A method for intelligent reflecting surface assisted multi-cell transmission with optimized energy efficiency

Abstract

The application discloses an intelligent reflecting surface assisted multi-cell transmission method for optimizing energy efficiency. The system to which the method is applied comprises multiple cells, and each cell base station has multiple antenna elements. Multiple single-antenna users in each cell are located at the cell edge weak coverage or signal blind area, and the intelligent reflecting surface arranged at the cell edge is used to assist the communication of the users in the area. First, the reflection phase shift matrix of the intelligent reflecting surface is fixed, and the beam forming vectors transmitted by each base station are designed. Then, the beam forming vectors transmitted by the base stations are fixed, and the reflection phase shift matrix of the intelligent reflecting surface is optimized. Through alternately optimizing the beam forming vectors transmitted by the base stations and the reflection phase shift matrix of the intelligent reflecting surface, the total energy efficiency of the system converges to an optimal value. The application can obtain higher energy efficiency with lower calculation complexity and is easy to implement.

Description

TECHNICAL FIELD

[0001] The application relates to an intelligent reflecting surface assisted multi-cell transmission method for optimizing energy efficiency, and belongs to the technical field of wireless communication. BACKGROUND

[0002] In a cellular network system, a base station can provide high transmission rate and low transmission delay for users distributed in the center of a cell. However, when a user is located at the edge of a cell, the distance between the user and the base station providing services for the user is far, the path loss of the transmission signal is increased, and the distance between the edge user and an interfering base station is reduced, and the interference received by the user is increased. In a cellular network, improving the performance of edge users has always been a challenge. Meanwhile, driven by the rapid development of advanced multimedia applications, the next generation of wireless networks must support high spectral efficiency and large-scale connection. Due to a large number of user accesses and high data rate requirements, energy loss has also become a challenging problem in wireless network design.

[0003] As an emerging technology in future 6G cellular networks, intelligent reflecting surfaces have attracted extensive attention from many researchers at home and abroad in recent years. An intelligent reflecting surface is a passive reflecting plate composed of a large number of adjustable reflecting elements. The intelligent reflecting surface not only has low power consumption but also can intelligently change the transmission environment of a wireless channel. By deploying an intelligent reflecting surface near the edge users of a cell, an additional transmission channel between a base station and the edge users is provided, thereby enhancing the received signal gain of the users and reducing the interference between the users. It is worth noting that since the intelligent reflecting surface also needs to consume energy to regulate the phase shift, as the number of intelligent reflecting elements increases, the spectral efficiency of the system will also increase, but the total power consumption of the intelligent reflecting surface will also increase. How to achieve a compromise between spectral efficiency and power consumption is also worth studying.

[0004] In summary, for the energy efficiency optimization problem in an intelligent reflecting surface assisted communication system, it is a suitable choice to jointly design the beamforming vector transmitted by the base station and the transmission scheme of the intelligent reflecting surface reflection phase shift matrix by using an intelligent reflecting surface assisted multi-cell transmission method. SUMMARY

[0005] Technical problem: The purpose of the application is to provide an intelligent reflecting surface assisted multi-cell transmission method for optimizing energy efficiency, which jointly optimizes the beamforming vector transmitted by the base station and the intelligent reflecting surface reflection phase shift matrix, so as to maximize the total energy efficiency of the system.

[0006] Technical solution: The application is an intelligent reflecting surface assisted multi-cell transmission method for optimizing energy efficiency, which is aimed at a system: there are J cells in the system, and each cell base station is deployed with a uniform antenna array containing M antenna elements; there are K single-antenna users in each cell at the edge of the cell with weak coverage or signal blind area, which need to be assisted in communication by the intelligent reflecting surface with N=N v ×N h reflective elements arranged at the edge of the cell, the intelligent reflecting surface is arranged with N v rows and N h columns of reflective elements, each reflective element is realized by a PIN transistor, the phase shift accuracy of each reflective element is B bits, and the possible reflective phase shift is The application first fixes the reflective phase shift matrix of the intelligent reflecting surface, and designs the beam forming vector sent by each base station; then, the beam forming vector sent by the base station is fixed, and the reflective phase shift matrix of the intelligent reflecting surface is optimized; the beam forming vector sent by the base station and the reflective phase shift matrix of the intelligent reflecting surface are alternately optimized until the total energy efficiency of the system converges to an optimal value. The method specifically includes the following steps:

[0007] Step one, set the convergence threshold ε, let the iteration number t=1; initialize the beam forming vector sent by the jth base station to the kth user in the jth cell Where j=1,…,J, k=1,…,K, 1 M×1 represents an M×1 vector with all elements being 1; the initial value of the reflective phase shift matrix of the intelligent reflecting surface is randomized, and the modulus values of the diagonal elements are all 1, represents the phase shift value of the nth reflective element after the tth iteration, and diag(·) represents generating a diagonal matrix;

[0008] Step two, calculate the total power consumption of the intelligent reflecting surface under the reflective phase shift matrix Φ (t-1) of the intelligent reflecting surface obtained in the t-1th iteration

[0009] Step three, calculate the total energy efficiency G of the system when the beam forming vector sent by the jth base station to the kth user in the jth cell is and the reflective phase shift matrix of the intelligent reflecting surface is Φ (t-1) after the t-1th iteration (t-1) :

[0010]

[0011] Where, is the equivalent channel from the jth base station to the kth user in the jth cell after the t-1th iteration, represents the channel from the jth base station to the intelligent reflecting surface, Hjk,t-1denotes the channel from the IRS to the kth user in the jth cell, Hjk,t-1denotes the equivalent channel from the qth base station to the kth user in the jth cell after the t-1th iteration, Hjk,t-1denotes the channel from the qth base station to the IRS, the superscript (·) H denotes the conjugate transpose, Vjk,t-1denotes the beamforming vector of the jth base station to its kth user after the t-1th iteration, Vjk,t-1denotes the beamforming vector of the qth base station to its kth user after the t-1th iteration, denotes the noise power at the kth user in the jth cell, v denotes the efficiency of the transmit power amplifier, P BS and P user denote the circuit power consumption of the base station and the user, respectively;

[0012] Step four, the IRS reflection phase shift matrix Φ (t-1) and the beamforming vector Vjk,t-1of the jth base station to its kth user are calculated using the IRS reflection phase shift matrix Φ Step five, the IRS reflection phase shift matrix Φ

[0013] Step six, the system total energy efficiency G is calculated when the beamforming vector Vjk,t of the jth base station to its kth user and the IRS reflection phase shift matrix Φ (t) after the tth iteration are

[0014] Step seven, determine whether the following formula is true: (t) : (t)

[0015]

[0016] where, Hjk,t denotes the equivalent channel from the jth base station to the kth user in the jth cell after the tth iteration, Hjk,t denotes the equivalent channel from the qth base station to the kth user in the jth cell after the tth iteration, Vjk,t denotes the beamforming vector of the jth base station to its kth user after the tth iteration, Vjk,t denotes the beamforming vector of the qth base station to its kth user after the tth iteration;

[0017] Step seven, determine whether the following formula is true: ​​

[0018]

[0019] If not, let t = t + 1, enter step four; otherwise, let The beamforming vector sent by the jth base station to its kth user is denoted as Φ (t) The smart reflecting surface reflection phase shift matrix.

[0020] In step two, after the t-1th iteration, the smart reflecting surface reflection phase shift matrix The total power consumption of the smart reflecting surface under is calculated by the following formula:

[0021]

[0022] Where P static and P are the static power consumption and dynamic power consumption of the smart reflecting surface respectively; the static power consumption is the power consumption of the control circuit; the dynamic power consumption changes dynamically with the coding of the reflecting unit, and the coding of the nth reflecting unit in the t-1th iteration is determined by its phase shift value ; the phase shift value of each reflecting unit of the smart reflecting surface corresponds to 2 B coding values, i.e.

[0023]

[0024] Where, is one of the 2 B coding values corresponding to the nth reflecting unit, and the dynamic power consumption can be expressed as:

[0025]

[0026] Where, represents the number of "1"s in the coding corresponding to the nth reflecting unit, and P PIN represents the power consumption of the PIN transistor when the coding is "1".

[0027] In step four, the beamforming vector (t-1) sent by the jth base station to its kth user in the tth iteration is calculated using the smart reflecting surface reflection phase shift matrix Φ obtained in the t-1th iteration and the beamforming vector includes the following sub-steps:

[0028] a1) Calculate the intermediate variable

[0029]

[0030] where, is the additive white Gaussian noise power received by the kth user in the jth cell;

[0031] a2) Calculate the mean square error of the kth user in the jth cell in the tth iteration using the following formula:

[0032]

[0033] a3) Calculate the auxiliary variable in the tth iteration

[0034] a4) Calculate the auxiliary variable in the tth iteration according to the following formula: (t) ,

[0035]

[0036] where the auxiliary variable is calculated using the following formula:

[0037]

[0038] ν is the efficiency of the transmit power amplifier, denotes the total power consumption of the intelligent reflecting surface under the phase shift matrix Φ (t-1) denotes the total power consumption of the intelligent reflecting surface under the phase shift matrix Φ BS and P user denote the circuit power consumption of the base station and the user, respectively;

[0039] a5) Calculate the eigenvector matrix obtained in the tth iteration by singular value decomposition (SVD):

[0040]

[0041] where Σ is a diagonal matrix with all positive diagonal elements, and I M denotes an M x M dimensional identity matrix;

[0042] a6) Calculate the auxiliary variable in the tth iteration (t) = [η1 (t) ,…,η J (t) ] Upper bound of each element:

[0043]

[0044] where P max,j denotes the maximum transmit power allowed at the jth base station;

[0045] a7) Calculate the auxiliary variable in the interval using the following formula: (t)performing a binary search, updating the beamforming vector sent by the jth base station to its kth user after the tth iteration

[0046]

[0047] in step five, according to the calculated beamforming vector computing the intelligent reflecting surface reflecting phase shift matrix Φ (t) comprising the following sub-steps:

[0048] b1) calculating the intermediate matrix after the tth iteration by using the following formula

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] b2) setting an inner loop convergence threshold ξ, initializing the inner loop iteration number r = 1, and initializing the intelligent reflecting surface reflecting phase shift vector v according to the intelligent reflecting surface reflecting phase shift matrix Φ (t-1) (0) is a vector composed of the diagonal elements of Φ (t-1) , where (·) T denotes the transpose of a vector;

[0055] b3) calculating the objective function obtained after the r-1th iteration:

[0056] f(v (r-1) )=(v (r-1) ) H (Α (t) ⊙(Β (t) ) T )v (r-1) -2Re{(v (r-1) ) H (d (t) ) *}

[0057] where (·) * denotes the conjugate of a vector, is a vector composed of the diagonal elements of D (t) ; and

[0058] b4) calculating the intermediate vector of the rth iteration​​

[0059]

[0060] wherein, λ max is the maximum eigenvalue of (A (t) ⊙(B (t) ) T ), I N denotes the N x N identity matrix, is the auxiliary matrix, is the vector consisting of the diagonal elements of ;

[0061] b5) Calculate the smart reflector phase shift vector of the rth iteration by using the following formula and performing a binary search on each element of the auxiliary matrix (r) μ

[0062]

[0063] wherein, arg(·) denotes the argument of a vector;

[0064] b6) Calculate the objective function obtained in the rth iteration,

[0065] f(v (r) ) = (v (r) ) H (A (t) ⊙(B (t) ) T ) v (r) - 2Re{ (v (r) ) H (d (t) ) *}

[0066] b7) Determine whether holds, if so, go to step b8), otherwise let r = r + 1 and go to step b4);

[0067] b8) Update the smart reflector phase shift matrix (t) Φ (r) = diag(v (r) ) obtained in the tth iteration.

[0068] Advantageous effects: The present application is a smart reflector assisted multi-cell transmission method for optimizing energy efficiency, which has the following advantages compared with the prior art:

[0069] (1) The present application proposes a practical smart reflector power consumption model, and models and calculates the power consumption of the smart reflector with discrete phase shifts.

[0070] (2) The design scheme of the beamforming vector sent by the base station and the intelligent reflecting surface reflection phase shift matrix in the application has low complexity, is easy to implement, and has good performance. BRIEF DESCRIPTION OF DRAWINGS

[0071] Figure 1 is a flowchart of an intelligent reflecting surface assisted multi-cell transmission method for optimizing energy efficiency. DETAILED DESCRIPTION

[0072] The technical solutions provided by the application will be described in detail below with reference to specific implementation cases. It should be understood that the following specific embodiments are only used to illustrate the application and are not used to limit the scope of the application.

[0073] The application relates to an intelligent reflecting surface assisted multi-cell transmission method for optimizing energy efficiency. v h The intelligent reflecting surface has N v rows and N h columns of reflecting units, and the reflecting phase precision of each reflecting unit is B bits, and the possible reflecting phase is The application first fixes the intelligent reflecting surface reflection phase shift matrix and designs the beamforming vectors sent by the base stations; then, the beamforming vectors sent by the base stations are fixed, and the intelligent reflecting surface reflection phase shift matrix is optimized; the beamforming vectors sent by the base stations and the intelligent reflecting surface reflection phase shift matrix are alternately optimized until the total energy efficiency of the system converges to an optimal value. The method specifically comprises the following steps:

[0074] Step one, set a convergence threshold epsilon, let the iteration number t=1; initialize the beamforming vector sent by the jth base station to the kth user thereof where j=1,...,J, k=1,...,K, 1 M×1 represents an Mx1-dimensional vector with all elements being 1; the initial value of the intelligent reflecting surface reflection phase shift matrix is randomized, and the modulus values of the diagonal elements are all 1, represents the phase shift value of the nth reflecting unit after the tth iteration, and diag(·) represents a diagonal matrix;

[0075] Step two, calculate the intelligent reflecting surface reflection phase shift matrix Phi (t-1) The total power consumption of the intelligent reflecting surface is which can be obtained by the following formula: ​

[0076]

[0077] where P static and are the static and dynamic power consumption of the IRS respectively; the static power consumption is the power consumption of the control circuit; the dynamic power consumption varies dynamically with the encoding of the reflecting elements, and the encoding of the nth reflecting element in the t-1th iteration is determined by its phase shift value ; the phase shift value of each reflecting element of the IRS corresponds to 2 B encoding values, i.e.

[0078]

[0079] where is one of the 2 B encoding values corresponding to the nth reflecting element, and the dynamic power consumption can be expressed as:

[0080]

[0081] where represents the number of "1"s in the encoding corresponding to the nth reflecting element, and P PIN represents the power consumption of the PIN transistor when the encoding is "1";

[0082] Step three, calculate the total energy efficiency G of the system when the beamforming vector sent by the jth base station to its kth user is (t-1) and the reflection phase shift matrix of the IRS is Φ (t-1) :

[0083]

[0084] where is the equivalent channel from the jth base station to the kth user in the jth cell after the t-1th iteration, represents the channel from the jth base station to the IRS, represents the channel from the IRS to the kth user in the jth cell, is the equivalent channel from the qth base station to the kth user in the jth cell after the t-1th iteration, represents the channel from the qth base station to the IRS, and the superscript (·) H represents the conjugate transpose, represents the beamforming vector sent by the jth base station to its lth user after the t-1th iteration, represents the beamforming vector sent by the qth base station to its lth user after the t-1th iteration, denotes the noise power at the kth user in the jth cell, v denotes the efficiency of the transmit power amplifier, P BS and P user denote the circuit power consumption of the base station and the user, respectively;

[0085] Step four, using the smart reflecting surface reflection phase shift matrix Φ (t-1) and the beamforming vector sent by the jth base station to its kth user calculate the beamforming vector sent by the jth base station to its kth user in the tth iteration Specifically, the following sub-steps are included:

[0086] a1) calculate the intermediate variable in the tth iteration

[0087]

[0088] wherein, is the additive white Gaussian noise power received by the kth user in the jth cell;

[0089] a2) calculate the mean square error of the kth user in the jth cell in the tth iteration using the following formula:

[0090]

[0091] a3) calculate the auxiliary variable in the tth iteration

[0092] a4) calculate the auxiliary variable λ in the tth iteration according to the following formula: (t) ,

[0093]

[0094] wherein, the auxiliary variable is calculated using the following formula:

[0095]

[0096] v is the efficiency of the transmit power amplifier, denotes the total power consumption of the smart reflecting surface under the smart reflecting surface reflection phase shift matrix Φ (t-1) , P BS and P user denote the circuit power consumption of the base station and the user, respectively;

[0097] a5) calculate the eigenvector matrix obtained in the tth iteration by singular value (SVD) decomposition

[0098]

[0099] where Σ is a diagonal matrix with positive diagonal elements, I M denotes an M x M dimensional identity matrix;

[0100] a6) Calculate the auxiliary variable η (t) = [η (t) 1 ,…,η J t (t) ] upper bound of each element:

[0101]

[0102] where P max,j denotes the maximum transmit power allowed at the jth base station;

[0103] a7) Perform a binary search on the auxiliary variable η j (t) in the interval |0,(η ub t | and update the beamforming vector (t) sent by the jth base station to its kth user after the tth iteration

[0104]

[0105] Step five, according to the beamforming vector calculated in step four , calculate the intelligent reflecting surface reflection phase shift matrix Φ (t) of the tth iteration and the total power consumption of the intelligent reflecting surface Specifically, the following sub-steps are included:

[0106] b1) Calculate the intermediate matrix

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] b2) Set the inner loop convergence threshold ξ, initialize the inner loop iteration number r = 1, and initialize the intelligent reflecting surface reflection phase shift vector (t-1) according to the intelligent reflecting surface reflection phase shift matrix Φ , v (0) is a vector composed of the diagonal elements of Φ (t-1) , where (·)T denotes the transpose of a vector;

[0113] b3) Calculate the objective function for the r-1th iteration:

[0114] f(v (r-1) ) = (v (r-1) ) H (A (t) ⊙(B (t) ) T )v (r-1) - 2Re{(v (r-1) ) H (d (t) ) *}

[0115] where (·) * denotes the conjugate of a vector, is a vector consisting of the diagonal elements of D (t) ;

[0116] b4) Calculate the intermediate vector for the rth iteration

[0117]

[0118] where λ max is the largest eigenvalue of (A (t) ⊙(B (t) ) T ), I N denotes the N x N identity matrix, is the auxiliary matrix, is a vector consisting of the diagonal elements of ;

[0119] b5) Calculate the SRS reflection phase shift vector for the rth iteration using the following equation and performing a binary search on each element of the auxiliary matrix μ (r) in the interval [0, 1]:

[0120]

[0121] where arg(·) denotes the argument of a vector;

[0122] b6) Calculate the objective function for the rth iteration,

[0123] f(v (r) ) = (v (r) ) H (A (t) ⊙(B (t) ) T )v (r) - 2Re{(v (r)) H (d (t) ) *}

[0124] b7) judge whether the following formula is established: if yes, go to step b8), otherwise let r=r+1 and go to step b4);

[0125] b8) update the smart reflecting surface reflection phase shift matrix Φ (t) =diag(v (r) ) obtained in the tth iteration;

[0126] Step six, calculate the system total energy efficiency G (t) when the beamforming vector sent by the jth base station to its kth user is (t) and the smart reflecting surface reflection phase shift matrix is Φ after the tth iteration:

[0127]

[0128] wherein, is the equivalent channel from the jth base station to the kth user in the jth cell after the tth iteration, is the equivalent channel from the qth base station to the kth user in the jth cell after the tth iteration, denotes the beamforming vector sent by the jth base station to its lth user after the tth iteration, denotes the beamforming vector sent by the qth base station to its lth user after the tth iteration.

[0129] Step seven, judge whether the following formula is established:

[0130]

[0131] if not, let t=t+1 and go to step four; otherwise, take as the beamforming vector sent by the jth base station to its kth user, and take Φ (t) as the smart reflecting surface reflection phase shift matrix.

[0132] In summary, by jointly designing the beamforming vector sent by the base station and the smart reflecting surface reflection phase shift matrix, the present application realizes a good compromise between spectrum efficiency and power consumption, maximizes the system total energy efficiency, and exceeds the traditional transmission design method in terms of running time complexity and system performance. A flowchart of the smart reflecting surface assisted multi-cell transmission method for optimizing energy efficiency is shown in Figure 1 .

[0133] The above merely describes the preferred embodiments of the present application, and it should be pointed out that those skilled in the art can make several improvements and refinements without departing from the principles of the present application, and these improvements and refinements should also be considered as the protection scope of the present application.

Claims

1. A method for intelligent reflecting surface assisted multi-cell transmission with optimized energy efficiency, the method comprising: The system to which the method is directed: there are J cells in the system, and each cell base station is deployed with a uniform antenna array containing M antenna elements; there are K single-antenna users in each cell at the edge of the cell with weak coverage or signal blind area, which need to be assisted in communication by the intelligent reflecting surface with N v rows h and N columns of reflecting units set at the edge of the cell, each reflecting unit being implemented by a PIN transistor, the phase shift accuracy of each reflecting unit being B bits, and the reflecting phase shift being The method specifically includes the following steps: Step one, set the convergence threshold ε, let the iteration number t = 1; initialize the beamforming vector sent by the jth base station to its kth user Where j = 1, …, J, k = 1, …, K, 1 M×1 Indicates an Mx1-dimensional vector with all elements being 1; initialize the intelligent reflecting surface reflection phase shift matrix Φ (0) ; Step two, calculate the smart surface reflection phase shift matrix Φ from the t-1th iteration (t-1) Total power consumption of the smart surface Step three, calculate the system total energy efficiency G of when the beamforming vector sent by the jth base station to its kth user is and the intelligent reflecting surface reflects the phase shift matrix Φ (t-1) at the t-1th iteration (t-1) : wherein, is the equivalent channel from the jth base station to the kth user within the jth cell after the t - 1th iteration, denotes the channel from the jth base station to the smart reflective surface, denotes the channel from the smart reflective surface to the kth user within the jth cell, is the equivalent channel from the qth base station to the kth user within the jth cell after the t - 1th iteration, denotes the channel from the qth base station to the smart reflective surface, superscript (·) H denotes the conjugate transpose, denotes the beamforming vector sent by the jth base station to its lth user after the t - 1th iteration, denotes the beamforming vector sent by the qth base station to its lth user after the t - 1th iteration, denotes the noise power at the kth user within the jth cell, v denotes the efficiency of the transmit power amplifier, P BS and P user denote the circuit power consumption of the base station and the user, respectively; Step four, utilizing Φ (t-1) and calculating the beamforming vector sent by the jth base station to its kth user in the tth iteration Step five, based on computing the smart surface reflection phase shift matrix Φ for the tth iteration (t) and the total power consumption of the smart surface Step six, calculate the beamforming vector sent by the jth base station to its kth user after the tth iteration as and the system total energy efficiency G (t) when the smart reflective surface reflects the phase shift matrix Φ (t) : wherein, is the equivalent channel from the jth base station to the kth user within the jth cell after the tth iteration, is the equivalent channel from the qth base station to the kth user within the jth cell after the tth iteration, denotes the beamforming vector sent by the jth base station to its lth user after the tth iteration, denotes the beamforming vector sent by the qth base station to its lth user after the tth iteration. Step seven, determine if the following is true: If not, let t = t + 1, go to step four; otherwise, set The beamforming vector transmitted by the jth base station to its kth user is denoted by Φ (t) The phase shift matrix as reflected by the intelligent reflecting surface.

2. The method for optimizing energy efficiency with intelligent reflective surface-assisted multi-cell transmission according to claim 1, characterized in that: The step two, after the t-1th iteration, the smart reflective surface reflects the phase shift matrix The total power consumption of the smart reflective surface under the phase shift matrix Is calculated by the following formula: P static and respectively, the static power consumption of the smart reflective surface and the dynamic power consumption of the smart reflective surface; the static power consumption is the power consumption of the control circuit; the dynamic power consumption dynamically changes with the encoding of the reflective unit, and the encoding of the nth reflective unit in the t-1th iteration is determined by the phase shift value of the nth reflective unit; B Each phase shift value of each reflective unit of the smart reflective surface corresponds to 2 wherein, 2n is the 2 B one of the encoding values, the dynamic power consumption can be expressed as: wherein, represents the number of "1"s in the nth reflection unit P PIN represents the power consumption of the PIN transistor when the code is "1".

3. The method for optimizing energy efficiency with intelligent reflective surface-assisted multi-cell transmission according to claim 1, characterized in that: In the fourth step, the smart reflecting surface reflection phase shift matrix Φ obtained in the t-1th iteration is used (t-1) and the beamforming vector transmitted by the jth base station to its kth user and the beamforming vector transmitted by the jth base station to its kth user in the tth iteration is calculated comprising the following sub-steps: a1 ) calculating an intermediate variable in the tth iteration wherein, Pjk is the additive white Gaussian noise power received by the kth user in the jth cell. a2) Calculate the mean square error for the kth user in the jth cell in the tth iteration using the following equation: a3) calculating the auxiliary variable of the t-th iteration a4) Calculate the auxiliary variable λ in the t-th iteration according to the formula (t) , where the auxiliary variable is calculated using the formula v is the efficiency of the transmit power amplifier, denotes the total power consumption of the intelligent reflecting surface under the phase shift matrix Φ (t 1) denotes the total power consumption of the intelligent reflecting surface under the phase shift matrix Φ BS and P user denote the circuit power consumption of the base station and the user, respectively; a5) by singular value (SVD) decomposition, compute the eigenvector matrix of the tth iteration where Σ is a diagonal matrix with positive diagonal entries, I M denotes the M x M identity matrix; a6) Compute the auxiliary variable η (t) = [η1 (t) ,…, η J (t) Upper bound of each element: where P max,j denotes the maximum transmit power allowed at the jth base station; a7) updating the beamforming vector sent by the jthbase station to its kthuser after the tthiteration j (t) ) ub ] using a binary search on the auxiliary variable η (t) ​

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