Integrated Communications and Localization for Massive MIMO LEO Satellite Systems
集成通信和大规模 MIMO 低地球轨道卫星系统的定位

Index Terms-Integrated communications and localization, 6G, non-geostationary satellite, LEO satellite, massive MIMO, hybrid precoding, squared position error bound.
综合通信和定位，6G，非地球静止轨道卫星，LEO 卫星，大规模 MIMO，混合预编码，位置误差平方界。

Fifth generation (5G) wireless networks are under deployment and the basic functionalities and capabilities are defined within the 5G standard [2]. However, there still exist many requirements that 5 G networks may not satisfy, and sixth generation (6G) wireless networks are envisioned to offer seamless and ubiquitous coverage, higher communication capability and sensing/localization precision, and enhanced intelligence and security level, etc. [2]-[6]. One of the potential application scenarios of 6 G networks is the integrated communications and localization (ICAL) on Internet of Everything (IoE),
第五代（5G）无线网络正在部署中，并且 5G 标准中定义了基本功能和能力[2]。然而，5G 网络仍然存在许多无法满足的要求，第六代（6G）无线网络预计将提供无缝和普遍覆盖，更高的通信能力和定位精度，以及增强的智能和安全性等[2]-[6]。6G 网络的一个潜在应用场景是万物互联（IoE）中的综合通信和定位（ICAL）。

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版权 © 2015 IEEE。个人使用此材料是允许的。然而，对于任何其他用途的使用许可必须从 IEEE 获得，通过发送请求至 pubs-permissions@ieee.org。

Part of this work was presented in ICC’2023 [1].
本研究的部分内容已在 ICC’2023 上展示[1]。
Li You, Xiaoyu Qiang, Yongxiang Zhu, Wenjin Wang, and Xiqi Gao are with the National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China, and also with the Purple Mountain Laboratories, Nanjing 211100, China (e-mail: lyou@seu.edu.cn; xyqiang@seu.edu.cn; zhuyx@seu.edu.cn; wangwj@seu.edu.cn; xqgao@seu.edu.cn).
李有、强小宇、朱永祥、王文晋和高希奇均来自东南大学移动通信国家重点实验室，南京 210096，中国，同时也来自南京紫金山实验室，南京 211100，中国（电子邮件：lyou@seu.edu.cn；xyqiang@seu.edu.cn；zhuyx@seu.edu.cn；wangwj@seu.edu.cn；xqgao@seu.edu.cn）。

Fan Jiang is with the Pengcheng Laboratory, Shenzhen 518000, China. He was with the School of Information Technology, Halmstad University, Halmstad 30118, Sweden (Email: jiangf02@pcl.ac.cn)
蒋帆来自鹏城实验室，深圳 518000，中国。他之前在瑞典哈尔姆斯塔德大学信息技术学院，哈尔姆斯塔德 30118，瑞典（电子邮件：jiangf02@pcl.ac.cn）。

Christos G. Tsinos is with the National and Kapodistrian University of Athens, Evia, 34400, Greece and also with the Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg City 2721, Luxembourg (e-mail: ctsinos@uoa.gr).
克里斯托斯·G·齐诺斯来自希腊埃维亚 34400 的雅典国立卡波迪斯提里亚大学，同时也来自卢森堡大学信安可靠性与信任跨学科中心（SnT），卢森堡市 2721，卢森堡（电子邮件：ctsinos@uoa.gr）。

Henk Wymeersch is with the Department of Electrical Engineering, Chalmers University of Technology, Gothenburg 41296, Sweden (e-mail: henkw@chalmers.se).
荷兰·维梅尔施是瑞典查尔默斯理工大学电气工程系的成员，瑞典哥特堡市 41296（电子邮件：henkw@chalmers.se）。

Björn Ottersten is with the Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg City 2721, Luxembourg (bjorn.ottersten@uni.lu).
伯恩·奥特森是卢森堡大学跨学科安全、可靠性和信任中心（SnT）的成员，卢森堡市 2721，卢森堡（电子邮件：bjorn.ottersten@uni.lu）。
including tracking of persons or robots in an industrial site, autonomous driving, emergency response, etc. In such use cases, communications and localization are simultaneously performed by by jointly designing the signal waveform for shared spectrum on one hardware platform, to improve the utilization of resources [2], [5].
包括在工业场地跟踪人员或机器人、自动驾驶、应急响应等场景。在这种应用场景中，通过在同一个硬件平台上联合设计信号波形来进行通信和定位，以提高资源的利用效率[2]，[5]。

One of the common application cases for ICAL on IoE is the terrestrial network [7]-[9]. However, the ICAL functionality in a terrestrial network is unavailable in some areas where ground infrastructure is infeasible to deploy, or the signals are easily blocked [10]. In these scenarios, satellite networks can provide an attractive and cost effective complement for the terrestrial networks since they can provide larger coverage, and support wideband communications and more flexible localization for the areas that terrestrial networks might have coverage issues. Thus, satellite networks are expected to support global communications and seamless localization, and will play an essential role in performing ICAL for 6 G networks [5], [11][13]. Generally, the satellite networks are divided into two categories, namely geostationary earth orbit (GEO) and nonGEO (NGEO) satellite networks [14]. The typical satellite networks, including several global navigation satellite systems (GNSSs), e.g., global positioning system (GPS), GLONASS, and BEIDOU, are commonly capable of offering primary navigation with wide converge [10]. Those satellite networks are generally based on GEO and medium earth orbit (MEO) satellites, and recently, low earth orbit (LEO) satellite constellations have attracted much attention in terms of their application into position, navigation, and timing (PNT) [15]. The LEO satellites are usually deployed at altitudes of $200-$$200-$200-200- 2000 km [16], and can be launched with low cost and high flexibility [10]. Moreover, due to lower propagation delay and smaller path loss and footprint, the LEO satellite networks can provide better communication capability and localization precision compared with GEO counterparts [10], [17]. So far, several large LEO satellite systems, e.g., OneWeb, SpaceX, have been launched by governments and corporations, and see a steady reduction in launch costs, which makes it possible to develop global LEO satellite systems, and complement GNSSs.
ICAL 在 IoE 中的一个常见应用场景是地面网络[7]-[9]。然而，在一些地基基础设施部署不可行或信号容易被阻挡的区域，地面网络中的 ICAL 功能是不可用的[10]。在这种情况下，卫星网络可以为地面网络提供一个有吸引力且成本效益高的补充，因为它们可以提供更大的覆盖范围，并支持宽带通信和更灵活的定位，而这些是地面网络可能无法覆盖的区域。因此，卫星网络有望支持全球通信和无缝定位，并将在为 6G 网络执行 ICAL 方面发挥重要作用[5]，[11][13]。通常，卫星网络分为两类，即地球静止轨道（GEO）和非地球静止轨道（NGEO）卫星网络[14]。典型的卫星网络包括几个全球导航卫星系统（GNSSs），例如全球定位系统（GPS）、GLONASS 和北斗，通常能够提供广泛的主导航服务[10]。 这些卫星网络通常基于地球静止轨道（GEO）和中地球轨道（MEO）卫星，最近，低地球轨道（LEO）卫星星座因其在位置、导航和定时（PNT）方面的应用而引起了广泛关注 [15]。LEO 卫星通常部署在海拔 $200-$$200-$200-200- 2000 公里的高度 [16]，可以以较低的成本和较高的灵活性发射 [10]。此外，由于较低的传播延迟、较小的路径损耗和占地面积，LEO 卫星网络在通信能力和定位精度方面比 GEO 卫星更具优势 [10]，[17]。截至目前，已经有多家政府和公司发射了多个大型 LEO 卫星系统，例如 OneWeb、SpaceX，发射成本持续下降，这使得开发全球 LEO 卫星系统并补充 GNSS 成为可能。

