A Distributed Beamforming Method for Decellularized MIMO Networks Assisted by Multiple Intelligent Reflectors

Abstract

This invention discloses a distributed beamforming method for decellularized MIMO networks assisted by multiple intelligent reflectors, comprising the following steps: Step 1, optimization problem modeling and variable initialization; Step 2, solving the base station beamforming subproblem; Step 3, solving the IRS control matrix subproblem; Step 4, distributed implementation and numerical analysis. This invention can enhance user reception and improve user-end communication quality by distributively optimizing the base station beamforming and the phase shift matrix of the passive reflection of the IRS, and reduces the solution complexity through a closed-form solution.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a distributed beamforming method for decellularized multiple-input multiple-output networks assisted by multiple intelligent reflectors. Background Technology

[0002] Cellular de-cellular networks are a highly promising technology in 5G and 6G communications. They enable all base stations to serve users simultaneously without being limited by the cellular edge, thus utilizing spectrum resources more efficiently than traditional cellular networks. Smart reflector technology is also a revolutionary technology that can be used to improve physical layer security and enhance the Quality of Service (QoS) of terminals in dead zones and at the cellular edge. Therefore, combining IRS with de-cellular networks holds great promise for increasing wireless network capacity.

[0003] Maximizing the weighted sum-rate (WRS) is an important research topic in IRS-assisted communication networks. Introducing an IRS leads to coupling between variables in the objective function and non-convex unit modulus phase shift constraints, a difficult problem to solve. Traditional methods such as semi-definite relaxation (SDR), second-order programming (SOCP), and successful convex approximation (SCA) for solving modulo-1 constraints result in high algorithmic complexity and are difficult to implement. Furthermore, these methods rarely yield closed-form solutions, hindering their application in distributed frameworks to reduce computational and equipment burden. Majorization-minimization (MM) methods for solving modulo-1 constraints involve eigenvalue decomposition when finding the upper bound of the objective function, potentially leading to even higher complexity with large IRS and unit numbers. Therefore, maximizing the weighted sum-rate is a crucial research topic in IRS-assisted communication networks. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a distributed beamforming method for decellularized MIMO networks assisted by multiple intelligent reflectors, which can enhance the received signal of users and improve the communication quality of users by optimizing the beamforming of the base station and the phase shift matrix of the passive reflection of the IRS.

[0005] To address the aforementioned technical problems, this invention provides a method for distributed beamforming of decellularized multi-input multi-output networks assisted by multiple intelligent reflectors, comprising the following steps:

[0006] Step 1: Optimization Problem Modeling and Variable Initialization; Considering the downlink scenario of an IRS-assisted cell-free MIMO system, evaluate the channel information of base station-user, base station-IRS, and IRS-user, randomly initialize the base station beamforming vector and the phase shift control matrix of the IRS, calculate the base station-user equivalent channel including the IRS link, and model the user received signal, signal-to-interference-plus-noise ratio, and achievable Shannon rate based on actual parameters such as the number of base stations, the number of users, the number of IRS, the number of base station antennas, and the user priority, thus completing the optimization problem modeling;

[0007] Step 2: Solving the base station beamforming subproblem; In the beamforming subproblem, by minimizing the mean square error MMSE and introducing auxiliary weights and decoding coefficient variables, the subproblem is equivalently transformed into a WMMSE convex problem. The optimal solutions for decoding coefficients, auxiliary weights, and beamforming vectors in each iteration are obtained sequentially using the block coordinate descent method (BCD).

[0008] Step 3: Solve the IRS control matrix subproblem; In the control matrix subproblem, the objective function is rearranged into a standard form, ignoring the constant terms, and the non-constant terms are analyzed and transformed. The element block coordinate descent method is used to solve each element on the diagonal of the control matrix in turn, and finally the optimal solution of the control matrix corresponding to each IRS in the subproblem is obtained.

[0009] Step 4: Distributed Implementation and Numerical Analysis; Determine the location of each node, model the channel model, record the base station beamforming vector, IRS control matrix and its corresponding weighted rate sum after each iteration update, compare the convergence speed of this algorithm with other centralized algorithms, and analyze the correlation between the weighted rate sum and different transmit power, different number of transmit antennas and different number of IRS elements.

