Nowadays, mobile applications such as mobile health computing, mobile object recognition and extended reality are emerging[1, 2]. Their requirements such as extremely high data rate, high quality-of-service (QoS), and ultra-low latency are driving the revolution of mobile wireless network. Fortunately, reconfigurable intelligent surfaces (RISs) or intelligent reflecting surfaces (IRSs) are envisioned as one of the most promising and revolutionizing technologies for improving the spectrum and energy efficiency in wireless systems. An RIS that consists of an array of passive reflecting elements can propagate the received signals towards the receiver by adjusting the phase shift of each reflecting element. Hence, one can flexibly enhance or weaken the signals at the receiver via adjusting the elements of RISs. Meanwhile, since the RIS reflecting elements only passively reflect the incoming signals without any signal processing (SP) operations, RISs can use much less power for signal transmission compared with relays.
Recently, a number of existing literature such as [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] have focused on the applications of RISs in wireless communication. In , the authors maximized the weighted sum-rate in RIS-aided multi-cell networks. The coverage of a downlink RIS-assisted network that consists of one base station (BS) and one user was analyzed and maximized in . The work in  optimized the resource allocation in a network that consists of a RIS-assisted wireless transmitter and multiple receivers. The performance of RIS-assisted nonorthogonal-multiple-access (NOMA) system is analyzed in [9, 10, 11, 12, 13]. The aforementioned works in [6, 7, 8, 9, 10, 11, 12, 13, 14, 15] studied the application of RISs in radio frequency (RF) communication. Meanwhile, the works  and [17, 18, 19, 20] studied the application of RISs in terahertz (THz) band and millimeter wave band, respectively. However, none of these existing works [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] studied the use of RISs for visible light communication (VLC) system.
VLC that utilizes the indensity of light to carry information has become an prevalent development trend in the future indoor scene due to the increasing shortage of radio spectrum resources[21, 22, 23]. VLC has advantages over RF on the aspects of huge bandwidth, excellent energy efficiency, no health hazards[24, 25]. Moreover, compared with RIS-aided RF, RIS-aided VLC can provide communications and illumination simultaneously. However, the transmitted signals must be real and non-negative in VLC, thus the channel capacity in VLC is different from that in RF. Therefore, the aforementioned conventional methods in RIS-aided RF [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] can not be directly employed in VLC due to its unique characteristics.
Furthermore, to enable VLC to be utilized in outdoor scenario, one can use unmanned aerial vehicles (UAVs) to provide both communications and illumination to ground users. A number of existing works has studied the problems related VLC-enabled UAVs. In particular, in , the power consumption of VLC-enabled UAVs that must provide communications and illumination is optimized. Authors in 
utilized machine learning (ML) technology to predict the illumination requirements of users so as to optimize the deployment of the VLC-enabled UAVs. In, the authors studied the use of NOMA techniques for VLC-enabled UAVs to maximize the sum rate of all users. However, the Optical Wireless Channel (OWC) consists of Line-of-Sight (LOS) channel, which represents the rectilinear propagation between transmitter and receiver, and Non-Line-of-Sight (NLOS) channel, which fades severely during the propagation via reflection, scattering and so on[29, 30]. In outdoor scenario, there exists a lot of obstacles such as buildings, large billboard and even trees. With the help of RIS, a UAV-RIS-user link which consists of two LOS sublinks can be constructed even there exists obstacles between UAV and ground users.
The main contribution of this work is a novel framework that enables the UAVs to jointly use RIS and VLC to efficiently serve ground users. The key contributions are listed as follows:
The optimization of deploying UAVs over a RISs-assisted visible light communication (VLC) system is studied. These UAVs must simultaneously provide communications and illumination for ground users. With the constraints of data rate and illumination demand, a mixed integer programming probem is formulated which jointly optimizes UAV deployment, phase shifts of RISs, user association and RIS association so as to minimize the transmit power of UAVs.
To solve this problem, an algorithm that alternately optimizes UAV deployment, phase shifts of RISs, user association and RIS association is proposed. In particular, first, phases alignment method and SDP algorithm are proposed to optimize the phase shift of RISs in two application scenarios, i.e. only one user is associated with one UAV and more than one users are associated with one UAV, respectively. Then, the noncave UAV deployment optimization problem is transformed to a convex problem which can be solved by CVX toolboox. Since the problems of user association and RIS association are integer programming, the fraction relaxation method is adopted before using dual method to find the optimal solution. For simplicity, a greedy algorithm is proposed as an alternative to optimize RIS association.
