# High-Precision Ranging Method of 5G NR Co-Band PRS in Industrial Internet Scenarios
## 3 Proposed Timing Recovery Scheme
### Multi-Path Delay Estimation  
For indoor multipath environments, path delay estimation is particularly important. We further analyze multipath delay by estimating the time-domain channel. In general, accurate channel estimation requires high-power pilot signals [28], while Co-Band PRS signals are inherently low-power. Although this paper reduces noise interference by implementing window filtering [29], it is not possible to eliminate the communication data that are superimposed on the Co-Band PRS signal using this method. However,  
Figure 3: Schematic of the rising cosine roll-off window in 5G NR.  
the communication data superimposed on the PRS localization signal become the main source of interference and cannot be eliminated in this way. In this regard, there are two approaches to consider. Firstly, increasing the number of subcarriers and using a short comb structure like Comb2 can enhance the localization signal correlation characteristics by extending the localization signal length. Secondly, this paper proposes improving the time delay estimation performance by pre-demodulating the data information and eliminating the data codes.  
Firstly, the Co-Band PRS signal in the i-th OFDM symbol is defined as \(\{\Psi_{i,q}|q=0,1\ldots Q\}\), where the value of Q is determined by the number of subcarriers occupied by the PRS of the i-th OFDM symbol in the frequency domain. And point signal \(\Phi_{i,q}\) may also contain communication data that can be given by  
\[\Phi_{i,q}=\Psi_{i,q}+\hat{d}_{k,l}^{(p,\mu)}=p_{k,l}^{(p,\mu)}+\hat{d}_{k,l}^{ (p,\mu)} \tag{15}\]  
\[k=mK_{comb}^{PRS}+\left(\left(k_{offset}^{PRS}+k^{\prime}\right)\text{ mod }K_{comb}^{PRS}\right) \tag{16}\]  
where \(\hat{d}_{k,l}^{(p,\mu)}\) is the estimated data code, obtained directly by Fourier transforming the signal after the initial coarse capture and decoding it. We perform an FFT on the received signal, and by utilizing time-frequency mapping, we can obtain  
\[\hat{\Psi}_{i,q}=\text{MAP}\left\{\text{FFT}\{y[n+\hat{\delta}]\}-\frac{\hat{ d}_{k,l}^{(p,\mu)}}{\gamma_{PL}}\right\} \tag{17}\]  
where \(\hat{\delta}\) is the time delay estimate obtained through coarse capture, and \(\gamma_{PL}\) denotes the path fading factor. Dividing this by the original pilot signal yields an estimate of the channel's frequency domain response as  
\[\hat{H}_{i,q}=\frac{\hat{\Psi}_{i,q}}{\Psi_{i,q}},\quad q=0,1\ldots Q. \tag{18}\]  
The estimated channel is passed through a Hamming window to minimize the effect of IFFT symbol leakage. It is then transformed to the time domain using a Q-point IFFT. The estimated channel impulse response can be obtained as  
\[\hat{P}_{k}=\frac{1}{I}\sum_{i=0}^{I-1}\left|\frac{1}{wQ}\sum_{q=0}^{Q-1}\hat{ H}_{i,q}\operatorname{Haming}(q)e^{|2\pi kq/(wQ)|}\right|^{2},\quad k=0,\ldots,wQ-1. \tag{19}\]  
Due to the influence of multipath, the channel time-domain impulse response contains multiple path components. Often, the strongest path is not the first path reached. To address this, we introduce a threshold, denoted as \(\Theta\). We consider the first path whose power exceeds this threshold as the first reach path and update the timing estimation by  
\[\hat{\theta}=\frac{1}{w}\arg\min_{k}\left\{\hat{P}_{k}>\Theta\right\} \tag{20}\]  
For the integer part of \(\hat{\theta}\), it will be sent back to the FFT window block in Figure 2 to correct the window function position. The fractional part of \(\hat{\theta}\) will be sent to the sequence phase rotation block in Figure 2 to correct the Co-Band PRS phase. If the integer part of \(\hat{\theta}\) exists, the data \(\hat{d}_{k,l}^{(p,\mu)}\) also need to be re-estimated according to the new FFT window position.