# Multistatic ISAC Localization Accuracy Improvement in LoS/NLoS Scenario using PRS

Keivan Khosroshahi, Philippe Sehier, Sami Mekki, Michael Suppa

► To cite this version:

Keivan Khosroshahi, Philippe Sehier, Sami Mekki, Michael Suppa. Multistatic ISAC Localization Accuracy Improvement in LoS/NLoS Scenario using PRS. IEEE 22nd Consumer Communications & Networking Conference (CCNC 2025), Jan 2025, Las Vegas, NV, United States. 10.1109/CCNC54725.2025.10976025. [hal-05066626](https://hal.science/hal-05066626v1)

HAL Id: hal-05066626

https://hal.science/hal-05066626v1

Submitted on 16 May 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Multistatic ISAC: Localization Accuracy Improvement in LoS/NLoS Scenario using PRS

Keivan Khosroshahi*†, Philippe Sehier†, Sami Mekki†, and Michael Suppa‡

* Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes, Gif-sur-Yvette, France

† Nokia Standards, Massy, France

‡ Roboception GmbH, Munich, Germany

keivan.khosroshahi@centralesupelec.fr, {philippe.sehier, sami.mekki}@nokia.com, michael.suppa@roboception.de

**Abstract**—A major challenge for integrated sensing and communication (ISAC) systems is the degradation in localization accuracy caused by unfavorable propagation conditions, such as multipath effects and non-line-of-sight (NLoS) environments. These conditions can introduce outlier measurements that significantly affect localization performance. This paper explores ways to enhance target localization accuracy in multistatic ISAC systems under both line-of-sight (LoS) and NLoS conditions. We utilize the positioning reference signal (PRS) as the sensing signal. A new algorithm is proposed to improve localization accuracy by reducing the influence of outliers in range measurements and PRS range resolution. Finally, simulation results confirm the superiority of the proposed method compared to least squares (LS) method.

**Index Terms**—Multistatic ISAC, PRS, LS, localization, 3GPP

## I. INTRODUCTION

Radio signal-based sensing has attracted considerable attention in beyond fifth-generation (B5G) and sixth-generation (6G) technologies. Integrated sensing and communication (ISAC) is expected to become a key technology in future wireless systems, enabling a wide range of sensing applications such as remote healthcare, weather monitoring, target tracking, gesture recognition, autonomous vehicles, and augmented reality (AR) [1]. Reference signals in wireless communication systems are recognized for their strong passive detection capabilities and high resilience to noise, prompting growing interest in developing sensing techniques based on these signals [2]. Among the various reference signals in 5G networks, positioning reference signals (PRS) stands out for sensing applications due to its extensive time-frequency resources and flexible configuration. The PRS was introduced in 3rd generation partnership project (3GPP) release 16 of the fifth-generation (5G) specification to improve the positioning accuracy of connected user equipment (UEs) [3]. This work focuses on enhancing the localization accuracy of an unconnected target in multistatic ISAC systems under line-of-sight (LoS) and non-line-of-sight (NLoS) conditions. We employ the PRS as the sensing signal. We propose a novel algorithm that improves target localization accuracy by addressing the impact of outliers and range estimation errors caused by PRS range resolution. Simulation results show the effectiveness of our method, showing significant improvements in the average localization error compared to the least square (LS) method.

This work was funded by the European Commission through the H2020 MSCA 5GSmartFact project under grant agreement number 956670.

<figure><img src="image_2.png" /><figcaption>Fig. 1: Multistatic ISAC scenario where red, green and yellow dashed lines indicate blocked LoS, LoS and NLoS links between gNBs, UEs, and the target, respectively.</figcaption></figure>

## II. MULTISTATIC ISAC SYSTEM MODEL

We consider a multistatic ISAC scenario comprising *S* transmitters, *K* receivers, and one passive point-like target as in Fig. 1. The UEs are configured to receive the echoes from the LoS or NLoS target. The locations of the gNBs and UEs are assumed to be known. The location of the UEs can be determined by the positioning service provided by gNBs [3]. The location of the *k*-th UE is denoted as $\mathbf{u}_k = (x_{k,u}, y_{k,u})$, $\mathbf{u}_k \in \mathbb{R}^2$, $k \in \{1, 2, ..., K\}$. The point-like target is placed at $\mathbf{x}_0 = (x_0, y_0)$, $\mathbf{x}_0 \in \mathbb{R}^2$ and *s*-th gNB is located at $\mathbf{g}_s = (x_{s,g}, y_{s,g})$, $\mathbf{g}_s \in \mathbb{R}^2$, $s \in \{1, 2, ..., S\}$. We assume that the clocks of the gNBs could be synchronized by global positioning system (GPS) clock module [4]. We define $\hat{r}_{s,k}$ as the estimated bistatic distance of the target, i.e., the distance between gNB *s* and target and from target to UE *k*.