[0010] Preferably, in step 1, the optimization problem modeling and variable initialization specifically involve: considering the downlink of an IRS-assisted decellularized MIMO system, where B base stations simultaneously serve K users with the assistance of R IRSs. Assume each base station and user is equipped with N... t There are one transmit antenna and one receive antenna. It is assumed that the IRS can only change the phase of the incident signal. Each IRS has N elements, and the phase shift matrix of the r-th IRS is expressed as... in Let be the phase shift coefficient of the nth cell of the r-th IRS. The channels from base station b to the r-th IRS, from base station b to user k, and from the r-th IRS to user k are respectively... This implies that the channel state information between every node in the system is known.

[0011] The equivalent channel from base station b to user k is represented as:

[0012]

[0013] in,

[0014]

[0015] This represents the symbol information sent by all base stations to the k-th user, and The transmit beamforming vector from base station b to user k is expressed as: Therefore, the signal received by user k can be represented as:

[0016]

[0017] Where n k This represents the Gaussian white noise received by user k.

[0018] The signal-to-interference-plus-noise ratio at user k can be written as:

[0019]

[0020] in, Represents noise n k The power.

[0021] The optimization problem is represented as:

[0022]

[0023] in, It is the set of beamforming vectors for all base stations, α k ,P b ,θ n These are the priority weight of user k, the maximum transmit power of base station b, and the k-th element of θ, respectively.

[0024] Since the variables in the constraints are separable, the block coordinate descent method is used to solve the problem. A distributed, low-complexity algorithm based on the block coordinate descent method is used to maximize the WSR. In each iteration, θ is first determined to optimize F, and then θ is calculated using the obtained F.

[0025] Preferably, in step 2, the solution to the base station beamforming problem specifically involves: given θ, This represents the decoding coefficients for user k. This represents the estimated signal. Therefore, the mean square error of user k is expressed as:

[0026]

[0027] By using the minimum mean square error receiver MMSE, problem (4) with respect to F is equivalently transformed into the WMMSE problem, i.e.

[0028]

[0029] in, Let (6) represent the auxiliary weighting variables and the set of decoding coefficients, respectively. Since (6) is convex for each variable in w, u, and F, the BCD method is used to solve (6).

[0030] By u k By calculating the gradient and setting it to zero, we can obtain the optimal MMSE receiver. Right now

[0031]

[0032] From (6), the auxiliary weighted variable w can be obtained through the optimality condition. k The optimal value:

[0033]

[0034] When w k ,u k , Given the WMMSE problem, it is rewritten as:

[0035]

[0036] Problem (9) is now a convex quadratic constrained quadratic programming problem with a monotonic gradient. It can be solved using the bisection method, and its Lagrangian function is written as (10), where λ b C1 and f are the components of the dual variable with respect to base station b, respectively. b,k Irrelevant constant terms, through the optimality condition, yield f b,k It is λ b The function, as shown in (11), is determined by the dual variable λ. b The beamforming vector f is obtained by reverse calculation. b,k ;

[0037]

[0038]

[0039] Obviously, Rewritten as:

[0040] Tr[(Λ b +λ b I) -2 Ω b ] = P b (12)

[0041] in,

[0042]

[0043]

[0044] D b Λ b D b H For matrix The eigenvalue decomposition of can therefore yield

[0045]

[0046] The left side of equation (15) follows λ b The value of λ increases and then decreases monotonically. The value of λ can be found using the bisection method. b Thus, the optimal solution for beamforming in the loop is obtained by reverse deduction according to equation (11).

[0047] Preferably, in step 3, the solution of the IRS control matrix subproblem is as follows: when F is given, w and u are solved by (7) and (8), then the WMMSE problem with respect to θ is rewritten as:

[0048]

[0049] From (1) and (5), we know that problem (16) is a quadratic programming problem. Due to the modulo 1 constraint, this problem is a non-convex problem, which can be rewritten as:

[0050]

[0051] Where C2 is a constant independent of θ, and Z,q are shown in equations (18) and (19);

[0052]

[0053]

[0054] By employing the element block coordinate descent method, given an element in θ, we process another element within it, and this approach yields a closed-form solution.

