RIS-Assisted Network Slicing Resource Optimization Algorithm for Coexistence of eMBB and URLLC

Abstract

Enhanced mobile broadband (eMBB) and Ultra-Reliable and Low-Latency Communications (URLLC) are the two main services in the fifth-generation mobile network. URLLC services have stringent latency and reliability requirements, while eMBB services are designed to provide extremely high data rates for content delivery. The differentiated Quality of Service (QoS) requirements of the two services make their coexistence on the same bandwidth resources a challenging issue. To meet this challenge, we introduce reconfigurable intelligent surface (RIS) technology to assist in solving the resource allocation problem. The problem is formulated as two optimization problems. For the eMBB allocation problem, we jointly optimize the resource block allocation, power allocation, and RIS phase shift matrix and propose a two-stage alternating iterative algorithm to maximize the total traversal capacity of eMBB users. For the URLLC allocation problem, we maximize the URLLC packet reception rate and minimize the amount of eMBB rate loss while ensuring the quality of service for eMBB and URLLC. A heuristic URLLC allocation algorithm based on pre-configured RIS is proposed. Simulation results show that the proposed algorithm can meet the strict delay requirements of URLLC even when the URLLC packet reception rate is nearly 95.5%. Meanwhile, the total loss rate of eMBB service caused by the reuse of URLLC service is less than 6%. Thus, the applicability of the proposed solution to the coexistence problem is demonstrated.

1. Introduction

Three types of service application scenarios for 5G include enhanced mobile broadband (eMBB), massive machine type communications (mMTC), and ultra-reliable and low-latency communications (URLLC) [1]. An efficient goal of the 5G new radio (NR) evolution is to enable the efficient coexistence of services with different quality of service (QoS) [2], which is a significant challenge in the 5G network and will be upgraded in the upcoming 6G network.

The 3GPP (3rd Generation Partnership Project) standard proposed the puncture technique [3] to solve the above coexistence problems, which has laid the foundation for most scholars’ related research. This technology gives higher priority to URLLC services, but this will affect the transmission of eMBB services and lead to a decrease in the frequency efficiency of the whole system. Based on this, more efficient resource allocation schemes are proposed to balance heterogeneous QoS requirements and system frequency spectrum efficiency. Zhang et al. [4] proposed an iterative algorithm for joint resource allocation based on the puncturing technique, which can satisfy both eMBB data rate and URLLC interruption probability requirements. Wang et al. [5] formulated a joint URLLC and eMBB resource scheduling problem based on user clustering. An adaptive iterative power allocation algorithm was proposed based on successive convex approximations and convex functional difference programming to solve this scheduling problem. Bairagi et al. [6,7] used heuristic algorithms and one-sided matching games to solve optimization problems, followed by penalty continuous upper bound minimization algorithms and transmission models. In addition, many scholars have used deep reinforcement learning (DRL) to solve resource allocation and optimization problems in cellular networks [8,9,10,11], such as deep deterministic policy-based gradient algorithms and deep Q-learning algorithms. The channel quality for eMBB and URLLC users in coexistence scenarios directly determines their performance, i.e., data rate, reliability, and latency. The above methods can show good performance when the channel conditions are good. However, when faced with a complex wireless communication environment, they do not accurately derive the terminal rates based on the actual puncture states and channel conditions of the two services.

Reconfigurable intelligent surface (RIS) has attracted much academic attention as a possible paradigm in future wireless networks. Its ability to control and configure the wireless propagation environment stands out. RIS can effectively solve the problems of high energy consumption of relay communication and the severe difficulty of building 5G base stations, so the study of this technology is introduced for 6G mobile communication development [12]. In existing research, RIS has converged with several communication frontier technologies [13], including multiple-input multiple-output (MIMO), non-orthogonal multiple access (NOMA), mobile edge computing (MEC), and unmanned aerial vehicle (UAV) technologies.

Given the ability of RIS to actively modify the wireless communication environment, numerous studies have investigated RIS-assisted wireless networks for the eMBB and URLLC services. The literature [14,15,16,17] studied only single service class application scenarios, i.e., only eMBB or URLLC services. Wu et al. [14] verified that RIS-assisted MIMO systems could achieve the same performance as large-scale MIMO systems (without RIS assistance) while significantly reducing the active antenna and RF chain. Ranjha et al. [15] used UAV-assisted short data URLLC as an example. With the passive beam forming function of the RIS unit and direct search method, the UAV’s optimal location and block length are determined in the theoretical model, and the total decoding BER is reduced. Melgarejo et al. [16] proposed an authorization-free access scheme assisted by RIS to enhance the reliability of URLLC. Ghanem et al. [17] proposed a suboptimal iterative algorithm that uses a new iterative rank minimization method to optimize all variables in each iteration jointly. This algorithm simplifies the URLLC services and yields a significant performance gain. AL-Mekhlafi et al. [18] went further to investigate the coexistence of eMBB and URLLC services in RIS-assisted cellular networks. It can be seen that there are fewer studies related to RIS technology for achieving the coexistence of eMBB and URLLC services in wireless networks.

Based on the above analysis, RIS technology which can reshape the wireless propagation environment and the coexistence multiplexing issue of URLLC and eMBB are both essential components in the future 6G network. Combining the two for efficient operation to fully utilize the network’s potential and realize the coexistence of heterogeneous services is the focus of our current attention. The main contributions of this paper are as follows:

• We study the problem of achieving efficient multiplexing URLLC and eMBB in RIS-assisted wireless networks. The resource allocation problem in the coexistence scenario is formulated as two optimization problems, while the performance tradeoff between different services is considered.
• The eMBB allocation problem is solved in two stages. The first stage determines the RB allocation. The second stage jointly optimizes the power allocation and RIS phase shift matrix. However, since the RIS optimization takes a long time, the RIS phase shift matrix is pre-configured.
• For URLLC services, we propose a heuristic URLLC allocation algorithm based on pre-configured RIS. The pre-configured RIS phase shift matrix is sequentially substituted into the URLLC allocation problem to obtain the optimal power and frequency allocation strategy to maximize the URLLC packet reception rate.
• Simulation results show that the heuristic algorithm based on RIS pre-configured proposed in this paper achieves a better URLLC packet reception rate than other allocation methods while satisfying the delay requirements. Then, the performance of four different types of RIS configurations is compared to prove the effectiveness of RIS.

The composition of this paper is as follows: Section 2 presents the system model. Section 3 presents two optimization problems, i.e., the eMBB and URLLC allocation problems. Section 4 converts and solves these two problems separately and introduces the optimal RIS phase shift matrix design. Section 5 conducts simulation experiments and analyzes the experimental results. Section 6 concludes the whole paper and considers the outlook for this work.

