Beamforming and user selection method based on distributed irss-aided MIMO communication system

Abstract

The present invention belongs to the technical field of wireless communications, and particularly relates to a beamforming and user selection method based on a distributed IRSs-aided MIMO communication system. The method comprises: constructing a distributed IRSs-aided MIMO communication system model; constructing a joint optimization problem P for active beamforming at a base station, phase shifts of IRSs, and a user selection strategy; decoupling the joint optimization problem P into a joint optimization subproblem P1 for a user selection strategy and active beamforming at the base station, and an optimization subproblem P2 for phase shifts of the IRSs; solving the joint optimization subproblem P1 to obtain a user selection strategy and a beamforming vector at the base station; solving the optimization subproblem P2 to obtain phase shifts of the IRSs; and repeatedly executing the solving steps until the joint optimization problem P converges, so as to obtain an optimal user selection strategy, an optimal beamforming vector at the base station, and optimal phase shifts of the IRSs, and then executing same. While ensuring the user service quality, the present invention significantly reduces the transmitting power of a base station, thereby improving the system performance.

Description

A beamforming and user selection method based on a distributed IRSs assisted MIMO communication system TECHNICAL FIELD

[0001] The application belongs to the technical field of wireless communication, and particularly relates to a beamforming and user selection method based on a distributed IRSs assisted MIMO communication system. BACKGROUND

[0002] With the rapid development of wireless communication technology, people's expectations for wireless communication technology are constantly increasing. The fifth generation mobile communication (5G) system widely deployed at present meets people's requirements for high speed and low latency communication to a large extent. However, this generation of mobile communication system has the disadvantages of high hardware cost, high power consumption and high complexity, which not only brings many inconveniences to the deployment, operation and maintenance of operators, but also greatly reduces the cost-effective experience of users. The goal of the sixth generation mobile communication (6G) is to meet higher requirements than 5G, such as massive access of communication devices, ultra-high traffic, ultra-low latency and ultra-high reliability. As one of the most representative new technologies, intelligent reflecting surface (IRS) can change the wireless transmission environment in real time to achieve extended coverage, interference elimination and enhanced energy efficiency. Compared with other technologies of 6G network, IRS has attracted widespread attention due to its small size, low energy consumption and easy deployment.

[0003] IRS is a passive device, and the introduction of IRS aims to increase a design dimension of a wireless communication system, to intervene in the channel, so as to achieve a "certain degree" of controllable channel. This "degree" depends on the corresponding algorithm after IRS is integrated into the system and its coverage density. The emergence of IRS will greatly reduce the propagation energy consumption of electromagnetic waves, expand the communication coverage, resist interference noise, and significantly improve the spectrum utilization.

[0004] With the rapid development of global mobile Internet, the number of mobile broadband users has shown explosive growth, and massive communication devices access the network simultaneously, which requires how to effectively allocate and manage network resources. However, most of the current research on IRS-assisted communication systems does not consider massive devices accessing the network simultaneously, ignores that the number of users in the hotspot area is much larger than the number of antennas at the base station (BS) end, and still considers that the base station in the cell can serve massive communication devices under the same frequency resource block. Although many schemes have designed the joint optimization of beamforming at the base station and user selection in the cellular network without IRS, these algorithms cannot be applied to IRS-assisted networks because for the selected users, the channel can be reconfigured by controlling the amplitude and phase of the IRS elements, so a new user selection algorithm is needed to optimize the system performance in the IRS-assisted communication system. On the other hand, when the direct link of the communication system is severely blocked and large-scale centralized deployment is difficult, it is particularly necessary to use distributed multiple intelligent reflecting surfaces (IRSs) to improve system performance. In the distributed IRSs-assisted MIMO communication network, there are massive communication devices, and how to jointly select the user selection strategy, the active beamforming of the base station and the passive beamforming of the IRSs is still a challenge. SUMMARY

[0005] In view of the deficiencies in the prior art, the present application proposes a beamforming and user selection method based on a distributed IRSs-assisted MIMO communication system, which comprises:

[0006] S1: constructing a distributed IRSs-assisted MIMO communication system model;

[0007] S2: based on the distributed IRSs-assisted MIMO communication system model, taking the minimum transmission power of the base station as the optimization objective, constructing a joint optimization problem P of the active beamforming at the base station, the phase shift of the IRSs and the user selection strategy;

