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RIS-assisted High-Speed Railway Integrated Sensing and Communication System

Panpan Li, Yong Niu, , Hao Wu, , Zhu Han, , Guiqi Sun, Ning Wang, , and Zhangdui Zhong,  Bo Ai,  Copyright (c) 2015 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org. This work was in part by the Fundamental Research Funds for the Central Universities 2023JBMC030; in part by the Fundamental Research Funds for the Central Universities under Grant 2022JBXT001 and Grant 2022JBQY004; in part by the National Key Research and Development Program of China under Grant 2020YFB1806903; in part by the National Key Research and Development Program of China under Grant 2021YFB2900301; in part by the National Natural Science Foundation of China under Grant 62221001, Grant 62231009, Grant U21A20445; in part by Fundamental Research Funds for the Central Universities 2022JBQY004; in part by Science and Technology Research and Development Program of China National Railway Group Corporation K2022G018; supported by State Key Laboratory of Advanced Rail Autonomous Operation; supported by Frontiers Science Center for Smart High-speed Railway System; and supported by Beijing Engineering Research Center of High-speed Railway Broadband Mobile Communications. (Corresponding author: Yong Niu.) P. Li, H. Wu, G. Sun, Z. Zhong, and B. Ai are with the State Key Laboratory of Advanced Rail Autonomous Operation, Beijing Jiaotong University, Beijing 100044, China (e-mail: 19111023@bjtu.edu.cn; hwu@bjtu.edu.cn; guiqisun@bjtu.edu.cn; zhdzhong@bjtu.edu.cn; aibo@ieee.org). Y. Niu is with the State Key Laboratory of Advanced Rail Autonomous Operation, Beijing Jiaotong University, Beijing 100044, China, and also with the National Mobile Communications Research Laboratory, Southeast University, Nanjing 211189, China (e-mail: niuy11@163.com). Z. Han is with the Department of Electrical and Computer Engineering at the University of Houston, Houston, TX 77004 USA, and also with the Department of Computer Science and Engineering, Kyung Hee University, Seoul, South Korea, 446-701. (e-mail: hanzhu22@gmail.com). N. Wang is with the School of Information Engineering, Zhengzhou University, Zhengzhou 450001, China (e-mail: ienwang@zzu.edu.cn).
Abstract

One technology that has the potential to improve wireless communications in years to come is integrated sensing and communication (ISAC). In this study, we take advantage of reconfigurable intelligent surface’s (RIS) potential advantages to achieve ISAC while using the same frequency and resources. Specifically, by using the reflecting elements, the RIS dynamically modifies the radio waves’ strength or phase in order to change the environment for radio transmission and increase the ISAC systems’ transmission rate. We investigate a single cell downlink communication situation with RIS assistance. Combining the ISAC base station’s (BS) beamforming with RIS’s discrete phase shift optimization, while guaranteeing the sensing signal, The aim of optimizing the sum rate is specified. We take advantage of alternating maximization to find practical solutions with dividing the challenge into two minor issues. The first power allocation subproblem is non-convex that CVX solves by converting it to convex. A local search strategy is used to solve the second subproblem of phase shift optimization. According to the results of the simulation, using RIS with adjusted phase shifts can significantly enhance the ISAC system’s performance.

Index Terms:
Integrated Sensing and Communication (ISAC), mmWave band, RIS-assisted, High-Speed Railway (HSR).

I Introduction

IN the upcoming wireless network generation, sensing services will be ubiquitous, such as the Internet of Vehicles, smart home, intelligent manufacturing, human-computer interaction, etc.[1]. The requirements for the quality of wireless connections are also increasing. The trend towards bandwidth communication and high-density sensing has resulted in wireless spectrum resources being more restricted. In order to solve this problem, integrated sensing and communication (ISAC) have received more and more attention. ISAC indicates a new type of information processing technology. It can realize the coordination of sensing and communication functions through software and hardware resource sharing or information sharing. By integrating the communication and sensing functions into a single system, ISAC aims to significantly increase energy and spectrum efficiency while lowering hardware and signal expenses. The integration of communications and sensing services, as well as the pursuit of trade-offs and shared performance benefits, are ISAC’s ultimate objectives. And ISAC can even pursure greater integration patterns. In this mode, the two functions are designed not just to coexist, rather for the advantage of both parties, i.e., communication-aided sensing or sensing-aided communication.

With the increasing mileage of high-speed rail running, it is particularly important to ensure the safety of the train. Foreign objects intrusion is one of the factors that seriously threaten the railway safety. The use of radar sensing enables the detection of foreign objects around the track and on the train, and some other functions such as sensing the position of the train. However, as the mileage of high-speed railway operations continues to increase, achieving the full railway sensing is a significant challenge in terms of hardware costs. Moreover, in the era of smart railways, the demand for high-capacity connectivity is rising for services like high-definition video monitoring and railway Internet of Things (IoT). Applicating ISAC to the high-speed railway (HSR) system can greatly reduce the hardware costs. It can also solve the problem of tight wireless spectrum resources in the railway private networks.

With its capacity to change wireless communication conditions, reconfigurable intelligent surface (RIS) has received a lot of interest recently. A huge number of passive reflection elements make up the parallel theme known as RIS, every one of which may reflect the received signal with a programmable phase shift. RIS may efficiently enhance the expected signal or suppress the unexpected signal by continuously or discretely modifying the incident signal’s amplitude, phase, or both[2].

The application of RIS to ISAC can also serve as reciprocal. One the one hand, the wireless channel connecting the transmitter and the receiver/target is always a determining factor in the sensing and communication performance of ISAC. Sensing targets without or with poor light of sight (LoS) links is a challenging problem. In this case, RIS can be used to provide additional reflective links, improving the sensing accuracy and the transmission rates. On the other hand, a key challenge for wireless communication systems with RIS assistance is the need for perfect channel state information (CSI), which in HSR systems is challenging. If the sensing function of ISAC is used to measure parameters at the receiver (such as the angle of departure/ arrival), it will contribute to the passive beamforming of RIS.

This research examines the communication issue between the ground base station (BS) and the HSR. We installed several mobile relays (MRs) as communication relays on the train’s roof since wireless signals can hardly get through the train body. The MRs receive wireless signals from the BS and serve passengers inside the carriages. Trackside BS have both communication and sensing functions, and utilize RIS to raise the system’s efficiency. increase network transmission speed with guaranteeing the transmitting power and sensing efficiency thresholds. The optimization variables are composed of the continuous transmitting power of the BS and a finite number of discontinuous RIS phase shifts. They are coupled in the defined optimization objective. The problem is challenging to be solved, and therefore we decompose it into two subproblems and subsequently resolve them..

The following is a summary of the paper’s contributions.