Massive multiple-input multiple-output (MIMO) can provide numerous degrees of freedom in both temporal and spatial domains [5]. Besides, it can provide sufficient link budget to potentially support wideband communications to mobile terminals without dedicated antennas, and provide multiple links to do localization and tracking. Therefore, it has gained much attention for pure communications and localization, to improve the spectral efficiency (SE) and the precision of localization
大规模多输入多输出（MIMO）可以在时域和空域提供大量的自由度[5]。此外，它还可以提供足够的链路预算，潜在地支持宽频带通信到移动终端，而无需专用天线，并提供多条链路进行定位和跟踪。因此，它在纯通信和定位方面引起了广泛关注，以提高频谱效率（SE）和定位精度。
[17]-[19], which motivates us to adopt the massive MIMO technology for ubiquitous ICAL [5], [8], [20]. However, the implementation of fully digital transceivers in massive MIMO requires a large number of radio frequency (RF) chains, and might lead to high power consumption. Generally, this issue can be circumvented by developing a hybrid precoding architecture [21]. Recently, AST SpaceMobile has reported the successful deployment of the 693-square-foot MIMO array on its BlueWalker 3 LEO satellite [22]. Motivated by this, we combine the LEO satellite networks with the employment of massive MIMO in 6G, to support ICAL with the terrestrial user terminals (UTs) in the remote areas [4].
[17]-[19]，这促使我们采用大规模 MIMO 技术用于泛在 ICAL[5]，[8]，[20]。然而，大规模 MIMO 中全数字收发器的实现需要大量的射频（RF）链路，可能会导致高功耗。通常，可以通过开发混合预编码架构来解决这个问题[21]。最近，AST SpaceMobile 在其 BlueWalker 3 低地球轨道（LEO）卫星上成功部署了 693 平方英尺的 MIMO 阵列[22]。受此启发，我们将 LEO 卫星网络与 6G 中的大规模 MIMO 结合使用，以支持远程地区的陆地用户终端（UTs）的泛在 ICAL[4]。

In this work, we propose to implement ICAL in the massive MIMO LEO satellite systems, to trade-off between the communication capability and the localization precision, which are evaluated by the SE and the squared position error bound (SPEB), respectively [5]. Though the precoding designs for the downlink of the ICAL systems have been already investigated in the terrestrial networks [7]-[9], the signal propagation properties in such systems differs from that of the LEO satellite ones, and thus can not be applied directly. Specifically, owing to the mobility of the transceivers and the long satellite-to-UTs distance, there exist large Doppler shifts and a long propagation latency in the considered scenario [17], [23]. Thus, the instantaneous channel state information (iCSI) between the satellite and the UTs is time-varying, which may be difficult to estimate. Moreover, the estimated iCSI might be outdated [24], which makes it challenging to use iCSI for downlink precoding in such system. Motivated by these characteristics, we investigate the precoding design by exploiting the statistical CSI (sCSI), which is relatively slowvarying.
在本文中，我们提出在大规模 MIMO 低地球轨道（LEO）卫星系统中实现 ICAL，以在通信能力和定位精度之间进行权衡，分别通过 SE 和位置误差平方界（SPEB）进行评估[5]。尽管 ICAL 系统的下行链路预编码设计已经在陆地网络中进行了研究[7]-[9]，但此类系统中的信号传播特性与 LEO 卫星系统不同，因此不能直接应用。具体来说，由于收发器的移动性和卫星到用户终端（UTs）的长距离，所考虑的场景中存在较大的多普勒频移和长传播延迟[17]，[23]。因此，卫星与 UTs 之间的即时信道状态信息（iCSI）是时变的，可能难以估计。此外，估计的 iCSI 可能会过时[24]，这使得使用 iCSI 进行下行链路预编码变得具有挑战性。受这些特性的启发，我们通过利用统计信道状态信息（sCSI）来研究预编码设计，sCSI 相对缓慢变化。

Inspired by the aforementioned motivations, a hybrid analog/digital transmitter is proposed for wideband massive MIMO LEO satellite systems to perform ubiquitous ICAL by exploiting sCSI. The main contributions of the paper are summarized as follows:
受到上述动机的启发，本文为宽带大规模 MIMO 低地球轨道卫星系统提出了一种混合模拟/数字发射机，以利用 sCSI 执行普遍的 ICAL。本文的主要贡献总结如下：

