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TSN-5G 网络中 5G 透明时钟的实证评估
Empirical Evaluation of a 5G Transparent Clock for Time Synchronization in a TSN-5G Network · 2025-09-08
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Time synchronization distribution is an essential service for the Industrial Internet of Things (IIoT), playing a crucial role in the evolution towards Industry 4.0 and 5.0. Applications in these sectors depend on precise synchronization for reliable communication, low latency and operational efficiency to optimize automation and interaction between robots, sensors and machinery, as well as accurate sensor data analysis. The Time Sensitive Networking (TSN) standard, defined by IEEE 802.1 [ 1 ], enables synchronization accuracy below 100 μ s 100\ \mu s [ 2 ], ensuring deterministic and reliable operation. However, the growing need for mobility in industrial, Internet of Things (IoT) and robotics sectors presents new challenges, as TSN was conceived for wired networks. As a solution, 3GPP Release 16 proposes integrating Fifth Generation (5G) with TSN to provide wireless communication and mobile flexibility without compromising synchronization requirements.
时间同步分发是工业物联网（IIoT）的一项基本服务，在向工业 4.0 和工业 5.0 演进的过程中发挥着关键作用。这些领域中的应用依赖精确同步，以实现可靠通信、低时延和运行效率，从而优化机器人、传感器和机械之间的自动化与交互，以及准确的传感器数据分析。由 IEEE 802.1 [1] 定义的时间敏感网络（TSN）标准能够实现低于 100 μs 的同步精度 [2]，从而确保确定性和可靠运行。然而，工业、物联网（IoT）和机器人领域对移动性的需求不断增长，带来了新的挑战，因为 TSN 最初是为有线网络构想的。作为一种解决方案，3GPP Release 16 提出将第五代移动通信（5G）与 TSN 集成，以在不损害同步要求的情况下提供无线通信和移动灵活性。
术语 IIoT、Industry 4.0/5.0、TSN、IEEE 802.1、IoT、3GPP Release 16、5G 均已保留；数字和单位“低于 100 μs”已保留；引用 [1]、[2] 已保留。原文中 “100 μ s 100\ \mu s”存在重复/排版残留，译文按一次“100 μs”处理，建议人工确认是否由公式抽取导致。
TSN functionalities such as IEEE 802.1 Qbv, IEEE 802.1 Qcc and IEEE 802.1 Qci rely on accurate time synchronization. However, 5G introduces challenges that degrade synchronization accuracy, such as high levels of jitter, asymmetries in Uplink (UL) and Downlink (DL) delays, variable processing times in devices like the Next-Generation Node B (gNB) and User Plane Function (UPF), and retransmissions. TS 22.104 [ 3 ] establishes the 5G System (5GS) requirements for industrial and IIoT networks, specifying a maximum time synchronization error of 900 900 ns and support for up to 32 32 simultaneous working clock domains. These domains provide high-precision time to the devices within them, allowing TSN devices to manage multiple clock domains simultaneously. While a global clock domain provides the date and time to the devices belonging to that domain. In some cases, the working and global clock domains may overlap. Meanwhile, 3GPP TS 23.501 [ 4 ] defines several configurations to enable TSN synchronization in the 5GS, which can be implemented as a time-aware system using the IEEE 802.1AS standard [ 5, 6 ], which uses the generic Precision Time Protocol (gPTP) protocol, or configured as a Boundary Clock (BC) or Transparent Clock (TC) following the IEEE 1588 standard [ 7 ].
IEEE 802.1Qbv、IEEE 802.1Qcc 和 IEEE 802.1Qci 等 TSN 功能依赖准确的时间同步。然而，5G 引入了一些会降低同步精度的挑战，例如较高水平的抖动、上行链路（UL）和下行链路（DL）时延中的非对称性、下一代 Node B（gNB）和用户面功能（UPF）等设备中的可变处理时间，以及重传。TS 22.104 [3] 规定了工业和 IIoT 网络的 5G 系统（5GS）要求，指定最大时间同步误差为 900 ns，并支持多达 32 个同时工作的工作时钟域。这些时钟域向其内部设备提供高精度时间，使 TSN 设备能够同时管理多个时钟域。而全局时钟域则向属于该域的设备提供日期和时间。在某些情况下，工作时钟域和全局时钟域可能会重叠。同时，3GPP TS 23.501 [4] 定义了若干种配置，以在 5GS 中实现 TSN 同步；这些配置可以使用 IEEE 802.1AS 标准 [5, 6] 作为时间感知系统来实现，该标准使用通用精确时间协议（gPTP），也可以按照 IEEE 1588 标准 [7] 配置为边界时钟（BC）或透明时钟（TC）。
IEEE 802.1Qbv/Qcc/Qci、UL、DL、gNB、UPF、TS 22.104、5GS、3GPP TS 23.501、IEEE 802.1AS、gPTP、IEEE 1588、BC、TC 均已保留；“900 ns”“32 个”已保留。原文中 “900 900 ns”“32 32”存在重复抽取痕迹，译文按一次处理；原文 “While a global clock domain...” 为不完整句式，译文按上下文补足逻辑，需人工确认。
Several studies have addressed the challenges of time synchronization distribution in TSN - 5G network. For example, Striffler et al. [ 8 ] analyze frequency drift and timing errors when 5GS operated as a TC, which can lead to non-compliance with time synchronization requirements. While Wang et al. [ 9 ] propose solutions to mitigate the effects of multi- gNB competition, retransmissions, and mobility in a 5GS modeled as TC. Shi et al. [ 10 ] investigate synchronization errors in 5GS configured as BC, focusing on the uncertainty due to reference time granularity and propagation delay estimation. Val et al. [ 11 ] demonstrate that, despite Wi-Fi variability, TSN -compatible synchronization accuracies are achieved through hardware-level modifications, although this approach is currently infeasible for commercial 5G networks.
已有若干研究讨论了 TSN-5G 网络中时间同步分发的挑战。例如，Striffler 等人 [8] 分析了当 5GS 作为 TC 运行时的频率漂移和定时误差，这可能导致不符合时间同步要求。Wang 等人 [9] 则提出了解决方案，用于减轻在建模为 TC 的 5GS 中多 gNB 竞争、重传和移动性的影响。Shi 等人 [10] 研究了配置为 BC 的 5GS 中的同步误差，重点关注由参考时间粒度和传播时延估计引起的不确定性。Val 等人 [11] 证明，尽管 Wi-Fi 存在可变性，仍可通过硬件级修改实现与 TSN 兼容的同步精度，尽管这种方法目前对于商用 5G 网络并不可行。
作者引用 [8]-[11]、TC、BC、5GS、gNB、Wi-Fi、TSN 等术语已保留；逻辑上分别对应 TC 运行、TC 建模、BC 配置和 Wi-Fi 硬件修改四类研究。原文 “TSN - 5G network” 单复数略不自然，译为“TSN-5G 网络”；未发现明显问题。
To our knowledge, there is no empirical evaluation of the TC in an integrated TSN - 5G network. Therefore, the objective of this paper is to empirically investigate the distribution of TSN time synchronization in a TSN - 5G network when the 5GS is configured as an End-to-End (E2E) TC. Our main contributions are as follows:
据我们所知，目前尚无关于集成 TSN-5G 网络中 TC 的实证评估。因此，本文的目标是在 5GS 被配置为端到端（E2E）TC 时，对 TSN-5G 网络中的 TSN 时间同步分发进行实证研究。我们的主要贡献如下：
“To our knowledge”译为“据我们所知”；TC、TSN-5G、5GS、End-to-End（E2E）TC 均已保留；研究目标和贡献引出关系准确。未发现明显问题。
• We analyze the various configurations of 5GS to support TSN synchronization transport, considering its implementation in commercial single-clock equipment. • We implement the E2E TC on commercial TSN switches. This implementation comprises two processes: the computation of the residence time introduced by the 5GS and the recovery of the TSN clock domain at the slave node. • We deploy a TSN - 5G network testbed with commercial equipment to evaluate time synchronization performance. • We performed an experimental evaluation of the time synchronization accuracy on the implemented testbed.
• 我们分析了 5GS 用于支持 TSN 同步传输的各种配置，并考虑其在商用单时钟设备中的实现。• 我们在商用 TSN 交换机上实现了 E2E TC。该实现包括两个过程：计算由 5GS 引入的驻留时间，以及在从节点处恢复 TSN 时钟域。• 我们使用商用设备部署了一个 TSN-5G 网络测试床，以评估时间同步性能。• 我们在所实现的测试床上对时间同步精度进行了实验评估。
四项贡献均已逐项翻译；5GS、TSN、E2E TC、TSN-5G 等缩写保留；“residence time”译为“驻留时间”，“slave node”译为“从节点”。该段与后续 P006-P009 内容重复，可能是列表抽取与分段抽取重复导致，但按输入要求保留并翻译；需人工确认是否应在最终论文译稿中去重。
We analyze the various configurations of 5GS to support TSN synchronization transport, considering its implementation in commercial single-clock equipment.
我们分析了 5GS 用于支持 TSN 同步传输的各种配置，并考虑其在商用单时钟设备中的实现。
术语 5GS、TSN 已保留；与 P005 第一项内容重复，可能为列表项被重复抽取。译文本身未发现明显问题，但段落重复需人工确认。
We implement the E2E TC on commercial TSN switches. This implementation comprises two processes: the computation of the residence time introduced by the 5GS and the recovery of the TSN clock domain at the slave node.
我们在商用 TSN 交换机上实现了 E2E TC。该实现包括两个过程：计算由 5GS 引入的驻留时间，以及在从节点处恢复 TSN 时钟域。
E2E TC、TSN、5GS 等术语已保留；“residence time”译为“驻留时间”，“slave node”译为“从节点”；与 P005 第二项内容重复，需人工确认是否为抽取重复。
We deploy a TSN - 5G network testbed with commercial equipment to evaluate time synchronization performance.
我们使用商用设备部署了一个 TSN-5G 网络测试床，以评估时间同步性能。
TSN-5G 和“testbed/测试床”译法一致；与 P005 第三项内容重复，需人工确认是否为抽取重复。
We performed an experimental evaluation of the time synchronization accuracy on the implemented testbed.
我们在所实现的测试床上对时间同步精度进行了实验评估。
“experimental evaluation”和“time synchronization accuracy”分别译为“实验评估”和“时间同步精度”；与 P005 第四项内容重复，需人工确认是否为抽取重复。
Our results indicate a peak-to-peak time synchronization of 500 500 ns, meeting industrial requirements (≤ 1 μ s \leq 1\ \mu s). Also, we note that, at certain Precision Time Protocol (PTP) message transmission rates, time offsets can be observed that may affect the time synchronization but do not exceed the requirements. These results are independent of whether the synchronizing transmitter (master node) is synchronized to an external reference (Global Navigation Satellite System (GNSS)) or operates with its internal clock (Free-running (FR)).
我们的结果表明，峰峰值时间同步为 500 ns，满足工业要求（≤ 1 μs）。此外，我们注意到，在某些精确时间协议（PTP）消息传输速率下，可以观察到可能影响时间同步的时间偏移，但这些偏移并未超过要求。无论同步发送端（主节点）是同步到外部参考源（全球导航卫星系统（GNSS）），还是使用其内部时钟运行（自由运行（FR）），这些结果都是独立成立的。
“peak-to-peak time synchronization”译为“峰峰值时间同步”；500 ns、≤ 1 μs、PTP、GNSS、FR 均已保留。原文中 “500 500 ns”存在重复抽取痕迹，译文按一次处理；“independent of whether...” 译为“不论……这些结果都是独立成立的”，逻辑已保留。需人工确认“peak-to-peak time synchronization”是否应按领域习惯译为“峰峰值时间同步误差”。
The rest of the paper is structured as follows: Section II presents the background and an analysis of time synchronization options in TSN - 5G networks. Section III describes the model and architecture of the integrated network. Section IV details the design and operation of the TC, along with PTP messages analysis and offset calculation. Section V describes the testbed and experimental setup. Section VI presents and discusses the results obtained. Finally, Section VII concludes with the main contributions.
本文其余部分组织如下：第 II 节介绍 TSN - 5G 网络中的背景知识以及时间同步选项分析。第 III 节描述集成网络的模型和架构。第 IV 节详细说明 TC 的设计与运行，并给出 PTP 消息分析和偏移量计算。第 V 节描述测试床和实验设置。第 VI 节呈现并讨论所获得的结果。最后，第 VII 节以主要贡献作为总结。
术语 TSN、5G、TC、PTP 均已保留；章节编号、逻辑顺序和“offset calculation”含义无明显风险；“concludes with the main contributions”译为“以主要贡献作为总结”基本准确。未发现明显问题。
In the TSN - 5G integrated network, there are two synchronization processes running in parallel, the 5G time synchronization process and the TSN time synchronization process [ 2, 12 ], as shown in Figure 1. The 5G synchronization process provides the temporal reference from the 5G Grandmaster (GM) to the 5GS devices, such as the UPF, gNB and User Equipment (UE). In paralell, the TSN synchronization process provides the TSN GM temporal reference to the TSN network devices. The two synchronization processes are considered to be independent, providing flexibility in the design and implementation of the synchronization process. Both processes are detailed below, but first we describe the 5GS architecture in the integrated TSN - 5G network proposed by 3GPP.
在 TSN - 5G 集成网络中，有两个同步过程并行运行，即 5G 时间同步过程和 TSN 时间同步过程 [2, 12]，如图 1 所示。5G 同步过程将来自 5G Grandmaster（GM）的时间参考提供给 5GS 设备，例如 UPF、gNB 和用户设备（User Equipment，UE）。与此同时，TSN 同步过程将 TSN GM 的时间参考提供给 TSN 网络设备。这两个同步过程被认为是相互独立的，从而为同步过程的设计和实现提供了灵活性。下面将详细说明这两个过程，但首先我们描述 3GPP 所提出的集成 TSN - 5G 网络中的 5GS 架构。
“temporal reference”统一译为“时间参考”；“paralell”为原文拼写错误，不影响翻译；5GS、UPF、gNB、UE、GM 等缩写已保留；引用 [2, 12] 和图 1 未遗漏。未发现明显问题。
According to 3GPP TS 23.501 [ 4 ], the 5GS acts as a PTP instance in the TSN network. As shown in Figure 1, the external network consists of end stations and TSN bridges, whose time reference is provided by a PTP or gPTP GM. In the 5G domain, a 5G GM synchronizes the gNB, which distributes the time reference to the UE over the radio link and to the UPF via the PTP -compliant 5G transport network. To integrate 5G with TSN, the UPF implements a TSN Translator (TT) (Network-Side Time Sensitive Networking Translator (NW-TT)) that interfaces with the external TSN bridge, while the UE connects to another TT (Device-Side Time Sensitive Networking Translator (DS-TT)) and this connects to a TSN end station. These TT ensure interoperability, allowing the 5GS to operate as a logical bridge in various modes without direct alignment with the TSN GM.
根据 3GPP TS 23.501 [4]，5GS 在 TSN 网络中充当一个 PTP 实例。如图 1 所示，外部网络由终端站和 TSN 网桥组成，其时间参考由 PTP 或 gPTP GM 提供。在 5G 域中，5G GM 对 gNB 进行同步，而 gNB 通过无线链路将时间参考分发给 UE，并通过符合 PTP 的 5G 传输网络将时间参考分发给 UPF。为了将 5G 与 TSN 集成，UPF 实现一个 TSN Translator（TT），即网络侧时间敏感网络转换器（Network-Side Time Sensitive Networking Translator，NW-TT），它与外部 TSN 网桥连接；同时 UE 连接到另一个 TT，即设备侧时间敏感网络转换器（Device-Side Time Sensitive Networking Translator，DS-TT），而该 DS-TT 又连接到一个 TSN 终端站。这些 TT 确保互操作性，使 5GS 能够在各种模式下作为逻辑网桥运行，而不需要与 TSN GM 直接对齐。
标准号 3GPP TS 23.501、引用 [4]、图 1、PTP/gPTP/GM/TT/NW-TT/DS-TT 均已保留；“logical bridge”译为“逻辑网桥”准确；“without direct alignment with the TSN GM”可能涉及时间基准不直接对齐，译文保留该含义。未发现明显问题。
The 5G time synchronization process is based on the internal distribution of the 5G GM reference across the 5GS transport network and the 5GS Radio Access Network (RAN) [ 13 ]. A straightforward solution in the 5G transport network is to install GNSS receivers in each gNB, which offers ± 100 \pm 100 ns accuracy [ 13 ], meeting the 5GS timing requirements. However, this method comes with high deployment and maintenance costs, indoor installation difficulties and vulnerability to jamming. Alternatively, synchronization protocols over packet networks, such as IEEE 1588 [ 7 ], with adapted profiles defined by ITU-T (e.g., G.8275.1 (PTP -aware) and G.8275.2 (non- PTP -aware)).
5G 时间同步过程基于 5G GM 参考在 5GS 传输网络和 5GS 无线接入网（Radio Access Network，RAN）中的内部分发 [13]。在 5G 传输网络中，一个直接的解决方案是在每个 gNB 中安装 GNSS 接收机，这可提供 ±100 ns 的精度 [13]，满足 5GS 定时要求。然而，该方法带来较高的部署和维护成本、室内安装困难以及易受干扰的脆弱性。作为替代方案，可以使用分组网络上的同步协议，例如 IEEE 1588 [7]，并采用 ITU-T 定义的适配配置文件，例如 G.8275.1（PTP-aware，感知 PTP）和 G.8275.2（non-PTP-aware，非感知 PTP）。
原文中“± 100 \pm 100 ns”疑似 PDF/LaTeX 抽取重复，译文按指标含义处理为“±100 ns”；最后一句原文语法不完整，译文根据上下文补足为“可以使用……协议”；GNSS、gNB、IEEE 1588、ITU-T、G.8275.1/G.8275.2 均已保留。由于原文公式/符号存在抽取异常且句子残缺，需人工复核。
In the 5G RAN, synchronization between the 5G GM and the UE is achieved through the gNB, as defined in TS 38.331. The gNB continuously updates the 5G GM reference [ 2, 13, 14 ] and periodically transmits it to the UE via System Information Block (SIB) or unicast Radio Resource Control (RRC) messages, identified via a System Frame Number (SFN). The SIB 9 message, which contains the time information in GPS and UTC formats, is transmitted at the boundary between two SFN, enabling synchronization of the devices. In addition, the 5G reference must be adjusted according to the cell size to compensate for DL propagation delay and minimize reception uncertainty. Accurate delay calculation and obtaining the SIB 9 reference are essential aspects, although they are not addressed in this study. For more information, see [ 14, 13 ].