2. System Model

2.1. RIS-Assisted Wireless Network Model

This paper is based on a downlink wireless network scenario with a single 5G base station (gNB) serving E eMBB users and U URLLC users. A RIS system with N tiny reflective elements is also deployed, and the base station controls and regulates the RIS through a microcontroller. Let $e\in \{1,\cdots ,E\}$ denote the eMBB service slice, $u\in \{1,\cdots ,U\}$ means the URLLC service slice, $n\in \{1,\cdots ,N\}$ represents the RIS reflection element, and $b\in \{1,\cdots ,B\}$ means the RBs in the network, where the bandwidth of each RB is W. Each time slot $t\in \{1,\cdots ,T-1\}$ has a duration of τ.

Assume that all communicating nodes’ channel state information (CSI) is completely known at the gNB. Assume that eMBB users and URLLC users are receivers (R_x) and base stations are transmitters (T_x), as shown in Figure 1. ${\theta }_n\in [0,2\pi )$ denotes the phase shift of the nth RIS reflective element, $\theta =[{\theta }_1,\cdots ,{\theta }_N]$ denotes the RIS phase shift vector, and $\mathsf{\Phi }=diag(e^{j{\theta }_1},\cdots ,e^{j{\theta }_N})$ denotes the phase shift matrix of the RIS. The RIS-assisted end-to-end channel matrix C is expressed as follows: C = GΦH + D, where G is the channel coefficient matrix between RIS and R_x, H is the channel coefficient matrix between T_x and RIS, and D represents the direct channel coefficient matrix between T_x and R_x. Then, the channel gain of eMBB user e in RB b can be expressed as C_e = |G_RIS,eΦ_eH_gNB,RIS + D_gNB,e|², where Φ_e denotes the RIS phase shift matrix of eMBB, G_RIS,e denotes the channel coefficient between RIS and eMBB user e, H_gNB,RIS denotes the channel coefficient between gNB and RIS, and D_gNB,e denotes the channel coefficient between eMBB user e and gNB. Similarly, the channel gain of URLLC user u in RB b can be expressed as C_u = |G_RIS,uΦ_uH_gNB,RIS + D_gNB,u|².

2.2. Multiplexing Model for eMBB-URLLC Services

Usually, eMBB transmission is allowed to span multiple time domains to improve spectral efficiency. In contrast, URLLC transmission can span multiple frequency channels to meet its time delay requirements [19]. In this paper, the URLLC user is scheduled with a short transmission time interval (sTTI), while the TTI size used to schedule the eMBB user is longer (slot duration is 1 ms). As shown in Figure 2, when URLLC services pass in and puncture the second (CB2) and sixth code block (CB6) of eMBB user 2, it degrades the eMBB quality of service. That is a serious problem faced in eMBB and URLLC coexistence scenarios [20], so appropriate mechanisms should be introduced to guarantee the quality of ongoing eMBB transmissions.

3. Problem Formulation

3.1. eMBB Allocation Problem

The objective of this problem is to jointly optimize RB allocation, power allocation, and RIS phase shift matrix to maximize the total ergodic capacity of eMBB users under constraints such as maximum transmission power and rate ratio. This paper uses Orthogonal Frequency Division Multiplexing (OFDM) as the primary modulation and demodulation technique. The channel gain C_e of eMBB user e in RB b is known. Assume that the channel is interfered with by Additive White Gaussian Noise (AWGN), denoted as σ² = N₀B, where N₀ is the noise power spectral density. The corresponding signal-to-noise ratio (SNR) of eMBB user e in RB b is expressed as:

$$h_e{}_b=C_e/{\sigma }^2$$

(1)

Then the received SNR of eMBB user e on RB b is:

$${\gamma }_{eb}=P_{eb}{h}_{eb}$$

(2)

where P_eb is the downlink transmission power of eMBB user e in RB b.

When M-ary quadrature amplitude modulation (M-QAM) is used, and the error probability is measured according to the Symbol Error Ratio (SER), the number of bits per symbol G [21] can be expressed as:

$$G={\log }_2(1+\frac{{\gamma }_{eb}}{\mathsf{\Gamma }})$$

(3)

where Γ is the signal-to-noise ratio gap, defined as: $\mathsf{\Gamma }=\frac{1}{3}{\left[Q^{-1}\left(\frac{SER}{4}\right)\right]}^2$, $Q\left(x\right)={\displaystyle {\int }_x^{\infty }\left(e^{-u^2/2}/\sqrt{2\pi }\right)}du$.

Thus, the data rate of eMBB user e on RB b at a given time slot can be approximated as:

$$r_{eb}=W{\log }_2(1+\frac{{\gamma }_{eb}}{\mathsf{\Gamma }})$$

(4)

Combining Equations (1)–(4), the data rate of eMBB user e on all assigned RB b is expressed as follows:

$$\begin{array}{l}{r}_e={\displaystyle \sum _{b\in B}{x}_{eb}W}{\log }_2(1+\frac{{\gamma }_{eb}}{\mathsf{\Gamma }})\\ ={\displaystyle \sum _{b\in B}{x}_{eb}W{\log }_2\left(1+\frac{P_{eb}|G_{RIS,e}{\mathsf{\Phi }}_e{H}_{gNB,RIS}+D_{gNB,e}{|}^2}{{\sigma }^2\mathsf{\Gamma }}\right)}\\ \end{array}$$

(5)

where the binary variable $x_{eb}=\left\{\begin{array}{cc}1,\hfill & \mathrm{if} \mathrm{user} \mathrm{e} \mathrm{is} \mathrm{assigned} \mathrm{RB} \mathrm{in} \mathrm{a} \mathrm{timeslot}\\ 0,\hfill & \mathrm{else}\end{array}\right.$ is the RB allocation indicator for eMBB user e in a time slot.

Therefore, the gNB traversal capacity of all eMBB users in a given time slot is issued by the following equation:

$$C_{gNB}=E\left({\displaystyle \sum _{\mathrm{e}=1}^{\epsilon }{r}_e}\right)$$

(6)

where E(·) is expected to cover all fading channels.