Communications - So far, the communications for the LEO satellite scenarios have been intensively investigated. In [17], the authors have formulated a massive MIMO communication scheme for both uplink and downlink of the LEO satellite systems based on the average signal-to-leakage-plus-noise ratio
通信 - 到目前为止，低地球轨道（LEO）卫星场景的通信已经进行了深入研究。在[17]中，作者们基于平均信号与泄漏加噪声比（SLNR）制定了适用于 LEO 卫星系统的上行链路和下行链路的大规模 MIMO 通信方案。
(ASLNR) and average signal-to-interference-plus-noise ratio (ASINR) maximization criteria, respectively. The downlink precoding designs for both fully digital and hybrid transmitters have been studied in [12], [24], [25], to maximize the downlink SE or the energy efficiency performance. Besides, joint user scheduling and beamforming frameworks have been investigated for the downlink of the massive MIMO LEO satellite systems [26], [27]. In [28], the authors focused on the research of the uplink transmit design for the massive MIMO LEO satellite systems.
(ASLNR)和平均信号与干扰加噪声比(ASINR)最大化准则分别。已有关于全数字和混合发射机下行链路预编码的设计研究，旨在最大化下行链路的谱效率或能量效率性能。此外，还研究了大规模 MIMO 低地球轨道卫星系统的下行链路联合用户调度和波束形成框架[26], [27]。在[28]中，作者专注于研究大规模 MIMO 低地球轨道卫星系统的上行链路传输设计。

Localization - Wireless localization can be performed with single anchor or multiple anchors, both of which have been extensively investigated in the terrestrial systems. In [29], [30], the authors have presented theoretical analyses for multiple anchor localizations. The CRLB for single anchor localization has been derived for both two-dimensional (2D) and threedimensional (3D) scenarios in [18], [31]. In [32], the authors have investigated the localization and orientation performance limits for the single anchor scenarios with massive MIMO transmission. In [33], the authors have studied the influence of synchronization errors and Doppler effects on single anchor localization systems.
定位 - 无线定位可以使用单个锚点或多个锚点进行，这两种方法在地面上的系统中已经被广泛研究。在[29]、[30]中，作者们已经对多锚点定位进行了理论分析。单锚点定位的 CRLB（最小方差无偏估计下界）已经在[18]、[31]中分别针对二维（2D）和三维（3D）场景进行了推导。在[32]中，作者们研究了大规模 MIMO 传输下单锚点定位和方向性能的极限。在[33]中，作者们研究了同步误差和多普勒效应对单锚点定位系统的影响。

ICAL - The existing ICAL studies mainly focus on terrestrial scenarios. In [7], [8], the authors have designed the beamforming vectors to simultaneously perform communications and localization during data transmission, based on rate maximization, SPEB minimization, or the transmission power minimization criteria. Besides, localization can not only be performed together with the data transmission, but also with the pilot transmission, at the same time of channel estimation. In [9], the authors have proposed a two-stage beamforming scheme, where in the first stage, pilot overhead signaling is minimized subject to localization precision constraints, and in the second stage, the data rate is maximized with the estimated CSI obtained from stage one.
ICAL - 目前的 ICAL 研究主要集中在陆地场景。在[7]、[8]中，作者设计了波束形成向量，在数据传输过程中同时进行通信和定位，基于速率最大化、SPEB 最小化或传输功率最小化标准。此外，定位不仅可以与数据传输同时进行，也可以与导频传输同时进行，在信道估计的同时进行。在[9]中，作者提出了一种两阶段波束形成方案，在第一阶段，导频开销信号最小化，同时满足定位精度约束；在第二阶段，利用第一阶段获得的 CSI 最大化数据速率。

The paper is organized as follows. Section II formulates the system model for the wideband massive MIMO LEO satellite ICAL system. The performance metrics for both communications and localization, i.e., SE and SPEB, are analyzed in Section III. An algorithmic framework is developed in Section IV to design the hybrid analog/digital precoders for the ICAL system enabling the trade-off between the communication and localization performance. Section V presents the simulation results and the paper is concluded briefly in Section VI.
论文组织如下。第二部分制定了宽频带大规模 MIMO 低地球轨道卫星 ICAL 系统的系统模型。第三部分分析了通信和定位性能指标，即 SE 和 SPEB。第四部分开发了一个算法框架，用于设计 ICAL 系统的混合模拟/数字预编码器，以实现通信和定位性能之间的权衡。第五部分呈现了仿真结果，第六部分简要总结了论文。