  • •

    We construct an HSR-to-ground communication network in which the trackside BS combines the roles of sensing and communication, and we deploy a RIS to offer reflecting pathways to enhance the sensing and communication effectiveness.

  • •

    By maximizing the ISAC BS’s transmitting power and the discrete phase shifts of the RIS elements, the system sum rate maximization problem is formulated within the minimal sensing threshold and the maximum transmitting power limitation of the BS. The coupling between the optimization variables makes it challenging to find a closed solution. To do this, we decompose it into two seperate issues and use an iterative alternating optimization approach to solve them.

  • •

    The waveform design subproblem is non-convex, and we convert it into a convex one by employing the first-order Taylor expansion, and then solve it with the CVX toolbox. The RIS phase shift design subproblem is solved by using a local search method to identify the appropriate phase shifts combination.

  • •

    We contrast the suggested algorithm’s performance with that of the solution achieved without RIS support and other benchmark methods. In comparison to the other three benchmark schemes, the simulation results demonstrate that the proposed method is able to obtain a higher sum rate under the same sensing signal threshold and other system parameters.

The remainder of the paper is structured as follows. In Section II, we provide an overview of the relevant works. In Section III, we create a model that details the system under investigation as well as its communication links. In Section IV, the system sum rate maximization issue is defined, together with its two subproblems—beamforming design subproblem and phase shift design subproblem. Then Section V tailors the optimization techniques to each of the two subproblems. the optimization algorithms are tailored to each of the two subproblems. Then the two subproblems are jointly optimized to achieve the optimal solution. In Section VI, we evaluate the proposed algorithm’s performance and contrast it with the various benchmarking algorithms. Finally, Section VII serves as the paper’s conclusion.

Notations: We represent column vectors with boldfaced lowercase letters, e.g., 𝐱\mathbf{x}, and boldfaced uppercase letters represent matrices, e.g., 𝐗\mathbf{X}. We let 𝐗T\mathbf{X}^{T} and 𝐗H\mathbf{X}^{H} denote the transpose and Hermitian operations performed on 𝐗\mathbf{X}, respectively. ℂn\mathbb{C}^{n} and ℝn\mathbb{R}^{n} stand for the set of n-dimensional complex and real vectors. [𝐗]i\left[\mathbf{X}\right]_{i}, [𝐗]i,j\left[\mathbf{X}\right]_{i,j} means the ii-th element of a vector x and the (i,ji,j)-th element of a matrix 𝐗\mathbf{X}. diag(𝐱)diag(\mathbf{x}) is a diagonal matrix whose diagonal elements are extracted from a vector x. While the Frobenius norm of a matrix 𝐗\mathbf{X} is denoted by ∥X∥F\left\|\textbf{X}\right\|_{F}. ⨂\bigotimes represents the Kronecker product of two matrices. Finally, we represent a set in flower letters, e.g, 𝒳\mathcal{X}.

II Related Work

Tan et al. [3] discussed novel applications, the major performance requirements, limitations, and future research objectives for ISAC design in 6-th generation mobile networks (6G). Zhang et al. [4] provided an extensive review of the latest technologies in ISAC systems from a signal processing standpoint, including three types: communication-centric, radar-centric, as well as cooperative design and optimization. Wang et al. [5] examined the ISAC enabling technologies, such as transmission waveform designing, signal processing, data processing, environmental modeling, and sensing sources. Xiong et al. [6] summarized the research status of ISAC waveform design. Hua et al. [7] studied transmission beamforming in downlink ISAC systems, and in particular, they considered two types of communication receivers, which differed in their ability to eliminate interference from a priori known specialized radar signals. Liu et al. [8] considered the omnidirectional and directional beampattern design of DFRC downlink communication, and further considered the weighted optimization for the flexible balance between communication and sensing quality based on the solved waveform closed solution. Liu et al. [9] used hybrid analog-to-digital (HAD) beamforming to create a transceiver design and frame structure for the mmWave dual-function radar communication (DFRC) BS. Islam et al. [10] provided a paradigm for collaborative optimization while developing analog/digital (A/D) transmission and reception beamformers. Liu et al. [11] studied the fundamental limitations of ISAC to grasp the mismatch between the restrictions and the existing technology. In order to improve ISAC’s system performance, [12, 13, 14, 15] conducted relevant research. Ouyang et al. [12] analyzed how well an uplink ISAC system performs and derived new expressions to describe the likelihood of an outage, the traversal communication capacity, and the perceived rate. Li et al. [13] investigated the feasibility of spatially-spread orthogonal time frequency space (SS-OTFS) modulation in the ISAC system. Liu et al. [14] characterized the effectiveness of ISAC by deriving the expressions of precise and asymptotic outage probability (OP), diversity order, approximate ergodic sum rate (ESR). Dong et al. [15] presented the idea of detecting quality of service (QoS) according to different applications, based on which a common structure is established for allocating ISAC resources. However, in the above study, the effectiveness limit of ISAC systems was related to the wireless channel’s quality. If the wireless propagation environment was improved, the system performance can be further improved. While none of the above studies took this into account.

RIS is an emerging panel composed of metamaterials that can be used to assist in wireless communications. It consists of a large number of elements much smaller in size than the wavelength, without power amplifiers, and at a very low cost. Based on this, the majority of scholars want to use RIS to enhance the communication quality inexpensively. Renzo et al. [16] introduced the emerging research area of RIS including wireless communication, proposed a framework for analyzing and optimizing RIS, and summarized the current status of RIS research as well as key research questions. Pan et al. [17] examined the role of RIS in the future 6G systems and suggested eight possible research directions. Tang et al. [18] developed a free-space path loss model for RIS-assisted communication for different scenarios, taking into account the distance, RIS panel size, and other factors. Dai et al. [19] verified the gain of a RIS panel with 256 elements for the low frequency 2.3 GHz and millimeter wave bands, respectively. Nadeem, Tang, Liu et al. [20, 21, 22] studied the sum rate improvement of RIS for MISO, MIMO, and Multiuser MIMO scenarios, respectively. Huang et al. [23] investigated the energy efficiency of RIS-assisted downlink multi-user communication with the aim of minimizing the link budget of individual users. Guo et al. [24] maximized all users’ weighted sum rate for multi-user multiple-input single-output (MISO) systems using RIS for both perfect and imperfect channel state information scenarios. Xing et al. [25] proposed a novel water filling algorithm design method, which can be used to deal with the constraints of various performance indicators and power in imperfect CSI systems. Wei et al. [26] gave a channel estimation framework for RIS-assisted cascade channels. Basar et al. [27] took RIS assistance for wireless communication deeper into the modulation phase and proposed the RIS-space shift keying (RIS-SSK) and RIS-spatial modulation (RIS-SM) schemes. Hou et al. [28] verified the performance gain of RIS for non-orthogonal multiple access (NOMA) systems. All the above studies considered the use of continuous RIS phase shifts. However, from the hardware point of view, the phase shift of the RIS is achieved by the switching of the PIN diodes, so the number of quantized bits of the phase shift is an integer multiple of 2. In fact, a discrete finite phase shift is more reasonable. Di et al. [29] considered the discrete RIS reflection phase shifts. Zhang et al. [30] investigated the effect of finite phase shifts on throughput and gave the number of phase shift quantization required for a given throughput constraint. Yang, Chen et al. [31, 32] increased the number of RISs in the system to enhance spatial reuse. Yang et al. [33] used a new active RIS, which not only reflected the signal but also amplified it compared to the passive RIS. There is also a lot of research on the integration of RIS with other technologies. Li et al. [34] used RIS to solve the UAV LoS link deterioration problem and jointly optimized the UAV trajectory and RIS reflection phase shift matrix to maximize the UAV communication system capacity. Huang et al. [35] used deep reinforcement learning to jointly optimize transmitter-side beamforming and RIS passive beamforming.