In summary, the eMBB resource allocation problem can be formulated as follows:

$$P1:\underset{{\mathsf{\Phi }}_e,P,x_{eb}}{\max }{C}_{gNB}$$

(7)

$$s.t.0\le P_{eb}\le P_{eb}^{max},\forall e\in E,\forall b\in B$$

(8)

$$x_{eb}=\{0,1\},\forall e\in E,\forall b\in B$$

(9)

$$r_i:r_j={\phi }_i:{\phi }_j,\forall i,j\in \left\{1,\cdots ,E\right\},i\ne j$$

(10)

$$\left|{\mathsf{\Phi }}_n\right|\le 1,0\le {\theta }_n\le 2\pi ,\forall n$$

(11)

where $P_{eb}^{max}$ in constraint (8) is the maximum transmission power of RB-eMBB. Constraint (9) is the eMBB user e allocation indicator. Constraint (10) is the proportional rate constraint, ${\displaystyle \sum _{e=1}^E{\phi }_e}=1$, where ${\phi }_1:{\phi }_2:\cdots :{\phi }_E$ is the normalized proportionality constant. Constraint (11) constrains the reflection coefficient of the RIS.

3.2. URLLC Allocation Problem

The goal of the problem is to maximize the reception rate of URLLC packets and minimize the amount of eMBB rate loss while ensuring QoS for eMBB users and URLLC packet rate requirements.

Assume that all incoming URLLC packets have the same size, denoted by i. L_m is the number of packets of URLLC at mini-slot m. $I_{e,l}^m$ means the number of RBs punctured from eMBB user e and assigned to URLLC packet l at mini-slot m.

The URLLC packet l arriving at mini-slot m must be completely and successfully transmitted to the relevant URLLC user. The expression for the QoS constraint for URLLC is as follows:

$$I_l^m{r}_l(P_l^m,{\mathsf{\Phi }}^m)\ge c_{th}$$

(12)

where $I_l^m={\displaystyle {\sum }_{e=1}^E{I}_{e,l}^m}$. r_l denotes the achievable rate per RB of URLLC packet l, and the expression is referred to Equation (4). Φ^m is the RIS phase shift matrix at mini-slot m. Let $c_{th}=\frac{i}{\tau }$.

In addition, it should be ensured that the QoS of eMBB is not degraded while accessing URLLC packets. The instantaneous achievable rate for eMBB user e is expressed as:

$$r_e^{\prime }=(1-\frac{I_e^m}{{\widehat{b}}_e})r_e$$

(13)

where $I_e^m={\displaystyle {\sum }_{l=1}^{L^m}{I}_{e,l}^m}$ denotes the total number of RBs punctured from eMBB user e at mini-slot m. ${\widehat{b}}_e$ denotes the number of RBs that eMBB user e has after RB allocation.

The QoS of eMBB can be expressed by the minimum data rate r_th [18], and it needs to be ensured that the eMBB losses due to puncturing the eMBB RB and designing the RIS phase shift matrix do not violate the eMBB rate requirement r_th. The expression is as follows:

$$r_e^{\prime }\ge r_{e,th}$$

(14)

$$r_{e,th}=\frac{M{r}_{th}}{{\widehat{b}}_e}-\left({\displaystyle \sum _i^{m-1}{r}_e^{\prime i}}+(M-m)r_e\right)$$

The number of URLLC packets received at mini-slot m can be expressed as:

$$f_1({\mathbf{k}}^m)={\displaystyle \sum _{l=1}^{L^m}{k}_l^m}$$

(15)

where ${\mathbf{k}}^m={[k_1^m,\cdots ,k_{L^m}^m]}^T$ is a L^m×1 binary vector. The binary variable $k_l^m\in \{0,1\}$ is the receipt indicator of the URLLC packet, $k_l^m=1$ if the URLLC packet l is received, and $k_l^m=0$ otherwise. The reception rate of the URLLC is denoted by $\eta =\frac{{\displaystyle {\sum }_m^M{\widehat{L}}^m}}{{\displaystyle {\sum }_m^M{L}^m}}$, where ${\widehat{L}}^m$ denotes the total number of URLLC packets successfully served at each mini-slot m.

Let ${\beta }_e^m\in \{0,1\}$ denotes the weight of the URLLC load assigned to eMBB user e at mini-slot m. Let ${\mathbf{I}}^m={(I_{e,l}^m)}_{1<e<E,1<l<L^m}$. Then, the total traffic loss of eMBB can be expressed as:

$$f_2\left({\mathbf{I}}^m\right)={\displaystyle \sum _{e=1}^E{I}_e^m{\beta }_e^m}$$

(16)

Based on the above, the URLLC allocation problem involves optimizing the power and frequency resource allocation and the RIS phase shift matrix. The URLLC allocation problem at the mini-slot m is represented as follows:

$$P2:\underset{{\mathsf{\Phi }}^m,{\mathbf{P}}_L^m,{\mathbf{k}}^m,{\mathbf{I}}^m}{\max }\left[f_1\left({\mathbf{k}}^m\right),-f_2\left({\mathbf{I}}^m\right)\right]$$

(17)

$$s.t.I_l^m{c}_l\ge k_l^m{c}_{th},\forall l\in L^m$$

(18)

$$r^{\prime }\ge r_{e,th},\forall e\in E$$

(19)

$$0\le P_l^m\le P_l^{m,max},\forall l\in L^m,\forall m\in M$$

(20)

$${\displaystyle \sum _{e=1}^E{P}_{eb}}+{\displaystyle \sum _{l=1}^{L^m}{P}_l^m}\le P_{gNB}$$

(21)

$$k_l^m\in \left\{0,1\right\},\forall l\in L^m$$

(22)

$$\frac{I_l^m}{B}\le k_l^m\le I_l^m,\forall l\in L^m$$

(23)

$$\left|{\mathsf{\Phi }}_n\right|\le 1,0\le {\theta }_n\le 2\pi ,\forall n$$

(24)

where $P_l{}^m$ denotes the transmission power of URLLC packet l at mini-slot m and ${\mathbf{P}}_L^m={[P_1^m,\cdots ,P_{L^m}^m]}^T$. $P_l^{m,max}$ represents the maximum transmission power of URLLC. Constraints (18) and (19) denote the QoS of the URLLC and eMBB, respectively. Constraint (20) indicates that the transmission power does not exceed the maximum. Constraint (21) means that the allocated eMBB and URLLC power should not exceed the total power of the BS. Constraint (22) indicates the reception indicator of the URLLC packet. Constraint (23) demonstrates that if URLLC packet l is received, i.e., $k_l^m=1$, the number of RBs allocated to URLLC packet l must be greater than zero, i.e., $I_l^m>0$.

4. Problem Conversion and Solution

4.1. Solution of eMBB Allocation Problem

Since there are three optimization variables in problem P1, i.e., P, Φ, and x_eb, the optimal global solution cannot be found directly. A two-stage alternating iterative eMBB allocation algorithm is proposed.

