A design method for intelligent metasurface-assisted transmission with maximized energy efficiency

Abstract

The present invention discloses a method for designing intelligent metasurface-assisted transmission that maximizes energy efficiency. The system includes multiple cells, and each cell base station has multiple antenna array elements. In each cell, there is a single-antenna user in a weak coverage or signal blind area at the cell edge. An intelligent metasurface set at the cell edge is used to assist users in communication within the area. First, the intelligent metasurface reflection phase shift is fixed, and the beamforming vectors sent by each base station are designed using statistical channel state information. Then, the beamforming vectors sent by the base station are fixed, and the intelligent metasurface reflection phase shift of the statistical channel state information is optimized. The beamforming vectors sent by the base station and the intelligent metasurface reflection phase shift are alternately optimized until the ergodic energy efficiency of the system converges to an optimal value. The present invention can achieve higher energy efficiency with lower computational complexity and is easy to implement.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication technology, and in particular relates to a design method for intelligent metasurface-assisted transmission with maximized energy efficiency. Background Art

[0002] In cellular network systems, base stations can provide high transmission rates and low transmission latency for users located in the cell center. However, when users are located at the cell edge, the distance from the base station serving them is greater, increasing the path loss of the transmitted signal. Furthermore, the distance between edge users and interfering base stations decreases, increasing the interference experienced by users. Improving the performance of edge users in cellular networks has always been a major challenge. Smart metasurfaces, an emerging technology for future 6G cellular networks, have recently garnered extensive attention from researchers both domestically and internationally. Smart metasurfaces are passive reflectors composed of a large number of reflective units with adjustable reflection phase shifts. By deploying smart metasurfaces near cell edge users, an additional transmission channel between the base station and edge users is provided, thereby enhancing the user's received signal gain while reducing interference between users. However, driven by the rapid development of advanced multimedia applications, next-generation wireless networks must support high spectral efficiency and large-scale connectivity. Due to the large number of users and the high data rate requirements, energy consumption has become a challenging issue in wireless network design. However, existing research on energy efficiency has mostly been based on an idealized RIS power consumption model, failing to consider the power consumption differences between different RIS hardware and different coding states.

[0003] In particular, in the scenario where the base station and the smart metasurface obtain accurate instantaneous channel state information, the base station needs to continuously obtain real-time channel state information and continuously adjust the smart metasurface reflection phase shift to ensure that the system energy efficiency is optimized. However, this will also lead to increased computational complexity and excessive overhead in obtaining channel state information.

[0004] In summary, for the energy efficiency optimization problem in the intelligent metasurface-assisted communication system, based on the measured RIS power consumption model, the intelligent metasurface-assisted multi-cell transmission method using statistical channel state information to jointly design the beamforming vector sent by the base station and the intelligent metasurface reflection phase shift matrix is ​​a suitable choice. Summary of the Invention

[0005] The purpose of the present invention is to provide a smart metasurface-assisted transmission design method that maximizes energy efficiency, jointly optimizes the beamforming vector sent by the base station and the smart metasurface reflection phase shift, so as to maximize the overall energy efficiency of the system and solve the technical problems mentioned in the background technology.

[0006] In order to solve the above technical problems, the specific technical solutions of the present invention are as follows:

[0007] A design method for intelligent metasurface-assisted transmission with maximum energy efficiency is proposed, characterized in that the method is targeted at a system with a total of J cells, and each cell base station deploys a uniform antenna array containing M antenna elements; in each cell, there is a single-antenna user in a weak coverage or signal blind area at the cell edge, which needs to be set at the cell edge with N=N v ×N h The intelligent metasurface with N reflective units is used to assist the user communication in the weak coverage or signal blind area at the edge of the cell. v Row N h The system consists of a series of reflection units, each of which is implemented using a PIN diode. The phase shift accuracy of each reflection unit is 2 bits, and the value set of its reflection phase shift is {0,π / 2,π,3π / 2}, and the corresponding 2-bit codes are {00,01,11,10}. First, the reflection phase shift of the smart metasurface is fixed, and the beamforming vectors sent by each base station are designed. Then, the beamforming vectors sent by the base station are fixed, and the reflection phase shift of the smart metasurface is optimized. The beamforming vectors sent by the base station and the reflection phase shift of the smart metasurface are alternately optimized until the ergodic energy efficiency of the system converges to the optimal value.