在 5G RAN 中，5G GM 与 UE 之间的同步通过 gNB 实现，如 TS 38.331 中所定义。gNB 持续更新 5G GM 参考 [2, 13, 14]，并通过系统信息块（System Information Block，SIB）或单播无线资源控制（Radio Resource Control，RRC）消息将其周期性地发送给 UE，该参考通过系统帧号（System Frame Number，SFN）进行标识。SIB 9 消息包含 GPS 和 UTC 格式的时间信息，并在两个 SFN 之间的边界处发送，从而实现设备同步。此外，必须根据小区大小调整 5G 参考，以补偿下行链路（DL）传播时延并最小化接收不确定性。准确的时延计算以及获得 SIB 9 参考是关键方面，尽管它们并未在本研究中处理。更多信息见 [14, 13]。
TS 38.331、SIB、RRC、SFN、SIB 9、GPS、UTC、DL 等术语和缩写已保留；“boundary between two SFN”译为“两个 SFN 之间的边界”可能需结合标准语境理解，但未改变原意；引用顺序 [14, 13] 保留。未发现明显问题。
TS 23.501 [ 4 ] defines several modes in which the 5GS can be configured to operate as one PTP instance [ 2 ], enabling TSN time synchronization in an integrated TSN - 5G network. Specifically, these clock modes are:
TS 23.501 [4] 定义了若干模式，在这些模式中，5GS 可以被配置为作为一个 PTP 实例运行 [2]，从而在集成 TSN - 5G 网络中实现 TSN 时间同步。具体而言，这些时钟模式为：
标准号 TS 23.501、引用 [4] 和 [2]、5GS、PTP、TSN - 5G 均已保留；“clock modes”译为“时钟模式”准确；该段引出后续列表，逻辑完整。未发现明显问题。
• 5GS as a Time-Aware System: The 5GS behaves as an IEEE 802.1AS-compliant node [ 5 ], participating in time synchronization using the gPTP protocol. NW-TT and DS-TT synchronize with both GM clocks (TSN GM and 5G GM), thus requiring two clocks, and manage gPTP messages (transmitted in Layer 2 (L2)) to ensure synchronization [ 2 ]. • 5GS as BC: The 5GS is configured as a BC according to the IEEE 1588 standard [ 7 ], actively participating in synchronization. That is, the 5GS maintains the PTP domain timescale and synchronizes the connected PTP time receivers (e.g., DS-TT, TSN Slave, etc.), acting as the time source. This mode provides higher accuracy and robustness, allowing network scalability and lower impact of jitter and propagation delay in multi-device scenarios, but is more complex. • 5GS as TC: The 5GS behaves as a TC according to the IEEE 1588 standard [ 7 ], without actively participating in time synchronization, but measures the residence time of PTP messages within the network and uses it to correct them before forwarding them. The TT manage the PTP messages and calculate the delay within the 5GS. There are two types of TC: Peer-to-Peer (P2P) or E2E. In P2P TC [ 15 ] the 5GS measures the delay between two directly connected neighboring node using Peer Delay Messages and calculates the residence time of the PTP messages within the 5G network. The sum of the residence time and the link delay along the path is reported to the PTP time receiver [ 6 ]. The E2E TC calculates the total E2E delay between the PTP transmitter and receiver by exchanging PTP messages. In the 5GS the residence time is calculated and the sum of the residence time over the entire path is added in the correction field of the PTP messages. This sum of residence times is relayed to the PTP time receiver. This way, the PTP receiver can calculate the total compensation based on the sum of residence times in the correction field of the messages. Therefore, P2P TC compensates for the latency between neighboring nodes while E2E TC compensates for the latency of the entire E2E path. P2P TC requires IEEE 1588 compatibility on all network devices, E2E TC does not.
• 5GS 作为 Time-Aware System：5GS 表现为一个符合 IEEE 802.1AS 的节点 [5]，使用 gPTP 协议参与时间同步。NW-TT 和 DS-TT 与两个 GM 时钟（TSN GM 和 5G GM）同步，因此需要两个时钟，并管理 gPTP 消息（在第 2 层（Layer 2，L2）中传输）以确保同步 [2]。• 5GS 作为 BC：5GS 按照 IEEE 1588 标准 [7] 被配置为 BC，主动参与同步。也就是说，5GS 维护 PTP 域时间尺度，并同步已连接的 PTP 时间接收器（例如 DS-TT、TSN Slave 等），充当时间源。该模式提供更高的精度和鲁棒性，支持网络可扩展性，并在多设备场景中降低抖动和传播时延的影响，但更为复杂。• 5GS 作为 TC：5GS 按照 IEEE 1588 标准 [7] 表现为 TC，并不主动参与时间同步，而是测量 PTP 消息在网络内的驻留时间，并在转发这些消息之前使用该驻留时间对其进行校正。TT 管理 PTP 消息并计算 5GS 内部的时延。TC 有两种类型：点到点（Peer-to-Peer，P2P）或端到端（E2E）。在 P2P TC [15] 中，5GS 使用 Peer Delay Messages 测量两个直接连接的相邻节点之间的时延，并计算 PTP 消息在 5G 网络内的驻留时间。沿路径的驻留时间与链路时延之和被报告给 PTP 时间接收器 [6]。E2E TC 通过交换 PTP 消息来计算 PTP 发送器与接收器之间的总 E2E 时延。在 5GS 中，会计算驻留时间，并将整个路径上的驻留时间之和加入到 PTP 消息的 correction field 中。该驻留时间之和被中继给 PTP 时间接收器。这样，PTP 接收器可以基于消息 correction field 中的驻留时间之和计算总补偿。因此，P2P TC 补偿相邻节点之间的时延，而 E2E TC 补偿整个 E2E 路径的时延。P2P TC 要求所有网络设备都兼容 IEEE 1588，而 E2E TC 不要求。
该段包含三个列表项且后续 P018-P020 又分别重复前三个列表项，可能是段落抽取重复或列表解析问题；BC、TC、P2P、E2E、correction field、Peer Delay Messages 等关键术语已保留；“neighboring node”原文单复数不一致，译文按“相邻节点”处理；逻辑上 P2P 与 E2E 的补偿范围区别已保留。由于该段与后续段落存在明显重复和列表上下文抽取风险，需人工复核。
5GS as a Time-Aware System: The 5GS behaves as an IEEE 802.1AS-compliant node [ 5 ], participating in time synchronization using the gPTP protocol. NW-TT and DS-TT synchronize with both GM clocks (TSN GM and 5G GM), thus requiring two clocks, and manage gPTP messages (transmitted in Layer 2 (L2)) to ensure synchronization [ 2 ].
5GS 作为 Time-Aware System：5GS 表现为一个符合 IEEE 802.1AS 的节点 [5]，使用 gPTP 协议参与时间同步。NW-TT 和 DS-TT 与两个 GM 时钟（TSN GM 和 5G GM）同步，因此需要两个时钟，并管理 gPTP 消息（在第 2 层（Layer 2，L2）中传输）以确保同步 [2]。
术语 Time-Aware System、IEEE 802.1AS、gPTP、NW-TT、DS-TT、GM、L2 均已保留；内容与 P017 中第一项重复，可能是输入抽取导致，但本段按要求独立翻译。未发现明显问题。
5GS as BC: The 5GS is configured as a BC according to the IEEE 1588 standard [ 7 ], actively participating in synchronization. That is, the 5GS maintains the PTP domain timescale and synchronizes the connected PTP time receivers (e.g., DS-TT, TSN Slave, etc.), acting as the time source. This mode provides higher accuracy and robustness, allowing network scalability and lower impact of jitter and propagation delay in multi-device scenarios, but is more complex.
5GS 作为 BC：5GS 按照 IEEE 1588 标准 [7] 被配置为 BC，主动参与同步。也就是说，5GS 维护 PTP 域时间尺度，并同步已连接的 PTP 时间接收器（例如 DS-TT、TSN Slave 等），充当时间源。该模式提供更高的精度和鲁棒性，支持网络可扩展性，并在多设备场景中降低抖动和传播时延的影响，但更为复杂。
BC、IEEE 1588、PTP domain timescale、PTP time receivers、DS-TT、TSN Slave 等术语已保留；“allowing network scalability”译为“支持网络可扩展性”合理；内容与 P017 第二项重复，属输入层面现象。未发现明显问题。
5GS as TC: The 5GS behaves as a TC according to the IEEE 1588 standard [ 7 ], without actively participating in time synchronization, but measures the residence time of PTP messages within the network and uses it to correct them before forwarding them. The TT manage the PTP messages and calculate the delay within the 5GS.
5GS 作为 TC：5GS 按照 IEEE 1588 标准 [7] 表现为 TC，并不主动参与时间同步，而是测量 PTP 消息在网络内的驻留时间，并在转发这些消息之前使用该驻留时间对其进行校正。TT 管理 PTP 消息并计算 5GS 内部的时延。
TC、IEEE 1588、PTP、TT、5GS 等术语已保留；“residence time”译为“驻留时间”符合 PTP/透明时钟语境；内容与 P017 第三项开头重复，属输入层面现象。未发现明显问题。
There are two types of TC: Peer-to-Peer (P2P) or E2E. In P2P TC [ 15 ] the 5GS measures the delay between two directly connected neighboring node using Peer Delay Messages and calculates the residence time of the PTP messages within the 5G network. The sum of the residence time and the link delay along the path is reported to the PTP time receiver [ 6 ]. The E2E TC calculates the total E2E delay between the PTP transmitter and receiver by exchanging PTP messages. In the 5GS the residence time is calculated and the sum of the residence time over the entire path is added in the correction field of the PTP messages. This sum of residence times is relayed to the PTP time receiver. This way, the PTP receiver can calculate the total compensation based on the sum of residence times in the correction field of the messages.
TC 有两种类型：Peer-to-Peer（P2P，对等）或 E2E（端到端）。在 P2P TC [15] 中，5GS 使用 Peer Delay Messages 测量两个直接连接的相邻节点之间的时延，并计算 PTP 消息在 5G 网络内的驻留时间。沿路径的驻留时间与链路时延之和会被报告给 PTP 时间接收器 [6]。E2E TC 通过交换 PTP 消息来计算 PTP 发送器与接收器之间的总 E2E 时延。在 5GS 中，会计算驻留时间，并将整条路径上的驻留时间总和加入 PTP 消息的 correction field 中。该驻留时间总和会被转发给 PTP 时间接收器。通过这种方式，PTP 接收器可以基于消息 correction field 中的驻留时间总和来计算总补偿量。
术语 P2P TC、E2E TC、5GS、PTP、Peer Delay Messages、correction field 均已保留；数字引用 [15]、[6] 未遗漏；“residence time and link delay along the path”译为“沿路径的驻留时间与链路时延之和”，逻辑一致。未发现明显问题。
Therefore, P2P TC compensates for the latency between neighboring nodes while E2E TC compensates for the latency of the entire E2E path. P2P TC requires IEEE 1588 compatibility on all network devices, E2E TC does not.
因此，P2P TC 补偿相邻节点之间的延迟，而 E2E TC 补偿整个 E2E 路径的延迟。P2P TC 要求所有网络设备都兼容 IEEE 1588，E2E TC 则不要求。
对比关系“while”已体现；IEEE 1588 标准编号保留；“latency”统一译为“延迟”，与上一段“时延”含义一致。未发现明显问题。
In this paper, we opt for the E2E TC mode in 5GS, as it allows transmission of multiple working clock domains from different GM s, a key requirement in industrial environments. The IEEE 802.1AS standard, requiring L2 transmission, has limitations for integration into commercial equipment. However, it has been demonstrated that an IEEE 802.1AS network can operate as distributed clock (BC, ordinary or TC) according to IEEE 1588 [ 15 ], facilitating the transport of multiple clock signals between domains. Moreover, the TC by operating independently, without the need to synchronize its own clocks simplifies the integration of 5GS into existing TSN networks or enables the incorporation of new 5G operators, thus ensuring greater flexibility in the deployment of TSN - 5G network.
在本文中，我们选择 5GS 中的 E2E TC 模式，因为它允许传输来自不同 GM 的多个工作时钟域，这是工业环境中的一项关键要求。要求 L2 传输的 IEEE 802.1AS 标准在集成到商用设备中时存在限制。然而，已有研究表明，IEEE 802.1AS 网络可以按照 IEEE 1588 [15] 作为分布式时钟（BC、ordinary 或 TC）运行，从而促进多个时钟信号在域之间的传输。此外，由于 TC 独立运行，不需要同步其自身时钟，因此简化了 5GS 集成到现有 TSN 网络中的过程，或者支持纳入新的 5G 运营商，从而确保 TSN-5G 网络部署具有更大的灵活性。
GM、L2、IEEE 802.1AS、IEEE 1588、BC、TC 等缩写已保留；“ordinary”原文可能指 ordinary clock，但原文只写 ordinary，保留以避免擅自补全；“GM s”疑似 OCR 空格问题，按 GMs 理解为多个 GM。未发现明显问题。
We consider the TSN - 5G system model as illustrated in Figure 2. The TSN system includes a TSN Master, synchronized with the TSN GM, which distributes the time reference to other TSN bridges and/or TSN end station. This synchronization is extended to a TSN Slave in another TSN domain, interconnected through the 5G network. This TSN Slave, once synchronized, distributes the synchronization to other TSN bridges or TSN end stations. The 5GS incorporates a 5G GM, which directly provides the time reference to the gNB and NW-TT, both connected through the UPF. Since commercial equipment does not integrate a UPF with NW-TT, the NW-TT is synchronized with the 5G GM and connected directly to the TSN Master. While the DS-TT, also synchronized to the 5G GM via the UE, connects to the TSN Slave. This differs from the model in Figure 1, as in this case the NW-TT and UPF are separate devices, and both the NW-TT and DS-TT are directly connected to the TSN Master and TSN Slave, respectively.
我们考虑如图 2 所示的 TSN-5G 系统模型。TSN 系统包括一个 TSN Master，它与 TSN GM 同步，并将时间参考分发给其他 TSN bridge 和/或 TSN end station。该同步被扩展到另一个 TSN 域中的 TSN Slave，该 TSN 域通过 5G 网络互连。该 TSN Slave 一旦完成同步，就会将同步分发给其他 TSN bridge 或 TSN end station。5GS 包含一个 5G GM，它直接向 gNB 和 NW-TT 提供时间参考，二者通过 UPF 连接。由于商用设备未集成带有 NW-TT 的 UPF，因此 NW-TT 与 5G GM 同步，并直接连接到 TSN Master。而 DS-TT 也通过 UE 同步到 5G GM，并连接到 TSN Slave。这与图 1 中的模型不同，因为在本情形中，NW-TT 和 UPF 是分离的设备，并且 NW-TT 与 DS-TT 分别直接连接到 TSN Master 和 TSN Slave。
TSN Master、TSN Slave、TSN GM、5G GM、gNB、NW-TT、UPF、DS-TT、UE 等关键实体均保留；图 2、图 1 对照关系未遗漏；“both connected through the UPF”按“二者通过 UPF 连接”翻译，但结合后文“NW-TT and UPF are separate devices”设备拓扑可能需结合图示确认。未发现明显问题。
Time synchronization in the TSN - 5G network is based on IEEE 1588 compliant PTP frame transmission [ 7 ]. In this paper, we use the E2E TC clock mechanism for time synchronization. We define ℱ \mathcal{F} as the set of PTP flows traversing the TSN - 5G network. Each PTP flow f i ∀ i ∈ ℱ f_{i}\ \forall\ i\in\mathcal{F} represent a bidirectional communication between a PTP transmitter node, synchronized with a GM and a PTP receiver node, not synchronized with the GM. We refer as a PTP transmitter node to the TSN Master and as a PTP receiver node to the TSN Slave. These PTP flows ensure that the PTP transmitter and the PTP receiver maintain the same time reference as the GM. Therefore, each flow f i ∀ i ∈ ℱ f_{i}\ \forall\ i\in\mathcal{F} is transmitted from the TSN Master to the TSN Slaves, traversing the 5G network. In our case, we focus on a single PTP flow f i f_{i} to evaluate synchronization. This f i f_{i} transmits a series of p ℰ f i p^{f_{i}}_{\mathcal{E}} PTP packets between the TSN Master and the Slave using the E2E TC mechanism detailed in Section IV. For clarity, henceforth, the superindex f i f_{i} will be omitted, meaning p ℰ f i = p ℰ p^{f_{i}}_{\mathcal{E}}=p_{\mathcal{E}} in all variables, since only a single PTP flow is considered.
TSN-5G 网络中的时间同步基于符合 IEEE 1588 的 PTP 帧传输 [7]。在本文中，我们使用 E2E TC 时钟机制进行时间同步。我们将 ℱ（\mathcal{F}）定义为穿越 TSN-5G 网络的 PTP 流集合。每个 PTP 流 \(f_i\)，其中 \(\forall i \in \mathcal{F}\)，表示在一个与 GM 同步的 PTP 发送节点和一个未与 GM 同步的 PTP 接收节点之间进行的双向通信。我们将 TSN Master 称为 PTP 发送节点，将 TSN Slave 称为 PTP 接收节点。这些 PTP 流确保 PTP 发送器和 PTP 接收器保持与 GM 相同的时间参考。因此，每个流 \(f_i\)，其中 \(\forall i \in \mathcal{F}\)，都从 TSN Master 传输到 TSN Slave，并穿越 5G 网络。在我们的情形中，我们聚焦于单个 PTP 流 \(f_i\) 来评估同步。该 \(f_i\) 使用第 IV 节详述的 E2E TC 机制，在 TSN Master 与 Slave 之间传输一系列 \(p^{f_i}_{\mathcal{E}}\) 个 PTP 分组。为清晰起见，下文将省略上标 \(f_i\)，即在所有变量中 \(p^{f_i}_{\mathcal{E}} = p_{\mathcal{E}}\)，因为只考虑单个 PTP 流。
公式符号 \(\mathcal{F}\)、\(f_i\)、\(\forall i \in \mathcal{F}\)、\(p^{f_i}_{\mathcal{E}}\)、\(p_{\mathcal{E}}\) 已保留；“represent”原文主谓数不一致，按语义译为“表示”；“PTP packets”译为“PTP 分组”。未发现明显问题。
In this scenario, as previously explained, two synchronization processes coexist [ 12 ]: TSN synchronization and 5G synchronization. We consider that each device within the TSN - 5G network has a single clock. The clocks of the TSN Master and Slave are synchronized with the TSN GM reference, while the TT are solely synchronized with the 5G GM. In 5G synchronization, the 5G GM reference is transmitted through the gNB to the UE and the UE transmits it to the DS-TT. In this paper, we do not focus on the 5G clock recovery by the UE and its subsequent transmission to the DS-TT, therefore, we assume perfect recovery from SIB 9 for synchronization at the UE and subsequently at the DS-TT.