In order to overcome the dependence of ISAC systems on wireless propagation environments, there have been some studies to apply RIS to ISAC to enhance the communication and sensing performance. Hu et al. [36] built an ISAC system based on distributed RIS and designed a detailed workflow, including the transmission protocols, position detection, and beamforming optimization. Maximizing the communication and sensing performance can be achieved by jointly optimizing transmit signal waveforms, sensing waveforms, and RIS phase shifts. The main metrics are transmission rate, Cramer-Rao bounded for angle estimation, and sensing mutual information (MI) [37, 38, 39, 40, 41]. He et al. [42] and Yu et al. [43] studied dual-RIS and multiple-RIS assisted ISAC systems, respectively. Zhang et al. [44] and Sankar et al. [45] studied the reflection and amplification of active-RIS and hybrid-RIS on communication and sensing signals, respectively. Salem et al. [46] studied the Multi-user MIMO (MU-MISO) physical layer security ISAC systems when eavesdropped by malicious unmanned aerial vehicles (UAVs). By jointly optimizing the radar receiving beamformer, RIS reflection coefficient, and transmit beamforming, the system’s achievable confidentiality could be maximized. Liu et al. [47] proposed an ISAC system supported by the IRS operating in the terahertz (THz) band. Unlike conventional downlinks, Liu et al. [48] considered an uplink ISAC system where a single-antenna user used distributed semi-passive RIS to transmit signals to a BS with multiple antennas. Two stages made up the transmission cycle according to the defined framework. The distributed semipassive RIS simultaneously performed position sensing and data transfer at each stage. Position sensing and beamforming design techniques that are straightforward and efficient were also suggested. However, in these above studies, some were not true ISAC, but the communication and sensing functions were deployed on the same base station, the signal was still separate. Moreover, RIS only assisted the communication signal, which did not help the sensing signal. In addition, few studies have taken into account poor quality LoS links, which are very typical in HSR systems.

However, in some extremely harsh communication environments, such as mountainous areas, it is not easy to deploy BS with direct link due to the terrain. Or due to weather, natural disasters, etc., the environment changes causing the original direct link to disappear. We want to achieve communication and sensing in a lower cost and more convenient way. In this paper, we study the impact of RIS in extremely harsh wireless communication environments. We try to use the intelligent reflection of RIS to achieve a certain degree of communication and sensing functions to ensure the safe operation of high-speed railway in the absence of a direct link.

Refer to caption
Figure 1: The RIS-aided HSR ISAC system.

III System Model

III-A System Description

As Fig. 1 shows that we take into account the downlink of a RIS-assisted ISAC system. An NN-antenna uniform line array (ULA) ISAC BS is present in the system, which combines sensing and communicating functions. Using the sensing echo signal of the ISAC BS, it can detect illegal targets on the train, tracks, and platforms, and can also achieve high-resolution positioning of carriages or illegal targets. Whether it is detection, estimation, or recognition, the accuracy is determined by the quality of the sensing echo signals. The BS provides services to KK single-antenna users, and concurrently detects or tracks targets by receiving echo signals. The direct connection of the ISAC BS to the user and target is disabled due to obstructions such as buildings or vegetation and the weak penetration characteristics of the mmWave. Therefore, we consider deploying a RIS panel in the system to help the signal reach the receivers with the reflection of the RIS. Moreover, the RIS can enhance the reflected signals by adjusting their amplitude and phase through a centralized controller to support communication and radar sensing tasks. The RIS panel with LL reflective elements is deployed on the side walls of the building and can maintain good channel conditions between the users and the targets through reasonable deployment. For the sake of simplicity, we make the assumption that the channel is quasi-static flat fading, where the channel fluctuates independently inside the coherent block and stays consistent during the transmission block. Additionally, we presume that the ISAC BS has complete channel information for every connection.

III-B Communication Model

The signal received by the kkth MR is:

yk=𝒉ir,k𝚽𝑯bi𝒘sk+n,y_{k}=\bm{h}_{ir,k}\bm{\Phi}\bm{H}_{bi}\bm{w}s_{k}+n, (1)

where 𝑯bi∈ℂL×N\bm{H}_{bi}\in\mathbb{C}^{L\times N} and 𝑯ir=[hir,1,⋯hir,K]T∈ℂK×L\bm{H}_{ir}=\left[h_{ir,1},\cdots h_{ir,K}\right]^{T}\in\mathbb{C}^{K\times L} represent the coefficients of the ISAC BS-RIS and RIS-MRs channels, respectively, 𝒘∈ℂN×1\bm{w}\in\mathbb{C}^{N\times 1} represents the transmitting beamforming vector, sks_{k} represents the information sent to user kk, and n∼CN(0,σ2)n\sim CN(0,\sigma^{2}) is the circularly summetric complex Gaussian (CSCG) noise. 𝚽≜diag[ejϕ1,ejϕ2,⋯,ejϕL]\bm{\Phi}\triangleq diag\left[e^{j\phi_{1}},e^{j\phi_{2}},\cdots,e^{j\phi_{L}}\right] is a diagonal matrix that considers the phase shift that is actually produced about by all RIS components.. ϕl=2mlπ2e\phi_{l}=\frac{2m_{l}\pi}{2^{e}} represents the phase shift of the llth element where l=1,⋯,L,ml∈{0,1,⋯,2e−1}l=1,\cdots,L,m_{l}\in\left\{0,1,\cdots,2^{e}-1\right\}, and ee is the quantity of quantization bits. It is believed that all channels at the ISAC BS are correctly estimated using the inserted pilot symbols. Moreover, all channels are presumed to be perfectly estimated. at the ISAC BS through the inserted pilot symbols. So the signal to interference plus noise ratio (SINR) that user kk has received is:

γk=∥𝒉ir,k𝚽𝑯bi𝒘∥σ2.\gamma_{k}=\frac{\left\|\bm{h}_{ir,k}\bm{\Phi H}_{bi}\bm{w}\right\|}{\sigma^{2}}. (2)

All users’ communication sum rate is:

∑k∈𝒦Rk=∑k∈𝒦CkB=∑k∈𝒦log2(1+γk),\sum_{k\in\mathcal{K}}R_{k}=\sum_{k\in\mathcal{K}}\frac{C_{k}}{B}=\sum_{k\in\mathcal{K}}log_{2}(1+\gamma_{k}), (3)

where 𝒦\mathcal{K} is the set of all users. The system communication throughput is represented by CC and the spectrum’s limited bandwidth by BB, correspondingly.