Outliers can arise in three different scenarios: 1) The target is in NLoS of the UEs. 2) The target is in NLoS of the gNBs. 3) The target is in NLoS of both the gNBs and the UEs. Since we lack priori knowledge about the occurrence of these scenarios, we account for all of them in the optimization that will be introduced later in this section.

1) *Target and UEs in NLoS:* In the case that the target is in NLoS with some UEs, we remove all paths between the target and all the UEs to mitigate the influence of the potentially erroneous measurements that could cause outliers, as we do
not know which UEs are in NLoS with the target. This can be done as

$$
\begin{align}
\hat{r}_{s,s',k} &= \hat{r}_{s',k} - \hat{r}_{s,k} = \|\mathbf{x}_0 - \mathbf{g}_s\| + \zeta_{0,k} + \gamma_{s',k} \nonumber \\
&\quad - (\|\mathbf{x}_0 - \mathbf{g}_{s'}\| + \zeta_{0,k} + \gamma_{s,k}) \tag{1} \\
&= \|\mathbf{x}_0 - \mathbf{g}_s\| - \|\mathbf{x}_0 - \mathbf{g}_{s'}\| + \gamma_{s',k} - \gamma_{s,k} \nonumber \\
\forall s, s' &\in \{1, 2, \dots, S\}, s \neq s', \forall k \in \{1, 2, \dots, K\} \tag{2}
\end{align}
$$

where $\zeta_{0,k}$ represents the NLoS distance that the sig-
nal travels to reach UE $k$ from the target, and $\gamma_{s,k} \sim
U(-\frac{c_0}{2\Delta f_M}, \frac{c_0}{2\Delta f_M})$, $\forall s \in \{1, 2, \dots, S\}, \forall k \in \{1, 2, \dots, K\}$
denotes the range estimation error caused by the PRS range
resolution defined in [5, Eq. 10] between $k$-th UE and $s$-th
gNB. By removing the paths between the target and the UEs,
we alleviate the potential error from PRS range estimation.

2) Target and gNBs in NLoS: When the target is in NLoS of some gNBs, to remove the potential error from the range estimation using PRS, we need to remove all the paths between the target and the gNBs since we are not aware which gNBs are in NLoS with the target. This can be achieved by

$$
\begin{align}
\hat{r}_{s,k,k'} &= \hat{r}_{s,k} - \hat{r}_{s,k'} = \zeta_{s,0} + \|\mathbf{x}_0 - \mathbf{u}_k\| + \gamma_{s,k} \nonumber \\
&\quad - (\zeta_{s,0} + \|\mathbf{x}_0 - \mathbf{u}_{k'}\| + \gamma_{s,k'}) \tag{3} \\
&= \|\mathbf{x}_0 - \mathbf{u}_k\| - \|\mathbf{x}_0 - \mathbf{u}_{k'}\| + \gamma_{s,k} - \gamma_{s,k'} \nonumber \\
\forall s &\in \{1, 2, \dots, S\}, \forall k, k' \in \{1, 2, \dots, K\}, k \neq k' \tag{4}
\end{align}
$$

where $\zeta_{s,0}$ denotes the NLoS distance that the signal travels from gNB $s$ to the target. It is important to note that while removing the paths as described in II-1 and II-2 reduces error in PRS range estimation by eliminating NLoS paths, it maintains the correctness of the range measurements when the target is in LoS with the gNBs or UEs. Considering the calculated $\hat{r}_{s,s',k}$ and $\hat{r}_{s,s',k}$ as (2) and (4), respectively, we solve the following optimization problem:

$$
\begin{equation}
\begin{split}
\min_{\mathbf{x}_0} & \left[ \sum_{s=1}^{S} \sum_{k=1}^{K-1} \sum_{k'=k+1}^{K} (\hat{r}_{s,k,k'} - (\|\mathbf{x}_0 - \mathbf{u}_k\| - \|\mathbf{x}_0 - \mathbf{u}_{k'}\|))^2 \right. \\
& \left. + \sum_{k=1}^{K} \sum_{s=1}^{S-1} \sum_{s'=s+1}^{S} (\hat{r}_{s,s',k} - (\|\mathbf{x}_0 - \mathbf{g}_s\| - \|\mathbf{x}_0 - \mathbf{g}_{s'}\|))^2 \right]
\end{split}
\tag{5}
\end{equation}
$$