在该场景中，如前所述，两个同步过程共存 [12]：TSN 同步和 5G 同步。我们认为 TSN-5G 网络中的每个设备都有一个单一时钟。TSN Master 和 Slave 的时钟与 TSN GM 参考同步，而 TT 仅与 5G GM 同步。在 5G 同步中，5G GM 参考通过 gNB 传输到 UE，UE 再将其传输到 DS-TT。在本文中，我们不关注 UE 对 5G 时钟的恢复以及随后将其传输到 DS-TT 的过程，因此，我们假设 UE 以及随后 DS-TT 处用于同步的 SIB 9 恢复是完美的。
TSN 同步与 5G 同步的并行关系保留；TT、5G GM、gNB、UE、DS-TT、SIB 9 均保留；“perfect recovery from SIB 9”译为“从 SIB 9 完美恢复”，含义可能依赖 5G 系统信息块上下文，但无公式残缺。未发现明显问题。
In TSN synchronization, the p ℰ p_{\mathcal{E}} include a timestamp. Specifically, each p e e ∈ ℰ p_{e}\ e\in\mathcal{E} contains a timestamp that records the moment the TSN Master sends the packet e e. However, due to delays caused by software and hardware packet processing in the TSN Master, the timestamp in p e p_{e} may lack precision. Then, the transmission timestamp of p e p_{e} is included in p e + 1 p_{e+1}, recording the precise moment (t 1 t_{1}) when p e p_{e} exits the TSN Master. When the TSN Slave receives p e p_{e}, it records the timestamp (t 2 t_{2}).
在 TSN 同步中，\(p_{\mathcal{E}}\) 包含时间戳。具体而言，每个 \(p_e\)，其中 \(e \in \mathcal{E}\)，都包含一个时间戳，用于记录 TSN Master 发送分组 \(e\) 的时刻。然而，由于 TSN Master 中的软件和硬件分组处理所造成的延迟，\(p_e\) 中的时间戳可能缺乏精度。随后，\(p_e\) 的发送时间戳会被包含在 \(p_{e+1}\) 中，记录 \(p_e\) 离开 TSN Master 的精确时刻（\(t_1\)）。当 TSN Slave 接收到 \(p_e\) 时，它记录时间戳（\(t_2\)）。
\(p_{\mathcal{E}}\)、\(p_e\)、\(e \in \mathcal{E}\)、\(p_{e+1}\)、\(t_1\)、\(t_2\) 已保留；“packet e”译为“分组 e”；逻辑上体现了后续消息携带前一分组精确发送时间戳。未发现明显问题。
In addition, p ℰ p_{\mathcal{E}} packets when traversing the 5G network experience variable delays (jitter), compromising the timing accuracy and affecting the correct operation of the TSN nodes. This present a challenge to accurately estimate the time reference. To address this issue, the delay experienced by the p ℰ p_{\mathcal{E}} while traversing the 5G network is calculated. This delay is referred to as the residence time in the 5G network (d r e s d_{res}). Its calculation involves generating timestamps for certain p e p_{e} packet at the TT. The NW-TT generates an ingress timestamp (t i n t_{in}) based on the 5GS reference time, while the DS-TT generates an egress timestamp (t e g t_{eg}) also based on the 5GS reference time. The residence time (d r e s d_{res}) is defined as: d r e s = t e g − t i n d_{res}=t_{eg}-t_{in} (1) Since the 5G network is asymmetric in its links, meaning the UL and DL delays differ depending on the radio channel’s characteristics, a specific residence time is defined for each link. The residence time for the UL is denoted as d r e s, u p d_{res,up}, and for the DL as d r e s, d o w n d_{res,down}.
此外，\(p_{\mathcal{E}}\) 分组在穿越 5G 网络时会经历可变延迟（jitter，抖动），这会损害定时精度并影响 TSN 节点的正确运行。这给准确估计时间参考带来了挑战。为解决这一问题，需要计算 \(p_{\mathcal{E}}\) 在穿越 5G 网络时经历的延迟。该延迟被称为在 5G 网络中的驻留时间（\(d_{res}\)）。其计算涉及在 TT 处为某些 \(p_e\) 分组生成时间戳。NW-TT 基于 5GS 参考时间生成 ingress timestamp（\(t_{in}\)，入口时间戳），而 DS-TT 同样基于 5GS 参考时间生成 egress timestamp（\(t_{eg}\)，出口时间戳）。驻留时间（\(d_{res}\)）定义为：\(d_{res}=t_{eg}-t_{in}\)（1）。由于 5G 网络在链路上是不对称的，即 UL 和 DL 延迟会随无线信道特性而不同，因此为每条链路定义特定的驻留时间。UL 的驻留时间表示为 \(d_{res,up}\)，DL 的驻留时间表示为 \(d_{res,down}\)。
jitter、TT、NW-TT、DS-TT、5GS、UL、DL 等术语保留并补充中文；公式 \(d_{res}=t_{eg}-t_{in}\) 与编号（1）保留；“This present”原文语法错误，按“This presents”语义翻译；“for certain \(p_e\) packet”单复数不一致，按“某些分组”处理。未发现明显问题。
Each TSN node incorporates an internal oscillator that may introduce noise to the device’s internal clock due to physical disturbances, causing clock skew. To mitigate this clock drift, PTP messages are generated with cycle T T.
每个 TSN 节点都包含一个内部振荡器，该振荡器可能因物理扰动而向设备内部时钟引入噪声，从而导致时钟偏斜。为减轻这种时钟漂移，PTP 消息以周期 \(T\) 生成。
“internal oscillator”“clock skew”“clock drift”分别译为“内部振荡器”“时钟偏斜”“时钟漂移”；原文末尾为“cycle T T”，疑似 OCR 重复或公式识别问题，译为周期 \(T\)，需核对原 PDF 是否为 \(T\) 或其他符号。
We focus on the distribution of time synchronization in an integrated TSN - 5G network, implementing E2E TC mode in the 5GS. With this approach, 5G devices do not need to synchronize with the TSN GM time reference, as the 5G common time reference is used to accurately calculate the residence times (d r e s, u p d_{res,up}, d r e s, d o w n d_{res,down}) of p ℰ p_{\mathcal{E}} traversing the network. As explained in Section III, it is essential that the NW-TT and DS-TT share the same time reference derived from the 5G GM. This allows that the TC mechanism to operate in a manner equivalent to a standalone switch, ensuring consistency in the calculation of residence times from the timestamps generated on devices located at opposite ends of 5GS. Any failure to propagate a common time reference could lead to inconsistencies or invalid synchronization results between TSN systems at the edges. The following section details the PTP messages exchanged and the procedure to be followed to calculate the offset and residence time.
我们聚焦于在集成 TSN-5G 网络中分发时间同步，并在 5GS 中实现 E2E TC 模式。采用这种方法时，5G 设备不需要与 TSN GM 时间参考同步，因为 5G 公共时间参考被用于准确计算穿越网络的 \(p_{\mathcal{E}}\) 的驻留时间（\(d_{res,up}\)、\(d_{res,down}\)）。如第 III 节所述，NW-TT 和 DS-TT 必须共享由 5G GM 派生出的同一时间参考。这使得 TC 机制能够以等同于独立交换机的方式运行，确保根据位于 5GS 两端设备上生成的时间戳来计算驻留时间时具有一致性。任何未能传播公共时间参考的情况，都可能导致边缘 TSN 系统之间出现不一致或无效的同步结果。下一节将详细说明所交换的 PTP 消息，以及计算 offset 和驻留时间所需遵循的过程。
E2E TC、5GS、TSN GM、5G GM、NW-TT、DS-TT、PTP、offset 等术语保留；\(d_{res,up}\)、\(d_{res,down}\)、\(p_{\mathcal{E}}\) 保留；“allows that the TC mechanism”原文语法不顺，按“使得 TC 机制能够”处理；逻辑关系与第 III 节衔接完整。未发现明显问题。
The E2E TC solution implemented in the 5GS exchanges PTP messages between the nodes of the distributed architecture, as illustrated in Figure 3. The TSN Master initiates synchronization by transmitting “Announce” messages, followed by “Sync” and “Follow-Up”. The TSN Slave then sends “Delay Request” and receives a “Delay Response” in reply. This exchange enables the measurement of the residence time on the 5GS, through the time stamping and delay estimation capabilities of the NW-TT and DS-TT, and the recovery of the TSN clock domain at the TSN Slave. Both functionalities are key to the operation of the TC and to perform TC on commercial switches, we have implemented both functionalities in these devices. Each functionality is detailed below:
在 5GS 中实现的 E2E TC 解决方案在分布式架构的节点之间交换 PTP 消息，如图 3 所示。TSN Master 通过发送“Announce”消息来发起同步，随后发送“Sync”和“Follow-Up”。然后，TSN Slave 发送“Delay Request”，并接收作为回复的“Delay Response”。这一交换使得能够通过 NW-TT 和 DS-TT 的时间戳标记与时延估计能力，测量 5GS 上的驻留时间，并在 TSN Slave 处恢复 TSN 时钟域。这两项功能对于 TC 的运行都是关键的；为了在商用交换机上执行 TC，我们已在这些设备中实现了这两项功能。下面详细说明每项功能：
术语 E2E TC、5GS、PTP、TSN Master、TSN Slave、NW-TT、DS-TT、TSN 时钟域均已保留；消息名按原文保留。逻辑上“交换消息→测量驻留时间→恢复时钟域→实现于商用交换机”完整。未发现明显问题。
1 Calculation of the 5GS residence time: NW-TT and DS-TT assign timestamps to the “Sync” packets at the ingress (t 1 ′ t_{1^{\prime}}) and egress (t 2 ′ t_{2^{\prime}}) of the 5GS, respectively. These timestamps determine the DL residence time (d r e s, d o w n d_{res,down}), as detailed in equation (2). The value of d r e s, d o w n d_{res,down} is temporarily stored in DS-TT until the arrival of the “Follow-Up” packet, where DS-TT updates the Correction Field (CF) with the value of d r e s, d o w n d_{res,down}. This procedure allows the TSN Slave to compensate for the delay introduced by the “Sync” packets within the 5GS for its estimates of the total link delay. An analogous process is applied for the “Delay Request” and “Delay Reply” packets, allowing the UL residence time (d r e s, u p d_{res,up}) estimation using the timestamps of “Delay Request” and the CF update in “Delay Reply”, as shown in Figure 3. The UL and DL residence time are calculated as: d r e s, d o w n = t 2 ′ − t 1 ′ d r e s, u p = t 4 ′ − t 3 ′ \begin{split}d_{res,down}=t_{2^{\prime}}-t_{1^{\prime}}\\ d_{res,up}=t_{4^{\prime}}-t_{3^{\prime}}\end{split} (2) 2 Clock recovery at the TSN Slave: several operations are necessary [ 7 ]. First, we decouple the delay of the PTP packets sent from the TSN Master to the TSN Slave from the variable residence time of the 5GS. That is, due to the residence time calculation, the 5GS introduces variable jitter in the UL and DL, generating different delays for PTP packets. We call D e, d o w n D_{e,down} the DL delay of the “Sync” packet, while D e, u p D_{e,up} is the UL delay of the “Delay Request” packet. The sum of both delays determines the p ℰ p_{\mathcal{E}} transmission delay (D ℰ D_{\mathcal{E}}). D e, d o w n D_{e,down}, D e, u p D_{e,up} and D ℰ D_{\mathcal{E}} are calculated as: D e, d o w n = t 2 − t 2 ′ + t 1 ′ − t 1 = t 2 − t 1 − d r e s, d o w n \displaystyle D_{e,down}=t_{2}-t_{2^{\prime}}+t_{1^{\prime}}-t_{1}=t_{2}-t_{1}-d_{res,down} (3) D e, u p = t 4 − t 4 ′ + t 3 ′ − t 3 = t 4 − t 3 − d r e s, u p \displaystyle D_{e,up}=t_{4}-t_{4^{\prime}}+t_{3^{\prime}}-t_{3}=t_{4}-t_{3}-d_{res,up} (4) D ℰ = D e, d o w n + D e, u p \displaystyle D_{\mathcal{E}}=D_{e,down}+D_{e,up} (5) d r e s, d o w n d_{res,down} and d r e s, u p d_{res,up} mitigate the associated problem of having different latencies in UL and DL. The TSN Slave requires a response time (d r e s p o n s e d_{response}) after receiving the “Sync” before generating the “Delay Request”, as shown in Figure 3. This d r e s p o n s e d_{response} is calculated as: d r e s p o n s e = t 3 − t 2 \begin{split}d_{response}=t_{3}-t_{2}\end{split} (6) The TSN Slave calculates the time offset (β \beta) with respect to the TSN Master from all timestamps, the residence time and the response time, as follows: β = (t 2 − t 1) − D ℰ 2 − d r e s, d o w n \begin{split}\beta=(t_{2}-t_{1})-\frac{D_{\mathcal{E}}}{2}-d_{res,down}\end{split} (7)
1 5GS 驻留时间的计算：NW-TT 和 DS-TT 分别在 5GS 的入口（\(t_{1'}\)）和出口（\(t_{2'}\)）处为“Sync”数据包分配时间戳。这些时间戳确定 DL 驻留时间（\(d_{res,down}\)），如公式（2）所详述。\(d_{res,down}\) 的值被临时存储在 DS-TT 中，直到“Follow-Up”数据包到达；在该数据包中，DS-TT 使用 \(d_{res,down}\) 的值更新 Correction Field（CF）。该过程使 TSN Slave 能够在其总链路时延估计中，补偿“Sync”数据包在 5GS 内引入的时延。对于“Delay Request”和“Delay Reply”数据包，也应用类似过程，从而能够利用“Delay Request”的时间戳以及“Delay Reply”中的 CF 更新来估计 UL 驻留时间（\(d_{res,up}\)），如图 3 所示。UL 和 DL 驻留时间计算如下： \[ \begin{split} d_{res,down}=t_{2'}-t_{1'}\\ d_{res,up}=t_{4'}-t_{3'} \end{split} \tag{2} \] 2 TSN Slave 处的时钟恢复：需要若干操作 [7]。首先，我们将从 TSN Master 发送到 TSN Slave 的 PTP 数据包时延与 5GS 的可变驻留时间解耦。也就是说，由于驻留时间计算，5GS 在 UL 和 DL 中引入可变抖动，从而为 PTP 数据包产生不同的时延。我们将“Sync”数据包的 DL 时延称为 \(D_{e,down}\)，而 \(D_{e,up}\) 是“Delay Request”数据包的 UL 时延。这两个时延之和确定 \(p_{\mathcal{E}}\) 传输时延（\(D_{\mathcal{E}}\)）。\(D_{e,down}\)、\(D_{e,up}\) 和 \(D_{\mathcal{E}}\) 计算如下： \[ D_{e,down}=t_2-t_{2'}+t_{1'}-t_1=t_2-t_1-d_{res,down} \tag{3} \] \[ D_{e,up}=t_4-t_{4'}+t_{3'}-t_3=t_4-t_3-d_{res,up} \tag{4} \] \[ D_{\mathcal{E}}=D_{e,down}+D_{e,up} \tag{5} \] \(d_{res,down}\) 和 \(d_{res,up}\) 缓解了 UL 和 DL 中具有不同时延这一相关问题。如图 3 所示，TSN Slave 在接收“Sync”之后、生成“Delay Request”之前，需要一个响应时间（\(d_{response}\)）。该 \(d_{response}\) 计算如下： \[ d_{response}=t_3-t_2 \tag{6} \] TSN Slave 根据所有时间戳、驻留时间和响应时间，计算其相对于 TSN Master 的时间偏移（\(\beta\)），如下： \[ \beta=(t_2-t_1)-\frac{D_{\mathcal{E}}}{2}-d_{res,down} \tag{7} \]
输入段落 P032 似乎合并了后续 P033-P035 的内容，包含编号 1、编号 2 以及公式（2）至（7），存在段落切分重复风险。公式符号中 \(t_{1'}\)、\(t_{2'}\)、\(t_{3'}\)、\(t_{4'}\) 按可读数学形式整理；原文有 “p ℰ \(p_{\mathcal{E}}\) transmission delay” 识别较异常，已保留为 \(p_{\mathcal{E}}\) 传输时延，但需结合论文原版确认是否 OCR 错误。状态需人工复核。
Calculation of the 5GS residence time: NW-TT and DS-TT assign timestamps to the “Sync” packets at the ingress (t 1 ′ t_{1^{\prime}}) and egress (t 2 ′ t_{2^{\prime}}) of the 5GS, respectively. These timestamps determine the DL residence time (d r e s, d o w n d_{res,down}), as detailed in equation (2). The value of d r e s, d o w n d_{res,down} is temporarily stored in DS-TT until the arrival of the “Follow-Up” packet, where DS-TT updates the Correction Field (CF) with the value of d r e s, d o w n d_{res,down}. This procedure allows the TSN Slave to compensate for the delay introduced by the “Sync” packets within the 5GS for its estimates of the total link delay. An analogous process is applied for the “Delay Request” and “Delay Reply” packets, allowing the UL residence time (d r e s, u p d_{res,up}) estimation using the timestamps of “Delay Request” and the CF update in “Delay Reply”, as shown in Figure 3. The UL and DL residence time are calculated as: d r e s, d o w n = t 2 ′ − t 1 ′ d r e s, u p = t 4 ′ − t 3 ′ \begin{split}d_{res,down}=t_{2^{\prime}}-t_{1^{\prime}}\\ d_{res,up}=t_{4^{\prime}}-t_{3^{\prime}}\end{split} (2)
5GS 驻留时间的计算：NW-TT 和 DS-TT 分别在 5GS 的入口（\(t_{1'}\)）和出口（\(t_{2'}\)）处为“Sync”数据包分配时间戳。这些时间戳确定 DL 驻留时间（\(d_{res,down}\)），如公式（2）所详述。\(d_{res,down}\) 的值被临时存储在 DS-TT 中，直到“Follow-Up”数据包到达；在该数据包中，DS-TT 使用 \(d_{res,down}\) 的值更新 Correction Field（CF）。该过程使 TSN Slave 能够在其总链路时延估计中，补偿“Sync”数据包在 5GS 内引入的时延。对于“Delay Request”和“Delay Reply”数据包，也应用类似过程，从而能够利用“Delay Request”的时间戳以及“Delay Reply”中的 CF 更新来估计 UL 驻留时间（\(d_{res,up}\)），如图 3 所示。UL 和 DL 驻留时间计算如下： \[ \begin{split} d_{res,down}=t_{2'}-t_{1'}\\ d_{res,up}=t_{4'}-t_{3'} \end{split} \tag{2} \]
术语和消息名称已保留；DL/UL 驻留时间、CF 更新、DS-TT 临时存储的因果链完整。该段与 P032 的前半部分重复，可能是输入切分或抽取重复导致；公式中的撇号下标已按数学排版归一。状态需人工复核。
Clock recovery at the TSN Slave: several operations are necessary [ 7 ]. First, we decouple the delay of the PTP packets sent from the TSN Master to the TSN Slave from the variable residence time of the 5GS. That is, due to the residence time calculation, the 5GS introduces variable jitter in the UL and DL, generating different delays for PTP packets. We call D e, d o w n D_{e,down} the DL delay of the “Sync” packet, while D e, u p D_{e,up} is the UL delay of the “Delay Request” packet. The sum of both delays determines the p ℰ p_{\mathcal{E}} transmission delay (D ℰ D_{\mathcal{E}}). D e, d o w n D_{e,down}, D e, u p D_{e,up} and D ℰ D_{\mathcal{E}} are calculated as: D e, d o w n = t 2 − t 2 ′ + t 1 ′ − t 1 = t 2 − t 1 − d r e s, d o w n \displaystyle D_{e,down}=t_{2}-t_{2^{\prime}}+t_{1^{\prime}}-t_{1}=t_{2}-t_{1}-d_{res,down} (3) D e, u p = t 4 − t 4 ′ + t 3 ′ − t 3 = t 4 − t 3 − d r e s, u p \displaystyle D_{e,up}=t_{4}-t_{4^{\prime}}+t_{3^{\prime}}-t_{3}=t_{4}-t_{3}-d_{res,up} (4) D ℰ = D e, d o w n + D e, u p \displaystyle D_{\mathcal{E}}=D_{e,down}+D_{e,up} (5) d r e s, d o w n d_{res,down} and d r e s, u p d_{res,up} mitigate the associated problem of having different latencies in UL and DL. The TSN Slave requires a response time (d r e s p o n s e d_{response}) after receiving the “Sync” before generating the “Delay Request”, as shown in Figure 3. This d r e s p o n s e d_{response} is calculated as: d r e s p o n s e = t 3 − t 2 \begin{split}d_{response}=t_{3}-t_{2}\end{split} (6)
TSN Slave 处的时钟恢复：需要若干操作 [7]。首先，我们将从 TSN Master 发送到 TSN Slave 的 PTP 数据包时延与 5GS 的可变驻留时间解耦。也就是说，由于驻留时间计算，5GS 在 UL 和 DL 中引入可变抖动，从而为 PTP 数据包产生不同的时延。我们将“Sync”数据包的 DL 时延称为 \(D_{e,down}\)，而 \(D_{e,up}\) 是“Delay Request”数据包的 UL 时延。这两个时延之和确定 \(p_{\mathcal{E}}\) 传输时延（\(D_{\mathcal{E}}\)）。\(D_{e,down}\)、\(D_{e,up}\) 和 \(D_{\mathcal{E}}\) 计算如下： \[ D_{e,down}=t_2-t_{2'}+t_{1'}-t_1=t_2-t_1-d_{res,down} \tag{3} \] \[ D_{e,up}=t_4-t_{4'}+t_{3'}-t_3=t_4-t_3-d_{res,up} \tag{4} \] \[ D_{\mathcal{E}}=D_{e,down}+D_{e,up} \tag{5} \] \(d_{res,down}\) 和 \(d_{res,up}\) 缓解了 UL 和 DL 中具有不同时延这一相关问题。如图 3 所示，TSN Slave 在接收“Sync”之后、生成“Delay Request”之前，需要一个响应时间（\(d_{response}\)）。该 \(d_{response}\) 计算如下： \[ d_{response}=t_3-t_2 \tag{6} \]
公式（3）至（6）的变量、上下行方向、消息对应关系已逐项保留。原文 “p ℰ \(p_{\mathcal{E}}\) transmission delay” 存在 OCR 或排版识别风险，译文保留但需人工核对；该段与 P032 中间部分重复，也提示输入段落切分异常。状态需人工复核。
The TSN Slave calculates the time offset (β \beta) with respect to the TSN Master from all timestamps, the residence time and the response time, as follows: β = (t 2 − t 1) − D ℰ 2 − d r e s, d o w n \begin{split}\beta=(t_{2}-t_{1})-\frac{D_{\mathcal{E}}}{2}-d_{res,down}\end{split} (7)
TSN Slave 根据所有时间戳、驻留时间和响应时间，计算其相对于 TSN Master 的时间偏移（\(\beta\)），如下： \[ \beta=(t_2-t_1)-\frac{D_{\mathcal{E}}}{2}-d_{res,down} \tag{7} \]
时间偏移 \(\beta\)、\(D_{\mathcal{E}}/2\)、\(d_{res,down}\) 均已保留；公式编号（7）保留。该段与 P032 末尾重复，但本段自身无明显翻译问题。由于依赖前文公式上下文，建议人工核对公式排版。
Thus, the TSN Slave compensates for its clock offset to set the TSN GM time. This procedure compensates for latency variability in the propagation of time references in 5GS, ensuring accurate synchronization throughout the network, essential for industrial applications and the IIoT. Both functionalities have been implemented in commercial equipment that make up the TT and the TSN Slave.