III-C Radar Model

Considering the terrible situation where The target is obscured from the ISAC BS’s line of sight (LoS) connection, we use the RIS to create a virtual LoS link. Using the beampattern gain from the RIS toward the target, we evaluate the efficiency of the sensing system. For a RIS equipped with LxL_{x} rows and LyL_{y} columns (Lx×Ly=LL_{x}\times L_{y}=L), its response in the direction of θa,θe\theta_{a},\theta_{e} is:

𝒂(θa,θe)⊗𝒂z(θe),\bm{a}\left(\theta_{a},\theta_{e}\right)\otimes\bm{a}_{z}(\theta_{e}), (4)

where,

𝒂y(θa,θe)≜1Ly[1,ejπsinθacosθe,⋯,ejπ(Ly−1)sinθacosθe]T,\bm{a}_{y}(\theta_{a},\theta_{e})\triangleq\frac{1}{\sqrt{L_{y}}}\left[1,e^{j\pi sin\theta_{a}cos\theta_{e}},\cdots,e^{j\pi(L_{y}-1)sin\theta_{a}cos\theta_{e}}\right]^{T}, (5)
𝒂z(θe)≜1Lx[1,ejπcosθe,⋯,ejπ(Lx−1)cosθe]T,\bm{a}_{z}(\theta_{e})\triangleq\frac{1}{\sqrt{L_{x}}}\left[1,e^{j\pi cos\theta_{e}},\cdots,e^{j\pi(L_{x}-1)cos\theta_{e}}\right]^{T}, (6)

and the target’s angles contacts with the RIS in the azimuth and elevation planes are denoted by θa\theta_{a} and θe\theta_{e}, accordingly. Then the RIS-to-target beampattern gain is:

𝒢(θa,θe)=\displaystyle\mathcal{G}(\theta_{a},\theta_{e})= 𝔼(|𝒂H(θa,θe)𝚽𝑯bi𝒘|2)\displaystyle\mathbb{E}\left(\left|\bm{a}^{H}(\theta_{a},\theta_{e})\bm{\Phi H}_{bi}\bm{w}\right|^{2}\right) (7)
=\displaystyle= 𝒂H(θa,θe)𝚽𝑯bi𝒘𝒘H𝑯biH𝚽H𝒂(θa,θe).\displaystyle\bm{a}^{H}(\theta_{a},\theta_{e})\bm{\Phi H}_{bi}\bm{ww}^{H}\bm{H}_{bi}^{H}\bm{\Phi}^{H}\bm{a}(\theta_{a},\theta_{e}).

III-D Channel Model

There have been many studies on the estimation of channel state information for RIS-assisted channels, so in this paper it is assumed that the ISAC BS and the RIS central controller have perfect CSI. Suppose there are both LoS and non-light of sight (NLoS) constituents in the system, and all links follow Rician fading. In this work, we suppose that the ISAC BS-RIS link’s CSI can be accurately predicted. The channel coefficient between the ISAC BSto the RIS can be denoted as Rice fading matrix 𝑯bi\bm{H}_{bi}:

𝑯bi=KRKR+1𝑯biLoS+1KR+1𝑯biNLoS,\bm{H}_{bi}=\sqrt{\frac{K_{R}}{K_{R}+1}}\bm{H}_{bi}^{LoS}+\sqrt{\frac{1}{K_{R}+1}}\bm{H}_{bi}^{NLoS}, (8)

where KR=4K_{R}=4 is the Rician factor. 𝑯biLoS∈ℂL×N\bm{H}_{bi}^{LoS}\in\mathbb{C}^{L\times N} is the LoS component connecting the RIS and the ISAC BS, which is related to the link distance and remains stable in each time slot. And 𝑯biNLoS∈ℂL×N\bm{H}_{bi}^{NLoS}\in\mathbb{C}^{L\times N} represents the NLoS Rayleigh fading component. 𝑯biLoS\bm{H}_{bi}^{LoS} and 𝑯biNLoS\bm{H}_{bi}^{NLoS} can be expressed, respectively, as:

[𝑯biLoS]l,n=β0(dbi)−α1e−jψl,n,\displaystyle\left[\bm{H}_{bi}^{LoS}\right]_{l,n}=\sqrt{\beta_{0}(d_{bi})^{-\alpha_{1}}}e^{-j\psi_{l,n}}, (9)
l∈{1,⋯,L},n∈{1,⋯,N},\displaystyle l\in\left\{1,\cdots,L\right\},n\in\left\{1,\cdots,N\right\},
𝑯biLoS=β0(dbi−α2)𝑯~biNLoS,\bm{H}_{bi}^{LoS}=\sqrt{\beta_{0}(d_{bi}^{-\alpha_{2}})}\widetilde{\bm{H}}_{bi}^{NLoS}, (10)

where β0=−61.3849\beta_{0}=-61.3849dB indicates the path loss at a distance of 11m, dbid_{bi} is the distance between the ISAC BS and RIS, α1=2.5\alpha_{1}=2.5, α2=3.6\alpha_{2}=3.6 are the exponent of path loss in LoS and NLoS scenarios, ψl,n\psi_{l,n} is the randomly distributed phase within [0,2π)[0,2\pi), and each term of 𝑯~biNLoS\widetilde{\bm{H}}_{bi}^{NLoS} is a complicated, circularly-symmetrical, zero-mean, unit-variance random variable to characterize small-scale fading.

Similarly, the channel 𝒉ir,k∈ℂ1×L\bm{h}_{ir,k}\in\mathbb{C}^{1\times L} of RIS-MR kk may be written as:

𝒉ir,k=KRKR+1𝒉ir,kLoS+1KR+1𝒉ir,kNLoS.\bm{h}_{ir,k}=\sqrt{\frac{K_{R}}{K_{R}+1}}\bm{h}_{ir,k}^{LoS}+\sqrt{\frac{1}{K_{R}+1}}\bm{h}_{ir,k}^{NLoS}. (11)

IV Problem Formulation

In this section, using the aforementioned system model, we start by stating the optimization problem, and to effectively find a sub-optimal solution, we divide the challenging optimization problem into two smaller issues.