Matrices and vectors are denoted by upper and lower case boldface letters, respectively. ${\mathbb{C}}^{m\times n}$${\mathbb{C}}^{m\times n}$C^(m xx n)\mathbb{C}^{m \times n} represents the $m\times n$$m\times n$m xx nm \times n dimension unitary space. The left-hand side of $\triangleq$$\triangleq$≜\triangleq is defined by the right-hand side. $\otimes$$\otimes$ox\otimes denotes the Kronecker product. $\exp \{\cdot \}$$\exp \{\cdot \}$exp{*}\exp \{\cdot\} and $\log \{\cdot \}$$\log \{\cdot \}$log{*}\log \{\cdot\} are the exponential and logarithmic operators, respectively. ${\mathbf{I}}_N$${\mathbf{I}}_N$I_(N)\mathbf{I}_{N} stands for $N\times N$$N\times N$N xx NN \times N identity matrix. $(\cdot {)}^T,(\cdot {)}^{\ast }$$(\cdot {)}^T,(\cdot {)}^{\ast }$(*)^(T),(*)^(**)(\cdot)^{T},(\cdot)^{*}, and $(\cdot {)}^H$$(\cdot {)}^H$(*)^(H)(\cdot)^{H} represent the transpose, conjugate, and conjugate transpose operations, respectively. $|x|,\mathrm{\angle }x,\mathrm{\Re }\{x\}$$|x|,\mathrm{\angle }x,\mathrm{\Re }\{x\}$|x|,/_x,ℜ{x}|x|, \angle x, \Re\{x\}, and $\lceil x\rceil$$\lceil x\rceil$|~x~|\lceil x\rceil denote the amplitude, the angle, the real part, and the ceiling
矩阵和向量分别用粗体大写字母和粗体小写字母表示。 ${\mathbb{C}}^{m\times n}$${\mathbb{C}}^{m\times n}$C^(m xx n)\mathbb{C}^{m \times n} 表示 $m\times n$$m\times n$m xx nm \times n 维单位空间。 $\triangleq$$\triangleq$≜\triangleq 的左侧由右侧定义。 $\otimes$$\otimes$ox\otimes 表示克罗内克积。 $\exp \{\cdot \}$$\exp \{\cdot \}$exp{*}\exp \{\cdot\} 和 $\log \{\cdot \}$$\log \{\cdot \}$log{*}\log \{\cdot\} 分别表示指数和对数运算。 ${\mathbf{I}}_N$${\mathbf{I}}_N$I_(N)\mathbf{I}_{N} 表示 $N\times N$$N\times N$N xx NN \times N 单位矩阵。 $(\cdot {)}^T,(\cdot {)}^{\ast }$$(\cdot {)}^T,(\cdot {)}^{\ast }$(*)^(T),(*)^(**)(\cdot)^{T},(\cdot)^{*} 和 $(\cdot {)}^H$$(\cdot {)}^H$(*)^(H)(\cdot)^{H} 分别表示转置、共轭和共轭转置操作。 $|x|,\mathrm{\angle }x,\mathrm{\Re }\{x\}$$|x|,\mathrm{\angle }x,\mathrm{\Re }\{x\}$|x|,/_x,ℜ{x}|x|, \angle x, \Re\{x\} 和 $\lceil x\rceil$$\lceil x\rceil$|~x~|\lceil x\rceil 分别表示幅度、角度、实部和上取整。
value of $x$$x$xx, respectively. The circular symmetric complexvalued zero-mean Gaussian distribution with variance ${\sigma }^2$${\sigma }^2$sigma^(2)\sigma^{2} is given by $\mathcal{C}\mathcal{N}(0,{\sigma }^2).\mathbb{E}\{\cdot \},\mathrm{Tr}\{\cdot \}$$\mathcal{C}\mathcal{N}\left(0,{\sigma }^2\right).\mathbb{E}\{\cdot \},\mathrm{Tr}\{\cdot \}$CN(0,sigma^(2)).E{*},Tr{*}\mathcal{C N}\left(0, \sigma^{2}\right) . \mathbb{E}\{\cdot\}, \operatorname{Tr}\{\cdot\}, and blkdiag $\}$$\}$}\} represent the expectation, the trace, and the block diagonal operators. rank $\{\mathbf{X}\}$$\{\mathbf{X}\}${X}\{\mathbf{X}\} stands for the rank of the matrix $\mathbf{X}.\Vert \cdot {\Vert }_2$$\mathbf{X}.\Vert \cdot {\Vert }_2$X.||*||_(2)\mathbf{X} .\|\cdot\|_{2} and $\Vert \cdot {\Vert }_F$$\Vert \cdot {\Vert }_F$||*||_(F)\|\cdot\|_{F} denote the ${\ell }_2$${\ell }_2$ℓ_(2)\ell_{2}-norm and Frobenius-norm, respectively. The $(i,j)$$(i,j)$(i,j)(i, j) th element of the matrix $\mathbf{A}$$\mathbf{A}$A\mathbf{A} is given by $[\mathbf{A}{]}_{i,j}.\mathbf{A}⪰\mathbf{B}$$[\mathbf{A}{]}_{i,j}.\mathbf{A}⪰\mathbf{B}$[A]_(i,j).A>-=B[\mathbf{A}]_{i, j} . \mathbf{A} \succeq \mathbf{B} refers to the positive semidefinite property of the matrix $\mathbf{A}-\mathbf{B}$$\mathbf{A}-\mathbf{B}$A-B\mathbf{A}-\mathbf{B}. $\partial$$\partial$del\partial denotes the partial derivative operation.
分别为 $x$$x$xx 。具有方差 ${\sigma }^2$${\sigma }^2$sigma^(2)\sigma^{2} 的圆对称复值零均值高斯分布由 $\mathcal{C}\mathcal{N}(0,{\sigma }^2).\mathbb{E}\{\cdot \},\mathrm{Tr}\{\cdot \}$$\mathcal{C}\mathcal{N}\left(0,{\sigma }^2\right).\mathbb{E}\{\cdot \},\mathrm{Tr}\{\cdot \}$CN(0,sigma^(2)).E{*},Tr{*}\mathcal{C N}\left(0, \sigma^{2}\right) . \mathbb{E}\{\cdot\}, \operatorname{Tr}\{\cdot\} 给出，blkdiag $\}$$\}$}\} 代表期望、迹和块对角运算。rank $\{\mathbf{X}\}$$\{\mathbf{X}\}${X}\{\mathbf{X}\} 表示矩阵 $\mathbf{X}.\Vert \cdot {\Vert }_2$$\mathbf{X}.\Vert \cdot {\Vert }_2$X.||*||_(2)\mathbf{X} .\|\cdot\|_{2} 的秩， $\Vert \cdot {\Vert }_F$$\Vert \cdot {\Vert }_F$||*||_(F)\|\cdot\|_{F} 表示 ${\ell }_2$${\ell }_2$ℓ_(2)\ell_{2} 范数和 Frobenius 范数，分别。矩阵 $\mathbf{A}$$\mathbf{A}$A\mathbf{A} 的 $[\mathbf{A}{]}_{i,j}.\mathbf{A}⪰\mathbf{B}$$[\mathbf{A}{]}_{i,j}.\mathbf{A}⪰\mathbf{B}$[A]_(i,j).A>-=B[\mathbf{A}]_{i, j} . \mathbf{A} \succeq \mathbf{B} 元素由给出， $\mathbf{A}-\mathbf{B}$$\mathbf{A}-\mathbf{B}$A-B\mathbf{A}-\mathbf{B} 表示矩阵的半正定性质。 $\partial$$\partial$del\partial 表示部分导数运算。

We propose to simultaneously perform communications and localization for the massive MIMO LEO satellite systems, as depicted in Fig. 1. The system is operated at carrier frequency
我们提议同时进行大规模 MIMO 低地球轨道卫星系统的通信和定位，如图 1 所示。系统在载波频率下运行