[0008] S3: decoupling the joint optimization problem P into a user selection strategy and base station active beamforming joint optimization sub-problem P1 and an IRSs phase shift optimization sub-problem P2;

[0009] S4: given the phase shift of the IRSs, solving the user selection strategy and base station beamforming joint optimization sub-problem P1 to obtain the user selection strategy and base station beamforming vector;

[0010] S5: solving the IRSs phase shift optimization sub-problem P2 according to the user selection strategy and base station beamforming vector to obtain the phase shift of the IRSs;

[0011] S6: repeat steps S4-S5 until the joint optimization problem P converges, obtaining the optimal user selection strategy, the optimal beamforming vectors at the base station and the optimal phase shifts of the IRSs and performing.

[0012] Preferably, the distributed IRSs-assisted MIMO communication system model comprises: 1 base station, L IRSs and K single-antenna users, the base station is equipped with M antenna arrays adopting a uniform linear array structure; each IRS is configured with N=N x N y reflective elements, adopting a uniform planar array form, wherein N x and N y are the number of reflective elements in the horizontal and vertical directions respectively, and N is the total number of reflective elements.

[0013] Preferably, the joint optimization problem of the active beamforming at the base station, the phase shift of the IRSs and the user selection strategy is:

[0014] wherein c k represents whether the kth user is selected by the base station, w k represents the beamforming vector sent by the BS to the kth user, K represents the number of users, Θ l represents the diagonal reflection matrix of the lth IRS, SINR k represents the signal-to-interference-and-noise ratio of the kth user, γ k represents the minimum signal-to-noise ratio constraint at user k, θ l,n represents the reflection coefficient of the nth reflective element of the lth IRS, L represents the number of IRSs, and N represents the number of reflective elements on the IRS.

[0015] Preferably, the joint optimization sub-problem of the user selection strategy and the beamforming at the base station is:

[0016] wherein c k represents whether the kth user is selected by the base station, w k represents the beamforming vector sent by the base station to the kth user, K represents the number of users, c j represents whether the jth user is selected by the base station, w j represents the beamforming vector sent by the base station to the jth user, represents the noise variance of the kth user, represents the channel gain of the combined channel between the kth user and the base station, γ k represents the minimum signal-to-noise ratio constraint at user k.

[0017] Preferably, step S4 comprises:

[0018] Given the phase shift of IRSs, introduce the number of selected users, rewrite the user selection strategy and the joint optimization of beamforming at the base station as a problem P3.

[0019] Transform the constraints in problem P3 into convex constraints;

[0020] Take the reciprocal of the base station transmit power as the fitness value, and solve problem P3 using the artificial bee colony algorithm to obtain the user selection strategy and the beamforming vector at the base station.

[0021] Further, the problem P3 after the constraints are transformed into convex constraints is represented as:

[0022] Wherein, w k represents the beamforming vector sent by the base station to the kth user, γ k represents the minimum signal-to-noise ratio constraint at the user k, represents the noise variance of the kth user, represents the channel gain of the combined channel between the kth user and the base station, represents the real part, w j represents the beamforming vector sent by the base station to the jth user, K opt represents the number of selected users.

[0023] Preferably, the process of solving problem P3 using the artificial bee colony algorithm includes:

[0024] Step 1: initialization phase: randomly initialize multiple honey source matrices, set the number of iterations; calculate the fitness value of the honey source, and find the minimum fitness value and its corresponding honey source position;

[0025] Step 2: employed bee phase: each employed bee randomly generates a new honey source and calculates the fitness value of the honey source, if the fitness value of the new honey source is greater than the minimum value of the fitness value of the original honey source, then replace the original honey source with the new honey source;

[0026] Step 3: observer bee phase: each observer bee selects a honey source according to the honey source selection probability, and randomly selects an element with a value of 1 and an element with a value of 0 in the selected honey source to change; calculate the fitness value of the new honey source, if the fitness value of the new honey source is greater than the fitness value of the original honey source, then replace the original honey source with the new honey source; otherwise, do not replace; if the honey source has not been replaced after LIMIT times of selection, then discard the honey source and randomly generate a new honey source;

[0027] Step 4: judge whether the maximum number of iterations is reached, if reached, select the honey source with the maximum fitness value as the optimal solution to obtain the user selection strategy and the beamforming vector at the base station; otherwise, return to step 3.