To solve (5) using the gradient descent, denoting the objective function as $f(\mathbf{x}_0)$, we can iteratively update $\mathbf{x}_0$ as:

$$
\mathbf{x}_{0}^{(i+1)} = \mathbf{x}_{0}^{(i)} - \alpha \nabla f(\mathbf{x}_{0}^{(i)}) \quad (6)
$$

where $\alpha$ is the step size.

3) Target, gNBs and UEs in NLoS: If the target is in NLoS of all gNBs and UEs, the range measurements are subject to significant errors. However, applying the methods described in Sections II-1 and II-2 can improve accuracy.

III. SIMULATION RESULTS

To validate the introduced approach, we use Matlab 5G
toolboxes to make this work 3GPP standards compliant. We
simulate a scenario where multiple gNBs, UEs and a target
are randomly distributed in 400m × 400m, 200m × 200m and

<figure><img src="image_3.png" /><figcaption>(a) CDFs of different methods</figcaption></figure>

<caption>(b) Outlier sensitivity</caption>

<caption>Fig. 2: Comparison of the proposed method with LS.</caption>

150m × 150m area, respectively. The carrier frequency is set to 28GHz, subcarrier spacing is 120kHz and physical resource block (PRB) of PRS is equal to 66 which corresponds to 100MHz in frequency range 2 (FR2) transmission bandwidth configurations defined in TS 38.104 [6]. The PRS comb size is set to 12. Given such configuration, PRS range resolution is 3.15m. We also set α to 0.001. In the simulations, the number of outliers is uniformly distributed between zero and S + K.

In Fig. 2a, we present the cumulative distribution function (CDF) of different methods while the number of gNBs and UEs is 6. To simulate the effect of outliers, we randomly add outliers in the range estimations, with values up to 10m using uniform distribution. The results demonstrate that the proposed method outperforms the LS method. Fig. 2b provides useful insight on the sensitivity of the different algorithms based on the maximum added outlier. We randomly added outliers from 4m to 18m with uniform distribution to the random paths between the gNBs and the target and between target and UEs, with the number of gNBs and UEs fixed at 6. The results reveal that the proposed method significantly enhances target localization accuracy.

IV. CONCLUSION

In this work, we introduced a novel method to improve the
accuracy of target localization in multistatic ISAC scenario
using PRS when the target is in LoS or NLoS of the UEs and
gNBs. We used PRS as the sensing signal. We validated our
methods using the MATLAB 5G toolbox, ensuring compliance
with 3GPP standards.

REFERENCES

[1] A. Behravan et al., “Positioning and sensing in 6G: Gaps, challenges, and opportunities,” *IEEE Vehicular Technology Magazine*, vol. 18, no. 1, pp. 40–48, 2022.

[2] Z. Wei et al., “5G PRS-based sensing: A sensing reference signal approach for joint sensing and communication system,” *IEEE Transactions on Vehicular Technology*, vol. 72, no. 3, pp. 3250–3263, 2022.

[3] 3GPP, “Study on NR positioning support,” 3rd Generation Partnership Project (3GPP), Technical Specification (TS) 38.855, 2019, v16.0.0.

[4] P. Vyskocil and J. Sebesta, “Relative timing characteristics of GPS timing modules for time synchronization application,” in *IEEE International workshop on satellite and space communications*, 2009, pp. 230–234.

[5] K. Khosroshahi, P. Sehier, and S. Mekki, “Leveraging PRS and PDSCH for integrated sensing and communication systems,” *IEEE Global Communications Conference (GLOBECOM)*, 2024. [Online]. Available: https://arxiv.org/abs/2408.00667.

[6] 3GPP, “NR; base station (BS) radio transmission and reception,” 3rd Generation Partnership Project (3GPP), Technical Specification (TS) 38.104, 2024, v18.6.0.