因此，TSN Slave 补偿其时钟偏移，以设置 TSN GM 时间。该过程补偿了 5GS 中时间参考传播的时延可变性，确保整个网络中的精确同步，而这对于工业应用和 IIoT 是必不可少的。这两项功能已经在构成 TT 和 TSN Slave 的商用设备中实现。
“clock offset”“TSN GM time”“latency variability”“time references”“IIoT”等关键术语均已对应翻译或保留。逻辑上“偏移补偿→设置时间→补偿时延可变性→支持精确同步→已在商用设备实现”完整。未发现明显问题。
We implemented a TSN - 5G testbed to evaluate time synchronization performance, illustrated in Figure 4, where we only considered PTP traffic. The TSN systems are composed of TSN Master and TSN Slave nodes, implemented on commercial TSN switches (Z16 from Safran). These devices integrate time-sensitive networking features according to the specifications set forth in [ 1 ]. TSN Slave contains modifications to implement the TSN clock recovery functionality, as detailed in Section IV-A. For PTP packet encapsulation and exchange, these devices use the User Datagram Protocol (UDP) protocol over IPv4 in unicast mode with the E2E mechanism, a modality widely adopted in 5G networks with commercial devices. In this UDP/IPv4 mode, the source and destination IP addresses of the PTP packets are the addresses assigned to the TSN Master and TSN Slave ports, respectively. The PTP packet transmission rate varies depending on the experiment. The TSN Master is synchronized with the TSN GM, implemented by a time and frequency reference server (Safran’s Secure Sync). The time synchronization between the TSN GM and the TSN Master is performed by coaxial cables, using the Pulse Per Second (PPS) and 10 10 MHz signals.
我们实现了一个 TSN-5G 测试床来评估时间同步性能，如图 4 所示，其中我们只考虑 PTP 流量。TSN 系统由 TSN Master 和 TSN Slave 节点组成，并在商用 TSN 交换机（Safran 的 Z16）上实现。这些设备根据 [1] 中规定的规范集成了时间敏感网络功能。TSN Slave 包含用于实现 TSN 时钟恢复功能的修改，如第 IV-A 节所详述。对于 PTP 数据包的封装和交换，这些设备在单播模式下使用 IPv4 之上的 User Datagram Protocol（UDP）协议，并采用 E2E 机制；这是 5G 网络中使用商用设备时被广泛采用的一种方式。在这种 UDP/IPv4 模式下，PTP 数据包的源 IP 地址和目的 IP 地址分别是分配给 TSN Master 和 TSN Slave 端口的地址。PTP 数据包传输速率随实验而变化。TSN Master 与 TSN GM 同步，TSN GM 由时间和频率参考服务器（Safran 的 Secure Sync）实现。TSN GM 与 TSN Master 之间的时间同步通过同轴电缆执行，使用 Pulse Per Second（PPS）和 10 MHz 信号。
设备型号 Safran Z16、Secure Sync，协议 UDP/IPv4、unicast、E2E、PPS、10 MHz 均已保留。原文出现 “10 10 MHz” 疑似 OCR 重复，译为 10 MHz；需人工核对原 PDF。其余数字、引用 [1]、章节 IV-A 均保留。
5GS consists of the TT, also implemented with commercial TSN switches (Safran’s Z16), both modified to implement TC. These TT are synchronized with the 5G clock provided by a second Safran Secure Sync server, which acts as the 5G GM. Since the 5G GM only has a single PPS and 10 10 MHz output, an auxiliary TSN switch (Z16-TSN) is required to distribute the time reference to the TT. This switch is synchronized with the 5G GM via coaxial cables connected to the PPS and 10 10 MHz signals, see Figure 4. Subsequently, the switch transmits the time reference to the NW-TT and DS-TT via L2, using an E2E mechanism with a PTP message transmission rate of 1 packet/s. The 5GS also consist of a Base Station (BS) and a 5G core, both integrated in a PC with two 50 50 MHz PCLe SDR Amarisoft cards and an AMARI NW 600 license. The BS operates in the frequency band n78, using a Sub-Carrier Spacing (SCS) of 30 kHz and a Time Division Duplex (TDD) mode, with a TDD pattern of 1,0. The UE consists of a Quectel RM500Q-GL modem connected to an Intel NUC 10 NUC10i7FNKN, which acts as a Customer Premise Equipment (CPE). This device contains an Intel i7-10710U processor with 16 GB of RAM and 512 GB of SSD memory, and runs Ubuntu 22.04.
5GS 由 TT 组成，TT 同样使用商用 TSN 交换机（Safran 的 Z16）实现，且二者均经过修改以实现 TC。这些 TT 与第二台 Safran Secure Sync 服务器提供的 5G 时钟同步，该服务器充当 5G GM。由于 5G GM 只有一个 PPS 和 10 MHz 输出，因此需要一个辅助 TSN 交换机（Z16-TSN）来向 TT 分发时间参考。该交换机通过连接到 PPS 和 10 MHz 信号的同轴电缆与 5G GM 同步，见图 4。随后，该交换机通过 L2 将时间参考传输到 NW-TT 和 DS-TT，使用 E2E 机制，PTP 消息传输速率为 1 packet/s。5GS 还由一个 Base Station（BS）和一个 5G core 组成，二者都集成在一台 PC 中，该 PC 配有两块 50 MHz PCIe SDR Amarisoft 卡和一个 AMARI NW 600 许可证。BS 工作在 n78 频段，使用 30 kHz 的 Sub-Carrier Spacing（SCS）和 Time Division Duplex（TDD）模式，TDD pattern 为 1,0。UE 由连接到 Intel NUC 10 NUC10i7FNKN 的 Quectel RM500Q-GL 调制解调器组成，该 Intel NUC 作为 Customer Premise Equipment（CPE）。该设备包含 Intel i7-10710U 处理器、16 GB RAM 和 512 GB SSD 存储，并运行 Ubuntu 22.04。
TT、TC、5G GM、Z16-TSN、NW-TT、DS-TT、L2、BS、5G core、PCIe SDR、AMARI NW 600、n78、SCS、TDD、UE、CPE 等术语和型号均已保留。原文 “10 10 MHz” 与 “50 50 MHz PCLe SDR” 存在 OCR 风险，分别译为 10 MHz 和 50 MHz PCIe SDR；“PCLe” 也疑似应为 “PCIe”。状态需人工复核。
All experiments are performed inside a LABIFIX Faraday cage, where the BS antennas are connected to a SDR via SMA connectors and the Quectel modem is connected via USB. This cage avoids radiation within the licensed frequency bands. The connections between the rest of the equipment are made using 1 Gbps optical fiber, except for the connections between the NW-TT and DS-TT to the gNB and UE, respectively, which use 1 Gbps RJ-45 cables, as shown in Figure 4.
所有实验均在 LABIFIX 法拉第笼内进行，其中 BS 天线通过 SMA 连接器连接到 SDR，Quectel 调制解调器通过 USB 连接。该法拉第笼避免了在许可频段内产生辐射。其余设备之间的连接使用 1 Gbps 光纤完成，但 NW-TT 到 gNB、DS-TT 到 UE 的连接除外；这些连接分别使用 1 Gbps RJ-45 电缆，如图 4 所示。
LABIFIX、Faraday cage、BS、SMA、SDR、Quectel、USB、licensed frequency bands、1 Gbps、RJ-45、gNB、UE 均已保留或准确翻译。连接例外关系“NW-TT 和 DS-TT 分别到 gNB 和 UE”已明确表达。未发现明显问题。
We have performed two experiments to evaluate the performance of TC and the accuracy of TSN time synchronization. The first experiment analyzes the synchronization between the TSN Master and the TSN Slave when varying the PTP packet transmission rates. The second experiment compares the time synchronization when the TSN Master is synchronized to the TSN GM, locked to a GNSS reference, versus when operating in FR, using its own internal clock. In both cases, we measured the offset between the TSN Master and TSN Slave clocks for 20 20 min with a high precision counter. Table I summarizes the configurations used in the experiments.
我们进行了两个实验，以评估 TC 的性能和 TSN 时间同步的准确性。第一个实验分析在改变 PTP 数据包传输速率时 TSN Master 与 TSN Slave 之间的同步。第二个实验比较了两种情况下的时间同步：一种是 TSN Master 与锁定到 GNSS 参考的 TSN GM 同步，另一种是在 FR 中运行、使用其自身内部时钟。在这两种情况下，我们都使用高精度计数器测量 TSN Master 与 TSN Slave 时钟之间的偏移，测量时长为 20 min。表 I 总结了实验中使用的配置。
两个实验目标、变量和比较条件均已保留；GNSS、FR、高精度计数器、20 min、表 I 均保留。原文 “20 20 min” 疑似 OCR 重复，译为 20 min；FR 缩写未在本段定义，需结合上下文人工确认其含义。状态需人工复核。
The measured offset results of the TC mechanism, with the GM synchronized to a GNSS, are presented in Table II for the tests “0” to “2”, showing the average, maximum, minimum and standard deviation of the offset in each case. In particular, the measured offset at a rate of 1 1 p/s is illustrated in Figure 5, whose distribution follows approximately a Gaussian distribution. Similar behavior is observed for the rest of the tests. The data demonstrate very good synchronization performance for the E2E TC mechanism, with overall jitter below 500 500 ns and offset in the range of hundreds of nanoseconds. The best performance is obtained in the test “1”, while lower transmission rates generate slower offset correction, degrading accuracy. Conversely, higher rates cause packet accumulation in the TT, which alters the residence time measurement at 5GS, inducing errors in the TSN Slave clock correction. Remarkably, all test meets the synchronization requirements of industrial applications, validating the effectiveness of our the distributed E2E TC system, even in a high variability and non-deterministic medium, such as 5GS.
在 GM 与 GNSS 同步的情况下，TC 机制的实测偏移结果见表 II 中测试“0”至“2”，其中给出了每种情况下偏移的平均值、最大值、最小值和标准差。特别地，图 5 展示了在 1 1 p/s 速率下测得的偏移，其分布近似服从高斯分布。其余测试也观察到了类似行为。数据表明，E2E TC 机制具有非常好的同步性能，整体抖动低于 500 500 ns，偏移处于数百纳秒范围内。最佳性能出现在测试“1”中，而较低的传输速率会产生较慢的偏移校正，从而降低精度。相反，较高的速率会导致 TT 中的数据包累积，这会改变 5GS 中的驻留时间测量，进而在 TSN Slave 时钟校正中引入误差。值得注意的是，所有测试都满足工业应用的同步要求，验证了我们的分布式 E2E TC 系统的有效性，即使是在 5GS 这样具有高可变性且非确定性的介质中也是如此。
原文中“1 1 p/s”和“500 500 ns”疑似 PDF/OCR 重复识别，已按原样保留；“all test meets”存在语法问题，按“所有测试都满足”理解；“our the distributed”存在原文冗余，译为“我们的分布式”。术语 GM、GNSS、TC、E2E TC、TT、5GS、TSN Slave 均已保留。需结合表 II 和图 5 确认速率与数值是否应为单个“1 p/s”和“500 ns”。
The measured offset results when TSN Master operates in FR are presented in test “3” of Table II, showing a Gaussian-like distribution, similar to that illustrated in Figure 5. Comparison of results with test “2” shows an equivalent temporal accuracy. Although FR seems to offer slightly better stability, this could be attributed to the absence of adjustments to the internal oscillator of the TSN Master to follow the GNSS reference, which avoids additional fluctuations. However, this does not imply higher accuracy as it is not compared to the global time reference. Since the 5GS introduces significant latency variations, the differences in offset between FR and GNSS are negligible. Thus, we conclude that the E2E TC mechanism operates equivalently under both references without significant impacts on synchronization.
当 TSN Master 运行于 FR 时的实测偏移结果见表 II 的测试“3”，其呈现出类似高斯的分布，与图 5 所示相似。与测试“2”的结果比较表明，二者具有等效的时间精度。尽管 FR 似乎提供了略好的稳定性，但这可能归因于 TSN Master 的内部振荡器无需进行调整以跟随 GNSS 参考，从而避免了额外波动。然而，这并不意味着更高的准确度，因为它并未与全局时间参考进行比较。由于 5GS 引入了显著的时延变化，FR 与 GNSS 之间的偏移差异可以忽略不计。因此，我们得出结论：E2E TC 机制在两种参考下等效运行，对同步没有显著影响。
FR 缩写原文未在本段展开，保留不译，需依赖前文确认含义；“temporal accuracy”译为“时间精度”，“accuracy”后文译为“准确度”以区分稳定性语境；测试“2”“3”、表 II、图 5 引用均已保留。逻辑上先比较稳定性，再说明不代表相对于全局参考的准确度更高，未发现明显问题。
This paper empirically evaluates an E2E TC in a TSN - 5G network, implemented on commercial TSN switches with a single clock. The solution contains the computation of the residence time within 5GS (NW-TT and DS-TT), and the recovery of the TSN clock domain at the slave node. We have deployed a TSN - 5G testbed with commercial equipment to analyze time synchronization at different PTP message rates. The results show a peak-to-peak accuracy of 500 500 ns, meeting industrial requirements, and show that certain transmission rates can induce offsets without exceeding the allowed margins, regardless of the reference (GNSS or FR). This work represents a first step to demonstrate the feasibility of E2E TC in an integrated TSN - 5G network. Future research will explore synchronization under traffic load and extraction of the SIB 9 reference to align the UE with the 5G GM clock of gNB.
本文在一个 TSN - 5G 网络中对 E2E TC 进行了实证评估，该 E2E TC 在带有单一时钟的商用 TSN 交换机上实现。该解决方案包含对 5GS 内部驻留时间的计算（NW-TT 和 DS-TT），以及在从节点处恢复 TSN 时钟域。我们部署了一个采用商用设备的 TSN - 5G 测试平台，用于分析不同 PTP 消息速率下的时间同步。结果显示峰峰值准确度为 500 500 ns，满足工业要求，并表明某些传输速率可能诱发偏移，但无论参考源是 GNSS 还是 FR，都不会超过允许裕量。本文工作是证明在集成 TSN - 5G 网络中实现 E2E TC 可行性的第一步。未来研究将探索存在流量负载时的同步，以及提取 SIB 9 参考以使 UE 与 gNB 的 5G GM 时钟对齐。
“500 500 ns”疑似 PDF/OCR 重复识别，已按原样保留，需结合论文表格或正文上下文确认是否应为“500 ns”；“single clock”译为“单一时钟”，可能指交换机内部单时钟架构；NW-TT、DS-TT、PTP、GNSS、FR、SIB 9、UE、gNB、5G GM 均已保留；“peak-to-peak accuracy”按“峰峰值准确度”翻译，需人工确认是否应按计量习惯译为“峰峰值精度”。
中文逐段译稿
时间同步分发是工业物联网（IIoT）的一项基本服务，在向工业 4.0 和工业 5.0 演进的过程中发挥着关键作用。这些领域中的应用依赖精确同步，以实现可靠通信、低时延和运行效率，从而优化机器人、传感器和机械之间的自动化与交互，以及准确的传感器数据分析。由 IEEE 802.1 [1] 定义的时间敏感网络（TSN）标准能够实现低于 100 μs 的同步精度 [2]，从而确保确定性和可靠运行。然而，工业、物联网（IoT）和机器人领域对移动性的需求不断增长，带来了新的挑战，因为 TSN 最初是为有线网络构想的。作为一种解决方案，3GPP Release 16 提出将第五代移动通信（5G）与 TSN 集成，以在不损害同步要求的情况下提供无线通信和移动灵活性。
术语 IIoT、Industry 4.0/5.0、TSN、IEEE 802.1、IoT、3GPP Release 16、5G 均已保留；数字和单位“低于 100 μs”已保留；引用 [1]、[2] 已保留。原文中 “100 μ s 100\ \mu s”存在重复/排版残留，译文按一次“100 μs”处理，建议人工确认是否由公式抽取导致。
IEEE 802.1Qbv、IEEE 802.1Qcc 和 IEEE 802.1Qci 等 TSN 功能依赖准确的时间同步。然而，5G 引入了一些会降低同步精度的挑战，例如较高水平的抖动、上行链路（UL）和下行链路（DL）时延中的非对称性、下一代 Node B（gNB）和用户面功能（UPF）等设备中的可变处理时间，以及重传。TS 22.104 [3] 规定了工业和 IIoT 网络的 5G 系统（5GS）要求，指定最大时间同步误差为 900 ns，并支持多达 32 个同时工作的工作时钟域。这些时钟域向其内部设备提供高精度时间，使 TSN 设备能够同时管理多个时钟域。而全局时钟域则向属于该域的设备提供日期和时间。在某些情况下，工作时钟域和全局时钟域可能会重叠。同时，3GPP TS 23.501 [4] 定义了若干种配置，以在 5GS 中实现 TSN 同步；这些配置可以使用 IEEE 802.1AS 标准 [5, 6] 作为时间感知系统来实现，该标准使用通用精确时间协议（gPTP），也可以按照 IEEE 1588 标准 [7] 配置为边界时钟（BC）或透明时钟（TC）。
IEEE 802.1Qbv/Qcc/Qci、UL、DL、gNB、UPF、TS 22.104、5GS、3GPP TS 23.501、IEEE 802.1AS、gPTP、IEEE 1588、BC、TC 均已保留；“900 ns”“32 个”已保留。原文中 “900 900 ns”“32 32”存在重复抽取痕迹，译文按一次处理；原文 “While a global clock domain...” 为不完整句式，译文按上下文补足逻辑，需人工确认。
已有若干研究讨论了 TSN-5G 网络中时间同步分发的挑战。例如，Striffler 等人 [8] 分析了当 5GS 作为 TC 运行时的频率漂移和定时误差，这可能导致不符合时间同步要求。Wang 等人 [9] 则提出了解决方案，用于减轻在建模为 TC 的 5GS 中多 gNB 竞争、重传和移动性的影响。Shi 等人 [10] 研究了配置为 BC 的 5GS 中的同步误差，重点关注由参考时间粒度和传播时延估计引起的不确定性。Val 等人 [11] 证明，尽管 Wi-Fi 存在可变性，仍可通过硬件级修改实现与 TSN 兼容的同步精度，尽管这种方法目前对于商用 5G 网络并不可行。
作者引用 [8]-[11]、TC、BC、5GS、gNB、Wi-Fi、TSN 等术语已保留；逻辑上分别对应 TC 运行、TC 建模、BC 配置和 Wi-Fi 硬件修改四类研究。原文 “TSN - 5G network” 单复数略不自然，译为“TSN-5G 网络”；未发现明显问题。
据我们所知，目前尚无关于集成 TSN-5G 网络中 TC 的实证评估。因此，本文的目标是在 5GS 被配置为端到端（E2E）TC 时，对 TSN-5G 网络中的 TSN 时间同步分发进行实证研究。我们的主要贡献如下：
“To our knowledge”译为“据我们所知”；TC、TSN-5G、5GS、End-to-End（E2E）TC 均已保留；研究目标和贡献引出关系准确。未发现明显问题。
• 我们分析了 5GS 用于支持 TSN 同步传输的各种配置，并考虑其在商用单时钟设备中的实现。• 我们在商用 TSN 交换机上实现了 E2E TC。该实现包括两个过程：计算由 5GS 引入的驻留时间，以及在从节点处恢复 TSN 时钟域。• 我们使用商用设备部署了一个 TSN-5G 网络测试床，以评估时间同步性能。• 我们在所实现的测试床上对时间同步精度进行了实验评估。
四项贡献均已逐项翻译；5GS、TSN、E2E TC、TSN-5G 等缩写保留；“residence time”译为“驻留时间”，“slave node”译为“从节点”。该段与后续 P006-P009 内容重复，可能是列表抽取与分段抽取重复导致，但按输入要求保留并翻译；需人工确认是否应在最终论文译稿中去重。
我们分析了 5GS 用于支持 TSN 同步传输的各种配置，并考虑其在商用单时钟设备中的实现。
术语 5GS、TSN 已保留；与 P005 第一项内容重复，可能为列表项被重复抽取。译文本身未发现明显问题，但段落重复需人工确认。
我们在商用 TSN 交换机上实现了 E2E TC。该实现包括两个过程：计算由 5GS 引入的驻留时间，以及在从节点处恢复 TSN 时钟域。
E2E TC、TSN、5GS 等术语已保留；“residence time”译为“驻留时间”，“slave node”译为“从节点”；与 P005 第二项内容重复，需人工确认是否为抽取重复。
我们使用商用设备部署了一个 TSN-5G 网络测试床，以评估时间同步性能。
TSN-5G 和“testbed/测试床”译法一致；与 P005 第三项内容重复，需人工确认是否为抽取重复。
我们在所实现的测试床上对时间同步精度进行了实验评估。
“experimental evaluation”和“time synchronization accuracy”分别译为“实验评估”和“时间同步精度”；与 P005 第四项内容重复，需人工确认是否为抽取重复。
我们的结果表明，峰峰值时间同步为 500 ns，满足工业要求（≤ 1 μs）。此外，我们注意到，在某些精确时间协议（PTP）消息传输速率下，可以观察到可能影响时间同步的时间偏移，但这些偏移并未超过要求。无论同步发送端（主节点）是同步到外部参考源（全球导航卫星系统（GNSS）），还是使用其内部时钟运行（自由运行（FR）），这些结果都是独立成立的。
“peak-to-peak time synchronization”译为“峰峰值时间同步”；500 ns、≤ 1 μs、PTP、GNSS、FR 均已保留。原文中 “500 500 ns”存在重复抽取痕迹，译文按一次处理；“independent of whether...” 译为“不论……这些结果都是独立成立的”，逻辑已保留。需人工确认“peak-to-peak time synchronization”是否应按领域习惯译为“峰峰值时间同步误差”。
本文其余部分组织如下：第 II 节介绍 TSN - 5G 网络中的背景知识以及时间同步选项分析。第 III 节描述集成网络的模型和架构。第 IV 节详细说明 TC 的设计与运行，并给出 PTP 消息分析和偏移量计算。第 V 节描述测试床和实验设置。第 VI 节呈现并讨论所获得的结果。最后，第 VII 节以主要贡献作为总结。
术语 TSN、5G、TC、PTP 均已保留；章节编号、逻辑顺序和“offset calculation”含义无明显风险；“concludes with the main contributions”译为“以主要贡献作为总结”基本准确。未发现明显问题。
在 TSN - 5G 集成网络中，有两个同步过程并行运行，即 5G 时间同步过程和 TSN 时间同步过程 [2, 12]，如图 1 所示。5G 同步过程将来自 5G Grandmaster（GM）的时间参考提供给 5GS 设备，例如 UPF、gNB 和用户设备（User Equipment，UE）。与此同时，TSN 同步过程将 TSN GM 的时间参考提供给 TSN 网络设备。这两个同步过程被认为是相互独立的，从而为同步过程的设计和实现提供了灵活性。下面将详细说明这两个过程，但首先我们描述 3GPP 所提出的集成 TSN - 5G 网络中的 5GS 架构。
“temporal reference”统一译为“时间参考”；“paralell”为原文拼写错误，不影响翻译；5GS、UPF、gNB、UE、GM 等缩写已保留；引用 [2, 12] 和图 1 未遗漏。未发现明显问题。
根据 3GPP TS 23.501 [4]，5GS 在 TSN 网络中充当一个 PTP 实例。如图 1 所示，外部网络由终端站和 TSN 网桥组成，其时间参考由 PTP 或 gPTP GM 提供。在 5G 域中，5G GM 对 gNB 进行同步，而 gNB 通过无线链路将时间参考分发给 UE，并通过符合 PTP 的 5G 传输网络将时间参考分发给 UPF。为了将 5G 与 TSN 集成，UPF 实现一个 TSN Translator（TT），即网络侧时间敏感网络转换器（Network-Side Time Sensitive Networking Translator，NW-TT），它与外部 TSN 网桥连接；同时 UE 连接到另一个 TT，即设备侧时间敏感网络转换器（Device-Side Time Sensitive Networking Translator，DS-TT），而该 DS-TT 又连接到一个 TSN 终端站。这些 TT 确保互操作性，使 5GS 能够在各种模式下作为逻辑网桥运行，而不需要与 TSN GM 直接对齐。
标准号 3GPP TS 23.501、引用 [4]、图 1、PTP/gPTP/GM/TT/NW-TT/DS-TT 均已保留；“logical bridge”译为“逻辑网桥”准确；“without direct alignment with the TSN GM”可能涉及时间基准不直接对齐，译文保留该含义。未发现明显问题。
5G 时间同步过程基于 5G GM 参考在 5GS 传输网络和 5GS 无线接入网（Radio Access Network，RAN）中的内部分发 [13]。在 5G 传输网络中，一个直接的解决方案是在每个 gNB 中安装 GNSS 接收机，这可提供 ±100 ns 的精度 [13]，满足 5GS 定时要求。然而，该方法带来较高的部署和维护成本、室内安装困难以及易受干扰的脆弱性。作为替代方案，可以使用分组网络上的同步协议，例如 IEEE 1588 [7]，并采用 ITU-T 定义的适配配置文件，例如 G.8275.1（PTP-aware，感知 PTP）和 G.8275.2（non-PTP-aware，非感知 PTP）。
原文中“± 100 \pm 100 ns”疑似 PDF/LaTeX 抽取重复，译文按指标含义处理为“±100 ns”；最后一句原文语法不完整，译文根据上下文补足为“可以使用……协议”；GNSS、gNB、IEEE 1588、ITU-T、G.8275.1/G.8275.2 均已保留。由于原文公式/符号存在抽取异常且句子残缺，需人工复核。
在 5G RAN 中，5G GM 与 UE 之间的同步通过 gNB 实现，如 TS 38.331 中所定义。gNB 持续更新 5G GM 参考 [2, 13, 14]，并通过系统信息块（System Information Block，SIB）或单播无线资源控制（Radio Resource Control，RRC）消息将其周期性地发送给 UE，该参考通过系统帧号（System Frame Number，SFN）进行标识。SIB 9 消息包含 GPS 和 UTC 格式的时间信息，并在两个 SFN 之间的边界处发送，从而实现设备同步。此外，必须根据小区大小调整 5G 参考，以补偿下行链路（DL）传播时延并最小化接收不确定性。准确的时延计算以及获得 SIB 9 参考是关键方面，尽管它们并未在本研究中处理。更多信息见 [14, 13]。
TS 38.331、SIB、RRC、SFN、SIB 9、GPS、UTC、DL 等术语和缩写已保留；“boundary between two SFN”译为“两个 SFN 之间的边界”可能需结合标准语境理解，但未改变原意；引用顺序 [14, 13] 保留。未发现明显问题。
TS 23.501 [4] 定义了若干模式，在这些模式中，5GS 可以被配置为作为一个 PTP 实例运行 [2]，从而在集成 TSN - 5G 网络中实现 TSN 时间同步。具体而言，这些时钟模式为：
标准号 TS 23.501、引用 [4] 和 [2]、5GS、PTP、TSN - 5G 均已保留；“clock modes”译为“时钟模式”准确；该段引出后续列表，逻辑完整。未发现明显问题。
• 5GS 作为 Time-Aware System：5GS 表现为一个符合 IEEE 802.1AS 的节点 [5]，使用 gPTP 协议参与时间同步。NW-TT 和 DS-TT 与两个 GM 时钟（TSN GM 和 5G GM）同步，因此需要两个时钟，并管理 gPTP 消息（在第 2 层（Layer 2，L2）中传输）以确保同步 [2]。• 5GS 作为 BC：5GS 按照 IEEE 1588 标准 [7] 被配置为 BC，主动参与同步。也就是说，5GS 维护 PTP 域时间尺度，并同步已连接的 PTP 时间接收器（例如 DS-TT、TSN Slave 等），充当时间源。该模式提供更高的精度和鲁棒性，支持网络可扩展性，并在多设备场景中降低抖动和传播时延的影响，但更为复杂。• 5GS 作为 TC：5GS 按照 IEEE 1588 标准 [7] 表现为 TC，并不主动参与时间同步，而是测量 PTP 消息在网络内的驻留时间，并在转发这些消息之前使用该驻留时间对其进行校正。TT 管理 PTP 消息并计算 5GS 内部的时延。TC 有两种类型：点到点（Peer-to-Peer，P2P）或端到端（E2E）。在 P2P TC [15] 中，5GS 使用 Peer Delay Messages 测量两个直接连接的相邻节点之间的时延，并计算 PTP 消息在 5G 网络内的驻留时间。沿路径的驻留时间与链路时延之和被报告给 PTP 时间接收器 [6]。E2E TC 通过交换 PTP 消息来计算 PTP 发送器与接收器之间的总 E2E 时延。在 5GS 中，会计算驻留时间，并将整个路径上的驻留时间之和加入到 PTP 消息的 correction field 中。该驻留时间之和被中继给 PTP 时间接收器。这样，PTP 接收器可以基于消息 correction field 中的驻留时间之和计算总补偿。因此，P2P TC 补偿相邻节点之间的时延，而 E2E TC 补偿整个 E2E 路径的时延。P2P TC 要求所有网络设备都兼容 IEEE 1588，而 E2E TC 不要求。
该段包含三个列表项且后续 P018-P020 又分别重复前三个列表项，可能是段落抽取重复或列表解析问题；BC、TC、P2P、E2E、correction field、Peer Delay Messages 等关键术语已保留；“neighboring node”原文单复数不一致，译文按“相邻节点”处理；逻辑上 P2P 与 E2E 的补偿范围区别已保留。由于该段与后续段落存在明显重复和列表上下文抽取风险，需人工复核。
5GS 作为 Time-Aware System：5GS 表现为一个符合 IEEE 802.1AS 的节点 [5]，使用 gPTP 协议参与时间同步。NW-TT 和 DS-TT 与两个 GM 时钟（TSN GM 和 5G GM）同步，因此需要两个时钟，并管理 gPTP 消息（在第 2 层（Layer 2，L2）中传输）以确保同步 [2]。
术语 Time-Aware System、IEEE 802.1AS、gPTP、NW-TT、DS-TT、GM、L2 均已保留；内容与 P017 中第一项重复，可能是输入抽取导致，但本段按要求独立翻译。未发现明显问题。
5GS 作为 BC：5GS 按照 IEEE 1588 标准 [7] 被配置为 BC，主动参与同步。也就是说，5GS 维护 PTP 域时间尺度，并同步已连接的 PTP 时间接收器（例如 DS-TT、TSN Slave 等），充当时间源。该模式提供更高的精度和鲁棒性，支持网络可扩展性，并在多设备场景中降低抖动和传播时延的影响，但更为复杂。
BC、IEEE 1588、PTP domain timescale、PTP time receivers、DS-TT、TSN Slave 等术语已保留；“allowing network scalability”译为“支持网络可扩展性”合理；内容与 P017 第二项重复，属输入层面现象。未发现明显问题。
5GS 作为 TC：5GS 按照 IEEE 1588 标准 [7] 表现为 TC，并不主动参与时间同步，而是测量 PTP 消息在网络内的驻留时间，并在转发这些消息之前使用该驻留时间对其进行校正。TT 管理 PTP 消息并计算 5GS 内部的时延。
TC、IEEE 1588、PTP、TT、5GS 等术语已保留；“residence time”译为“驻留时间”符合 PTP/透明时钟语境；内容与 P017 第三项开头重复，属输入层面现象。未发现明显问题。
TC 有两种类型：Peer-to-Peer（P2P，对等）或 E2E（端到端）。在 P2P TC [15] 中，5GS 使用 Peer Delay Messages 测量两个直接连接的相邻节点之间的时延，并计算 PTP 消息在 5G 网络内的驻留时间。沿路径的驻留时间与链路时延之和会被报告给 PTP 时间接收器 [6]。E2E TC 通过交换 PTP 消息来计算 PTP 发送器与接收器之间的总 E2E 时延。在 5GS 中，会计算驻留时间，并将整条路径上的驻留时间总和加入 PTP 消息的 correction field 中。该驻留时间总和会被转发给 PTP 时间接收器。通过这种方式，PTP 接收器可以基于消息 correction field 中的驻留时间总和来计算总补偿量。
术语 P2P TC、E2E TC、5GS、PTP、Peer Delay Messages、correction field 均已保留；数字引用 [15]、[6] 未遗漏；“residence time and link delay along the path”译为“沿路径的驻留时间与链路时延之和”，逻辑一致。未发现明显问题。
因此，P2P TC 补偿相邻节点之间的延迟，而 E2E TC 补偿整个 E2E 路径的延迟。P2P TC 要求所有网络设备都兼容 IEEE 1588，E2E TC 则不要求。
对比关系“while”已体现；IEEE 1588 标准编号保留；“latency”统一译为“延迟”，与上一段“时延”含义一致。未发现明显问题。
在本文中，我们选择 5GS 中的 E2E TC 模式，因为它允许传输来自不同 GM 的多个工作时钟域，这是工业环境中的一项关键要求。要求 L2 传输的 IEEE 802.1AS 标准在集成到商用设备中时存在限制。然而，已有研究表明，IEEE 802.1AS 网络可以按照 IEEE 1588 [15] 作为分布式时钟（BC、ordinary 或 TC）运行，从而促进多个时钟信号在域之间的传输。此外，由于 TC 独立运行，不需要同步其自身时钟，因此简化了 5GS 集成到现有 TSN 网络中的过程，或者支持纳入新的 5G 运营商，从而确保 TSN-5G 网络部署具有更大的灵活性。
GM、L2、IEEE 802.1AS、IEEE 1588、BC、TC 等缩写已保留；“ordinary”原文可能指 ordinary clock，但原文只写 ordinary，保留以避免擅自补全；“GM s”疑似 OCR 空格问题，按 GMs 理解为多个 GM。未发现明显问题。
我们考虑如图 2 所示的 TSN-5G 系统模型。TSN 系统包括一个 TSN Master，它与 TSN GM 同步，并将时间参考分发给其他 TSN bridge 和/或 TSN end station。该同步被扩展到另一个 TSN 域中的 TSN Slave，该 TSN 域通过 5G 网络互连。该 TSN Slave 一旦完成同步，就会将同步分发给其他 TSN bridge 或 TSN end station。5GS 包含一个 5G GM，它直接向 gNB 和 NW-TT 提供时间参考，二者通过 UPF 连接。由于商用设备未集成带有 NW-TT 的 UPF，因此 NW-TT 与 5G GM 同步，并直接连接到 TSN Master。而 DS-TT 也通过 UE 同步到 5G GM，并连接到 TSN Slave。这与图 1 中的模型不同，因为在本情形中，NW-TT 和 UPF 是分离的设备，并且 NW-TT 与 DS-TT 分别直接连接到 TSN Master 和 TSN Slave。
TSN Master、TSN Slave、TSN GM、5G GM、gNB、NW-TT、UPF、DS-TT、UE 等关键实体均保留；图 2、图 1 对照关系未遗漏；“both connected through the UPF”按“二者通过 UPF 连接”翻译，但结合后文“NW-TT and UPF are separate devices”设备拓扑可能需结合图示确认。未发现明显问题。
TSN-5G 网络中的时间同步基于符合 IEEE 1588 的 PTP 帧传输 [7]。在本文中，我们使用 E2E TC 时钟机制进行时间同步。我们将 ℱ（\mathcal{F}）定义为穿越 TSN-5G 网络的 PTP 流集合。每个 PTP 流 \(f_i\)，其中 \(\forall i \in \mathcal{F}\)，表示在一个与 GM 同步的 PTP 发送节点和一个未与 GM 同步的 PTP 接收节点之间进行的双向通信。我们将 TSN Master 称为 PTP 发送节点，将 TSN Slave 称为 PTP 接收节点。这些 PTP 流确保 PTP 发送器和 PTP 接收器保持与 GM 相同的时间参考。因此，每个流 \(f_i\)，其中 \(\forall i \in \mathcal{F}\)，都从 TSN Master 传输到 TSN Slave，并穿越 5G 网络。在我们的情形中，我们聚焦于单个 PTP 流 \(f_i\) 来评估同步。该 \(f_i\) 使用第 IV 节详述的 E2E TC 机制，在 TSN Master 与 Slave 之间传输一系列 \(p^{f_i}_{\mathcal{E}}\) 个 PTP 分组。为清晰起见，下文将省略上标 \(f_i\)，即在所有变量中 \(p^{f_i}_{\mathcal{E}} = p_{\mathcal{E}}\)，因为只考虑单个 PTP 流。
公式符号 \(\mathcal{F}\)、\(f_i\)、\(\forall i \in \mathcal{F}\)、\(p^{f_i}_{\mathcal{E}}\)、\(p_{\mathcal{E}}\) 已保留；“represent”原文主谓数不一致，按语义译为“表示”；“PTP packets”译为“PTP 分组”。未发现明显问题。
在该场景中，如前所述，两个同步过程共存 [12]：TSN 同步和 5G 同步。我们认为 TSN-5G 网络中的每个设备都有一个单一时钟。TSN Master 和 Slave 的时钟与 TSN GM 参考同步，而 TT 仅与 5G GM 同步。在 5G 同步中，5G GM 参考通过 gNB 传输到 UE，UE 再将其传输到 DS-TT。在本文中，我们不关注 UE 对 5G 时钟的恢复以及随后将其传输到 DS-TT 的过程，因此，我们假设 UE 以及随后 DS-TT 处用于同步的 SIB 9 恢复是完美的。
TSN 同步与 5G 同步的并行关系保留；TT、5G GM、gNB、UE、DS-TT、SIB 9 均保留；“perfect recovery from SIB 9”译为“从 SIB 9 完美恢复”，含义可能依赖 5G 系统信息块上下文，但无公式残缺。未发现明显问题。
在 TSN 同步中，\(p_{\mathcal{E}}\) 包含时间戳。具体而言，每个 \(p_e\)，其中 \(e \in \mathcal{E}\)，都包含一个时间戳，用于记录 TSN Master 发送分组 \(e\) 的时刻。然而，由于 TSN Master 中的软件和硬件分组处理所造成的延迟，\(p_e\) 中的时间戳可能缺乏精度。随后，\(p_e\) 的发送时间戳会被包含在 \(p_{e+1}\) 中，记录 \(p_e\) 离开 TSN Master 的精确时刻（\(t_1\)）。当 TSN Slave 接收到 \(p_e\) 时，它记录时间戳（\(t_2\)）。
\(p_{\mathcal{E}}\)、\(p_e\)、\(e \in \mathcal{E}\)、\(p_{e+1}\)、\(t_1\)、\(t_2\) 已保留；“packet e”译为“分组 e”；逻辑上体现了后续消息携带前一分组精确发送时间戳。未发现明显问题。
此外，\(p_{\mathcal{E}}\) 分组在穿越 5G 网络时会经历可变延迟（jitter，抖动），这会损害定时精度并影响 TSN 节点的正确运行。这给准确估计时间参考带来了挑战。为解决这一问题，需要计算 \(p_{\mathcal{E}}\) 在穿越 5G 网络时经历的延迟。该延迟被称为在 5G 网络中的驻留时间（\(d_{res}\)）。其计算涉及在 TT 处为某些 \(p_e\) 分组生成时间戳。NW-TT 基于 5GS 参考时间生成 ingress timestamp（\(t_{in}\)，入口时间戳），而 DS-TT 同样基于 5GS 参考时间生成 egress timestamp（\(t_{eg}\)，出口时间戳）。驻留时间（\(d_{res}\)）定义为：\(d_{res}=t_{eg}-t_{in}\)（1）。由于 5G 网络在链路上是不对称的，即 UL 和 DL 延迟会随无线信道特性而不同，因此为每条链路定义特定的驻留时间。UL 的驻留时间表示为 \(d_{res,up}\)，DL 的驻留时间表示为 \(d_{res,down}\)。
jitter、TT、NW-TT、DS-TT、5GS、UL、DL 等术语保留并补充中文；公式 \(d_{res}=t_{eg}-t_{in}\) 与编号（1）保留；“This present”原文语法错误，按“This presents”语义翻译；“for certain \(p_e\) packet”单复数不一致，按“某些分组”处理。未发现明显问题。
每个 TSN 节点都包含一个内部振荡器，该振荡器可能因物理扰动而向设备内部时钟引入噪声，从而导致时钟偏斜。为减轻这种时钟漂移，PTP 消息以周期 \(T\) 生成。
“internal oscillator”“clock skew”“clock drift”分别译为“内部振荡器”“时钟偏斜”“时钟漂移”；原文末尾为“cycle T T”，疑似 OCR 重复或公式识别问题，译为周期 \(T\)，需核对原 PDF 是否为 \(T\) 或其他符号。
我们聚焦于在集成 TSN-5G 网络中分发时间同步，并在 5GS 中实现 E2E TC 模式。采用这种方法时，5G 设备不需要与 TSN GM 时间参考同步，因为 5G 公共时间参考被用于准确计算穿越网络的 \(p_{\mathcal{E}}\) 的驻留时间（\(d_{res,up}\)、\(d_{res,down}\)）。如第 III 节所述，NW-TT 和 DS-TT 必须共享由 5G GM 派生出的同一时间参考。这使得 TC 机制能够以等同于独立交换机的方式运行，确保根据位于 5GS 两端设备上生成的时间戳来计算驻留时间时具有一致性。任何未能传播公共时间参考的情况，都可能导致边缘 TSN 系统之间出现不一致或无效的同步结果。下一节将详细说明所交换的 PTP 消息，以及计算 offset 和驻留时间所需遵循的过程。
E2E TC、5GS、TSN GM、5G GM、NW-TT、DS-TT、PTP、offset 等术语保留；\(d_{res,up}\)、\(d_{res,down}\)、\(p_{\mathcal{E}}\) 保留；“allows that the TC mechanism”原文语法不顺，按“使得 TC 机制能够”处理；逻辑关系与第 III 节衔接完整。未发现明显问题。
在 5GS 中实现的 E2E TC 解决方案在分布式架构的节点之间交换 PTP 消息，如图 3 所示。TSN Master 通过发送“Announce”消息来发起同步，随后发送“Sync”和“Follow-Up”。然后，TSN Slave 发送“Delay Request”，并接收作为回复的“Delay Response”。这一交换使得能够通过 NW-TT 和 DS-TT 的时间戳标记与时延估计能力，测量 5GS 上的驻留时间，并在 TSN Slave 处恢复 TSN 时钟域。这两项功能对于 TC 的运行都是关键的；为了在商用交换机上执行 TC，我们已在这些设备中实现了这两项功能。下面详细说明每项功能：
术语 E2E TC、5GS、PTP、TSN Master、TSN Slave、NW-TT、DS-TT、TSN 时钟域均已保留；消息名按原文保留。逻辑上“交换消息→测量驻留时间→恢复时钟域→实现于商用交换机”完整。未发现明显问题。
1 5GS 驻留时间的计算：NW-TT 和 DS-TT 分别在 5GS 的入口（\(t_{1'}\)）和出口（\(t_{2'}\)）处为“Sync”数据包分配时间戳。这些时间戳确定 DL 驻留时间（\(d_{res,down}\)），如公式（2）所详述。\(d_{res,down}\) 的值被临时存储在 DS-TT 中，直到“Follow-Up”数据包到达；在该数据包中，DS-TT 使用 \(d_{res,down}\) 的值更新 Correction Field（CF）。该过程使 TSN Slave 能够在其总链路时延估计中，补偿“Sync”数据包在 5GS 内引入的时延。对于“Delay Request”和“Delay Reply”数据包，也应用类似过程，从而能够利用“Delay Request”的时间戳以及“Delay Reply”中的 CF 更新来估计 UL 驻留时间（\(d_{res,up}\)），如图 3 所示。UL 和 DL 驻留时间计算如下： \[ \begin{split} d_{res,down}=t_{2'}-t_{1'}\\ d_{res,up}=t_{4'}-t_{3'} \end{split} \tag{2} \] 2 TSN Slave 处的时钟恢复：需要若干操作 [7]。首先，我们将从 TSN Master 发送到 TSN Slave 的 PTP 数据包时延与 5GS 的可变驻留时间解耦。也就是说，由于驻留时间计算，5GS 在 UL 和 DL 中引入可变抖动，从而为 PTP 数据包产生不同的时延。我们将“Sync”数据包的 DL 时延称为 \(D_{e,down}\)，而 \(D_{e,up}\) 是“Delay Request”数据包的 UL 时延。这两个时延之和确定 \(p_{\mathcal{E}}\) 传输时延（\(D_{\mathcal{E}}\)）。\(D_{e,down}\)、\(D_{e,up}\) 和 \(D_{\mathcal{E}}\) 计算如下： \[ D_{e,down}=t_2-t_{2'}+t_{1'}-t_1=t_2-t_1-d_{res,down} \tag{3} \] \[ D_{e,up}=t_4-t_{4'}+t_{3'}-t_3=t_4-t_3-d_{res,up} \tag{4} \] \[ D_{\mathcal{E}}=D_{e,down}+D_{e,up} \tag{5} \] \(d_{res,down}\) 和 \(d_{res,up}\) 缓解了 UL 和 DL 中具有不同时延这一相关问题。如图 3 所示，TSN Slave 在接收“Sync”之后、生成“Delay Request”之前，需要一个响应时间（\(d_{response}\)）。该 \(d_{response}\) 计算如下： \[ d_{response}=t_3-t_2 \tag{6} \] TSN Slave 根据所有时间戳、驻留时间和响应时间，计算其相对于 TSN Master 的时间偏移（\(\beta\)），如下： \[ \beta=(t_2-t_1)-\frac{D_{\mathcal{E}}}{2}-d_{res,down} \tag{7} \]
输入段落 P032 似乎合并了后续 P033-P035 的内容，包含编号 1、编号 2 以及公式（2）至（7），存在段落切分重复风险。公式符号中 \(t_{1'}\)、\(t_{2'}\)、\(t_{3'}\)、\(t_{4'}\) 按可读数学形式整理；原文有 “p ℰ \(p_{\mathcal{E}}\) transmission delay” 识别较异常，已保留为 \(p_{\mathcal{E}}\) 传输时延，但需结合论文原版确认是否 OCR 错误。状态需人工复核。
5GS 驻留时间的计算：NW-TT 和 DS-TT 分别在 5GS 的入口（\(t_{1'}\)）和出口（\(t_{2'}\)）处为“Sync”数据包分配时间戳。这些时间戳确定 DL 驻留时间（\(d_{res,down}\)），如公式（2）所详述。\(d_{res,down}\) 的值被临时存储在 DS-TT 中，直到“Follow-Up”数据包到达；在该数据包中，DS-TT 使用 \(d_{res,down}\) 的值更新 Correction Field（CF）。该过程使 TSN Slave 能够在其总链路时延估计中，补偿“Sync”数据包在 5GS 内引入的时延。对于“Delay Request”和“Delay Reply”数据包，也应用类似过程，从而能够利用“Delay Request”的时间戳以及“Delay Reply”中的 CF 更新来估计 UL 驻留时间（\(d_{res,up}\)），如图 3 所示。UL 和 DL 驻留时间计算如下： \[ \begin{split} d_{res,down}=t_{2'}-t_{1'}\\ d_{res,up}=t_{4'}-t_{3'} \end{split} \tag{2} \]
术语和消息名称已保留；DL/UL 驻留时间、CF 更新、DS-TT 临时存储的因果链完整。该段与 P032 的前半部分重复，可能是输入切分或抽取重复导致；公式中的撇号下标已按数学排版归一。状态需人工复核。
TSN Slave 处的时钟恢复：需要若干操作 [7]。首先，我们将从 TSN Master 发送到 TSN Slave 的 PTP 数据包时延与 5GS 的可变驻留时间解耦。也就是说，由于驻留时间计算，5GS 在 UL 和 DL 中引入可变抖动，从而为 PTP 数据包产生不同的时延。我们将“Sync”数据包的 DL 时延称为 \(D_{e,down}\)，而 \(D_{e,up}\) 是“Delay Request”数据包的 UL 时延。这两个时延之和确定 \(p_{\mathcal{E}}\) 传输时延（\(D_{\mathcal{E}}\)）。\(D_{e,down}\)、\(D_{e,up}\) 和 \(D_{\mathcal{E}}\) 计算如下： \[ D_{e,down}=t_2-t_{2'}+t_{1'}-t_1=t_2-t_1-d_{res,down} \tag{3} \] \[ D_{e,up}=t_4-t_{4'}+t_{3'}-t_3=t_4-t_3-d_{res,up} \tag{4} \] \[ D_{\mathcal{E}}=D_{e,down}+D_{e,up} \tag{5} \] \(d_{res,down}\) 和 \(d_{res,up}\) 缓解了 UL 和 DL 中具有不同时延这一相关问题。如图 3 所示，TSN Slave 在接收“Sync”之后、生成“Delay Request”之前，需要一个响应时间（\(d_{response}\)）。该 \(d_{response}\) 计算如下： \[ d_{response}=t_3-t_2 \tag{6} \]
公式（3）至（6）的变量、上下行方向、消息对应关系已逐项保留。原文 “p ℰ \(p_{\mathcal{E}}\) transmission delay” 存在 OCR 或排版识别风险，译文保留但需人工核对；该段与 P032 中间部分重复，也提示输入段落切分异常。状态需人工复核。
TSN Slave 根据所有时间戳、驻留时间和响应时间，计算其相对于 TSN Master 的时间偏移（\(\beta\)），如下： \[ \beta=(t_2-t_1)-\frac{D_{\mathcal{E}}}{2}-d_{res,down} \tag{7} \]
时间偏移 \(\beta\)、\(D_{\mathcal{E}}/2\)、\(d_{res,down}\) 均已保留；公式编号（7）保留。该段与 P032 末尾重复，但本段自身无明显翻译问题。由于依赖前文公式上下文，建议人工核对公式排版。
因此，TSN Slave 补偿其时钟偏移，以设置 TSN GM 时间。该过程补偿了 5GS 中时间参考传播的时延可变性，确保整个网络中的精确同步，而这对于工业应用和 IIoT 是必不可少的。这两项功能已经在构成 TT 和 TSN Slave 的商用设备中实现。
“clock offset”“TSN GM time”“latency variability”“time references”“IIoT”等关键术语均已对应翻译或保留。逻辑上“偏移补偿→设置时间→补偿时延可变性→支持精确同步→已在商用设备实现”完整。未发现明显问题。
我们实现了一个 TSN-5G 测试床来评估时间同步性能，如图 4 所示，其中我们只考虑 PTP 流量。TSN 系统由 TSN Master 和 TSN Slave 节点组成，并在商用 TSN 交换机（Safran 的 Z16）上实现。这些设备根据 [1] 中规定的规范集成了时间敏感网络功能。TSN Slave 包含用于实现 TSN 时钟恢复功能的修改，如第 IV-A 节所详述。对于 PTP 数据包的封装和交换，这些设备在单播模式下使用 IPv4 之上的 User Datagram Protocol（UDP）协议，并采用 E2E 机制；这是 5G 网络中使用商用设备时被广泛采用的一种方式。在这种 UDP/IPv4 模式下，PTP 数据包的源 IP 地址和目的 IP 地址分别是分配给 TSN Master 和 TSN Slave 端口的地址。PTP 数据包传输速率随实验而变化。TSN Master 与 TSN GM 同步，TSN GM 由时间和频率参考服务器（Safran 的 Secure Sync）实现。TSN GM 与 TSN Master 之间的时间同步通过同轴电缆执行，使用 Pulse Per Second（PPS）和 10 MHz 信号。
设备型号 Safran Z16、Secure Sync，协议 UDP/IPv4、unicast、E2E、PPS、10 MHz 均已保留。原文出现 “10 10 MHz” 疑似 OCR 重复，译为 10 MHz；需人工核对原 PDF。其余数字、引用 [1]、章节 IV-A 均保留。
5GS 由 TT 组成，TT 同样使用商用 TSN 交换机（Safran 的 Z16）实现，且二者均经过修改以实现 TC。这些 TT 与第二台 Safran Secure Sync 服务器提供的 5G 时钟同步，该服务器充当 5G GM。由于 5G GM 只有一个 PPS 和 10 MHz 输出，因此需要一个辅助 TSN 交换机（Z16-TSN）来向 TT 分发时间参考。该交换机通过连接到 PPS 和 10 MHz 信号的同轴电缆与 5G GM 同步，见图 4。随后，该交换机通过 L2 将时间参考传输到 NW-TT 和 DS-TT，使用 E2E 机制，PTP 消息传输速率为 1 packet/s。5GS 还由一个 Base Station（BS）和一个 5G core 组成，二者都集成在一台 PC 中，该 PC 配有两块 50 MHz PCIe SDR Amarisoft 卡和一个 AMARI NW 600 许可证。BS 工作在 n78 频段，使用 30 kHz 的 Sub-Carrier Spacing（SCS）和 Time Division Duplex（TDD）模式，TDD pattern 为 1,0。UE 由连接到 Intel NUC 10 NUC10i7FNKN 的 Quectel RM500Q-GL 调制解调器组成，该 Intel NUC 作为 Customer Premise Equipment（CPE）。该设备包含 Intel i7-10710U 处理器、16 GB RAM 和 512 GB SSD 存储，并运行 Ubuntu 22.04。
TT、TC、5G GM、Z16-TSN、NW-TT、DS-TT、L2、BS、5G core、PCIe SDR、AMARI NW 600、n78、SCS、TDD、UE、CPE 等术语和型号均已保留。原文 “10 10 MHz” 与 “50 50 MHz PCLe SDR” 存在 OCR 风险，分别译为 10 MHz 和 50 MHz PCIe SDR；“PCLe” 也疑似应为 “PCIe”。状态需人工复核。
所有实验均在 LABIFIX 法拉第笼内进行，其中 BS 天线通过 SMA 连接器连接到 SDR，Quectel 调制解调器通过 USB 连接。该法拉第笼避免了在许可频段内产生辐射。其余设备之间的连接使用 1 Gbps 光纤完成，但 NW-TT 到 gNB、DS-TT 到 UE 的连接除外；这些连接分别使用 1 Gbps RJ-45 电缆，如图 4 所示。
LABIFIX、Faraday cage、BS、SMA、SDR、Quectel、USB、licensed frequency bands、1 Gbps、RJ-45、gNB、UE 均已保留或准确翻译。连接例外关系“NW-TT 和 DS-TT 分别到 gNB 和 UE”已明确表达。未发现明显问题。
我们进行了两个实验，以评估 TC 的性能和 TSN 时间同步的准确性。第一个实验分析在改变 PTP 数据包传输速率时 TSN Master 与 TSN Slave 之间的同步。第二个实验比较了两种情况下的时间同步：一种是 TSN Master 与锁定到 GNSS 参考的 TSN GM 同步，另一种是在 FR 中运行、使用其自身内部时钟。在这两种情况下，我们都使用高精度计数器测量 TSN Master 与 TSN Slave 时钟之间的偏移，测量时长为 20 min。表 I 总结了实验中使用的配置。
两个实验目标、变量和比较条件均已保留；GNSS、FR、高精度计数器、20 min、表 I 均保留。原文 “20 20 min” 疑似 OCR 重复，译为 20 min；FR 缩写未在本段定义，需结合上下文人工确认其含义。状态需人工复核。
在 GM 与 GNSS 同步的情况下，TC 机制的实测偏移结果见表 II 中测试“0”至“2”，其中给出了每种情况下偏移的平均值、最大值、最小值和标准差。特别地，图 5 展示了在 1 1 p/s 速率下测得的偏移，其分布近似服从高斯分布。其余测试也观察到了类似行为。数据表明，E2E TC 机制具有非常好的同步性能，整体抖动低于 500 500 ns，偏移处于数百纳秒范围内。最佳性能出现在测试“1”中，而较低的传输速率会产生较慢的偏移校正，从而降低精度。相反，较高的速率会导致 TT 中的数据包累积，这会改变 5GS 中的驻留时间测量，进而在 TSN Slave 时钟校正中引入误差。值得注意的是，所有测试都满足工业应用的同步要求，验证了我们的分布式 E2E TC 系统的有效性，即使是在 5GS 这样具有高可变性且非确定性的介质中也是如此。
原文中“1 1 p/s”和“500 500 ns”疑似 PDF/OCR 重复识别，已按原样保留；“all test meets”存在语法问题，按“所有测试都满足”理解；“our the distributed”存在原文冗余，译为“我们的分布式”。术语 GM、GNSS、TC、E2E TC、TT、5GS、TSN Slave 均已保留。需结合表 II 和图 5 确认速率与数值是否应为单个“1 p/s”和“500 ns”。
当 TSN Master 运行于 FR 时的实测偏移结果见表 II 的测试“3”，其呈现出类似高斯的分布，与图 5 所示相似。与测试“2”的结果比较表明，二者具有等效的时间精度。尽管 FR 似乎提供了略好的稳定性，但这可能归因于 TSN Master 的内部振荡器无需进行调整以跟随 GNSS 参考，从而避免了额外波动。然而，这并不意味着更高的准确度，因为它并未与全局时间参考进行比较。由于 5GS 引入了显著的时延变化，FR 与 GNSS 之间的偏移差异可以忽略不计。因此，我们得出结论：E2E TC 机制在两种参考下等效运行，对同步没有显著影响。
FR 缩写原文未在本段展开，保留不译，需依赖前文确认含义；“temporal accuracy”译为“时间精度”，“accuracy”后文译为“准确度”以区分稳定性语境；测试“2”“3”、表 II、图 5 引用均已保留。逻辑上先比较稳定性，再说明不代表相对于全局参考的准确度更高，未发现明显问题。
本文在一个 TSN - 5G 网络中对 E2E TC 进行了实证评估，该 E2E TC 在带有单一时钟的商用 TSN 交换机上实现。该解决方案包含对 5GS 内部驻留时间的计算（NW-TT 和 DS-TT），以及在从节点处恢复 TSN 时钟域。我们部署了一个采用商用设备的 TSN - 5G 测试平台，用于分析不同 PTP 消息速率下的时间同步。结果显示峰峰值准确度为 500 500 ns，满足工业要求，并表明某些传输速率可能诱发偏移，但无论参考源是 GNSS 还是 FR，都不会超过允许裕量。本文工作是证明在集成 TSN - 5G 网络中实现 E2E TC 可行性的第一步。未来研究将探索存在流量负载时的同步，以及提取 SIB 9 参考以使 UE 与 gNB 的 5G GM 时钟对齐。
“500 500 ns”疑似 PDF/OCR 重复识别，已按原样保留，需结合论文表格或正文上下文确认是否应为“500 ns”；“single clock”译为“单一时钟”，可能指交换机内部单时钟架构；NW-TT、DS-TT、PTP、GNSS、FR、SIB 9、UE、gNB、5G GM 均已保留；“peak-to-peak accuracy”按“峰峰值准确度”翻译，需人工确认是否应按计量习惯译为“峰峰值精度”。
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Time synchronization distribution is an essential service for the Industrial Internet of Things (IIoT), playing a crucial role in the evolution towards Industry 4.0 and 5.0. Applications in these sectors depend on precise synchronization for reliable communication, low latency and operational efficiency to optimize automation and interaction between robots, sensors and machinery, as well as accurate sensor data analysis. The Time Sensitive Networking (TSN) standard, defined by IEEE 802.1 [ 1 ], enables synchronization accuracy below 100 μ s 100\ \mu s [ 2 ], ensuring deterministic and reliable operation. However, the growing need for mobility in industrial, Internet of Things (IoT) and robotics sectors presents new challenges, as TSN was conceived for wired networks. As a solution, 3GPP Release 16 proposes integrating Fifth Generation (5G) with TSN to provide wireless communication and mobile flexibility without compromising synchronization requirements.
TSN functionalities such as IEEE 802.1 Qbv, IEEE 802.1 Qcc and IEEE 802.1 Qci rely on accurate time synchronization. However, 5G introduces challenges that degrade synchronization accuracy, such as high levels of jitter, asymmetries in Uplink (UL) and Downlink (DL) delays, variable processing times in devices like the Next-Generation Node B (gNB) and User Plane Function (UPF), and retransmissions. TS 22.104 [ 3 ] establishes the 5G System (5GS) requirements for industrial and IIoT networks, specifying a maximum time synchronization error of 900 900 ns and support for up to 32 32 simultaneous working clock domains. These domains provide high-precision time to the devices within them, allowing TSN devices to manage multiple clock domains simultaneously. While a global clock domain provides the date and time to the devices belonging to that domain. In some cases, the working and global clock domains may overlap. Meanwhile, 3GPP TS 23.501 [ 4 ] defines several configurations to enable TSN synchronization in the 5GS, which can be implemented as a time-aware system using the IEEE 802.1AS standard [ 5, 6 ], which uses the generic Precision Time Protocol (gPTP) protocol, or configured as a Boundary Clock (BC) or Transparent Clock (TC) following the IEEE 1588 standard [ 7 ].
Several studies have addressed the challenges of time synchronization distribution in TSN - 5G network. For example, Striffler et al. [ 8 ] analyze frequency drift and timing errors when 5GS operated as a TC, which can lead to non-compliance with time synchronization requirements. While Wang et al. [ 9 ] propose solutions to mitigate the effects of multi- gNB competition, retransmissions, and mobility in a 5GS modeled as TC. Shi et al. [ 10 ] investigate synchronization errors in 5GS configured as BC, focusing on the uncertainty due to reference time granularity and propagation delay estimation. Val et al. [ 11 ] demonstrate that, despite Wi-Fi variability, TSN -compatible synchronization accuracies are achieved through hardware-level modifications, although this approach is currently infeasible for commercial 5G networks.
To our knowledge, there is no empirical evaluation of the TC in an integrated TSN - 5G network. Therefore, the objective of this paper is to empirically investigate the distribution of TSN time synchronization in a TSN - 5G network when the 5GS is configured as an End-to-End (E2E) TC. Our main contributions are as follows:
• We analyze the various configurations of 5GS to support TSN synchronization transport, considering its implementation in commercial single-clock equipment. • We implement the E2E TC on commercial TSN switches. This implementation comprises two processes: the computation of the residence time introduced by the 5GS and the recovery of the TSN clock domain at the slave node. • We deploy a TSN - 5G network testbed with commercial equipment to evaluate time synchronization performance. • We performed an experimental evaluation of the time synchronization accuracy on the implemented testbed.
We analyze the various configurations of 5GS to support TSN synchronization transport, considering its implementation in commercial single-clock equipment.
We implement the E2E TC on commercial TSN switches. This implementation comprises two processes: the computation of the residence time introduced by the 5GS and the recovery of the TSN clock domain at the slave node.
We deploy a TSN - 5G network testbed with commercial equipment to evaluate time synchronization performance.
We performed an experimental evaluation of the time synchronization accuracy on the implemented testbed.
Our results indicate a peak-to-peak time synchronization of 500 500 ns, meeting industrial requirements (≤ 1 μ s \leq 1\ \mu s). Also, we note that, at certain Precision Time Protocol (PTP) message transmission rates, time offsets can be observed that may affect the time synchronization but do not exceed the requirements. These results are independent of whether the synchronizing transmitter (master node) is synchronized to an external reference (Global Navigation Satellite System (GNSS)) or operates with its internal clock (Free-running (FR)).
The rest of the paper is structured as follows: Section II presents the background and an analysis of time synchronization options in TSN - 5G networks. Section III describes the model and architecture of the integrated network. Section IV details the design and operation of the TC, along with PTP messages analysis and offset calculation. Section V describes the testbed and experimental setup. Section VI presents and discusses the results obtained. Finally, Section VII concludes with the main contributions.
In the TSN - 5G integrated network, there are two synchronization processes running in parallel, the 5G time synchronization process and the TSN time synchronization process [ 2, 12 ], as shown in Figure 1. The 5G synchronization process provides the temporal reference from the 5G Grandmaster (GM) to the 5GS devices, such as the UPF, gNB and User Equipment (UE). In paralell, the TSN synchronization process provides the TSN GM temporal reference to the TSN network devices. The two synchronization processes are considered to be independent, providing flexibility in the design and implementation of the synchronization process. Both processes are detailed below, but first we describe the 5GS architecture in the integrated TSN - 5G network proposed by 3GPP.
According to 3GPP TS 23.501 [ 4 ], the 5GS acts as a PTP instance in the TSN network. As shown in Figure 1, the external network consists of end stations and TSN bridges, whose time reference is provided by a PTP or gPTP GM. In the 5G domain, a 5G GM synchronizes the gNB, which distributes the time reference to the UE over the radio link and to the UPF via the PTP -compliant 5G transport network. To integrate 5G with TSN, the UPF implements a TSN Translator (TT) (Network-Side Time Sensitive Networking Translator (NW-TT)) that interfaces with the external TSN bridge, while the UE connects to another TT (Device-Side Time Sensitive Networking Translator (DS-TT)) and this connects to a TSN end station. These TT ensure interoperability, allowing the 5GS to operate as a logical bridge in various modes without direct alignment with the TSN GM.
The 5G time synchronization process is based on the internal distribution of the 5G GM reference across the 5GS transport network and the 5GS Radio Access Network (RAN) [ 13 ]. A straightforward solution in the 5G transport network is to install GNSS receivers in each gNB, which offers ± 100 \pm 100 ns accuracy [ 13 ], meeting the 5GS timing requirements. However, this method comes with high deployment and maintenance costs, indoor installation difficulties and vulnerability to jamming. Alternatively, synchronization protocols over packet networks, such as IEEE 1588 [ 7 ], with adapted profiles defined by ITU-T (e.g., G.8275.1 (PTP -aware) and G.8275.2 (non- PTP -aware)).
In the 5G RAN, synchronization between the 5G GM and the UE is achieved through the gNB, as defined in TS 38.331. The gNB continuously updates the 5G GM reference [ 2, 13, 14 ] and periodically transmits it to the UE via System Information Block (SIB) or unicast Radio Resource Control (RRC) messages, identified via a System Frame Number (SFN). The SIB 9 message, which contains the time information in GPS and UTC formats, is transmitted at the boundary between two SFN, enabling synchronization of the devices. In addition, the 5G reference must be adjusted according to the cell size to compensate for DL propagation delay and minimize reception uncertainty. Accurate delay calculation and obtaining the SIB 9 reference are essential aspects, although they are not addressed in this study. For more information, see [ 14, 13 ].
TS 23.501 [ 4 ] defines several modes in which the 5GS can be configured to operate as one PTP instance [ 2 ], enabling TSN time synchronization in an integrated TSN - 5G network. Specifically, these clock modes are:
• 5GS as a Time-Aware System: The 5GS behaves as an IEEE 802.1AS-compliant node [ 5 ], participating in time synchronization using the gPTP protocol. NW-TT and DS-TT synchronize with both GM clocks (TSN GM and 5G GM), thus requiring two clocks, and manage gPTP messages (transmitted in Layer 2 (L2)) to ensure synchronization [ 2 ]. • 5GS as BC: The 5GS is configured as a BC according to the IEEE 1588 standard [ 7 ], actively participating in synchronization. That is, the 5GS maintains the PTP domain timescale and synchronizes the connected PTP time receivers (e.g., DS-TT, TSN Slave, etc.), acting as the time source. This mode provides higher accuracy and robustness, allowing network scalability and lower impact of jitter and propagation delay in multi-device scenarios, but is more complex. • 5GS as TC: The 5GS behaves as a TC according to the IEEE 1588 standard [ 7 ], without actively participating in time synchronization, but measures the residence time of PTP messages within the network and uses it to correct them before forwarding them. The TT manage the PTP messages and calculate the delay within the 5GS. There are two types of TC: Peer-to-Peer (P2P) or E2E. In P2P TC [ 15 ] the 5GS measures the delay between two directly connected neighboring node using Peer Delay Messages and calculates the residence time of the PTP messages within the 5G network. The sum of the residence time and the link delay along the path is reported to the PTP time receiver [ 6 ]. The E2E TC calculates the total E2E delay between the PTP transmitter and receiver by exchanging PTP messages. In the 5GS the residence time is calculated and the sum of the residence time over the entire path is added in the correction field of the PTP messages. This sum of residence times is relayed to the PTP time receiver. This way, the PTP receiver can calculate the total compensation based on the sum of residence times in the correction field of the messages. Therefore, P2P TC compensates for the latency between neighboring nodes while E2E TC compensates for the latency of the entire E2E path. P2P TC requires IEEE 1588 compatibility on all network devices, E2E TC does not.
5GS as a Time-Aware System: The 5GS behaves as an IEEE 802.1AS-compliant node [ 5 ], participating in time synchronization using the gPTP protocol. NW-TT and DS-TT synchronize with both GM clocks (TSN GM and 5G GM), thus requiring two clocks, and manage gPTP messages (transmitted in Layer 2 (L2)) to ensure synchronization [ 2 ].
5GS as BC: The 5GS is configured as a BC according to the IEEE 1588 standard [ 7 ], actively participating in synchronization. That is, the 5GS maintains the PTP domain timescale and synchronizes the connected PTP time receivers (e.g., DS-TT, TSN Slave, etc.), acting as the time source. This mode provides higher accuracy and robustness, allowing network scalability and lower impact of jitter and propagation delay in multi-device scenarios, but is more complex.
5GS as TC: The 5GS behaves as a TC according to the IEEE 1588 standard [ 7 ], without actively participating in time synchronization, but measures the residence time of PTP messages within the network and uses it to correct them before forwarding them. The TT manage the PTP messages and calculate the delay within the 5GS.
There are two types of TC: Peer-to-Peer (P2P) or E2E. In P2P TC [ 15 ] the 5GS measures the delay between two directly connected neighboring node using Peer Delay Messages and calculates the residence time of the PTP messages within the 5G network. The sum of the residence time and the link delay along the path is reported to the PTP time receiver [ 6 ]. The E2E TC calculates the total E2E delay between the PTP transmitter and receiver by exchanging PTP messages. In the 5GS the residence time is calculated and the sum of the residence time over the entire path is added in the correction field of the PTP messages. This sum of residence times is relayed to the PTP time receiver. This way, the PTP receiver can calculate the total compensation based on the sum of residence times in the correction field of the messages.
Therefore, P2P TC compensates for the latency between neighboring nodes while E2E TC compensates for the latency of the entire E2E path. P2P TC requires IEEE 1588 compatibility on all network devices, E2E TC does not.
In this paper, we opt for the E2E TC mode in 5GS, as it allows transmission of multiple working clock domains from different GM s, a key requirement in industrial environments. The IEEE 802.1AS standard, requiring L2 transmission, has limitations for integration into commercial equipment. However, it has been demonstrated that an IEEE 802.1AS network can operate as distributed clock (BC, ordinary or TC) according to IEEE 1588 [ 15 ], facilitating the transport of multiple clock signals between domains. Moreover, the TC by operating independently, without the need to synchronize its own clocks simplifies the integration of 5GS into existing TSN networks or enables the incorporation of new 5G operators, thus ensuring greater flexibility in the deployment of TSN - 5G network.