IV-A Problem Formulation

This paper’s objective is to simultaneously optimize the ISAC BS beamforming vector along with the RIS phase shift matrix to maximize the system throughput of communication while ensuring the effectiveness of radar sensing. The radar performance can be characterized by the beampattern gain of the RIS. The optimization issue can be described as follows:

max𝒘,𝚽∑k∈𝒦log2(1+∥𝒉ir,k𝚽𝑯bi𝒘∥2σ2)\displaystyle\underset{\bm{w},\bm{\Phi}}{\textup{max}}\sum_{k\in\mathcal{K}}\log_{2}\left(1+\frac{\left\|\bm{h}_{ir,k}\bm{\Phi H}_{bi}\bm{w}\right\|^{2}}{\sigma^{2}}\right) (12)
s.t.\displaystyle s.t. (a)mink∈𝒦𝒂H(θa,θe)𝚽𝑯bi𝒘𝒘H𝑯biH𝚽H𝒂(θa,θe)≥γth,\displaystyle(a)\underset{k\in\mathcal{K}}{\min}\bm{a}^{H}(\theta_{a},\theta_{e})\bm{\Phi H}_{bi}\bm{ww}^{H}\bm{H}_{bi}^{H}\bm{\Phi}^{H}\bm{a}(\theta_{a},\theta_{e})\geq\gamma_{th},
(b)∥𝒘22∥≤Pmax,\displaystyle(b)\left\|\bm{w}_{2}^{2}\right\|\leq P_{max},
(c)[𝚽]l,l=ejϕl,ϕl=2mlπ2e−1,\displaystyle(c)\left[\bm{\Phi}\right]_{l,l}=e^{j\phi_{l}},\phi_{l}=\frac{2m_{l}\pi}{2^{e}-1},

where constraint (aa) indicates that the minimum beampattern gain of the received signal by the radar detector must be greater than the threshold γth\gamma_{th}; constraint (bb) is the maximum ISAC BS transmitting power, and 𝒘\bm{w} is the beamforming vector; and constraint (cc) represents the RIS elements’ discrete phase shift.

IV-B Problem Decomposition

Obviously, the optimization problem in (12) is non-convex that contains two optimization variables, the beamforming parameter 𝒘\bm{w} and the RIS phase shift matrix 𝚽\bm{\Phi}. During the optimization process of maximizing the communication sum rate, the two optimization variables 𝒘\bm{w} and 𝚽\bm{\Phi} are coupled to each other, consequently, simultaneous optimization is challenging. Thus, we take into account the alternating optimization procedure. Firstly, optimize 𝒘\bm{w} with fixed 𝚽\bm{\Phi}, then optimize 𝚽\bm{\Phi} with fixed 𝒘\bm{w}, and finally find the optimal 𝒘\bm{w} and 𝚽\bm{\Phi} that meet the constraints such that the communication sum rate is maximum.

1) Optimization of 𝐰\bm{w} for Given 𝚽\bm{\Phi}: The subproblem is to reasonably optimize the ISAC BS transmitting beamforming vector to maximize the communication sum rate based on meeting the minimal SINR constraint of the radar echo signal and the maximum transmitting power constraint. When another optimization variable 𝚽\bm{\Phi} is fixed, the optimization issue in (12) can be rewritten as the new form below about the transmitting beamforming vector 𝒘\bm{w}:

max𝒘∑k∈𝒦log2(1+∥𝒉ir,k𝚽𝑯bi𝒘∥2σ2)\displaystyle\underset{\bm{w}}{\textup{max}}\sum_{k\in\mathcal{K}}\log_{2}\left(1+\frac{\left\|\bm{h}_{ir,k}\bm{\Phi H}_{bi}\bm{w}\right\|^{2}}{\sigma^{2}}\right) (13)
s.t.\displaystyle s.t. (a)mink∈𝒦𝒂H(θa,θe)𝚽𝑯bi𝒘𝒘H𝑯biH𝚽H𝒂(θa,θe)≥γth,\displaystyle(a)\underset{k\in\mathcal{K}}{\textup{min}}\bm{a}^{H}(\theta_{a},\theta_{e})\bm{\Phi H}_{bi}\bm{ww}^{H}\bm{H}_{bi}^{H}\bm{\Phi}^{H}\bm{a}(\theta_{a},\theta_{e})\geq\gamma_{th},
(b)∥𝒘22∥≤Pmax.\displaystyle(b)\left\|\bm{w}_{2}^{2}\right\|\leq P_{max}.

2) Optimization of 𝚽\bm{\Phi} for Given 𝐰\bm{w}: When 𝒘\bm{w} is fixed, the optimization problem can be transformed into selecting the best phase shift from 2e2^{e} phase shifts for maximizing the communication sum rate. Then, the optimization subproblem is formulated as follows:

max𝚽∑k∈𝒦log2(1+∥𝒉ir,k𝚽𝑯bi𝒘∥2σ2)\displaystyle\underset{\bm{\Phi}}{\textup{max}}\sum_{k\in\mathcal{K}}\log_{2}\left(1+\frac{\left\|\bm{h}_{ir,k}\bm{\Phi H}_{bi}\bm{w}\right\|^{2}}{\sigma^{2}}\right) (14)
s.t.\displaystyle s.t. [𝚽]l,l=ejϕl,ϕl=2mlπ2e−1.\displaystyle\left[\bm{\Phi}\right]_{l,l}=e^{j\phi_{l}},\phi_{l}=\frac{2m_{l}\pi}{2^{e}-1}.

For the above two optimization subproblems, in the next sections, we will construct appropriate optimization strategies to address them, so as to accomplish the objective of boosting communication total rate while fulfilling restrictions.

V Design of RIS-Assisted Wireless ISAC System

In this section, we first address the two aforementioned subproblems, followed by a sum rate maximization solution. It alternately handles these two subproblems iteratively until the algorithm converges and a suboptimal result is obtained.