[0028] Preferably, the IRSs phase shift optimization sub-problem is:

[0029] wherein, represents the IRS diagonal block matrix, represents the phase of the lth IRS, and represents the amplitude of the lth IRS. l,n represents the reflection coefficient of the nth reflecting element of the lth IRS, represents the channel gain from the base station to the kth user, represents the channel gain from the base station to the IRSs, r,k represents the channel gain from the IRSs to the kth user, represents the channel gain from the base station to the IRSs, and represents the beamforming vector of the base station to the kth user. k represents the beamforming vector of the base station to the jth user, j represents the beamforming vector of the base station to the jth user, represents the noise variance of the kth user, represents the minimum signal-to-noise ratio constraint at user k, and represents the number of users selected as the honey source. k represents the minimum signal-to-noise ratio constraint at user k, and represents the number of users selected as the honey source. opt represents the number of users selected as the honey source.

[0030] The present application has the beneficial effects that: the present application provides a beamforming and user selection method based on a distributed IRSs assisted MIMO communication system, which is used to solve the problem that there are a large number of users in the cell edge area, and the number of users is much larger than the number of base station antennas. The present application reconfigures the channel by appropriately selecting users and controlling the amplitude and phase of the IRS elements, realizes significantly reducing the transmission power of the base station under the premise of guaranteeing the quality of service of the users, and thus improves the system performance. BRIEF DESCRIPTION OF DRAWINGS

[0031] Fig. 1 is a flow chart of the beamforming and user selection method based on a distributed IRSs assisted MIMO communication system in the present application;

[0032] Fig. 2 is a schematic diagram of a distributed IRSs assisted MIMO communication system model in the present application;

[0033] Fig. 3 is a graph of the change of power with the number of iterations in the solving process of a preferred embodiment of the present application. DETAILED DESCRIPTION

[0034] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0035] The present application provides a beamforming and user selection method based on a distributed IRSs assisted MIMO communication system, as shown in Fig. 1, which includes the following contents:

[0036] S1: Construct a distributed IRSs-assisted MIMO communication system model.

[0037] As shown in FIG. 2, in a distributed IRSs-assisted MIMO communication system, including 1 base station (BS), L IRSs and K single-antenna users, the base station is equipped with M antenna arrays, adopts a uniform linear array (ULA) structure, each IRS is configured with N=N x N y reflective elements, adopts a uniform planar array (UPA) form configuration, where N x and N y are the number of reflective elements in the horizontal and vertical directions, respectively. Assuming a crowded hotspot scenario, there are many cell edge users, the number of which is much larger than the number of BS antennas, i.e. K>>M. Assuming that the direct link from the base station to the user is not blocked by obstacles, the user can receive the superimposed signal from the BS-user direct link and the BS-IRSs-user reflected link. Define Θ l = diag(θ l,1 ,…,θ l,N ) as the diagonal reflection matrix of the lth IRS, where represents the phase shift of the nth reflective element of the lth IRS. and respectively represent the channel gain from the BS to the lth IRS, the channel gain from the BS to the user k and the channel gain from the lth IRS to the user k. In order to fully utilize the time-frequency resources of the system, it is assumed that the BS can only select M users within each time-frequency resource block. For this purpose, define the binary selection vector c = {c1, …, c K} T :

[0038] The signal y k received at the kth user can be represented as:

[0039] where s k is the information sent by the base station to the kth user, and satisfies E{|s k | 2} = 1, is the beamforming vector of the BS to the kth user, represents the additive white Gaussian noise at the receiver of user k, represents the noise variance of the kth user, based on the above formula, the signal-to-interference-and-noise ratio of the kth user can be obtained as:

[0040] S2: Based on the distributed IRSs assisted MIMO communication system model, a joint optimization problem P of active beamforming at the base station, passive beamforming at the IRS and user selection strategy is constructed with the minimum transmission power of the base station as the optimization objective.

[0041] With the minimum transmission power of the BS as the objective, a joint optimization problem P of active beamforming at the base station, phase shift of the IRSs and user selection strategy is constructed under the constraint of meeting the QoS at the user:

[0042] Wherein, c k represents whether the kth user is selected by the base station, γ k represents the minimum signal-to-noise ratio constraint at the user k, L represents the number of IRSs, and N represents the number of reflecting elements on the IRS.