4.1.1. Stage 1: RB Allocation

For any given power allocation P and RIS phase shift matrix Φ, we propose a greedy algorithm-based RB allocation method to complete the optimal allocation of RBs. The algorithm solves the problem that the resource allocation cannot be completed properly in the case of a relatively low number of resources. Assume that all eMBB users have the same transmit power and satisfy the constraint (8). Each eMBB user selects and determines the RB allocation based on the channel condition and proportion. In each round of RB allocation, the eMBB user with the smallest proportional capacity has the priority. The detailed process is described in Algorithm 1.

Algorithm 1. RB allocation based on greedy algorithm

Input Number of RB R; Proportionality constants $\xi =\left[{\phi }_1:{\phi }_2:\cdots :{\phi }_E\right]$

Output the allocation result

Procedure

/* Step 1: Determine the number of RBs initially assigned to the user */

initialize each user number of RB Re, make its meet: $R_1:R_2:\cdots :R_E={\phi }_1:{\phi }_2:\cdots :{\phi }_E$

for e = 1:E

$R_e=⌊{\phi }_{e}R⌋$

$R^{\prime }={\Sigma }_{e=1}^E{R}_e$ /* Number of allocated RBs*/

$R^{″}=R\mathsf{-}{R}^{\prime }$ /* Number of unassigned RBs*/

end for

for e = 1:E

if Re = 0

Re = 1

$R^{″}=R^{″}-1$

end if

end for

Allocate RBs to users based on proportions */

for e = 1: E

Allocate unallocated RBs with maximum gain to users

Re = Re − 1

end for

for e = 1:E & Re ≠ 0

Divide by $\xi$ to calculate the capacity

According to the greedy strategy, get the minimum capacity in each iteration,

and choose the best RB for it

end for

/* Step 3: Allocate the remaining RB according to the effective channel SNR of all users from best to worst, and each user can get at most one unallocated RB*/

4.1.2. Stage 2: Joint Optimization of Power Allocation and RIS Phase Shift Matrix

After RB assignment, problem P1 is reduced to maximization of the variable P_eb and optimization of the RIS phase shift matrix, as follows:

$$P1.1:\underset{P,{\mathsf{\Phi }}_e}{\max } E\left({\displaystyle \sum _{e=1}^E{\displaystyle \sum _{u\in U}Wlo{g}_2\left(1+\frac{P_{eb}|G_{RIS,e}{\mathsf{\Phi }}_e{H}_{gNB,RIS}+D_{gNB,e}{|}^2}{{\sigma }^2\mathsf{\Gamma }}\right)}}\right)$$

(25)

$$s.t.0\le P_{eb}\le P_{eb}^{max},\forall e\in E,\forall b\in B$$

(26)

$$\left|{\mathsf{\Phi }}_n\right|\le 1,0\le {\theta }_n\le 2\pi ,\forall n$$

(27)

Since the objective function of P1.1 and its constraints are non-convex, the relaxation variable S is introduced to handle its non-convexity and satisfies the following equation:

$$\frac{P_{eb}|G_{RIS,e}{\mathsf{\Phi }}_e{H}_{gNB,RIS}+D_{gNB,e}{|}^2}{{\sigma }^2{\mathsf{\Gamma }}^{\prime }}\ge S_{e,b},\forall e,b$$

(28)

$$s.t.S=\left\{S_{e,b}=\frac{P_{eb}|G_{RIS,e}{\mathsf{\Phi }}_e{H}_{gNB,RIS}+D_{gNB,e}{|}^2}{{\sigma }^2{\mathsf{\Gamma }}^{\prime }},\forall e,b\right\}$$

(29)

Thus, problem P1.1 can be equivalently transformed into:

$$\begin{array}{l}P1.2:\underset{P,{\mathsf{\Phi }}_e,S}{\max }E\left({\displaystyle \sum _{e=1}^E{\displaystyle \sum _{u\in U}Wlo{g}_2\left(1+S_{e,b}\right)}}\right)\\ s.t.0\le P_{eb}\le P_{eb}^{max},\forall e\in E,\forall b\in B\\ \left|{\mathsf{\Phi }}_n\right|\le 1,0\le {\theta }_n\le 2\pi ,\forall n\\ S=\left\{S_{e,b}=\frac{P_{eb}|G_{RIS,e}{\mathsf{\Phi }}_e{H}_{gNB,RIS}+D_{gNB,e}{|}^2}{{\sigma }^2{\mathsf{\Gamma }}^{\prime }},\forall e,b\right\}\end{array}$$

(30)

The nonconvex problem P1.2 remains unsolvable because the variables P_eb and Φ are coupled. To make the problem approachable, decompose it into two subproblems as follows:

$$\begin{array}{l}P\mathrm{1.2.1}:\underset{P,S}{\max } E\left({\displaystyle \sum _{e=1}^E{\displaystyle \sum _{u\in U}Wlo{g}_2\left(1+S_{e,b}\right)}}\right)\\ s.t.0\le P_{eb}\le P_{eb}^{max},\forall e\in E,\forall b\in B\\ S=\left\{S_{e,b}=\frac{P_{eb}|G_{RIS,e}{\mathsf{\Phi }}_e{H}_{gNB,RIS}+D_{gNB,e}{|}^2}{{\sigma }^2{\mathsf{\Gamma }}^{\prime }},\forall e,b\right\}\end{array}$$

(31)

$$\begin{array}{l}P\mathrm{1.2.2}:Find{\mathsf{\Phi }}_e\\ s.t.\left|{\mathsf{\Phi }}_n\right|\le 1,0\le {\theta }_n\le 2\pi ,\forall n\\ S=\left\{S_{e,b}=\frac{P_{eb}|G_{RIS,e}{\mathsf{\Phi }}_e{H}_{gNB,RIS}+D_{gNB,e}{|}^2}{{\sigma }^2{\mathsf{\Gamma }}^{\prime }},\forall e,b\right\}\end{array}$$

(32)

Problem P1.2.1 is a convex optimization problem that convex optimization tools (e.g., CVX [22]) can efficiently solve to obtain an optimal solution. The problem P1.2.2 will be solved in Section 4.2.1.