V-A Beamforming Design Sub-Problem Algorithm

To simplify the problem, we denote 𝑮k=diag(𝒉ir,k)𝑯bi,𝑾=𝒘𝒘H,𝒖=[ejϕ1,⋯,ejϕL]\bm{G}_{k}=diag(\bm{h}_{ir,k})\bm{H}_{bi},\bm{W}=\bm{ww}^{H},\bm{u}=\left[e^{j\phi_{1}},\cdots,e^{j\phi_{L}}\right], and then we obtain the following equation:

max𝒘∑k∈𝒦log2(1+∥𝒉ir,k𝚽𝑯bi𝒘∥2σ2)\displaystyle\underset{\bm{w}}{\max}\sum_{k\in\mathcal{K}}\log_{2}\left(1+\frac{\left\|\bm{h}_{ir,k}\bm{\Phi H}_{bi}\bm{w}\right\|^{2}}{\sigma^{2}}\right) (15)
=\displaystyle= max𝑾∑k∈𝒦log2(1+Tr(𝑾𝑮kH𝒖𝒖H𝑮k)σ2)\displaystyle\underset{\bm{W}}{\max}\sum_{k\in\mathcal{K}}\log_{2}\left(1+\frac{\textbf{Tr}(\bm{WG}_{k}^{H}\bm{uu}^{H}\bm{G}_{k})}{\sigma^{2}}\right)
=\displaystyle= min𝑾∑k∈𝒦(F1(𝑾)−log2(σ2)),\displaystyle\underset{\bm{W}}{\min}\sum_{k\in\mathcal{K}}\left(F_{1}(\bm{W})-\log_{2}(\sigma^{2})\right),

where where F1(𝑾)≜log2(Tr(𝑾𝑮kH𝒖𝒖H𝑮k)+σ2)F_{1}(\bm{W})\triangleq\log_{2}\left(\textbf{Tr}\left(\bm{WG}_{k}^{H}\bm{uu}^{H}\bm{G}_{k}\right)+\sigma^{2}\right). Now, we rewrite the initial optimization issue in (13) into an equivalent form to make using the alternating optimization algorithm easier:

min𝑾(F1(𝑾)−log2(σ2))\displaystyle\underset{\bm{W}}{\min}\left(F_{1}(\bm{W})-\log_{2}(\sigma^{2})\right) (16)
s.t.\displaystyle s.t. (a)mink∈𝒦𝒂H(θa,θe)𝚽𝑯bi𝑾𝑯biH𝚽H𝒂(θa,θe)≥γth,\displaystyle(a)\underset{k\in\mathcal{K}}{\textup{min}}\bm{a}^{H}(\theta_{a},\theta_{e})\bm{\Phi H}_{bi}\bm{W}\bm{H}_{bi}^{H}\bm{\Phi}^{H}\bm{a}(\theta_{a},\theta_{e})\geq\gamma_{th},
(b)Tr(𝑾)≤Pmax,\displaystyle(b)\textup{Tr}(\bm{W})\leq P_{max},
(c)𝑾⪰0,\displaystyle(c)\bm{W}\succeq 0,
(d)Rank(𝑾)≤1.\displaystyle(d)Rank(\bm{W})\leq 1.

The problem, known as the difference of concave functions (DC) problem, is still challenging to resolve. To do this, we make an attempt to transform it into a convex function utilizing the Taylor expansion of the first order. That is, in order to estimate the ideal solution from the upper limit, one must first establish a rough upper limit for the optimization problem and minimize it as much as possible. By this approximation, the original goal function can be converted into a convex function with respect to 𝑾\bm{W}. Specifically, the objective function F1(𝑾)F_{1}(\bm{W}) at the ii-th iteration of the first-order Taylor expansion may be represented as:

F1(𝑾)=\displaystyle F_{1}(\bm{W})= F1(𝑾i)+Tr(▽𝑾F1(𝑾i)H(𝑾−𝑾i))\displaystyle F_{1}(\bm{W}^{i})+\textup{Tr}\left(\triangledown_{\bm{W}}F_{1}(\bm{W}^{i})^{H}(\bm{W}-\bm{W}^{i})\right) (17)
≜\displaystyle\triangleq F1~(𝑾,𝑾i),\displaystyle\widetilde{F_{1}}(\bm{W},\bm{W}^{i}),
▽𝑾F1(𝑾i)=𝑮kH𝒖𝒖H𝑮kσ2ln2.\triangledown_{\bm{W}}F_{1}(\bm{W}^{i})=\frac{\bm{G}_{k}^{H}\bm{uu}^{H}\bm{G}_{k}}{\sigma^{2}ln2}. (18)

Currently, the nonconvexity of the optimization problem in (19) is only from a rank-one constraint in (16dd). First, we release the non-convex restriction in (16dd) in order to resolve this problem with SDR and obtain its relaxed version, and then the problem can be solved with the CVX solver directly.

Input: the number of quantization bits ee, the sensing threshold γth\gamma_{th}, convergence threshold δ\delta
1 Initialize the initial iteration index i=1i=1, 𝚽i\bm{\Phi}^{i}, 𝑾i\bm{W}^{i}
2 for Ri+1−Ri>δR^{i+1}-R^{i}>\delta do
3       Solve (16) for specified 𝑾i\bm{W}^{i} and record the interim answer 𝑾\bm{W}
4       Set i=i+1i=i+1 and 𝑾i=𝑾\bm{W}^{i}=\bm{W}
5 end for
Output: 𝑾∗=𝑾i\bm{W}^{*}=\bm{W}^{i}
Algorithm 1 Successive Convex Approximation-Based Algorithm

V-B Phase Shift Design Sub-problem Algorithm

The initial optimization issue takes on a new form with the fixed transmission beamforming vector, such (14), where only RIS discrete phase shift matrix remains. It is still non-convex, making it challenging to resolve via convex optimization. Considering the complexity of the problem, the simplest straightforward method for solving this non-convex problem is the exhaustive algorithm. However, it is clear that the exhaustive algorithm’s complexity rises exponentially as the set of practical solutions increases [49]. The temporal complexity of the local search method and the exhaustive search algorithm are contrasted. Fortunately, the local search algorithm has much lower time complexity than the exhaustive algorithm. Therefore, we choose the local search algorithm in Algorithm 2 to solve this optimization subproblem. Especially, we firstly fix the phase shift of the other L−1L-1 elements unchanged, then traverse all possible values for each RIS unit θl\theta_{l} and select the most suitable value θl∗\theta_{l}^{*} that satisfies the central objective, that is, optimizing the communication sum rate. The other elements are then optimized in the same manner, until all phase shifts in the array have been entirely optimized.

V-C Sum Rate Maximization

We provide a summary of the discrete phase shift optimization and beamforming vector designing subproblem algorithms discussed above and present a sum rate maximization solution. According to Algorithm V-C, we randomly set the initial state and then alternately modify the transmitting beamforming parameters and phase shift matrix as long as the algorithm is not yet convergent, i.e. the system transmission rate differential between two subsequent rounds is less than a specified limit |R(i+1)−R(i)|<min{ϑ,θ}\left|R^{(i+1)}-R^{(i)}\right|<\min\{\vartheta,\theta\}.

