# Evaluation of 5G Positioning Based on Uplink SRS and Downlink PRS Under LOS and NLOS Environments
## 2 Methodology
### The 5G Signal Design of SRS  
According to the 3 GPP standard TS 138.211 V17.1.0 [41], SRS originates according to the Zadoff-Chu sequence, with each sequence entry assigned to a particular period and bandwidth unit based on set configurations. Once a Zadoff-Chu sequence has been selected, its entries are allocated to the physical resource unit within an RB. The Zadoff-Chu-based SRS maintains a constant amplitude and zero-autocorrelation property, which minimizes the peak-to-average power ratio and enhances its robustness against interference. This renders the SRS well-suited for high-precision positioning via time-based measurements. According to 3 GPP Release 17, the SRS is designated as the primary uplink positioning signal. The SRS functions as a Physical Reference Signal, enabling mmWave gNBs to assess channel quality and dynamically adjust uplink transmission parameters. The flexibility of the system is further demonstrated through configurable timing and subcarrier allocation within the subframe. The configuration of SRS resources is subject to the oversight of higher-layer parameters. The number of consecutive occupied OFDM symbols, denoted by \(N_{symb}^{SRS}\in\{1,2,4,8,12\}\) serve as the index of the OFDM symbol within a slot allocated for SRS transmission. \[l_{o}=N_{symb}^{SRS}-1-l_{offset} \tag{1}\]  
where \(l_{offset}=\in\{0,1,\ldots,13\}\) counting the OFDM symbols backward from the end of the slot, and starting from the frequency domain position \(k_{o}\), defining the initial resource element. These parameters facilitate precise regulation of the SRS pattern. The SRS is mapped to OFDM symbols within a slot by assigning it to symbol indices \(l\in\left\{0,1,\ldots,N_{symb}^{SRS}-1\right\}\). \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **SRS/PRS Value** & **Description** \\ \hline \hline \(\text{N}_{\text{frame}}\) & 1 & Number of frames. \\ \hline \(\text{f}_{\text{c}}\) & 28 GHz & Carrier frequency. \\ \hline SNR & 15 dB & Signal-to-noise ratio. \\ \hline \(\text{N}_{\text{symbol}}\) & 12 & Number of OFDM symbols used. \\ \hline \(\text{S}_{\text{start}}\) & 0 & Starting symbol index. \\ \hline \(\text{S}_{\text{spacing}}\) & 30 kHz & Subcarrier spacing. \\ \hline \(\text{C}_{\text{prefix}}\) & Normal & Type of cyclic prefix. \\ \hline \(\text{C}_{\text{size}}\) & 2 & Frequency domain comb size. \\ \hline \(\text{NS}_{\text{Grid}}\) & 52 & Number of resource blocks. \\ \hline \(\text{R}_{\text{timegap}}\) & 1 ms & Time gap between signal transmissions. \\ \hline \(\text{R}_{\text{period}}\) & [10, 0] & PRS and SRS transmission periodicity. \\ \hline \(\text{N}_{\text{runs}}\) & 100 & Number of independent simulation runs. \\ \hline \(\text{B}_{\text{carrier}}\) & 20 MHz & Bandwidth of the NR carrier. \\ \hline \(\text{F}_{\text{sampling}}\) & 30.72 MHz & Used for signal digitization. \\ \hline \(\text{N}_{\text{estimation}}\) & 12 symbols & Length of the estimation window. \\ \hline \(\text{M}_{\text{fading}}\) & TDL-C & 3 GPP TDL-C model. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Calculation and simulation parameters for UL-SRS and DL-PRS signals. This mapping employs a Gold sequence \(r^{\mu}(n,l)\) generated through a rotational transformation of a base sequence, where \(0\leq n\leq M^{SRS}-1\). The Gold sequence is subsequently mapped to physical resource elements according to the established relation. \[a_{kJ}^{\mu}=\beta^{SRS}.r^{\mu}(k,l) \tag{2}\]  
For \(k=0,1,\ldots,M^{SRS}-1,l=0,1,\ldots,N_{symb}^{SRS}-1\), the sequence initialization begins at the RE indexed by \(r^{\mu}(0,l)\) and \(\beta^{SRS}\) denotes an amplitude scaling factor. As illustrated in Figure 6, a potential resource grid allocation of SRS and comb size is presented. The comb size is a critical factor in determining the spacing of tones across the frequency domain, thereby shaping the density of reference signals and their effectiveness in positioning applications.