4.1.3. Alternating Iteration-Based eMBB Allocation Algorithm

Based on the results in the previous two subsections, an alternating iteration-based eMBB allocation algorithm is proposed for problem P1. Specifically, in the (r + 1)th iteration, the optimal RB allocation is achieved in the first stage based on a fixed power allocation and RIS phase shift matrix, i.e., $\{P_{{}^{eb}}^{(r)},{\mathsf{\Phi }}_{{}^e}^{(r)}\}$, to produce the gNB traversal capacity $C_{gNB}(P_{{}^{eb}}^{(r)},{\mathsf{\Phi }}_{{}^e}^{(r)},x_{eb}^{(r+1)})$. Then, based on $\left\{x_{eb}^{(r+1)}\right\}$ determined in the previous stage, $\{P_{{}^{eb}}^{(r+1)},{\mathsf{\Phi }}_{{}^e}^{(r+1)}\}$ and the pseudo-optimal gNB traversal capacity, i.e., $C_{gNB}(P_{{}^{eb}}^{(r+1)},{\mathsf{\Phi }}_{{}^e}^{(r+1)},x_{eb}^{(r+1)})$, are obtained in the second stage. When the change in the target value is below the threshold $\epsilon$, the algorithm stops iterating, denoted as $(C_{gNB}^{(r+1)}-C_{gNB}^{(r)})/C_{gNB}^{(r+1)}\le \epsilon$. Algorithm 2 summarizes the process of the alternating iteration-based eMBB allocation algorithm.

Algorithm 2. Alternating iteration-based eMBB allocation algorithm

Input Number of RB

Output Optimal solution

Procedure

Initialize and set r = 0 as the number of iterations

if $(C_{gNB}^{(r+1)}-C_{gNB}^{(r)})/C_{gNB}^{(r+1)}>\epsilon$ then

/* Stage 1 */

fix $\{P_{{}^{eb}}^{(r)},{\mathsf{\Phi }}_{{}^e}^{(r)}\}$, then determine RB allocation according to Algorithm 1

obtain $C_{gNB}(P_{{}^{eb}}^{(r)},{\mathsf{\Phi }}_{{}^e}^{(r)},x_{eb}^{(r+1)})$

/* Stage 2 */

use the determined $\left\{x_{eb}^{(r+1)}\right\}$ to solve the problem P1.1

obtain $C_{gNB}(P_{{}^{eb}}^{(r+1)},{\mathsf{\Phi }}_{{}^e}^{(r+1)},x_{eb}^{(r+1)})$

r = r + 1

end

4.2. Optimization of RIS Phase Shift Matrix

RIS can control the channel conditions for eMBB and URLLC users to improve their performance. We propose three criteria to optimize the phase shift matrix to meet each mini-slot’s existing eMBB and upcoming URLLC service requirements. However, the RIS phase shift matrix design may increase the latency. To resolve this issue, we pre-configure the RIS phase shift matrix. The optimal design of the three types of phase shift matrices is also executed in parallel in order not to generate additional delay effects.

4.2.1. RIS Phase Shift Matrix for eMBB ${\mathsf{\Phi }}_e^{*}$

The problem formulation is given in P1.2.2, and the slack variables are introduced to solve the problem, ${\kappa }_e=\mathrm{Re}(G_{RIS,e}{\mathsf{\Phi }}_e{H}_{gNB,RIS}+D_{gNB,e})$,${\epsilon }_e=\mathrm{Im}(G_{RIS,e}{\mathsf{\Phi }}_e{H}_{gNB,RIS}+D_{gNB,e})$.

Then problem P1.2.2 can be expressed as a feasibility check problem:

$$P\mathrm{1.2.3}:Find{\mathsf{\Phi }}_e$$

(33)

$$s.t.\left|{\mathsf{\Phi }}_n\right|\le 1,0\le {\theta }_n\le 2\pi ,\forall n$$

(34)

$${\kappa }_e=\mathrm{Re}(G_{RIS,e}{\mathsf{\Phi }}_e{H}_{gNB,RIS}+D_{gNB,e}),\forall e$$

(35)

$${\epsilon }_e=\mathrm{Im}(G_{RIS,e}{\mathsf{\Phi }}_e{H}_{gNB,RIS}+D_{gNB,e}),\forall e$$

(36)

$$\frac{P_{eb}\left({\kappa }_e^2+{\epsilon }_e^2\right)}{{\sigma }^2{\mathsf{\Gamma }}^{\prime }}\ge S_{e,b},\forall e,b$$

(37)

To solve the non-convexity of problem P1.2.3, the successive convex approximation (SCA) technique is applied in each iteration. For a given local point $\left({\kappa }_{e,b}^{(r)}+{\epsilon }_{e,b}^{(r)}\right)$, a lower bound on $\left({\kappa }_e^2+{\epsilon }_e^2\right)$ can be found according to the first-order Taylor expansion [22] and denoted by ${\psi }_e$:${\kappa }_e^2+{\epsilon }_e^2\ge {\left({\kappa }_e^{(r)}\right)}^2+{\left({\epsilon }_e^{(r)}\right)}^2+2{\kappa }_e^{(r)}\left({\kappa }_e-{\kappa }_e^{(r)}\right)+2{\epsilon }_e^{(r)}\left({\epsilon }_e-{\epsilon }_e^{(r)}\right)={\psi }_e$.

Thus, the problem P1.2.3 can be further formulated as:

$$P\mathrm{1.2.4}:Find{\mathsf{\Phi }}_e$$

(38)

$$s.t.\left|{\mathsf{\Phi }}_n\right|\le 1,0\le {\theta }_n\le 2\pi ,\forall n$$

(39)

$${\epsilon }_e=\mathrm{Im}(G_{RIS,e}{\mathsf{\Phi }}_e{H}_{gNB,RIS}+D_{gNB,e}),\forall e$$

(40)

$${\kappa }_e=\mathrm{Re}(G_{RIS,e}{\mathsf{\Phi }}_e{H}_{gNB,RIS}+D_{gNB,e}),\forall e$$

(41)

$$\frac{P_{eb}{\psi }_e}{{\sigma }^2{\mathsf{\Gamma }}^{\prime }}\ge S_{e,b},\forall e,b$$

(42)

At this point, problem P1.2.4 is a convex optimization problem that can be solved efficiently using CVX.