Through extensive numerical study, the proposed two schemes demonstrate the superior performance of and energy consumption reduction over the case without RIS, respectively. Our results also show that by associating each RIS with the closest UAV, one can achieve the minimum transmit power of all the UAVs.
The remainder of this paper is organized as follows. The system model and problem formulation are described in Section II. The joint UAV deployment and resource allocation is presented in Section III. Simulation results are analyzed in Section IV. Conclusions are drawn in Section V.
Ii System Model
Consider a VLC-enabled UAV network which consists of a set of UAVs in a specific area with a set of reconfigurable intelligent surfaces (RISs), as shown in Fig. 1. In this model, each UAV must simultaneously provide communication and illumination to ground users. For communication service, each UAV can directly transmit the data to the ground users or it can transmit the signal to RISs that will forward the data to the ground users. Hereinafter, we use aerial area to refer to the service area of each UAV. Note that each UAV does not serve ground users until it moves to the optimal location. Thus, the UAVs can be seen as static aerial base station during wireless transmission.
Ii-a Transmission Model
For simplicity, the time of each UAV flying from one place to anothor is ignored. The rotary-wing UAV is considered in this paper and each UAV can hover over one specific location to serve the users. At time slot , consider a ground user located at and a flying UAV located at , where is the altitude of each UAV, which is assumed to be equal and fixed for all UAVs. In our model, we consider two types of data transmission: UAV-ground users and UAV-RIS-ground users. The LOS channel gain between UAV and user can be expressed as:
where denotes the Lambertian emission order with being the semi angle at half-power of the transmitter. denotesis the physical area of the PD in each receiver and represents the distance between UAV and ground user . In (1), and represent the light emission angle and the incidence angle from UAV to ground user , respectively. In (1), denotes the field of view of the receiver, and the gain of the optical concentrator is defined as:
where denotes internal reflective index. From (2), we can see that is a constant when .
Let us consider a scene where there exists one or more RISs in the aerial area of UAV . For tractabilty, let denote the association between UAV and RIS . If RIS is in the aerial area of UAV at time , we have ; otherwise, . Since each RIS can be located in only one UAV’s aerial area, then we have the following equation:
In this case, there eixts not only LOS link, but also RIS-reflecting links between UAV and ground user . As shown in Fig. 2, the RISs are deployed on the buildings. The location of RIS is denoted by . Without loss of generality, the height of all RISs is assumed to be the same.
Assuming that all the RISs are equipped with a uniform linear array (ULA) of reflecting elements as well as a controller in the UAV to intelligently adjust the phase shifts. Denoting as the diagonal phase-shift matrix for RIS at time , where is the phase shift of the th reflecting element of RIS at time , and the phase shift is assumed to be continuously controllable.
Assuming the links from the UAV to the RIS (U-R link) and the links from the RIS to the ground user (R-G link) are both LOS channels. Hence, the channel gain of the U-R link between UAV and RIS at time , denoted by , is given by:
where the right-most term is the array reponse of an -element ULA, represents the cosine of the angle of arrival (AoA) of the signal from UAV to the ULA at RIS at time , is the antenna separation, and is the carrier wavelength. In (4), represents the path loss of the U-R link at time which can be expressed according to the Lambertian emission model:
where represents the distance between UAV and RIS at time , and represent the light emission angle and the incidence angle from UAV to RIS at time , respectively.
Similarly, the channel gain of the R-G link between RIS and ground user at time , denoted by , is given by:
where represents the cosine of the angle of departure (AoD) of the signal from RIS to ground user at time , represents the path loss of the R-G link at time which can also be expressed according to the Lambertian emission model:
where represents the distance between RIS and ground user at time , and represent the light emission angle and the incidence angle from RIS to ground user at time , respectively.
After obtaining the channel gains of both the LOS links and the RISs-reflecting links, we can further derive the total channel gain which is the sum of channel gain of LOS link and that of all the RIS-reflecting links:
where represents the position of UAV at time .
We consider the user association among multiple UAVs and users. Specifically, denote as the association for UAV and ground user at time . If , ground user is served by UAV at time ; otherwise, . Since each ground user can be served by only one UAV, we have the following equation:
Consider that when ground users are served by UAVs, they are all static, the mobility energy consumption of all the UAVs is not taken into account. Due to the limited energy of UAVs, their deployment must be optimized to minimize the transmit power while meeting the data rate and illumination requirements of ground users.