Fig. 1. 3D geometric model of the massive MIMO LEO satellite ICAL system with known satellite position and orientation, unknown UTs position.
图 1. 大规模 MIMO 低地球轨道卫星 ICAL 系统的 3D 几何模型，已知卫星位置和姿态，未知用户终端位置。
$f_{\mathrm{c}}$$f_{\mathrm{c}}$f_(c)f_{\mathrm{c}} and the corresponding wavelength is given by ${\lambda }_{\mathrm{c}}=c/f_{\mathrm{c}}$${\lambda }_{\mathrm{c}}=c/f_{\mathrm{c}}$lambda_(c)=c//f_(c)\lambda_{\mathrm{c}}=c / f_{\mathrm{c}}, where $c$$c$cc denotes the speed of the light. We assume $K$$K$KK singleantenna UTs, at unknown position ${\mathbf{p}}_k={[p_k^{\mathrm{x}},p_k^{\mathrm{y}},p_k^{\mathrm{z}}]}^T$${\mathbf{p}}_k={\left[p_k^{\mathrm{x}},p_k^{\mathrm{y}},p_k^{\mathrm{z}}\right]}^T$p_(k)=[p_(k)^(x),p_(k)^(y),p_(k)^(z)]^(T)\mathbf{p}_{k}=\left[p_{k}^{\mathrm{x}}, p_{k}^{\mathrm{y}}, p_{k}^{\mathrm{z}}\right]^{T} and velocity ${\dot{\mathbf{p}}}_k={[{\dot{p}}_k^{\mathrm{x}},{\dot{p}}_k^{\mathrm{y}},{\dot{p}}_k^{\mathrm{z}}]}^T,k=1,\dots ,K$${\dot{\mathbf{p}}}_k={\left[{\dot{p}}_k^{\mathrm{x}},{\dot{p}}_k^{\mathrm{y}},{\dot{p}}_k^{\mathrm{z}}\right]}^T,k=1,\dots ,K$p^(˙)_(k)=[p^(˙)_(k)^(x),p^(˙)_(k)^(y),p^(˙)_(k)^(z)]^(T),k=1,dots,K\dot{\mathbf{p}}_{k}=\left[\dot{p}_{k}^{\mathrm{x}}, \dot{p}_{k}^{\mathrm{y}}, \dot{p}_{k}^{\mathrm{z}}\right]^{T}, k=1, \ldots, K, are served by a single LEO satellite with known position $\mathbf{q}={[q^{\mathrm{x}},q^{\mathrm{y}},q^{\mathrm{z}}]}^T$$\mathbf{q}={\left[q^{\mathrm{x}},q^{\mathrm{y}},q^{\mathrm{z}}\right]}^T$q=[q^(x),q^(y),q^(z)]^(T)\mathbf{q}=\left[q^{\mathrm{x}}, q^{\mathrm{y}}, q^{\mathrm{z}}\right]^{T} and orientation angle $\mathbf{o}={[{\phi }_1,{\phi }_2]}^T,{}^1$$\mathbf{o}={\left[{\phi }_1,{\phi }_2\right]}^T,{}^1$o=[varphi_(1),varphi_(2)]^(T),^(1)\mathbf{o}=\left[\varphi_{1}, \varphi_{2}\right]^{T},{ }^{1} where ${\phi }_2$${\phi }_2$varphi_(2)\varphi_{2} and ${\phi }_1$${\phi }_1$varphi_(1)\varphi_{1} refer to the rotation around positive y - and negative ${\mathrm{x}}^{\prime }$${\mathrm{x}}^{\prime }$x^(')\mathrm{x}^{\prime}-axes, ${}^2$${}^2$^(2){ }^{2} respectively, as depicted in Fig. 1. We assume fixed positions and velocities of the UTs over the observed interval and update them according to the large movements of the UTs. A uniform planar array (UPA) of $N_{\mathrm{t}}=N_{\mathrm{t}}^{\mathrm{x}}{N}_{\mathrm{t}}^{\mathrm{y}}$$N_{\mathrm{t}}=N_{\mathrm{t}}^{\mathrm{x}}{N}_{\mathrm{t}}^{\mathrm{y}}$N_(t)=N_(t)^(x)N_(t)^(y)N_{\mathrm{t}}=N_{\mathrm{t}}^{\mathrm{x}} N_{\mathrm{t}}^{\mathrm{y}} antennas with half-wavelength separation is applied at the LEO satellite transmitter, where $N_{\mathrm{t}}^{\mathrm{x}}$$N_{\mathrm{t}}^{\mathrm{x}}$N_(t)^(x)N_{\mathrm{t}}^{\mathrm{x}} and $N_{\mathrm{t}}^{\mathrm{y}}$$N_{\mathrm{t}}^{\mathrm{y}}$N_(t)^(y)N_{\mathrm{t}}^{\mathrm{y}} denote the number of antennas at the x - and y -axes, respectively. The satellite transmitter is supported by a hybrid precoder with $N_{\mathrm{rf}}(K\le N_{\mathrm{rf}}\le N_{\mathrm{t}})$$N_{\mathrm{rf}}\left(K\le N_{\mathrm{rf}}\le N_{\mathrm{t}}\right)$N_(rf)(K <= N_(rf) <= N_(t))N_{\mathrm{rf}}\left(K \leq N_{\mathrm{rf}} \leq N_{\mathrm{t}}\right) RF chains.
$f_{\mathrm{c}}$$f_{\mathrm{c}}$f_(c)f_{\mathrm{c}} 和对应的波长由 ${\lambda }_{\mathrm{c}}=c/f_{\mathrm{c}}$${\lambda }_{\mathrm{c}}=c/f_{\mathrm{c}}$lambda_(c)=c//f_(c)\lambda_{\mathrm{c}}=c / f_{\mathrm{c}} 给出，其中 $c$$c$cc 表示光速。我们假设有 $K$$K$KK 个单天线用户终端（UT），其未知位置为 ${\mathbf{p}}_k={[p_k^{\mathrm{x}},p_k^{\mathrm{y}},p_k^{\mathrm{z}}]}^T$${\mathbf{p}}_k={\left[p_k^{\mathrm{x}},p_k^{\mathrm{y}},p_k^{\mathrm{z}}\right]}^T$p_(k)=[p_(k)^(x),p_(k)^(y),p_(k)^(z)]^(T)\mathbf{p}_{k}=\left[p_{k}^{\mathrm{x}}, p_{k}^{\mathrm{y}}, p_{k}^{\mathrm{z}}\right]^{T} 和速度为 ${\dot{\mathbf{p}}}_k={[{\dot{p}}_k^{\mathrm{x}},{\dot{p}}_k^{\mathrm{y}},{\dot{p}}_k^{\mathrm{z}}]}^T,k=1,\dots ,K$${\dot{\mathbf{p}}}_k={\left[{\dot{p}}_k^{\mathrm{x}},{\dot{p}}_k^{\mathrm{y}},{\dot{p}}_k^{\mathrm{z}}\right]}^T,k=1,\dots ,K$p^(˙)_(k)=[p^(˙)_(k)^(x),p^(˙)_(k)^(y),p^(˙)_(k)^(z)]^(T),k=1,dots,K\dot{\mathbf{p}}_{k}=\left[\dot{p}_{k}^{\mathrm{x}}, \dot{p}_{k}^{\mathrm{y}}, \dot{p}_{k}^{\mathrm{z}}\right]^{T}, k=1, \ldots, K ，由一个具有已知位置 $\mathbf{q}={[q^{\mathrm{x}},q^{\mathrm{y}},q^{\mathrm{z}}]}^T$$\mathbf{q}={\left[q^{\mathrm{x}},q^{\mathrm{y}},q^{\mathrm{z}}\right]}^T$q=[q^(x),q^(y),q^(z)]^(T)\mathbf{q}=\left[q^{\mathrm{x}}, q^{\mathrm{y}}, q^{\mathrm{z}}\right]^{T} 和方向角 $\mathbf{o}={[{\phi }_1,{\phi }_2]}^T,{}^1$$\mathbf{o}={\left[{\phi }_1,{\phi }_2\right]}^T,{}^1$o=[varphi_(1),varphi_(2)]^(T),^(1)\mathbf{o}=\left[\varphi_{1}, \varphi_{2}\right]^{T},{ }^{1} 的单颗低地球轨道（LEO）卫星服务，其中 ${\phi }_2$${\phi }_2$varphi_(2)\varphi_{2} 和 ${\phi }_1$${\phi }_1$varphi_(1)\varphi_{1} 分别指绕正 y 轴和负 ${\mathrm{x}}^{\prime }$${\mathrm{x}}^{\prime }$x^(')\mathrm{x}^{\prime} 轴的旋转，如图 1 所示。我们假设在观测区间内 UT 的固定位置和速度，并根据 UT 的大范围移动进行更新。LEO 卫星发射机处应用了半波长间隔的均匀平面阵列（UPA），包含 $N_{\mathrm{t}}=N_{\mathrm{t}}^{\mathrm{x}}{N}_{\mathrm{t}}^{\mathrm{y}}$$N_{\mathrm{t}}=N_{\mathrm{t}}^{\mathrm{x}}{N}_{\mathrm{t}}^{\mathrm{y}}$N_(t)=N_(t)^(x)N_(t)^(y)N_{\mathrm{t}}=N_{\mathrm{t}}^{\mathrm{x}} N_{\mathrm{t}}^{\mathrm{y}} 个天线，其中 $N_{\mathrm{t}}^{\mathrm{x}}$$N_{\mathrm{t}}^{\mathrm{x}}$N_(t)^(x)N_{\mathrm{t}}^{\mathrm{x}} 和 $N_{\mathrm{t}}^{\mathrm{y}}$$N_{\mathrm{t}}^{\mathrm{y}}$N_(t)^(y)N_{\mathrm{t}}^{\mathrm{y}} 分别表示 x 轴和 y 轴上的天线数量。卫星发射机由 $N_{\mathrm{rf}}(K\le N_{\mathrm{rf}}\le N_{\mathrm{t}})$$N_{\mathrm{rf}}\left(K\le N_{\mathrm{rf}}\le N_{\mathrm{t}}\right)$N_(rf)(K <= N_(rf) <= N_(t))N_{\mathrm{rf}}\left(K \leq N_{\mathrm{rf}} \leq N_{\mathrm{t}}\right) 个射频（RF）链路组成的混合预编码器支持。