4.2.2. RIS Phase Shift Matrix for URLLC ${\mathsf{\Phi }}_u^{*}$

However, the ${\mathsf{\Phi }}_e^{*}$ obtained in question P1.2.2 does not consider the arrival of URLLC business. The ${\mathsf{\Phi }}_u^{*}$ is designed to improve the network’s channel gain for all URLLC users. Therefore, the objective of the RIS phase-shift matrix optimization problem is to maximize the minimum URLLC channel gain. The expression is as follows:

$$\begin{array}{l}P3:\underset{{\mathsf{\Phi }}_u}{\max }\underset{1\le u\le U}{\min }{\left|C\right|}^2\\ s.t.C=G_{RIS,u}{\mathsf{\Phi }}_u{H}_{gNB,RIS}+D_{gNB,u}\\ \left|{\mathsf{\Phi }}_n\right|\le 1,0\le {\theta }_n\le 2\pi ,\forall n\end{array}$$

(43)

Let $v^H={[v_1,\cdots ,v_N]}^H$, where $v_n=e^{j{\varphi }_n}$. It follows that

${\left|G_{RIS,u}{\mathsf{\Phi }}_u{H}_{gNB,RIS}+D_{gNB,u}\right|}^2={\left|v^H\mathsf{\Theta }+D_{gNB,u}\right|}^2$, where $\mathsf{\Theta }=diag(G_{RIS,u})H_{gNB,RIS}$.

$$\begin{array}{l}P3:\underset{{\mathsf{\Phi }}_u}{\max }\underset{1\le u\le U}{\min }{\left|C\right|}^2\\ s.t.C=G_{RIS,u}{\mathsf{\Phi }}_u{H}_{gNB,RIS}+D_{gNB,u}\\ \left|{\mathsf{\Phi }}_n\right|\le 1,0\le {\theta }_n\le 2\pi ,\forall n\end{array}$$

(44)

Thus, problem P3 is equivalent to:

$$\begin{array}{l}P3.1:\underset{v}{\max }\underset{1\le u\le U}{\min }{v}^H\mathsf{\Theta }{\mathsf{\Theta }}^{H}v+D_{gNB,u}{\mathsf{\Theta }}^{H}v\\ +v^H\mathsf{\Theta }{D}_{gNB,u}+{\left|D_{gNB,u}\right|}^2\\ s.t.{\left|v_n\right|}^2=1,\forall n\end{array}$$

(45)

Problem P3.1 is a nonconvex quadratic constrained quadratic programming (QCQP) problem, which can be transformed into a homogeneous QCQP. Specifically, by introducing an auxiliary variable $\delta$, problem P3.1 is equivalently written as:

$$\begin{array}{l}P3.2\underset{\overline{v}}{\max }\underset{1\le u\le U}{\min }{\overline{v}}^H{\mathsf{\Lambda }}_u\overline{v}+{\left|D_{gNB,u}\right|}^2\\ s.t.{\left|{\overline{v}}_n\right|}^2=1,n=1,\cdots ,N+1\end{array}$$

(46)

where ${\mathsf{\Lambda }}_u=\left[\begin{array}{cc}\mathsf{\Theta }{\mathsf{\Theta }}^H& \mathsf{\Theta }{D}_{gNB,u}\\ D_{gNB,u}{\mathsf{\Theta }}^H& 0\end{array}\right],\overline{v}=\left[\begin{array}{c}v\\ \delta \end{array}\right]$, let ${\overline{v}}^H{\mathsf{\Lambda }}_u\overline{v}=tr({\mathsf{\Lambda }}_u\overline{v}{\overline{v}}^H)$ and $V=\overline{v}{\overline{v}}^H$, and it needs to meet $V\succ 0,rank(V)=1$. Since the rank-1 constraint is nonconvex, the constraint can be slackened using the semi-definite relaxation (SDR) method. Thus, problem P3.2 can be simplified as follows:

$$\begin{array}{l}P3.3:\underset{V}{\max }\underset{1\le u\le U}{\min }tr({\mathsf{\Lambda }}_{u}V)+{\left|D_{gNB,u}\right|}^2\\ s.t.V_{n,n}=1,n=1,\cdots ,N+1\\ V\succ 0\end{array}$$

(47)

Obviously, we can also use CVX to solve problem P3.3. Given that it is a semi-definite programming (SDP) problem, usually, the optimal $\overline{v}$ obtained by solving this problem does not satisfy the rank-1 constraint and the rank-1 solution can be obtained by applying Gaussian randomization techniques [14].

4.2.3. RIS Phase Shift Matrix for Joint eMBB and URLLC ${\mathsf{\Phi }}_{e,u}^{*}$

The RIS phase shift matrix ${\mathsf{\Phi }}_u^{*}$ improves URLLC performance, which can severely impact eMBB performance. Therefore, a uniform RIS phase shift matrix is needed to enhance URLLC loads’ performance and reduce eMBB traffic performance degradation. Similar to problem P3, the ${\mathsf{\Phi }}_{e,u}^{*}$ optimization problem can be expressed as follows:

$$P4:\underset{{\mathsf{\Phi }}_{e,u}}{\max }\underset{1\le x\le E+U}{\min }{\left|C\right|}^2$$

(48)

$$\begin{array}{l}s.t.if:x\in E\\ C_{\begin{array}{l}e\\ \end{array}}=G_{RIS,x}^e{\mathsf{\Phi }}_{e,u}{H}_{RIS,gNB}+D_{x,gNB}^e,\end{array}$$

(49)

$$\begin{array}{l}if:x\in \{E+1,\cdots ,E+U\}\\ C_u=G_{RIS,x}^u{\mathsf{\Phi }}_{e,u}{H}_{RIS,gNB}+D_{x,gNB}^u,\end{array}$$

(50)

$$\left|{\mathsf{\Phi }}_n\right|\le 1,0\le {\theta }_n\le 2\pi ,\forall n$$

(51)

where constraint (49) denotes the representation of the channel gain when $x\in E$, i.e., x is an eMBB service. Similarly, constraint (50) indicates the representation of the channel gain when $x\in \{E+1,\cdots ,E+U\}$, i.e., x is a URLLC service. Problem P4 is solved in a similar way to problem P3.

4.3. Solution of URLLC Allocation Problem

At the beginning of each mini-slot, the above three types of RIS phase shift matrices are acquired, transferred, and stored in the RIS controller. When the RIS phase shift matrix Φ^m is one of the pre-configured RIS phase shift matrices, i.e., substitute it to solve problem P2. In other words, when the RIS is determined, the original problem becomes solving the optimal frequency and power allocation problem for URLLC services, expressed as follows:

$$P2.1:\underset{{\mathbf{P}}_L^m,{\mathbf{k}}^m,{\mathbf{I}}_L^m,{\mathbf{I}}_{{}_E}^m}{\max }\left[f_1\left({\mathbf{k}}^m\right),-f_2\left({\mathbf{I}}_E^m\right)\right]$$

(52)

$$s.t.I_l^m{c}_l\ge k_l^m{c}_{th},\forall l\in L^m$$

(53)

$$r^{\prime }\ge r_{e,th},\forall e\in E$$

(54)

$$0\le P_l^m\le P_l^{m,max},\forall l\in L^m,\forall m\in M$$

(55)

$${\displaystyle \sum _{e=1}^E{P}_{eb}}+{\displaystyle \sum _{l=1}^{L^m}{P}_l^m}\le P_{gNB}$$

(56)

$$k_l^m\in \left\{0,1\right\},\forall l\in L^m$$

(57)

$${\displaystyle \sum _{l=1}^{L^m}{I}_l^m}={\displaystyle \sum _{e=1}^E{I}_e^m}$$

(58)

where constraint (58) ensures that the number of punctured eMBB resources equals the number of resources allocated to URLLC traffic.