[0043] S3: The joint optimization problem P is decoupled into a joint optimization sub-problem P1 of user selection strategy and active beamforming at the base station, and an IRS phase shift optimization sub-problem P2.

[0044] Given the phase shift of the IRSs Θ l , 1≤l≤L, the optimization problem becomes P1:

[0045] Wherein represents the combined channel, i.e. the direct channel plus the reflected channel, c j represents whether the jth user is selected by the base station, w j represents the beamforming vector sent by the base station to the jth user.

[0046] Given c k and w k , the optimization problem can become P2:

[0047] Wherein, represents the IRS diagonal block matrix, K opt represents the number of selected users.

[0048] S4: Given the phase shift of the IRSs, the joint optimization sub-problem P1 of user selection strategy and beamforming at the base station is solved to obtain the user selection strategy and the beamforming vector at the base station.

[0049] The process of solving the sub-problem P1 includes:

[0050] The present application proposes to solve the optimal user selection vector based on the artificial bee colony algorithm. In the process of the artificial bee colony algorithm, the fitness value of the honey source needs to be calculated. The honey source is a feasible solution that meets the optimization problem, and the fitness value of the honey source refers to the minimum transmission power required to meet the QoS constraint of the selected user after the base station selects the honey source.

[0051] Given the phase shift of IRSs, introduce the number of selected users, i.e. when the selected user is the honey source, rewrite the user selection strategy and the joint optimization sub-problem of beamforming at the base station as problem P3:

[0052] The above problem can be effectively solved based on the second order cone program (SOCP). Specifically, in the optimization problem, the objective function is a convex function, and only the QoS constraint needs to be transformed into a convex constraint. Since the absolute value is needed in SINR, w k After adding the phase rotation The value of SINR is not affected, so the inner product can be transformed into a positive real number by phase rotation, i.e. Therefore, the constraint in problem P3 is transformed into a convex constraint, and the specific constraint is:

[0053] The problem P3 after the constraint in problem P3 is transformed into a convex constraint is represented as:

[0054] The reciprocal of the base station transmit power is used as the fitness value, and the artificial bee colony algorithm is used to solve problem P3 to obtain the user selection strategy and the beamforming vector at the base station; Specifically:

[0055] Step 1: initialization phase: randomly initialize multiple honey source matrices nec_source∈J SN×K , set the number of iterations; calculate the fitness value of the honey source, and find the minimum fitness value and its corresponding honey source position.

[0056] For the base station, randomly generate a honey source matrix nec_source∈J SN×K , J∈{0,1} represents the definition domain of the elements in the honey source matrix. When the element in the honey source matrix takes 0, it means that the BS does not select the user for transmission. When the element in the honey source matrix takes 1, it means that the BS selects the user for transmission.

[0057] According to the given IRSs phase shift Θ l ,1≤l≤L and the user selection of each honey source, calculate the initialized honey source to obtain a set of fitness values. According to the user selection of each honey source, solve the optimization problem P3 to obtain the beamforming vector that satisfies the current user signal-to-noise ratio constraint, and calculate the reciprocal of the power, i.e. calculate the fitness value of the honey source, and find the minimum fitness value and its corresponding honey source position.

[0058] Step 2: Employed bee phase: each employed bee randomly generates a new food source and solves the optimization problem P3 to obtain the beamforming vector satisfying the current user signal-to-noise ratio constraint and to obtain the reciprocal of the power to calculate the fitness value of the food source. If the fitness value of the new food source is greater than the minimum fitness value of the original food source, the new food source replaces the original food source with the minimum fitness value.

[0059] Step 3: Observer bee phase: each observer bee selects a food source according to the food source selection probability, and randomly selects an element with a value of 1 and a value of 0 in the selected food source to change (changes the element with a value of 1 to 0, and changes the element with a value of 0 to 1); solves the fitness value of the new food source according to the optimization problem P3, if the fitness value of the new food source is greater than the fitness value of the original food source, the new food source replaces the original food source; otherwise, no replacement is made; if the food source has not been replaced after LIMIT times of selection, the food source is discarded and a new food source is randomly generated.

[0060] Assuming the total number of food sources is SN, after obtaining the fitness value set {fit1, fit2,..., fit SN SN} of the food sources, in each observer bee phase, a food source needs to be selected with a certain probability, i.e. the food source selection probability. Assuming that the probability of selecting a food source x∈{1,2,...,SN} is:

[0061] LIMIT is self-set, i.e. the maximum number of selection times allowed for the food source without improvement in the observer bee phase.

[0062] Step 4: Determine whether the maximum number of iterations is reached, if so, select the food source with the maximum fitness value as the optimal solution, obtain the user selection strategy c={c1,…,c K} T and the beamforming vector w={w1,…,w K} at the base station; otherwise, return to step 3.

[0063] S5: Solve the IRSs phase shift optimization sub-problem P2 according to the user selection strategy and the beamforming vector at the base station to obtain the phase shift of the IRSs.

[0064] According to the above artificial bee colony algorithm, the optimal solution c k and w k can be obtained, and then the optimization of the phase shift Θ l of the IRSs is performed, 1≤l≤L. First, the channel is processed as follows:

[0065] where is a diagonal block matrix.

[0066] The constraint condition in the phase shift optimization sub-problem P2 of the IRSs can be converted into a quadratic constraint, and the SDR technology is used to efficiently approximate the solution of the problem to obtain the phase shift of the IRSs.

[0067] S6: Steps S4-S5 are repeatedly executed until the joint optimization problem P converges, and the optimal user selection strategy, the optimal beamforming vector at the base station and the optimal phase shift of the IRSs are obtained and executed.

[0068] The system executes the optimal user selection strategy, the optimal beamforming vector at the base station and the optimal phase shift of the IRSs, and the transmission power of the base station is minimized, thereby significantly reducing the transmission power of the base station and improving the system performance under the premise of ensuring the quality of service of the user.

[0069] The present application is evaluated:

[0070] The present application is simulated, and a three-dimensional coordinate single-cell network system is considered in the simulation scenario, wherein the BS is located at (0m, 0m, 25m), and the lth IRS is located at (d1(cos(2πl / L)), d1(sin(2πl / L)), 10m). K users are uniformly distributed in a ring-shaped area with a radius [R1, R2], and the height of all users is set to 0m. Small-scale fading is considered, and the following channel model is used for all channels:

[0071] wherein β is a Rician factor, G LoS and G NLoS are the deterministic LOS component and NLOS component, respectively.

[0072] Path loss is considered, and the path loss model is set as:

[0073] wherein C0 is the path loss at the reference distance D0 = 1m, d is the link distance, and α is the path loss factor. The number of IRS reflection units N and the number of BS transmission antennas M are set according to the simulation requirements, and the parameter values for system initialization are given in Table 1.

[0074] Table 1 System initialization parameters

[0075] The number of reflection units of each IRSs is set to N = 30, the number of BS antennas is set to M = 8, d1 = 80m, R1 = 60m, R2 = 100m, the maximum number of iterations is set to 50, and the initial phase shift of the IRSs is set to a random phase shift. The simulation is shown in FIG. 3, and the power required by the proposed algorithm decreases with the increase of the number of iterations, thereby proving the convergence of the proposed algorithm.

[0076] The above examples further illustrate the objects, technical solutions and advantages of the present application. It should be understood that the above examples are only preferred embodiments of the present application and are not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made to the present application within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for beamforming and user selection based on distributed IRSs-aided MIMO communication system, characterized in that, The method comprises the following steps: S1: constructing a distributed IRSs-assisted MIMO communication system model; S2: based on the distributed IRSs-assisted MIMO communication system model, constructing a joint optimization problem P of active beamforming at the base station, phase shift of the IRSs and user selection strategy with the minimum transmission power of the base station as an optimization objective; S3: decoupling the joint optimization problem P into a user selection strategy and active beamforming joint optimization sub-problem P1 at the base station and an IRSs phase shift optimization sub-problem P2; S4: given the phase shift of the IRSs, solving the user selection strategy and active beamforming joint optimization sub-problem P1 to obtain the user selection strategy and the beamforming vector at the base station; S5: solving the IRSs phase shift optimization sub-problem P2 according to the user selection strategy and the beamforming vector at the base station to obtain the phase shift of the IRSs; S6: repeating steps S4-S5 until the joint optimization problem P converges to obtain the optimal user selection strategy, the optimal beamforming vector at the base station and the optimal phase shift of the IRSs and perform.