[0055] Due to modulo 1 constraints Regarding θ n Problem (17) can be rewritten as:

[0056]

[0057] in Since it is a complex number, the closed-form solution of equation (20) is: Therefore, the focus of the following work is to determine the value of κ, let f(θ) = θ H Zθ-2Re{θ H q}+C2,f(θ) with respect to θ n The complex derivative is calculated as follows:

[0058]

[0059] Similarly, the complex gradient of f(θ) with respect to θ is calculated as follows:

[0060]

[0061] From (21) and (22), we get:

[0062]

[0063] in[·] m,n Let [·] represent the element in the m-th row and n-th column of the matrix. n This represents the nth element of the vector;

[0064] Expand the left side of equation (23) and compare the two sides. The coefficients are obtained. Therefore, the κ value is updated as follows:

[0065]

[0066] Preferably, in step 4, the distributed implementation and numerical analysis specifically involve: assuming the base station is located at (0,0) with a radius of R. c On the circle, the user and IRS are randomly generated positions within the circle, and the large-scale path loss in dB is determined by... Given that d is the distance from transmitter to receiver, d0 = 1m is the reference distance, PL0 = 30dB is the path loss at the reference distance d0, the path loss exponent β of BS-UE link (LoS) and BS-IRS, IRS-UE link (NLoS) are set to 3.75 and 2.2 respectively, and B = 4, R = 5, K = 6, R c =125m, α K =1, And assume the base station is located in (R) c ,0), (0,R c ), (-R c ,0), (0,-R c ).

[0067] The beneficial effects of this invention are as follows: (1) This invention independently designs a distributed beamforming method for decellularized multi-input multi-output networks assisted by multiple intelligent reflectors, thereby enhancing the user's received signal and improving the communication quality of the user end; (2) The algorithm can be implemented in a distributed manner, which is more stable than the traditional centralized algorithm and effectively alleviates the computational pressure of a single computing node; (3) The algorithm complexity is reduced by the closed-form solution method, which is conducive to hardware implementation. Attached Figure Description

[0068] Figure 1 This is a schematic diagram of the system model of the present invention.

[0069] Figure 2 This is a schematic diagram of the control matrix optimization algorithm of the present invention.

[0070] Figure 3 This is a schematic diagram of the overall optimization algorithm of the present invention.

[0071] Figure 4 This is a schematic diagram of the overall distributed architecture of the present invention.

[0072] Figure 5 This diagram illustrates the convergence speed comparison between the present invention and other benchmark distributed algorithms.

[0073] Figure 6 This is a schematic diagram illustrating how the weighted sum rate of the present invention varies with the number of base station antennas and the transmit power.

[0074] Figure 7 This is a schematic diagram illustrating how the weighted sum rate of the present invention varies with the number of IRSs and the base station transmit power. Detailed Implementation

[0075] A distributed beamforming method for decellularized multiple-input multiple-output networks assisted by multiple intelligent reflectors includes the following steps:

[0076] A. Optimization Problem Modeling and Variable Initialization

[0077] like Figure 1 As shown, this invention considers the downlink of an IRS-assisted decellularized MIMO system, where B base stations simultaneously serve K users with the assistance of R IRSs. It is assumed that each base station and user is equipped with N... t There are one transmit antenna and one receive antenna. It is also assumed that the IRS can only change the phase of the incident signal, and each IRS has N elements. The phase shift matrix of the r-th IRS is expressed as... in Let be the phase shift coefficient of the nth unit of the r-th IRS. The channels from base station b to the r-th IRS, from base station b to user k, and from the r-th IRS to user k are respectively... This implies that the channel state information between every node in the system is known.

[0078] The equivalent channel from base station b to user k can be expressed as:

[0079]

[0080] in,

[0081]

[0082] This represents the symbol information sent by all base stations to the k-th user, and The transmit beamforming vector from base station b to user k is expressed as: Therefore, the signal received by user k can be represented as:

[0083]

[0084] Where n k This represents the Gaussian white noise received by user k.

[0085] The signal-to-interference-plus-noise ratio at user k can be written as:

[0086]

[0087] in, Represents noise n k The power.

[0088] The objective of this invention is to maximize the weighted sum-rate (WSR) by jointly optimizing the base station's transmit beam and the IRS's passive reflective beam (phase control matrix). The optimization problem can be expressed as:

[0089]

[0090] in, It is the set of beamforming vectors for all base stations, α k ,P b ,θ n These are the priority weight of user k, the maximum transmit power of base station b, and the kth element of θ, respectively.

[0091] Although the power constraint problem is a convex problem, it is still a non-convex problem and difficult to solve because the variables in the objective function and the modulo 1 constraint are coupled.

[0092] Since the variables in the constraints are separable, the algorithm of this invention utilizes the block coordinate descent method for solution. This section proposes a distributed, low-complexity algorithm based on block coordinate descent (BCD) to maximize the WSR. In each iteration, θ is first determined to optimize F, and then θ is calculated using the obtained F.

[0093] B. Solving the Base Station Beamforming Subsystem Problem

[0094] Given θ, This represents the decoding coefficients for user k. This represents the estimated signal. Therefore, the mean square error of user k can be expressed as:

[0095]

[0096] By using a minimum mean-square error receiver (MMSE), problem (4) concerning F can be equivalently transformed into a WMMSE problem, i.e.

[0097]

[0098] in, Let f(x) represent the auxiliary weighting variables and the set of decoding coefficients, respectively. Since (6) is convex for each variable in w, u, and F, the BCD method can be used to solve (6).

[0099] By u k By calculating the gradient and setting it to zero, we can obtain the optimal MMSE receiver. Right now

[0100]

[0101] From (6), the auxiliary weighted variable w can be obtained through the optimality condition. k The optimal value:

[0102]

[0103] When w k ,u k , Given the WMMSE problem, it can be rewritten as:

[0104]

[0105] Problem (9) is now a convex quadratic constrained quadratic programming problem with a monotonic gradient, which can be solved using the bisection method. Its Lagrangian function can be written as (10), where λ bC1 and f are the components of the dual variable with respect to base station b, respectively. b,k Irrelevant constant terms. Through the optimality condition, f can be obtained. b,k It is λ b The function, as shown in (11), is determined by the dual variable λ. b The beamforming vector f can be derived by reverse deduction. b,k .

[0106]

[0107]

[0108] Obviously, It can be rewritten as:

[0109] Tr[(Λ b +λ b I) -2 Ω b ] = P b (12)

[0110] in,

[0111]

[0112]

[0113] D b Λ b D b H For matrix The eigenvalue decomposition of can therefore yield

[0114]

[0115] The left side of equation (15) follows λ b The value of λ increases and then decreases monotonically; λ can be found using the bisection method. b Thus, the optimal solution for beamforming in the loop is obtained by reverse deduction according to equation (11).

[0116] C. Solving the IRS control matrix subproblem

[0117] When F is given, w and u can be solved using equations (7) and (8). Therefore, the WMMSE problem concerning θ can be rewritten as:

[0118]

[0119] From (1) and (5), we know that problem (16) is a quadratic programming problem. Due to the modulo 1 constraint, this problem is a non-convex problem and can be rewritten as:

[0120]

[0121] Where C2 is a constant independent of θ, and Z,q are shown in equations (18) and (19).

[0122]

[0123]

[0124] To avoid the high complexity and slow convergence speed caused by using eigenvalue decomposition to find the upper bound of MM, this invention utilizes the special structure of the problem and employs a cell block coordinate descent method, where one element in θ is given and another element is processed. This scheme can obtain a closed-form solution.

[0125] Due to the modulo-1 constraint |θ n |=1, Regarding θ n Problem (17) can be rewritten as:

[0126]

[0127] in It is a complex number. It is easy to see that the closed-form solution to equation (20) is... Therefore, the focus of the following work is to determine the value of κ. Let f(θ) = θ H Zθ-2Re{θ H q}+C2. f(θ) with respect to θ n The complex derivative can be calculated as

[0128]

[0129] Similarly, the complex gradient of f(θ) with respect to θ can be calculated as follows:

[0130]

[0131] From (21) and (22), we can obtain:

[0132]

[0133] in[·] m,n Let [·] represent the element in the m-th row and n-th column of the matrix. n This represents the nth element of the vector.

[0134] Expand the left side of equation (23) and compare the two sides. The coefficient can be obtained Therefore, the κ value is updated as follows:

[0135]

[0136] exist Figure 2The steps of the above-mentioned cell block coordinate descent method are summarized in the text. In step 5, the p value is updated using θ. The entire algorithm process can be found in [link to full text]. Figure 3 Since the algorithm of this invention has a closed-form solution at each step, the algorithm has low complexity.