According to constraint (54), at mini-slot m, the representation of the maximum number of available RBs allocated to URLLC packets by eMBB user e is given as follows:

$$I_e^{\max ,m}=\min \left(⌊{\widehat{b}}_e\left(1-\frac{r_{e,th}}{r_e}\right)⌋,{\widehat{b}}_e\right)$$

(59)

After determining the number of RB allocations for the URLLC packet l, the optimal power allocation expression is as follows:

$$P_l^{m*}=\frac{e^{\frac{k_l^m{c}_{th}}{\log (2)I_l^m}}-1}{h_l}$$

(60)

where $h_l=C_l/{\sigma }^2$.

Based on the above, P2.1 can be simplified as follows:

$$P2.2:\underset{{\mathbf{k}}^m,{\mathbf{I}}_L^m,{\mathbf{I}}_{{}_E}^m}{\max }\left[f_1\left({\mathbf{k}}^m\right),-f_2\left({\mathbf{I}}_E^m\right)\right]$$

(61)

$$s.t.k_l^m\in \left\{0,1\right\},\forall l\in L^m$$

(62)

$$\frac{I_l^m}{B}\le k_l^m\le I_l^m,\forall l\in L^m$$

(63)

$${\displaystyle \sum _{l=1}^{L^m}{I}_l^m}={\displaystyle \sum _{e=1}^E{I}_e^m}$$

(64)

$${\displaystyle \sum _{l=1}^{L^m}{I}_l^m{P}_l^{m*}\le }{\displaystyle \sum _{e=1}^E{I}_e^m{P}_e}$$

(65)

Given that URLLC services have strict latency requirements, low-complexity allocation algorithms are crucial for incoming URLLC packets. While ordinary iterative methods usually require a long computation time, this paper proposes low-complexity heuristic algorithms.

Firstly, to improve the URLLC packet admission rate, we consider preferentially assigning URLLCs with better channel conditions. C_ub is known to denote the channel gain of URLLC user u. Then the descending order of it is denoted as ${\mathit{C}}_{ub}=\{C_{ub}^{(1)},\cdots ,C_{ub}^{(U)}\}$. Similarly, ${\mathsf{\beta }}_e^m=\{{\beta }_e^{m(1)},\cdots ,{\beta }_e^{m(E)}\}$ means the ascending order of eMBB users according to their URLLC load allocation weights. Secondly, the algorithm allocates resources to URLLC users u by iterating over ordered eMBB users. The iterative process guarantees that the cumulative data rate of URLLC packets on a given eMBB user is below the rate threshold. Finally, these steps are repeated for all URLLC packets while satisfying the eMBB QoS.

The detailed steps of the pre-configured RIS-based heuristic allocation algorithm are given in Algorithm 3. The algorithm’s time complexity is related to the number of URLLC packets L^m, and the worst-case time complexity is O(L^m × E).

Algorithm 3. Heuristic URLLC allocation algorithm based on RIS

Input${\mathsf{\Phi }}^m\in \{{\mathsf{\Phi }}_e^{*},{\mathsf{\Phi }}_u^{*},{\mathsf{\Phi }}_{e,u}^{*}\}$

Output Optimal solution ${\mathbf{P}}_L^{m^{*}}({\mathsf{\Phi }}^m)$$,{\mathbf{I}}^{m^{*}}({\mathsf{\Phi }}^m)$$,{\mathbf{k}}^{m^{*}}({\mathit{\Phi }}^m)$

Procedure

for${\mathsf{\Phi }}^m\in \{{\mathsf{\Phi }}_e^{*},{\mathsf{\Phi }}_u^{*},{\mathsf{\Phi }}_{e,u}^{*}\}$do

/* solve problem P2 */

initialize ${\mathbf{I}}^m$ and ${\mathbf{P}}_L^m$, and calculate ${\mathbf{I}}^{\max ,m}$;

${\mathit{C}}_{ub}=\{C_{ub}^{(1)},\cdots ,C_{ub}^{(U)}\}$; /*descending order*/

${\mathsf{\beta }}_e^m=\{{\beta }_e^{m(1)},\cdots ,{\beta }_e^{m(E)}\}$; /*ascending order*/

for l = 1 : Lm do

$c_l^{temp}=0$;

for e = 1 : E do

$I_{e,l}^{temp}=⌈\frac{c_{th}-c_l^{temp}}{c_l(P_{eb})}⌉$;

if $I_{e,l}^{temp}\le I_e^{\max ,m}$ then

$I_{e,l}^m=I_{e,l}^{temp}$;

boolean = 1;break;

else

$I_{e,l}^m=I_e^{\max ,m}$;

$c_l^{temp}=c_l^{temp}+I_{e,l}^m\ast c_l(P_{eb})$

if boolean = 1 then

$P_l^m=\frac{{\displaystyle \sum _{e=1}^E{I}_{e,l}{P}_{eb}}}{{\displaystyle \sum _{e=1}^E{I}_{e,l}}}$;

update ${\mathbf{I}}^{\max ,m}$;

else

end

get the optimal solution ${\mathbf{P}}_L^{m^{*}}({\mathsf{\Phi }}^m)$$,{\mathbf{I}}^{m^{*}}({\mathsf{\Phi }}^m)$$,{\mathrm{k}}^{m^{*}}({\mathsf{\Phi }}^m)$

end

5. Simulation Results and Analysis

5.1. Simulation Experiments

This paper considers a RIS-assisted wireless network where a gNB is deployed in the center of the coverage area. The cellular cell radius is 300 m, and the RIS is located 20 m away to increase the base station’s coverage. The eMBB users are randomly distributed within the coverage area, and the URLLC traffic model is modeled as satisfying a Poisson distribution with parameter λ. Other relevant simulation parameters are set as shown in

Table 1. Parameter Settings.

Parameter	Value
Cell radius (r)	300 m
The total bandwidth (B)	20 MHz
RB bandwidth (BRB)	180 kHz
The base station transmitting power (PgNB)	46 dBm
URLLC maximum transmitting power (${\mathrm{P}}_{\mathrm{l}}^{\mathrm{m}}$)	23 dBm
eMBB maximum transmitting power (Peb)	23 dBm
Number of subcarriers per RB	12
URLLC transmission interval (sTTI)	0.1443 ms
eMBB transmission interval (TTI)	1 ms

, and the outdoor scenario is simulated using the SIMRIS channel simulator [23]. Other relevant parameters are described separately in each subsection.