The orthogonal frequency division multiplex (OFDM) modulation is employed for the downlink wideband transmission of the LEO satellite ICAL systems to mitigate the inter-symbol interference [17], [18]. We denote $B_{\mathrm{w}}$$B_{\mathrm{w}}$B_(w)B_{\mathrm{w}} and $T_{\mathrm{s}}=1/\left(2B_{\mathrm{w}}\right)$$T_{\mathrm{s}}=1/\left(2B_{\mathrm{w}}\right)$T_(s)=1//(2B_(w))T_{\mathrm{s}}=1 /\left(2 B_{\mathrm{w}}\right) as the system bandwidth and the sampling period, respectively. In particular, we assume each frame consists of $M_{\mathrm{s}}$$M_{\mathrm{s}}$M_(s)M_{\mathrm{s}} slots, and there are $M_{\mathrm{sp}}$$M_{\mathrm{sp}}$M_(sp)M_{\mathrm{sp}} and $M_{\mathrm{sd}}$$M_{\mathrm{sd}}$M_(sd)M_{\mathrm{sd}} OFDM symbols used for pilot
采用正交频分多址（OFDM）调制技术用于低地球轨道（LEO）卫星 ICAL 系统的下行宽带传输，以减轻符号间干扰[17]，[18]。我们将 $B_{\mathrm{w}}$$B_{\mathrm{w}}$B_(w)B_{\mathrm{w}} 和 $T_{\mathrm{s}}=1/\left(2B_{\mathrm{w}}\right)$$T_{\mathrm{s}}=1/\left(2B_{\mathrm{w}}\right)$T_(s)=1//(2B_(w))T_{\mathrm{s}}=1 /\left(2 B_{\mathrm{w}}\right) 分别表示为系统带宽和采样周期。特别地，我们假设每一帧由 $M_{\mathrm{s}}$$M_{\mathrm{s}}$M_(s)M_{\mathrm{s}} 个时隙组成，并且用于导频的 OFDM 符号有 $M_{\mathrm{sp}}$$M_{\mathrm{sp}}$M_(sp)M_{\mathrm{sp}} 个，用于数据传输的 OFDM 符号有 $M_{\mathrm{sd}}$$M_{\mathrm{sd}}$M_(sd)M_{\mathrm{sd}} 个。

