,TA\({}_{N}\)). The architecture of the Rx/Tx, which is composed of a receiver (Rx) and transmitter (Tx) components, is illustrated in Figure 2. The Rx component works as a general GPS receiver. Differently, its local carrier, code and navigation data of the receiver rather than positioning results are output to the next component (Tx). Figure 1: Indoor positioning system. The requirement, nowadays, can be satisfied by a software GNSS receiver. Figure 2 illustrates the signal processing in the Rx component. GPS radio frequency signals _RFGPS_ is received by the outdoor RA, and converted into intermediate frequency signals _IFGPS_ through down-conversion and Analog-Digital-Conversion (ADC). Since _IFGPS_ is a mixture of multiple satellites' signals, the Rx demodulates _IFGPS_ using multiple channels and each channel processes one satellite's signal. Through multiplying _IFGPS_ by the local carrier and C/A code, the Rx obtains navigation data and estimates the pseudorange measurement \(\rho_{i}^{\textit{GPS}}\) from each channel. It sends the local carrier, local C/A code and demodulated navigation data to the Tx component. Simultaneously, it delivers all the pseudorange measurements \(\rho_{i,2,-,N}^{\textit{GPS}}\), their corresponding PRN and channel number to the server via Wi-Fi (or another possible means). The Tx components mimic GPS satellites to generate and transmit RF. The navigation data, carrier and code signal are obtained from the signal processing channel of Rx. Thus, one Tx generates the GPS-like signal corresponding to one GPS satellite and one Rx channel. Figure 2 shows the process of the \(i\)-th Tx generating the RF signal. Firstly, Tx re-modulates IF signal using the local carrier, local C/A code and demodulated navigation data from the \(i\)-th channel of Rx. After re-modulation, the Tx obtains the digital intermediate frequency signal \(\textit{IF}_{i}^{\textit{RGPS}}\). Then, the signal \(\textit{IF}_{i}^{\textit{RGPS}}\) is converted from digital into analog signal using Digital-Analog-Conversion (DAC) and further from IF signals into RF signal \(\textit{RF}_{i}^{\textit{RGPS}}\) with L1 frequency (1575.42 MHz) using up-conversion. Finally, \(\textit{RF}_{i}^{\textit{RGPS}}\) is sent to user terminal via TA\({}_{i}\). In the system, more than four Tx are required for 3-D positioning and more than three Tx are required for 2-D positioning since one Tx corresponds to one satellite. Therefore, synchronization of all Tx units is required in the system. In Figure 2, the time of RF signal generation and the time of signal transmission from Tx to TA are the main factors causing asynchronization, also called as system delay biases. For the signal generation time, Rx and all Tx are controlled using one oscillator to ensure that all Tx units generate RF signals simultaneously. The remained system delay biases can be calibrated in the following two ways:  
(1) Pre-correction before installation of transmitting antennas  
In this method, all transmitting antennas are placed at the same position and their transmitting signals are received using one GPS receiver. Then, the difference between the indoor receiver's psuedorange  
Figure 2: Architecture of Rx/Tx Server in one channel. measurements and the Rx component for the same satellite (_i.e._, \(\rho_{i}^{\textit{RxPS}}-\rho_{i}^{\textit{GPS}}\), denoted as \(\Delta\rho_{i}\), which models will be detailed in Section 3, results from the processing time in Tx/Rx and propagation time from the transmitting antenna to the indoor receiver.