# Statistical Multipath Model Based on Experimental GNSS Data in Static Urban Canyon Environment
## 2 Multipath Parameters Extraction Method  
In the multipath environment, the received signal is composed of the LOS signal and multiple multipath rays. The compound signal can be expressed as [21]:  
\[\mathbf{s}(t)=Ax(t-\tau_{0})\cos(\omega_{0}t+\theta_{0})+A\sum_{k=1}^{N}\alpha_ {k}x(t-\tau_{0}-\tau_{k})\cos[\omega_{0}t+\theta_{0}+\Phi_{k}(t)] \tag{1}\]  
where \(A\) and \(\tau_{0}\) are the signal power and propagation time of LOS, respectively. The symbol \(x(. )\) represents the product of the navigation code and the spreading code. \(N\) is the multipath number. The parameter \(\alpha_{k}\) is the amplitude attenuation proportionality coefficient. \(\tau_{k}\) is the \(k\)-th multipath ray's time delay relative to LOS, and \(\Phi_{k}(t)\) is the \(k\)-th multipath ray's carrier phase difference relative to LOS. According to (1), it can be seen that the main parameters of multipath signal are \(\tau_{k}\), \(\alpha_{k}\) and \(\Phi_{k}(t)\). Thus, in the following paper, time delay \(\tau_{k}\), power attenuation \(20\log\alpha_{k}\), and fading frequency \(d\Phi_{k}(t)/2\pi dt\) are chosen as multipath parameter core features to be studied. To obtain multipath parameter features from the real satellite signal, a broadband intermediate frequency (IF) data sampling and recording device is designed to store both GPS L1 CA and BDS B1I raw IF signals at the same time. A one-stage, the direct down-conversion in-phase/quadrature orthogonal sampling technique is adopted with a local oscillator (LO) frequency of 1568 MHz. The sampling frequency is 62 MHz complex samples per second, with 8-bit quantization resolution. The 1 TByte capacity is able to support more than 2 h of continuous signal recording. The specifications of the signal recording device are shown in Table 1. This device is mounted on a van to record data in the scenarios of interest, which is shown in Figure 1. A right-hand circular polarization (RHCP) antenna is mounted on the top of the van. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Signal Sampling Device** & **GNSS Antenna (NovAtel GPS-703-GGG)** \\ \hline Constellation & BDS B1 \& GPS L1 & Polarization & RHCP \\ Sampling frequency & 62 MHz & Peak gain & 5.0 dBi \\ Signal bandwidth & 20 MHz & Directivity & Horizontal omnidirectional \\ Bit width & 8 bit & Axial ratio & \(<\)2.0 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the signal recording device. Figure 1: Global navigation satellite system (GNSS) signal intermediate frequency (IF) data recording platform. After collection in the field, the IF data were exported and processed off-line with a software receiver developed by our group. One of the algorithms implemented in this receiver is the Coupled Amplitude and Delay Lock Loop (CADLL) multipath estimation method, which can estimate multipath parameters by processing the raw IF data [22; 23]. The Block structure of the CADLL algorithm is shown in Figure 2. Instead of the traditional Delay Lock Loop (DLL), CADLL uses several units, which consist of one DLL and two Amplitude Lock Loops (ALL), to track the spreading code. Each unit can track one path ray, and unit always tracks the LOS signal. In every unit, DLL is used to estimate the code phase, and ALLs are used to estimate the normalized amplitude of I and Q branches. The time interval of each unit should be no less than 0.1 chip, so the maximum number \(N\) of multipath detection is ten in one chip. However, according to the analysis of experimental data, five channels for one satellite are enough to track most powerful multipath signals. Normally, the power of the rest multipath is too low to interfere with the positioning performance. According to (1), the code phase delay of the \(k\)-th multipath ray, with respect to the LOS signal, is calculated as  
\[\tau_{k}=\hat{\tau}_{k}-\hat{\tau}_{0}, \tag{2}\]  
where \(\hat{\tau}_{0}\) and \(\hat{\tau}_{k}\) are the estimated time delays of LOS and \(k\)-th multipath, respectively.