Fig. 2. The time-frequency structure for the transmitted pilot and data signals.
图 2. 发射导频和数据信号的时间-频率结构。
and data transmission in each slot, as depicted in Fig. 2. Thus, in each frame, $M_{\mathrm{p}}=M_{\mathrm{sp}}{M}_{\mathrm{s}}$$M_{\mathrm{p}}=M_{\mathrm{sp}}{M}_{\mathrm{s}}$M_(p)=M_(sp)M_(s)M_{\mathrm{p}}=M_{\mathrm{sp}} M_{\mathrm{s}} and $M_{\mathrm{d}}=M_{\mathrm{sd}}{M}_{\mathrm{s}}$$M_{\mathrm{d}}=M_{\mathrm{sd}}{M}_{\mathrm{s}}$M_(d)=M_(sd)M_(s)M_{\mathrm{d}}=M_{\mathrm{sd}} M_{\mathrm{s}} OFDM symbols are transmitted through the pilot and data transmission, respectively. Then, we assume $N_{\mathrm{sc}}$$N_{\mathrm{sc}}$N_(sc)N_{\mathrm{sc}} subcarriers are employed over the system bandwidth $B_{\mathrm{w}}$$B_{\mathrm{w}}$B_(w)B_{\mathrm{w}}, and the length of the cyclic prefix (CP) is set as $N_{\mathrm{cp}}$$N_{\mathrm{cp}}$N_(cp)N_{\mathrm{cp}}. Thus, we denote $f_{\mathrm{s}}$$f_{\mathrm{s}}$f_(s)f_{\mathrm{s}} as the subcarrier separation and the frequency of the $n$$n$nnth subcarrier is given by $f_n=(n-\frac{N_{\mathrm{sc}}+1}{2})f_{\mathrm{s}},n=1,\dots ,N_{\mathrm{sc}}$$f_n=\left(n-\frac{N_{\mathrm{sc}}+1}{2}\right)f_{\mathrm{s}},n=1,\dots ,N_{\mathrm{sc}}$f_(n)=(n-(N_(sc)+1)/(2))f_(s),n=1,dots,N_(sc)f_{n}=\left(n-\frac{N_{\mathrm{sc}}+1}{2}\right) f_{\mathrm{s}}, n=1, \ldots, N_{\mathrm{sc}}. Subsequently, the OFDM symbol length with and without CP is given by $T=N_{\mathrm{sc}}{T}_{\mathrm{s}}+N_{\mathrm{cp}}{T}_{\mathrm{s}}$$T=N_{\mathrm{sc}}{T}_{\mathrm{s}}+N_{\mathrm{cp}}{T}_{\mathrm{s}}$T=N_(sc)T_(s)+N_(cp)T_(s)T=N_{\mathrm{sc}} T_{\mathrm{s}}+N_{\mathrm{cp}} T_{\mathrm{s}} and $T_{\mathrm{sc}}=N_{\mathrm{sc}}{T}_{\mathrm{s}}$$T_{\mathrm{sc}}=N_{\mathrm{sc}}{T}_{\mathrm{s}}$T_(sc)=N_(sc)T_(s)T_{\mathrm{sc}}=N_{\mathrm{sc}} T_{\mathrm{s}}, respectively. In the following, let the subscript and superscript $g\in \{\mathrm{p},\mathrm{d}\}$$g\in \{\mathrm{p},\mathrm{d}\}$g in{p,d}g \in\{\mathrm{p}, \mathrm{d}\} represent the pilot and data transmission, respectively.
在每个时隙中，导频和数据传输的时间-频率结构如图 2 所示。因此，在每一帧中， $M_{\mathrm{p}}=M_{\mathrm{sp}}{M}_{\mathrm{s}}$$M_{\mathrm{p}}=M_{\mathrm{sp}}{M}_{\mathrm{s}}$M_(p)=M_(sp)M_(s)M_{\mathrm{p}}=M_{\mathrm{sp}} M_{\mathrm{s}} 个 OFDM 符号用于导频传输， $M_{\mathrm{d}}=M_{\mathrm{sd}}{M}_{\mathrm{s}}$$M_{\mathrm{d}}=M_{\mathrm{sd}}{M}_{\mathrm{s}}$M_(d)=M_(sd)M_(s)M_{\mathrm{d}}=M_{\mathrm{sd}} M_{\mathrm{s}} 个 OFDM 符号用于数据传输。然后，我们假设在系统带宽 $B_{\mathrm{w}}$$B_{\mathrm{w}}$B_(w)B_{\mathrm{w}} 上使用 $N_{\mathrm{sc}}$$N_{\mathrm{sc}}$N_(sc)N_{\mathrm{sc}} 个子载波，并将循环前缀（CP）的长度设置为 $N_{\mathrm{cp}}$$N_{\mathrm{cp}}$N_(cp)N_{\mathrm{cp}} 。因此，我们用 $f_{\mathrm{s}}$$f_{\mathrm{s}}$f_(s)f_{\mathrm{s}} 表示子载波间隔， $n$$n$nn 个子载波的频率由 $f_n=(n-\frac{N_{\mathrm{sc}}+1}{2})f_{\mathrm{s}},n=1,\dots ,N_{\mathrm{sc}}$$f_n=\left(n-\frac{N_{\mathrm{sc}}+1}{2}\right)f_{\mathrm{s}},n=1,\dots ,N_{\mathrm{sc}}$f_(n)=(n-(N_(sc)+1)/(2))f_(s),n=1,dots,N_(sc)f_{n}=\left(n-\frac{N_{\mathrm{sc}}+1}{2}\right) f_{\mathrm{s}}, n=1, \ldots, N_{\mathrm{sc}} 给出。随后，带 CP 和不带 CP 的 OFDM 符号长度分别表示为 $T=N_{\mathrm{sc}}{T}_{\mathrm{s}}+N_{\mathrm{cp}}{T}_{\mathrm{s}}$$T=N_{\mathrm{sc}}{T}_{\mathrm{s}}+N_{\mathrm{cp}}{T}_{\mathrm{s}}$T=N_(sc)T_(s)+N_(cp)T_(s)T=N_{\mathrm{sc}} T_{\mathrm{s}}+N_{\mathrm{cp}} T_{\mathrm{s}} 和 $T_{\mathrm{sc}}=N_{\mathrm{sc}}{T}_{\mathrm{s}}$$T_{\mathrm{sc}}=N_{\mathrm{sc}}{T}_{\mathrm{s}}$T_(sc)=N_(sc)T_(s)T_{\mathrm{sc}}=N_{\mathrm{sc}} T_{\mathrm{s}} 。在以下内容中，下标和上标 $g\in \{\mathrm{p},\mathrm{d}\}$$g\in \{\mathrm{p},\mathrm{d}\}$g in{p,d}g \in\{\mathrm{p}, \mathrm{d}\} 分别表示导频和数据传输。