We consider the TSN - 5G system model as illustrated in Figure 2. The TSN system includes a TSN Master, synchronized with the TSN GM, which distributes the time reference to other TSN bridges and/or TSN end station. This synchronization is extended to a TSN Slave in another TSN domain, interconnected through the 5G network. This TSN Slave, once synchronized, distributes the synchronization to other TSN bridges or TSN end stations. The 5GS incorporates a 5G GM, which directly provides the time reference to the gNB and NW-TT, both connected through the UPF. Since commercial equipment does not integrate a UPF with NW-TT, the NW-TT is synchronized with the 5G GM and connected directly to the TSN Master. While the DS-TT, also synchronized to the 5G GM via the UE, connects to the TSN Slave. This differs from the model in Figure 1, as in this case the NW-TT and UPF are separate devices, and both the NW-TT and DS-TT are directly connected to the TSN Master and TSN Slave, respectively.
Time synchronization in the TSN - 5G network is based on IEEE 1588 compliant PTP frame transmission [ 7 ]. In this paper, we use the E2E TC clock mechanism for time synchronization. We define ℱ \mathcal{F} as the set of PTP flows traversing the TSN - 5G network. Each PTP flow f i ∀ i ∈ ℱ f_{i}\ \forall\ i\in\mathcal{F} represent a bidirectional communication between a PTP transmitter node, synchronized with a GM and a PTP receiver node, not synchronized with the GM. We refer as a PTP transmitter node to the TSN Master and as a PTP receiver node to the TSN Slave. These PTP flows ensure that the PTP transmitter and the PTP receiver maintain the same time reference as the GM. Therefore, each flow f i ∀ i ∈ ℱ f_{i}\ \forall\ i\in\mathcal{F} is transmitted from the TSN Master to the TSN Slaves, traversing the 5G network. In our case, we focus on a single PTP flow f i f_{i} to evaluate synchronization. This f i f_{i} transmits a series of p ℰ f i p^{f_{i}}_{\mathcal{E}} PTP packets between the TSN Master and the Slave using the E2E TC mechanism detailed in Section IV. For clarity, henceforth, the superindex f i f_{i} will be omitted, meaning p ℰ f i = p ℰ p^{f_{i}}_{\mathcal{E}}=p_{\mathcal{E}} in all variables, since only a single PTP flow is considered.
In this scenario, as previously explained, two synchronization processes coexist [ 12 ]: TSN synchronization and 5G synchronization. We consider that each device within the TSN - 5G network has a single clock. The clocks of the TSN Master and Slave are synchronized with the TSN GM reference, while the TT are solely synchronized with the 5G GM. In 5G synchronization, the 5G GM reference is transmitted through the gNB to the UE and the UE transmits it to the DS-TT. In this paper, we do not focus on the 5G clock recovery by the UE and its subsequent transmission to the DS-TT, therefore, we assume perfect recovery from SIB 9 for synchronization at the UE and subsequently at the DS-TT.
In TSN synchronization, the p ℰ p_{\mathcal{E}} include a timestamp. Specifically, each p e e ∈ ℰ p_{e}\ e\in\mathcal{E} contains a timestamp that records the moment the TSN Master sends the packet e e. However, due to delays caused by software and hardware packet processing in the TSN Master, the timestamp in p e p_{e} may lack precision. Then, the transmission timestamp of p e p_{e} is included in p e + 1 p_{e+1}, recording the precise moment (t 1 t_{1}) when p e p_{e} exits the TSN Master. When the TSN Slave receives p e p_{e}, it records the timestamp (t 2 t_{2}).
In addition, p ℰ p_{\mathcal{E}} packets when traversing the 5G network experience variable delays (jitter), compromising the timing accuracy and affecting the correct operation of the TSN nodes. This present a challenge to accurately estimate the time reference. To address this issue, the delay experienced by the p ℰ p_{\mathcal{E}} while traversing the 5G network is calculated. This delay is referred to as the residence time in the 5G network (d r e s d_{res}). Its calculation involves generating timestamps for certain p e p_{e} packet at the TT. The NW-TT generates an ingress timestamp (t i n t_{in}) based on the 5GS reference time, while the DS-TT generates an egress timestamp (t e g t_{eg}) also based on the 5GS reference time. The residence time (d r e s d_{res}) is defined as: d r e s = t e g − t i n d_{res}=t_{eg}-t_{in} (1) Since the 5G network is asymmetric in its links, meaning the UL and DL delays differ depending on the radio channel’s characteristics, a specific residence time is defined for each link. The residence time for the UL is denoted as d r e s, u p d_{res,up}, and for the DL as d r e s, d o w n d_{res,down}.
Each TSN node incorporates an internal oscillator that may introduce noise to the device’s internal clock due to physical disturbances, causing clock skew. To mitigate this clock drift, PTP messages are generated with cycle T T.
We focus on the distribution of time synchronization in an integrated TSN - 5G network, implementing E2E TC mode in the 5GS. With this approach, 5G devices do not need to synchronize with the TSN GM time reference, as the 5G common time reference is used to accurately calculate the residence times (d r e s, u p d_{res,up}, d r e s, d o w n d_{res,down}) of p ℰ p_{\mathcal{E}} traversing the network. As explained in Section III, it is essential that the NW-TT and DS-TT share the same time reference derived from the 5G GM. This allows that the TC mechanism to operate in a manner equivalent to a standalone switch, ensuring consistency in the calculation of residence times from the timestamps generated on devices located at opposite ends of 5GS. Any failure to propagate a common time reference could lead to inconsistencies or invalid synchronization results between TSN systems at the edges. The following section details the PTP messages exchanged and the procedure to be followed to calculate the offset and residence time.
The E2E TC solution implemented in the 5GS exchanges PTP messages between the nodes of the distributed architecture, as illustrated in Figure 3. The TSN Master initiates synchronization by transmitting “Announce” messages, followed by “Sync” and “Follow-Up”. The TSN Slave then sends “Delay Request” and receives a “Delay Response” in reply. This exchange enables the measurement of the residence time on the 5GS, through the time stamping and delay estimation capabilities of the NW-TT and DS-TT, and the recovery of the TSN clock domain at the TSN Slave. Both functionalities are key to the operation of the TC and to perform TC on commercial switches, we have implemented both functionalities in these devices. Each functionality is detailed below:
1 Calculation of the 5GS residence time: NW-TT and DS-TT assign timestamps to the “Sync” packets at the ingress (t 1 ′ t_{1^{\prime}}) and egress (t 2 ′ t_{2^{\prime}}) of the 5GS, respectively. These timestamps determine the DL residence time (d r e s, d o w n d_{res,down}), as detailed in equation (2). The value of d r e s, d o w n d_{res,down} is temporarily stored in DS-TT until the arrival of the “Follow-Up” packet, where DS-TT updates the Correction Field (CF) with the value of d r e s, d o w n d_{res,down}. This procedure allows the TSN Slave to compensate for the delay introduced by the “Sync” packets within the 5GS for its estimates of the total link delay. An analogous process is applied for the “Delay Request” and “Delay Reply” packets, allowing the UL residence time (d r e s, u p d_{res,up}) estimation using the timestamps of “Delay Request” and the CF update in “Delay Reply”, as shown in Figure 3. The UL and DL residence time are calculated as: d r e s, d o w n = t 2 ′ − t 1 ′ d r e s, u p = t 4 ′ − t 3 ′ \begin{split}d_{res,down}=t_{2^{\prime}}-t_{1^{\prime}}\\ d_{res,up}=t_{4^{\prime}}-t_{3^{\prime}}\end{split} (2) 2 Clock recovery at the TSN Slave: several operations are necessary [ 7 ]. First, we decouple the delay of the PTP packets sent from the TSN Master to the TSN Slave from the variable residence time of the 5GS. That is, due to the residence time calculation, the 5GS introduces variable jitter in the UL and DL, generating different delays for PTP packets. We call D e, d o w n D_{e,down} the DL delay of the “Sync” packet, while D e, u p D_{e,up} is the UL delay of the “Delay Request” packet. The sum of both delays determines the p ℰ p_{\mathcal{E}} transmission delay (D ℰ D_{\mathcal{E}}). D e, d o w n D_{e,down}, D e, u p D_{e,up} and D ℰ D_{\mathcal{E}} are calculated as: D e, d o w n = t 2 − t 2 ′ + t 1 ′ − t 1 = t 2 − t 1 − d r e s, d o w n \displaystyle D_{e,down}=t_{2}-t_{2^{\prime}}+t_{1^{\prime}}-t_{1}=t_{2}-t_{1}-d_{res,down} (3) D e, u p = t 4 − t 4 ′ + t 3 ′ − t 3 = t 4 − t 3 − d r e s, u p \displaystyle D_{e,up}=t_{4}-t_{4^{\prime}}+t_{3^{\prime}}-t_{3}=t_{4}-t_{3}-d_{res,up} (4) D ℰ = D e, d o w n + D e, u p \displaystyle D_{\mathcal{E}}=D_{e,down}+D_{e,up} (5) d r e s, d o w n d_{res,down} and d r e s, u p d_{res,up} mitigate the associated problem of having different latencies in UL and DL. The TSN Slave requires a response time (d r e s p o n s e d_{response}) after receiving the “Sync” before generating the “Delay Request”, as shown in Figure 3. This d r e s p o n s e d_{response} is calculated as: d r e s p o n s e = t 3 − t 2 \begin{split}d_{response}=t_{3}-t_{2}\end{split} (6) The TSN Slave calculates the time offset (β \beta) with respect to the TSN Master from all timestamps, the residence time and the response time, as follows: β = (t 2 − t 1) − D ℰ 2 − d r e s, d o w n \begin{split}\beta=(t_{2}-t_{1})-\frac{D_{\mathcal{E}}}{2}-d_{res,down}\end{split} (7)
Calculation of the 5GS residence time: NW-TT and DS-TT assign timestamps to the “Sync” packets at the ingress (t 1 ′ t_{1^{\prime}}) and egress (t 2 ′ t_{2^{\prime}}) of the 5GS, respectively. These timestamps determine the DL residence time (d r e s, d o w n d_{res,down}), as detailed in equation (2). The value of d r e s, d o w n d_{res,down} is temporarily stored in DS-TT until the arrival of the “Follow-Up” packet, where DS-TT updates the Correction Field (CF) with the value of d r e s, d o w n d_{res,down}. This procedure allows the TSN Slave to compensate for the delay introduced by the “Sync” packets within the 5GS for its estimates of the total link delay. An analogous process is applied for the “Delay Request” and “Delay Reply” packets, allowing the UL residence time (d r e s, u p d_{res,up}) estimation using the timestamps of “Delay Request” and the CF update in “Delay Reply”, as shown in Figure 3. The UL and DL residence time are calculated as: d r e s, d o w n = t 2 ′ − t 1 ′ d r e s, u p = t 4 ′ − t 3 ′ \begin{split}d_{res,down}=t_{2^{\prime}}-t_{1^{\prime}}\\ d_{res,up}=t_{4^{\prime}}-t_{3^{\prime}}\end{split} (2)
Clock recovery at the TSN Slave: several operations are necessary [ 7 ]. First, we decouple the delay of the PTP packets sent from the TSN Master to the TSN Slave from the variable residence time of the 5GS. That is, due to the residence time calculation, the 5GS introduces variable jitter in the UL and DL, generating different delays for PTP packets. We call D e, d o w n D_{e,down} the DL delay of the “Sync” packet, while D e, u p D_{e,up} is the UL delay of the “Delay Request” packet. The sum of both delays determines the p ℰ p_{\mathcal{E}} transmission delay (D ℰ D_{\mathcal{E}}). D e, d o w n D_{e,down}, D e, u p D_{e,up} and D ℰ D_{\mathcal{E}} are calculated as: D e, d o w n = t 2 − t 2 ′ + t 1 ′ − t 1 = t 2 − t 1 − d r e s, d o w n \displaystyle D_{e,down}=t_{2}-t_{2^{\prime}}+t_{1^{\prime}}-t_{1}=t_{2}-t_{1}-d_{res,down} (3) D e, u p = t 4 − t 4 ′ + t 3 ′ − t 3 = t 4 − t 3 − d r e s, u p \displaystyle D_{e,up}=t_{4}-t_{4^{\prime}}+t_{3^{\prime}}-t_{3}=t_{4}-t_{3}-d_{res,up} (4) D ℰ = D e, d o w n + D e, u p \displaystyle D_{\mathcal{E}}=D_{e,down}+D_{e,up} (5) d r e s, d o w n d_{res,down} and d r e s, u p d_{res,up} mitigate the associated problem of having different latencies in UL and DL. The TSN Slave requires a response time (d r e s p o n s e d_{response}) after receiving the “Sync” before generating the “Delay Request”, as shown in Figure 3. This d r e s p o n s e d_{response} is calculated as: d r e s p o n s e = t 3 − t 2 \begin{split}d_{response}=t_{3}-t_{2}\end{split} (6)
The TSN Slave calculates the time offset (β \beta) with respect to the TSN Master from all timestamps, the residence time and the response time, as follows: β = (t 2 − t 1) − D ℰ 2 − d r e s, d o w n \begin{split}\beta=(t_{2}-t_{1})-\frac{D_{\mathcal{E}}}{2}-d_{res,down}\end{split} (7)
Thus, the TSN Slave compensates for its clock offset to set the TSN GM time. This procedure compensates for latency variability in the propagation of time references in 5GS, ensuring accurate synchronization throughout the network, essential for industrial applications and the IIoT. Both functionalities have been implemented in commercial equipment that make up the TT and the TSN Slave.
We implemented a TSN - 5G testbed to evaluate time synchronization performance, illustrated in Figure 4, where we only considered PTP traffic. The TSN systems are composed of TSN Master and TSN Slave nodes, implemented on commercial TSN switches (Z16 from Safran). These devices integrate time-sensitive networking features according to the specifications set forth in [ 1 ]. TSN Slave contains modifications to implement the TSN clock recovery functionality, as detailed in Section IV-A. For PTP packet encapsulation and exchange, these devices use the User Datagram Protocol (UDP) protocol over IPv4 in unicast mode with the E2E mechanism, a modality widely adopted in 5G networks with commercial devices. In this UDP/IPv4 mode, the source and destination IP addresses of the PTP packets are the addresses assigned to the TSN Master and TSN Slave ports, respectively. The PTP packet transmission rate varies depending on the experiment. The TSN Master is synchronized with the TSN GM, implemented by a time and frequency reference server (Safran’s Secure Sync). The time synchronization between the TSN GM and the TSN Master is performed by coaxial cables, using the Pulse Per Second (PPS) and 10 10 MHz signals.
5GS consists of the TT, also implemented with commercial TSN switches (Safran’s Z16), both modified to implement TC. These TT are synchronized with the 5G clock provided by a second Safran Secure Sync server, which acts as the 5G GM. Since the 5G GM only has a single PPS and 10 10 MHz output, an auxiliary TSN switch (Z16-TSN) is required to distribute the time reference to the TT. This switch is synchronized with the 5G GM via coaxial cables connected to the PPS and 10 10 MHz signals, see Figure 4. Subsequently, the switch transmits the time reference to the NW-TT and DS-TT via L2, using an E2E mechanism with a PTP message transmission rate of 1 packet/s. The 5GS also consist of a Base Station (BS) and a 5G core, both integrated in a PC with two 50 50 MHz PCLe SDR Amarisoft cards and an AMARI NW 600 license. The BS operates in the frequency band n78, using a Sub-Carrier Spacing (SCS) of 30 kHz and a Time Division Duplex (TDD) mode, with a TDD pattern of 1,0. The UE consists of a Quectel RM500Q-GL modem connected to an Intel NUC 10 NUC10i7FNKN, which acts as a Customer Premise Equipment (CPE). This device contains an Intel i7-10710U processor with 16 GB of RAM and 512 GB of SSD memory, and runs Ubuntu 22.04.
All experiments are performed inside a LABIFIX Faraday cage, where the BS antennas are connected to a SDR via SMA connectors and the Quectel modem is connected via USB. This cage avoids radiation within the licensed frequency bands. The connections between the rest of the equipment are made using 1 Gbps optical fiber, except for the connections between the NW-TT and DS-TT to the gNB and UE, respectively, which use 1 Gbps RJ-45 cables, as shown in Figure 4.
We have performed two experiments to evaluate the performance of TC and the accuracy of TSN time synchronization. The first experiment analyzes the synchronization between the TSN Master and the TSN Slave when varying the PTP packet transmission rates. The second experiment compares the time synchronization when the TSN Master is synchronized to the TSN GM, locked to a GNSS reference, versus when operating in FR, using its own internal clock. In both cases, we measured the offset between the TSN Master and TSN Slave clocks for 20 20 min with a high precision counter. Table I summarizes the configurations used in the experiments.
The measured offset results of the TC mechanism, with the GM synchronized to a GNSS, are presented in Table II for the tests “0” to “2”, showing the average, maximum, minimum and standard deviation of the offset in each case. In particular, the measured offset at a rate of 1 1 p/s is illustrated in Figure 5, whose distribution follows approximately a Gaussian distribution. Similar behavior is observed for the rest of the tests. The data demonstrate very good synchronization performance for the E2E TC mechanism, with overall jitter below 500 500 ns and offset in the range of hundreds of nanoseconds. The best performance is obtained in the test “1”, while lower transmission rates generate slower offset correction, degrading accuracy. Conversely, higher rates cause packet accumulation in the TT, which alters the residence time measurement at 5GS, inducing errors in the TSN Slave clock correction. Remarkably, all test meets the synchronization requirements of industrial applications, validating the effectiveness of our the distributed E2E TC system, even in a high variability and non-deterministic medium, such as 5GS.
The measured offset results when TSN Master operates in FR are presented in test “3” of Table II, showing a Gaussian-like distribution, similar to that illustrated in Figure 5. Comparison of results with test “2” shows an equivalent temporal accuracy. Although FR seems to offer slightly better stability, this could be attributed to the absence of adjustments to the internal oscillator of the TSN Master to follow the GNSS reference, which avoids additional fluctuations. However, this does not imply higher accuracy as it is not compared to the global time reference. Since the 5GS introduces significant latency variations, the differences in offset between FR and GNSS are negligible. Thus, we conclude that the E2E TC mechanism operates equivalently under both references without significant impacts on synchronization.
This paper empirically evaluates an E2E TC in a TSN - 5G network, implemented on commercial TSN switches with a single clock. The solution contains the computation of the residence time within 5GS (NW-TT and DS-TT), and the recovery of the TSN clock domain at the slave node. We have deployed a TSN - 5G testbed with commercial equipment to analyze time synchronization at different PTP message rates. The results show a peak-to-peak accuracy of 500 500 ns, meeting industrial requirements, and show that certain transmission rates can induce offsets without exceeding the allowed margins, regardless of the reference (GNSS or FR). This work represents a first step to demonstrate the feasibility of E2E TC in an integrated TSN - 5G network. Future research will explore synchronization under traffic load and extraction of the SIB 9 reference to align the UE with the 5G GM clock of gNB.