[0137] D. Distributed Implementation and Numerical Analysis

[0138] Assume the base station is located at (0,0) with radius R. c On the circle, the user and IRS are randomly generated positions within the circle, and the large-scale path loss in dB is determined by... Given that d is the distance from transmitter to receiver, d0 = 1m is the reference distance, and PL0 = 30dB is the path loss at the reference distance d0. The path loss exponent β for the BS-UE link (LoS) and BS-IRS, IRS-UE link (NLoS) is set to 3.75 and 2.2, respectively. For simplicity and without loss of generality, we set B = 4, R = 5, K = 6, R c =125m, α K =1, And assume the base station is located in (R) c ,0), (0,R c ), (-R c ,0), (0,-R c ).

[0139] Figure 4 This demonstrates the architecture of a distributed implementation of the algorithm, where at the start of each iteration, all users simultaneously update their respective u. k and w k And broadcast it to the base station. Then each base station updates the corresponding {f}. b,k}, Then, it is broadcast to other base stations and users after being combined with θ. The iterative information required by each base station includes KN. t dimensional beamforming vector f b,1 ,...f b,k And an NR-dimensional phase shift vector θ. Furthermore, at the start of each iteration, the user transmits 2K one-dimensional complex numbers u. k and w k Therefore, the amount of information required for each iteration is 2K+B(KN). t +NR).

[0140] Figure 5 The convergence performance of several algorithms is demonstrated. Centralized iteration refers to all base station variables being updated simultaneously by a centralized CPU, while distributed algorithm iteration refers to each base station updating its corresponding beamforming vector and phase shift matrix separately. From Figure 5As can be seen, because the centralized algorithm can update more variables in one iteration, the convergence speed of the distributed algorithm is slower than that of the centralized algorithm. This algorithm converges faster than other distributed algorithms, and all four algorithms mentioned above have closed-form solutions.

[0141] Figure 6 The relationship between the number of IRS cells, transmit power, and average WSR is illustrated. Each curve represents over 100 random channel samples. It can be seen that the higher the transmit power used by the base station, the higher the WSR the user can achieve. Increasing the number of IRS cells also improves system performance, and the algorithm outperforms the performance of using maximum transmit ratio under a random phase-shift IRS.

[0142] Figure 7 The paper demonstrates the relationship between average WSR and base station transmit power and the number of transmit antennas. Intuitively, increasing the number of transmit antennas at the base station can improve system performance.