Ii-B Problem Formulaion
In order to formulate the deployment problem of UAVs, first, the relationship between the transmit power of the UAV and the data rate required by the users must be obtained. Assuming the UAVs provide multicell channels to all the ground users, the required data rate for all the ground users at time can be formulated by:
where is Euler number, is illumination response factor of transmitter, denotes the power of the additive white Gaussion noise (AWGN). In (10), represents the transmit power of UAV at time . According to (10), thus, we obtain the minimum transmit power of UAV that meets the data rate requirements of its associated users:
With respect to the illumination requirements of ground users served by UAV , we must have:
where represents the illumination demand of ground user at time .
After giving the constrains of the data rate and illumination requirements of users, we can further formulate the deployment problem:
denotes the user association vector of UAV, denotes the RIS association vector of UAV , denotes the phase shift matrix which can be expressed as following:
and is the predefined minimum distance between any two UAVs. In (13), the objective function denotes the sum transmit power of all UAVs. Constraint (13a) represents the requirements of the illumination of ground users. The data requirement for each ground user is given in (13b). Constraint (13c) indicates that each ground user can only be served by one UAV at each time slot. Each RIS can be located in only one UAV’s aerial area as shown in (13d).
Assuming the data rate requirement and illumination reuqirement will not change in each time interval of ten minutes. Hence, in order to successfully meet the requirments of ground users, we must solve out the optimal deployment of UAVs at the beginning of each time interval.
Iii Optimization of UAV Deployment, User Association and Power Efficiency
According to the last section, the optimal deployment of each UAV at the beginning of each time interval can be calculated by solving the optimization problem formulated in (13). Note that (13) is a mixed integer programming problem, an iterative algorithm is proposed to tackle with this problem. Specifically, we first optimize and with fixed and . Afterwards, and can be optimized with fixed and .
Iii-a Phase Shift Matrix Optimization and UAV Deployment
With fixed user association and RIS association , the optimization problem (13) can be reduced to:
where . Problem (15) can be solved in two steps: passive beamforming optimization and UAV deployment optimization.
Iii-A1 Passive Beamforming Optimization
In order to futher reduce the computation complexity in passive beamforming optimization, we divide this subproblem in two application scenarios, i.e. only one user is associated with one UAV and more than one users are associated with one UAV.
Only one user is associated with UAV
In this case, it is obviously that in order to maximize the received signal energy, we can align the phases of the received signal at the ground user. Firstly, with fixed , the total channel gain in (8) can be further expressed as:
where denotes the set of RISs associated with UAV . Therefore, we can combine the signals from different paths coherently at ground user , i.e., , or re-expressed as:
In this way, the received signal energy is maximized through the phase alignment of the received signal. Hence, can be further written as:
More than one users are associated with UAV
When an UAV is serving more than one ground users, the aligned phase will vary from one user to another if utilizing phase alignment method, thus making it a trouble to tackle with problem (15). With fixed , and in (15), we can formulate the following problem for each UAV :
where denotes the set of ground users associated with UAV . Problem (19) is a nonlinear fractional programming which can be approximated as the following problem:
To solve problem (20), we utilize semidefinite program (SDP) algorithm. Denote . Then represents the matrix of all the that satisfy arranging in rows, where represents the number of elements in set . The constraint in (20) is equal to . Through introducing , can be transformed to . Then, the optimization problem (20) can be further written as:
Since is a scalar, then we can obtain:
Denote , , . Problem (21) can be further expressed as:
It can be inferred that , where denotes matrix trace. In order to solve problem (23), we denote as and needs to satisfy and . Then, we relax this rank-one constraint to convert problem (23) to a convex SDP problem:
Iii-A2 UAV deployment optimization
We further optimize the UAV deployment with fixed . Since in constraint (15b) is a convex function with respect to and , we can use the first-order Taylor expansion to convert it to a linear function with respect to and :
where the superscript represents the variable at the previous iteration. Then, we can denote:
where which is the coefficient of can be approximated by using the AoA of the signal at RIS at the previous iteration. In (31), only and are related with . Thus, we can further introduce a new group of variables into problem (30):
where represents the emission angle and the incidence angle at the previous iteration, respectively. Due to constraint (32b), (32d) and (32e) are still nonconvex, we also use the first-order Taylor expansion method as that in (27):
with all the stands for the value of at the previous iteration. Problem (33) is now a convex problem which can be figured out the global optimal point by using CVX toolbox in MATLAB.
Iii-B User and RIS Association Optimization
In the previous subsection, we optimize and with fixed and . In this subsection, We further optimize and with fixed and . Thus, the optimization problem (13) can be reduced to: