# A Joint Positioning Algorithm in Industrial IoT Environments with mm-Wave Communications
## 3 Overview of NR PRS and SRS-Pos Design  
### DL Positioning Reference Signal, DL-PRS  
In the DL positioning technology scheme (mainly based on DL-TDOA or DL-AoD), and the uplink-downlink joint positioning technology scheme, UE obtains the measurement value by detecting the PRSs from multiple base stations or transmission/reception points (TRPs). As a tradeoff of signaling overhead and flexible resource allocation under multiple TRP non-colliding transmissions to position a device, NR uses a hierarchy with positioning frequency layers, PRS resource sets and PRS resources to define the structure, as shown in Figure 1a. One positioning frequency layer consists of one or more PRS resource sets across one or more TRPs, all with the same carrier frequency, subcarrier spacing (SCS, i.e., OFDM numerology), PRS bandwidth and so on. A PRS resource set contains at most two PRS resources originating from the same TRP, and parameters comprising PRS repetition factor, resource offset, etc., are identical. Each PRS resource typically corresponds to a beam from the TRP. Then, by configuring a device to measure on a certain PRS resource from a PRS resource set, the location server obtains knowledge not only about which TRP the reported measurements correspond to, but also the particular beam from the TRP. \begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Explanation** \\ \hline \(L_{\text{PRS}}\) & consecutive OFDM symbols within a slot in time domain \\ \hline \(K_{\text{comb}}^{\text{PRS}}\) & frequency granularity of PRS resources \\ \hline \(n_{\text{SRS}}^{\text{cs,max}}\) & maximum number of cyclic shifts \\ \hline \(K_{\text{TC}}^{\text{SRS}}\) & comb structure of transmitted SRS-Pos \\ \hline \(\mathbb{C}^{m\times n}\) & a set of \(m\times n\) dimensional complex matrix \\ \hline \(\left(\cdot\right)^{\dagger}\) & conjugate transpose operation \\ \hline \(\left(\cdot\right)^{T}\) & transpose operation \\ \hline \(N_{\text{RE}}^{\text{SRS}}\) & SRS RE number \\ \hline \(N_{\text{RB}}^{\text{PRS}}\) & PRS RB number \\ \hline \(N_{\text{RB}}^{\text{SRS}}\) & SRS RB number \\ \hline \(\mathcal{CN}\big{(}\mu,\sigma^{2}\big{)}\) & normal distribution with mean \(\mu\) and variance \(\sigma^{2}\) \\ \hline
**I** & identity matrix \\ \hline \(\text{E}\{\cdot\}\) & the expectation operation \\ \hline \(\mathcal{O}(\cdot)\) & time complexity \\ \hline \(\Xi_{\text{TDOA}}\) & the algorithm complexity of UL-TDOA \\ \hline \(\Xi_{\text{AoA}}\) & the algorithm complexity of UL-AoA \\ \hline \(\Xi_{\text{joint}}\) & the algorithm complexity of joint UL-AoA + TDOA \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Notation description. For each PRS transmission, a frequency-time resource set with \(L_{\text{PRS}}\in\{2,4,6,12\}\) consecutive OFDM symbols within a slot in time domain and \(N_{\text{RB}}^{\text{PRS}}\in\{28,32,\ldots,272\}\) consecutive PRBs (Physical Resource Blocks) in the frequency domain is used. Note that the frequency resources are configured with a granularity of four PRBs [28]. Further, to allow simultaneous transmission of multiple PRS, a comb-based transmission is designed. \(K_{\text{comb}}^{\text{PRS}}\in\{2,4,6,12\}\) is the frequency granularity of PRS resources, i.e., the PRS utilizes every \(K_{\text{comb}}^{\text{PRS}}\)th subcarrier. Then, one device should listen to multiple TRPs for positioning. Figure 2a shows an example of PRS time-frequency resource element (RE) mapping under a comb-based design with \(K_{\text{comb}}^{\text{PRS}}=4\) and \(L_{\text{PRS}}=12\). Apart from the resource coordination, another near-far issue must be accounted for, since the device also needs to listen to PRSs from more distant TRPs. There is no sufficient dynamic range in the receiver to handle both a relatively weak signal from a distant TRP and a strong signal from a more closely located TRP simultaneously. Therefore, a mechanism to ensure that the near TRP is silent while measuring on the distant TRP is required.