An ICAL transmission protocol is developed for the LEO satellite systems. First, rough position knowledge of both the satellite and the UTs can be obtained at the LEO satellite side by, e.g., initial access or tracking [35], by exploiting which the satellite transmits precoded pilot and data signals to each UT. Then, the required channel parameters can be evaluated from the received pilot signals at the UT, and more precise localization knowledge can be derived from the estimated channel information [7], [18], [31], to further improve the localization precision and communication capacity.
为 LEO 卫星系统开发了一种 ICAL 传输协议。首先，通过例如初始接入或跟踪[35]，在 LEO 卫星端可以获得卫星和 UTs 的大致位置信息。然后，通过 UT 接收到的试点信号可以评估所需的信道参数，并通过估计的信道信息[7]、[18]、[31]进一步获得更精确的定位知识和通信容量。

In the wideband massive MIMO LEO satellite ICAL systems, the UPA response is not only dependent on the angles-of-departure (AoD) information, but also the frequency. Then, the UPA response ${\mathbf{v}}_{k,l}(f)$${\mathbf{v}}_{k,l}(f)$v_(k,l)(f)\mathbf{v}_{k, l}(f) for the $l$$l$ll th propagation path of the $k$$k$kk th UT at frequency $f$$f$ff is given by [36]
在宽带大规模 MIMO LEO 卫星 ICAL 系统中，UPA 响应不仅依赖于角度离散度(AoD)信息，还依赖于频率。则第 $k$$k$kk 个 UT 的第 $l$$l$ll 条传播路径在频率 $f$$f$ff 处的 UPA 响应 ${\mathbf{v}}_{k,l}(f)$${\mathbf{v}}_{k,l}(f)$v_(k,l)(f)\mathbf{v}_{k, l}(f) 为[36]

where ${\mathit{\theta }}_{k,l}=({\theta }_{k,l}^{\mathrm{x}},{\theta }_{k,l}^{\mathrm{y}})$${\mathit{\theta }}_{k,l}=\left({\theta }_{k,l}^{\mathrm{x}},{\theta }_{k,l}^{\mathrm{y}}\right)$theta_(k,l)=(theta_(k,l)^(x),theta_(k,l)^(y))\boldsymbol{\theta}_{k, l}=\left(\theta_{k, l}^{\mathrm{x}}, \theta_{k, l}^{\mathrm{y}}\right) denotes the AoD pair, as observed from Fig. 1. Besides, the array response vectors ${\mathbf{v}}_{\mathrm{x}}(f,{\mathit{\theta }}_{k,l})\in$${\mathbf{v}}_{\mathrm{x}}\left(f,{\mathit{\theta }}_{k,l}\right)\in$v_(x)(f,theta_(k,l))in\mathbf{v}_{\mathrm{x}}\left(f, \boldsymbol{\theta}_{k, l}\right) \in ${\mathbb{C}}^{N_{\mathrm{t}}^{\mathrm{x}}\times 1}$${\mathbb{C}}^{N_{\mathrm{t}}^{\mathrm{x}}\times 1}$C^(N_(t)^(x)xx1)\mathbb{C}^{N_{\mathrm{t}}^{\mathrm{x}} \times 1} and ${\mathbf{v}}_{\mathrm{y}}(f,{\mathit{\theta }}_{k,l})\in {\mathbb{C}}^{N_{\mathrm{t}}^{\mathrm{y}}\times 1}$${\mathbf{v}}_{\mathrm{y}}\left(f,{\mathit{\theta }}_{k,l}\right)\in {\mathbb{C}}^{N_{\mathrm{t}}^{\mathrm{y}}\times 1}$v_(y)(f,theta_(k,l))inC^(N_(t)^(y)xx1)\mathbf{v}_{\mathrm{y}}\left(f, \boldsymbol{\theta}_{k, l}\right) \in \mathbb{C}^{N_{\mathrm{t}}^{\mathrm{y}} \times 1} of the x - and y -axes can be expressed as [17], [36]
其中 ${\mathit{\theta }}_{k,l}=({\theta }_{k,l}^{\mathrm{x}},{\theta }_{k,l}^{\mathrm{y}})$${\mathit{\theta }}_{k,l}=\left({\theta }_{k,l}^{\mathrm{x}},{\theta }_{k,l}^{\mathrm{y}}\right)$theta_(k,l)=(theta_(k,l)^(x),theta_(k,l)^(y))\boldsymbol{\theta}_{k, l}=\left(\theta_{k, l}^{\mathrm{x}}, \theta_{k, l}^{\mathrm{y}}\right) 表示从图 1 观察到的角度离散度对， ${\mathbf{v}}_{\mathrm{x}}(f,{\mathit{\theta }}_{k,l})\in$${\mathbf{v}}_{\mathrm{x}}\left(f,{\mathit{\theta }}_{k,l}\right)\in$v_(x)(f,theta_(k,l))in\mathbf{v}_{\mathrm{x}}\left(f, \boldsymbol{\theta}_{k, l}\right) \in 、 ${\mathbb{C}}^{N_{\mathrm{t}}^{\mathrm{x}}\times 1}$${\mathbb{C}}^{N_{\mathrm{t}}^{\mathrm{x}}\times 1}$C^(N_(t)^(x)xx1)\mathbb{C}^{N_{\mathrm{t}}^{\mathrm{x}} \times 1} 和 ${\mathbf{v}}_{\mathrm{y}}(f,{\mathit{\theta }}_{k,l})\in {\mathbb{C}}^{N_{\mathrm{t}}^{\mathrm{y}}\times 1}$${\mathbf{v}}_{\mathrm{y}}\left(f,{\mathit{\theta }}_{k,l}\right)\in {\mathbb{C}}^{N_{\mathrm{t}}^{\mathrm{y}}\times 1}$v_(y)(f,theta_(k,l))inC^(N_(t)^(y)xx1)\mathbf{v}_{\mathrm{y}}\left(f, \boldsymbol{\theta}_{k, l}\right) \in \mathbb{C}^{N_{\mathrm{t}}^{\mathrm{y}} \times 1} 分别为 x 轴和 y 轴的阵列响应向量[17]、[36]