2. The method of claim 1, wherein, The distributed IRS-assisted MIMO communication system model comprises: 1 base station, L IRSs and K single-antenna users, the base station is equipped with M antenna arrays, adopts a uniform linear array structure; each IRS is configured with N=N x N y The number of reflection units, adopts a uniform planar array form, wherein N x And N y The number of reflection units in the horizontal and vertical directions respectively, N is the total number of reflection units.

3. The method of Claim 1, wherein, The joint optimization problem of the active beamforming, the IRSs phase shift, and the user selection strategy at the base station is: where c k denotes whether the kth user is selected by the base station, w k denotes the beamforming vector sent by the BS to the kth user, K denotes the number of users, Θ l denotes the diagonal reflection matrix of the lth IRS, SINR k denotes the signal-to-interference-and-noise ratio of the kth user, γ k denotes the minimum signal-to-noise ratio constraint at user k, θ l,n denotes the reflection coefficient of the nth reflecting element of the lth IRS, L denotes the number of IRSs, and N denotes the number of reflecting elements on an IRS.

4. The method of Claim 1, wherein, The user selection policy and base station at beamforming joint optimization sub-problem is: wherein c k represents whether the kth user is selected by the base station, w k represents the beamforming vector sent by the base station to the kth user, K represents the number of users, c j represents whether the jth user is selected by the base station, w j represents the beamforming vector sent by the base station to the jth user, denotes the noise variance of the kth user, channel gain representing the combined channel between the kth user and the base station, γ k denotes the minimum signal-to-noise ratio constraint at user k.

5. The method of claim 1, wherein, The step S4 comprises: Given the phase shift of the IRSs, introducing the number of selected users, rewriting the user selection strategy and active beamforming joint optimization sub-problem as a problem P3; Transforming the constraint in the problem P3 into a convex constraint; Taking the inverse of the transmission power of the base station as the fitness value, and solving the problem P3 by using the artificial bee colony algorithm to obtain the user selection strategy and the beamforming vector at the base station.

6. The method of claim 5, wherein, The constraints in problem P3 are transformed into convex constraints, and the problem P3 is denoted as: where w k represents the beamforming vector sent by the base station to the kth user, γ k represents the minimum signal-to-noise ratio constraint at user k, denotes the noise variance of the kth user, a channel gain representing a combined channel between the kth user and the base station, represents a real part, w j represents a beamforming vector given by a base station to the jth user, K opt represents a number of nectar source selection users.

7. The method of claim 1, wherein, The process of solving the problem P3 by using the artificial bee colony algorithm comprises: Step 1: initialization stage: randomly initializing a plurality of honey source matrices and setting the number of iterations; calculating the fitness value of the honey source and finding the minimum fitness value and the corresponding position of the honey source; Step 2: employed bee stage: each employed bee randomly generates a new honey source and calculates the fitness value of the honey source, if the fitness value of the new honey source is greater than the minimum value of the fitness value of the original honey source, then the new honey source replaces the original honey source with the minimum fitness value; Step 3: observation bee stage: each observation bee selects a honey source according to the honey source selection probability, and randomly selects an element with a value of 1 and an element with a value of 0 in the selected honey source to change; calculating the fitness value of the new honey source, if the fitness value of the new honey source is greater than the fitness value of the original honey source, then the new honey source replaces the original honey source; otherwise, no replacement is performed; if the honey source has not been replaced after being selected for LIMIT times, then the honey source is discarded and a new honey source is randomly generated; Step 4: judging whether the maximum number of iterations is reached, if yes, selecting the honey source with the maximum fitness value as the optimal solution to obtain the user selection strategy and the beamforming vector at the base station; otherwise, returning to step 3.

8. The method of claim 1, wherein, The IRSs phase shift optimization sub-problem is: where Θ represents the IRS diagonal block matrix, θ l,n denotes the reflection coefficient of the nth reflection element of the lth IRS, denotes the channel gain from the base station to the kth user, h r,k denotes the channel gain from the IRSs to the kth user, G denotes the channel gain from the base station to the IRSs, w k denotes the beamforming vector from the base station to the kth user, w j denotes the beamforming vector from the base station to the jth user, w denotes the noise variance of the kth user, γ k denotes the minimum signal-to-noise ratio constraint at user k, K opt denotes the number of nectar source selection users.

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