Input: the number of quantization bits ee, the sensing threshold γth\gamma_{th}, convergence threshold ϑ\vartheta
1 Initialize the initial iteration index i=1i=1, 𝚽i\bm{\Phi}^{i}, 𝑾i\bm{W}^{i}
2 for Ri+1−Ri>ϑR^{i+1}-R^{i}>\vartheta do
3       Give every possible value to ϕl\phi_{l}, and choose the value that maximizes the sum rate in problem (14), denoted as ϕl∗\phi_{l}^{*};
4       ϕl=ϕl∗\phi_{l}=\phi_{l}^{*};
5 end for
Output: 𝚽∗=𝚽i\bm{\Phi}^{*}=\bm{\Phi}^{i}
Algorithm 2 Phase Shift Design Sub-problem Algorithm Local Search-Based Algorithm
Input: Thresholds γth\gamma_{th}, θ\theta, ϑ\vartheta, randomly generate Φ\Phi, Φ∗\Phi^{*}=Φ\Phi, phase shift quantization bits ee, the initial iteration index i=1i=1
1 Update 𝐖\bm{{\rm W}}i+1{}_{i+1} by Algorithm 1 with given Φ\Phii{}_{i} ;
2 Update Φ\Phii+1{}_{i+1} by Algorithm 2with given 𝐖\bm{{\rm W}}i{}_{i};
3 if |R(i+1)−R(i)|<min{ϑ,θ}\left|R^{(i+1)}-R^{(i)}\right|<\min\{\vartheta,\theta\} then
4       R∗=R(i+1)R^{*}=R^{(i+1)};
5       Φ∗\Phi^{*}=Φ\Phii+1{}_{i+1};
6       W∗{\rm W^{*}}=W{\rm W}_i+1;
      Output: W∗,Φ∗,R∗;
7      
8else
9      i=i+1,andgotoStep1;
10endif
11      

    

V-D Complexity Analysis

13      The complexity of the method for maximizing the sum rate is not only determined by the number of iterations, which is configured to NouterN_{outer} for the convergence condition to be met |R(i+1)−R(i)|<min{ϑ,θ}\left|R^{(i+1)}-R^{(i)}\right|<\min\{\vartheta,\theta\}, but also in terms of the two subproblems. For the first, how often gradients are updated and the optimization of beamforming of all MRs in each gradient iteration create complexity. The number of receivers is MM, and we write NinnerN_{inner} for the number of gradient descent iterations. Thereby, the complexity of beamforming design subproblem is 𝒪(Ninner×M)\mathcal{O}(N_{inner}\times M). For the latter, the local search algorithm changes the value of element ll while keeping the other phase shifts constant and choosing the best one out of 2e2^{e} possible ones, and updates a value for ϕl\phi_{l}. Because the RIS contains LL elements, this part’s complexity is 𝒪(L×2e)\mathcal{O}(L\times 2^{e}). Consequently, we obtain 𝒪(Nouter×(Ninner×M+L×2e))\mathcal{O}(N_{outer}\times(N_{inner}\times M+L\times 2^{e})) for the suggested sum rate maximization algorithm’s complexity.

    

VI Performance Evaluation

In this section, we analyze how well the ISAC system is working with RIS. We get numerical data for various key parameters by comparing with other benchmark methods, which allows us to assess the efficiency of our suggested strategy, as well as analyze the influence of numerous essential aspects on effectiveness.

    

VI-A Simulation Setup

We take into account the mmWave HSR system. A high-speed train has eight carriages, each measuring 200 meters in length. The roof of the high-speed rail is evenly deployed with 11 MRs, of which each carriage is equipped with 1-2 MRs. A reflective link is provided by deploying a RIS between the ISAC BS and the MRs to assist in the transmission of communication and sensing signals. We construct a three-dimensional Cartesian coordinate system, as seen in Fig. 2. The high-speed rail and the MRs are parallel to the Y axis, while the RIS is set up in the X-Z plane. The ISAC BS and the MRs are located on different sides of the Y-axis. One Target is randomly distributed around 11 MRs. Table I shows the system simulation parameter settings.

16      
Refer to caption
Figure 2: The ISAC system’s cartesian coordinate with RIS assistance.
17      
TABLE I: Simulation Parameters
Parameter Symbol Value
Number of ISAC transmit antennas NN 8
Number of MRs KK 11
Amount of RIS components LL 64
Number of phase quantization bits ee 3
Carrier frequency ff 30GHz
Bandwidth WW 100MHz
Maximum transmitting power PP 23dBm
Radar SINR threshold γth\gamma_{th} 0.5×10−40.5\times 10^{-4}
Noise power spectral density N0/WN_{0}/W -134dBm/MHz
Noise power spectral density σ2\sigma^{2} -134dBm/MHz
Normalized antenna spacing δ\delta λ/2\lambda/2
Rician factor KRK_{R} 4
Path loss exponent β\beta 2
Height of the ISAC BS hBSh_{BS} 10m
Height of MRs hMRh_{MR} 2.5m
Height of RIS hRISh_{RIS} 2.5m

    

We contrast the proposed approach with the following algorithms to demonstrate how well it performs in the system

  • •

    Without-RIS: the technique does not deliver reflected signals via RIS, and the receiver may only receive signals through direct lines. In order to achieve our objectives, utilize the same power allocation algorithm.

  • •

    Random Phase Shift (RPS): for each element of RIS, the scheme chooses a set of functional phase shifts at random and maintains other elements throughout time. The most effective beamforming vector is then determined using algorithm 1 with the transmitting power of all links, and the goal of maximizing communication sum rate is explored.

  • •

    Average Power Transmission (APT): in the algorithm, every transmit antenna is given the same amount of transmission power, after which finds the RIS phase shift which optimizes the overall system communication throughput using a local search technique, and discusses the maximum communication sum rate and perception performance.

    

VI-B Performance Evaluation

20      In Fig. 3, we defined the quantity of quantization bits as e=3e=3, and the threshold of radar sensing beampattern gain γth=0.5×10−4\gamma_{th}=0.5\times 10^{-4}. We plot the communication sum rate curve as the RIS steadily expanded from 4 to 64 elements. The findings demonstrated that as the quantity of RIS components increases, we can see that the communication sum rate of the three RIS auxiliary schemes all increases. This indicates that more RIS elements can provide more reflective links and thus transmit more data. However, this upward trend gradually slows down with the increase of LL, which shows that the continuous expansion of the RIS panels cannot increase the sum rate indefinitely with other parameters unchanged. The communication sum rate provided by the reflective link is limited, which is mainly constrained by the transmission power, Shannon sum rate, system model, physical environment and other factors. The suggested algorithm with RIS has a highest communication sum rate than the previous three comparison algorithms. It shows the RIS’s ability to deliver reflected link auxiliary transmission when the ISAC BS’s direct connection to the MRs is interrupted by the harsh environment and cannot provide service. Compared to the RPS and APT schemes, the proposed scheme performs better, because the random RIS phase shifts do not give full play to the maximum advantage of the RIS elements. The channel variations between various MRs are also not taken into account by the average transmission power. As a result, when the sensing gain threshold is met, the proposed RIS-aided system outperforms the all baseline schemes in terms of communication performance.
21      
Refer to caption
Figure 3: Sum rate versus the quantity of RIS elements LL.
22      
Refer to caption
Figure 4: Sum rate versus the quantity of quantization bits ee.
23      
Refer to caption
Figure 5: Sum rate versus Sensing signal threshold.