5.2. Performance Evaluation of URLLC Allocation Policies

In this paper, the heuristic URLLC allocation algorithm based on RIS pre-configuration is simulated and compared with the following two types of schemes.

• Proportional Fair (PF) scheduling algorithm: The basic idea of this algorithm is to consider the ratio of instantaneous rate and long-term average rate when selecting users and to adjust different users by using the weight value. The final goal is to consider both system performance and user experience.
• Iterative algorithm for joint resource allocation (the algorithm proposed in the literature [4]): the transmission power of URLLC users is calculated to ensure the reliability constraint, and the resource allocation of URLLC users is done iteratively.

By varying the number of URLLC users, i.e., the URLLC service load, the URLLC packet reception rates under different methods are compared. As shown in Figure 3, the URLLC packet reception rate decreases significantly as the URLLC service load increases. That is because as more and more URLLC packets are accessed, the available resources obtained from puncturing are insufficient to accommodate all URLLC packets. As a result, to ensure the QoS of eMBB, some URLLC packets are rejected, leading to algorithm performance degradation. When the number of URLLC users is certain, the acceptance rate of the proposed scheme in this paper is higher; especially when the number of URLLC users is more, its superiority is more prominent.

As shown in Figure 4, the objective optimization using the heuristic algorithm can complete the allocation task within one mini-slot. In contrast, the time used by the algorithm proposed in the literature [4] increases significantly with the number of URLLC, which is highly likely to violate the URLLC delay requirement. That is because the algorithm proposed in the literature [4] uses a general iterative approach, which will significantly degrade the performance as the number of iterations increases. In contrast, this paper uses a heuristic algorithm based on an intuitive or empirical construction. Its characteristic is to give a feasible solution for each instance of the combinatorial optimization problem to be solved within an acceptable computational time. Therefore, combined with Figure 3 and Figure 4, the PF scheduling algorithm has a low URLLC packet acceptance rate and time complexity. In contrast, the algorithm proposed in the literature [4] has significantly lower performance and substantially higher latency as the URLLC load increases. Using the heuristic algorithm takes less time and has lower time complexity, which is more suitable for eMBB and URLLC coexistence scenario applications.

5.3. Impact of RIS Configuration

5.3.1. Performance Comparison of Four Types of RIS Solutions

We preset the following four scenarios to demonstrate the impact of different RIS configurations on the performance of URLLC and eMBB services. Scheme 1: Using RIS configuration ${\mathsf{\Phi }}_e^{*}$ for eMBB and URLLC throughout the time slot. Scheme 2: In each mini-slot, if URLLC packets are present, use RIS configuration ${\mathsf{\Phi }}_u^{*}$. Otherwise, use configuration ${\mathsf{\Phi }}_e^{*}$. Scheme 3: In each mini-slot, if URLLC packets are present, use RIS configuration ${\mathsf{\Phi }}_{e,u}^{*}$. Otherwise, use configuration ${\mathsf{\Phi }}_e^{*}$. Scheme 4 (chosen in this paper): In each mini-slot, the gNB selects the phase shift matrix ${\mathsf{\Phi }}^m\in \{{\mathsf{\Phi }}_e^{*},{\mathsf{\Phi }}_u^{*},{\mathsf{\Phi }}_{e,u}^{*}\}$ that maximizes the URLLC packet acceptance rate and minimizes the eMBB rate loss.

Figure 5 and Figure 6 show the URLLC packet acceptance rate curves and total eMBB loss rate with the number of RIS reflective elements for five different RIS phase shift matrix configurations. As seen from Figure 5, the URLLC packet admission rate increases with the number of RIS components for all four schemes except for the case without RIS. Among them, the result of Scheme 1 is relatively different from the other three schemes, with a difference of nearly 3%. Schemes 2 and 3 perform comparably to Scheme 4 selected in this paper at larger network sizes (i.e., a larger number of RIS elements in the network), with an acceptance rate close to 99.8%. However, as seen in Figure 6, the differences among the schemes gradually increase with the expansion of the network scale. When N is greater than 40, the total loss rate of eMBB of the selected scheme remains below 6%, while other schemes are close to or even over 10%; especially, when RIS is not deployed, the total loss rate of eMBB is close to 16%. In summary, the RIS assistance effectively improves the associated performance. This is because the assistance of RIS enables the gNB to configure RIS by selecting the phase shift matrix from the set ${\mathsf{\Phi }}^m\in \{{\mathsf{\Phi }}_e^{*},{\mathsf{\Phi }}_u^{*},{\mathsf{\Phi }}_{e,u}^{*}\}$ according to the URLLC traffic and its channel conditions, thus making a good tradeoff between maximizing URLLC packet admission rate and minimizing eMBB loss.

5.3.2. Traversal Achievable Rate Assisted by Different Number of RIS Reflection Elements

Combining Equations (1)–(3), the traversal achievable rate of this wireless cellular network is as follows:

$$\widehat{R}={\log }_2\det (I+{\gamma }_{eb})$$

(66)

where I denotes the unit matrix. It is assumed that the noise power is 100 dBm in this subsection, and the number of antenna configurations for the transmitter and receiver are 64 and 16, respectively. As shown in Figure 7, the RIS configuration achieves a better traversal achievable rate compared to the scenario without RIS deployment. As the number of reflective elements increases, the traversal achievable rate increases significantly, and the overall cost is lower due to the passive nature of the RIS elements. Many large-scale transmission scenarios, especially when mobile users use a large number of antennas in order to achieve a significant increase in traversal achievable rate, will increase the cost of signal processing and the required hardware. By using RIS in transmission, the cost can be reduced while ensuring the traversal achievable rate, so RIS has great potential for future wireless networks.

6. Summary

This paper aims to solve the resource allocation problem in the coexistence scenario of eMBB and URLLC services by combining RIS technology. The problem is described as two optimization problems, i.e., the eMBB allocation problem and the URLLC allocation problem. To overcome the nonconvexity of these problems, we propose a two-stage eMBB allocation algorithm based on alternating iterations and a heuristic URLLC allocation algorithm based on a preconfigured RIS phase shift matrix, respectively. Simulation results show that the proposed algorithm has lower time complexity than other scheduling methods when the URLLC packet reception rate reaches about 95.5%. And the larger the URLLC load is, the more prominent its superiority is. In addition, as the network scales up, the RIS scheme chosen in this paper is well suited to achieving the tradeoff between maximizing URLLC reception and minimizing eMBB loss compared to non-deployed RIS. In the future, we will try to apply the algorithm to the resource allocation problem of heterogeneous vehicle networks, the power resource planning and allocation problem, etc.