Claims

1. A distributed beamforming method for a cell-free multiple-input multiple-output (MIMO) network assisted by multiple-intelligent reflecting surfaces (M-IRSs), characterized in that, Includes the following steps: Step 1: Optimization Problem Modeling and Variable Initialization; Considering the downlink scenario of an IRS-assisted cell-free MIMO system, evaluate the channel information between base station and user, base station and IRS, and IRS and user. Randomly initialize the base station beamforming vector and the IRS phase shift control matrix, calculate the base station-user equivalent channel including the IRS link, and model the user received signal, signal-to-interference-plus-noise ratio, and achievable Shannon rate based on actual parameters such as the number of base stations, number of users, number of IRS, number of base station antennas, and user priority, thus completing the optimization problem modeling; Specifically, the optimization problem modeling and variable initialization consider the downlink of an IRS-assisted decellularized MIMO system, where... One base station With the assistance of one IRS, it simultaneously serves There are [number] users, assuming each base station and user are equipped with [equipment / services]. Each IRS has one transmit antenna and one receive antenna, and it is assumed that the IRS can only change the phase of the incident signal. Unit 1, the 1st The phase shift matrix of each IRS is expressed as: ,in For the first The first IRS Phase shift coefficient of each unit, base station To the One IRS channel, base station To users The channel and the first IRS to user The channels are respectively This implies that the channel state information between every node in the system is known. base station To users The equivalent channel is represented as: （1） in, , , This indicates that all base stations send to the first Symbolic information for each user, and Base station To users The transmitted beamforming vector is expressed as Therefore, users The received signal is represented as: （2） in Indicates user Received Gaussian white noise; user The signal-to-interference-to-noise ratio at this point is written as: （3） in, Indicates noise The power; The optimization problem is represented as: （4） in, It is the set of beamforming vectors for all base stations. users respectively Priority weights, base stations Maximum transmit power and The One element; Since the variables in the constraints are separable, the block coordinate descent method is used to solve the problem. A distributed, low-complexity algorithm based on the block coordinate descent method is used to maximize the WSR. In each iteration, the first step is to determine... To optimize And then through the obtained To calculate ; Step 2: Solving the base station beamforming subproblem; In the beamforming subproblem, by minimizing the mean square error (MMSE) and introducing auxiliary weights and decoding coefficient variables, the subproblem is equivalently transformed into a WMMSE convex problem. The optimal solutions for the decoding coefficients, auxiliary weights, and beamforming vector are obtained sequentially in each iteration using the block coordinate descent (BCD) method. Specifically, the solution to the base station beamforming subproblem is as follows: Given... , Indicates user Decoding coefficients, This indicates the estimated signal, therefore the user The mean square error is expressed as: （5） By using the minimum mean square error receiver (MMSE) to (4) about The problem is equivalently transformed into the WMMSE problem, that is... （6） in, Let them represent the auxiliary weighting variables and the set of decoding coefficients, respectively, because for... For each variable in (6), it is convex, so the BCD method is used to solve (6); Through the Find the gradient and set it equal to 0; that is, obtain the optimal MMSE receiver. ,Right now （7） The auxiliary weighted variables are obtained from (6) through the optimality condition. The optimal value: （8） when Given the WMMSE problem, it is rewritten as: （9） Problem (9) is now a convex quadratic constrained quadratic programming problem with a monotonic gradient. It is solved using the bisection method, and its Lagrangian function is written as (10), where These are the dual variables with respect to the base station. The amount, and Irrelevant constant terms are obtained through the optimality condition. yes The function, as shown in (11), is determined by defining the dual variable. The beamforming vector is obtained by reverse calculation. ; （10） （11） Obviously, Rewritten as: （12） in, （13） （14） For matrix The eigenvalue decomposition of can therefore yield （15） The left side of equation (15) follows The value of increases and then decreases monotonically. The result can be obtained using the bisection method. Thus, the optimal solution for beamforming in the loop is obtained by reverse deduction according to equation (11); Step 3: Solve the IRS control matrix subproblem; In the control matrix subproblem, the objective function is rearranged into a standard form, ignoring the constant terms, and the non-constant terms are analyzed and transformed. The element block coordinate descent method is used to solve each element on the diagonal of the control matrix in turn, and finally the optimal solution of the control matrix corresponding to each IRS in the subproblem is obtained. Step 4: Distributed Implementation and Numerical Analysis; Determine the location of each node, model the channel model, record the base station beamforming vector, IRS control matrix and its corresponding weighted rate sum after each iteration update, compare the convergence speed of this algorithm with other centralized algorithms, and analyze the correlation between the weighted rate sum and different transmit power, different number of transmit antennas and different number of IRS elements.

2. The distributed beamforming method for decellularized multi-input multi-output networks assisted by multiple intelligent reflectors as described in claim 1, characterized in that, In step 3, the solution to the IRS control matrix subproblem is specifically as follows: when Given, Solving for (7) and (8), then regarding The WMMSE problem can be rewritten as: （16） From (1) and (5), we know that problem (16) is a quadratic programming problem. Due to the modulo 1 constraint, this problem is a non-convex problem, which can be rewritten as: （17） in, Is with Irrelevant constants As shown in equations (18) and (19); （18） （19） Using the cell block coordinate descent method, given a... We can use one element from the set to process another element to obtain a closed-form solution. Due to modulo 1 constraints ,about Question (17) can be rewritten as: （20） in Since it is a complex number, the closed-form solution of equation (20) is: Therefore, the focus of the following work is to determine Value, let , About The complex derivative is calculated as follows: （21） Similarly, about The complex gradient is calculated as follows: （22） From (21) and (22), we get: （23） in Represents the first of the matrix OK List the elements, Then it represents the vector of the first position. One element; Expand the left side of equation (23) and compare the two sides. The coefficients are obtained. ,therefore, The value is updated to: （24）。 3. The distributed beamforming method for decellularized multi-input multi-output networks assisted by multiple intelligent reflectors as described in claim 1, characterized in that, In step 4, the distributed implementation and numerical analysis specifically involve: assuming the base station is located at (0,0) with a radius of... On the circle, the user and IRS are randomly generated positions within the circle, and the large-scale path loss in dB is determined by... Given, among which It is the distance from the transmitter to the receiver. This is a reference distance. Reference distance Path loss at the location, path loss index of BS-UE link (LoS) and BS-IRS, IRS-UE link (NLoS). Set them to 3.75 and 2.2 respectively. And assume the base station is located at ( ,0), (0, ), (- ,0), (0,- ).

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