    

Refer to caption
Figure 6: Sum rate versus transmitting power of the ISAC BS.
25      
Refer to caption
(a)
Refer to caption
(b)
Figure 7: (a) Sum rate versus distance between RIS and MRs. (b) Sum rate versus distance between RIS and MRs.
In Fig. 4, we set L=36/64L=36/64 and the radar sensing beampattern gain threshold is γth=0.5×10−4\gamma_{th}=0.5\times 10^{-4}. We show the variation in communication efficiency against the quantity of quantized RIS element phase shift bits. As shouwn in the figure, both the proposed scheme and the communication sum rate of APT hardly change with the increase of ee, while the float of the RPS scheme is large and irregular. This is because regardless of the number of quantization bits, the proposed algorithm and APT algorithm both find the optimal phase shift of each RIS element through the local optimization algorithm, and also consider the cooperation between all RIS elements. Through multiple iterations, the superior performance of the selected RIS phase shift matrix is guaranteed. This also may be due to the fact that the optimization of the transmission beamforming vector has a greater impact on the sum rate than the phase shift of the RIS. Therefore, after power optimization of the proposed scheme and the APT scheme, no matter what the quantization bits of RIS phase shift are, the optimal phase shift matrix can be found to maximize the sum rate. On the other hand, the RPS algorithm does not optimize the RIS phase shifts, but only randomly selects a phase shift for each RIS element, so there is no guarantee that the selected phase shift is suitable. Therefore, the strength of each reflected signal cannot be guaranteed, and the fluctuation is large. Correspondingly, the maximum sum rate cannot be guaranteed. Therefore, the sum rate of RPS fluctuates greatly. This also may be due to the fact that the optimization of the transmission beamforming vector has a greater impact on the sum rate than the phase shift of the RIS. Therefore, after power optimization of the proposed scheme and the APT scheme, no matter what the quantization bits of RIS phase shift are, the optimal phase shift matrix can be found to maximize the sum rate. On the other hand, the RPS algorithm does not optimize the RIS phase shifts, but only randomly selects a phase shift for each RIS element, so there is no guarantee that the selected phase shift is suitable. Therefore, the strength of each reflected signal cannot be guaranteed, and the fluctuation is large. Correspondingly, the maximum sum rate cannot be guaranteed. Therefore, the sum rate of RPS fluctuates greatly.
26      In Fig. 5, we set L=64L=64, and e=3e=3. We show the variation in sum rate as a function of the sensing beampattern gain threshold. As illustrated in Fig. 5, no matter the proposed algorithm, RPS, or APT, the sum rate rapidly declines as the sensing threshold rises. This is because as the sensing performance requirements for the target detection increase, the transmission power and the RIS phase shifts need to be adjusted to meet the higher threshold of sensing gain, and the communication sum rate will decrease accordingly. Morever, as the sensing gain threshold increases, the decrease in sum rate becomes more obvious. Among of the all three RIS-assisted algorithms, the RPS scheme has the most severe reduction in sum rate. This is because RPS selects RIS phase shifts randomly, and if an inappropriate RIS phase shift matrix is selected, the sensing performance needs to be compensated for by power allocation, and the sum rate will decrease accordingly.
27      In Fig. 6, we set L=64L=64, e=3e=3, and the radar sensing beampattern gain is γth=0.5×10−4\gamma_{th}=0.5\times 10^{-4}. We plot the sum rate according to the ISAC BS’s highest transmission power. As shown in Fig. 6, the sum rate of all RIS-assisted schemes increases with the maximum transmission power. Our suggested method has a substantially higher sum rate than the other three benchmark schemes. It should be noted that when the transmission power Pmax<=18dBP_{max}<=18dB, the sum rate of the RPS scheme is 0. This is because when the ISAC BS’s transmitting power is small, the randomly selected RIS phase shift matrix cannot meet the sensing gain threshold requirement, then the optimization problem we establish is not feasible, so the sum rate is 0.
28      In Fig. 7, we set L=64L=64, e=3e=3, and the radar sensing beampattern gain is γth=0.5×10−4\gamma_{th}=0.5\times 10^{-4}. We compare the sum rate and the sensing beampattern gain of all MRs. As shown in Fig. 7, from the first MR to the 11st MR, RIS and MRs are becoming further apart, and the path loss is getting worse, so the sum rate and the sensing beampattern gain gradually decrease. Among them, the decrease of the sensing beampattern gain is faster than that of the sum rate, because the sensing signal goes through the ISAC BS-RIS-Target and the Target-RIS-ISAC BS backhaul links. The path loss introduced by the doubling distance is much greater than that of the communication signal. Therefore, in order to ensure that the sensing performance of all possible targets meets the threshold requirements, the setting of the optimization parameters needs to pay more attention to the MR at the farthest location. This also ensures fairness in the sum rate to all MRs. While, the possible sum rate is not maximum correspondingly. This is the cost of balancing communication and sensing performance.

    

VII Conclusion

In this paper, we have focused on a downlink ISAC system with the aid of a RIS. To improve the system sum rate with meeting the realistic discrete phase shift, power, and sensing QoS limitations, We have looked into a hybrid beamforming architecture and RIS phase shift optimization problem. The specified issue is non-convex, hence we have provided a alternative optimization procedure to arrive at a sub-optimal solution. Finally, the proposed algorithm’s superiority has been confirmed by numerical results, and we have seen that RIS may improve the condition of a channel by giving numerous controlled signal reflections depending on how many RIS elements there are. In the future work, we will consider RIS-assisted multi-cell HSR integrated sensing and communication to improve the handover success rate and enhance the practicability.

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    [Uncaptioned image] Panpan Li was born in Henan, China, in 1997. She received the B.S. degree in communication engi- neering from North China Electric Power University, Baoding, China, in 2019. She is currently pursuing the Ph.D. degree with the State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiao- tong University, Beijing, China. Her current research includes millimeter-wave wireless communications, reconfigurable intelligent surfaces, convex optimiza- tion and wireless resource allocation.
    Algorithm 3 Sum Rate Maximization