[0008] The method specifically comprises the following steps:

[0009] Step 1: Set the convergence threshold ε and the number of iterations t = 1; initialize the beamforming vector sent by the j-th base station to the users in the cell. where j = 1,…,J,1 M×1 represents an M×1 dimensional vector with all elements equal to 1; the initial value of the smart metasurface reflection phase shift matrix Randomization is performed, diag(·) represents a diagonal matrix generated with the elements in the brackets as diagonal elements, Indicates the phase shift value of the nth reflector unit during initialization;

[0010] Step 2: Calculate the smart metasurface reflection phase shift matrix obtained at the t-1th iteration Total power consumption of the smart metasurface And establish a continuous relationship between the total power consumption of the smart metasurface and the discrete phase shift, represents the phase shift value of the nth reflector unit at the t-1th iteration;

[0011] Step 3: Use the following formula to calculate the beamforming vector sent by the jth base station to the user in the cell after the t-1th iteration: And the smart metasurface reflection phase shift matrix is ​​Φ (t-1) The system ergodic energy efficiency evaluation value G (t-1) :

[0012]

[0013] in, is the equivalent channel from the j-th base station to the user in the j-th cell after the t-1-th iteration, represents the line-of-sight path component of the channel from the jth base station to the smart metasurface, represents the line-of-sight path component from the smart metasurface to the user channel in the jth cell, represents the line-of-sight path component of the channel from the qth base station to the smart metasurface, represents the line-of-sight path component from the smart metasurface to the user channel in the qth cell, with the superscript (·) H represents the conjugate transpose, represents the beamforming vector sent by the j-th base station to its user after the t-1-th iteration, represents the beamforming vector sent by the qth base station to its user after the t-1th iteration, represents the noise power at the user in the jth cell, ν represents the efficiency of the transmitting power amplifier, P BS and P user Represent the circuit power consumption of base station and user respectively, represents the Ricean factor of the channel from the qth base station to the smart metasurface, κ j represents the Ricean factor of the channel from the smart metasurface to the user in the jth cell;

[0014] Step 4: Use the smart metasurface reflection phase shift matrix Φ obtained in the t-1th iteration (t-1) and the beamforming vector sent by the jth base station to its user Calculate the beamforming vector sent by the jth base station to its user in the tth iteration

[0015] Step 5: The beamforming vector calculated according to step 4 Calculate the smart metasurface reflection phase shift matrix Φ of the tth iteration (t) and the total power consumption of the smart metasurface

[0016] Step 6: Use the following formula to calculate the beamforming vector sent by the jth base station to the user in the cell after the tth iteration: And the smart metasurface reflection phase shift matrix is ​​Φ (t) The system ergodic energy efficiency evaluation value G (t) :

[0017]

[0018] in, represents the beamforming vector sent by the qth base station to its user after the tth iteration;

[0019] Step 7: Determine whether the following formula is true:

[0020]

[0021] If not, set t = t + 1 and go to step 4; otherwise, As the beamforming vector sent by the j-th base station to its user, Φ (t) As the smart metasurface reflection phase shift matrix, ε represents the threshold.

[0022] In the step 2, after the t-1th iteration, the intelligent metasurface reflection phase shift matrix Total power consumption of smart metasurface under Calculated by the following formula:

[0023]

[0024] Among them, P static and They are the static power consumption and dynamic power consumption of the intelligent metasurface respectively; the static power consumption is the power consumption of the control circuit; the dynamic power consumption is approximately calculated using the following formula

[0025]

[0026] in, represents the phase shift vector of the smart metasurface reflection after the t-1th iteration, P PIN Indicates the power consumption when the PIN tube is turned on, 1 N×1 Represents an N×1-dimensional vector of all ones.

[0027] In the step 4, the smart metasurface reflection phase shift matrix Φ obtained by the t-1th iteration is used. (t-1) and the beamforming vector sent by the jth base station to its user Calculate the beamforming vector sent by the jth base station to its user in the tth iteration The following sub-steps are included:

[0028] a1) Calculate the auxiliary variable in the tth iteration using the following formula

[0029]

[0030] a2) Calculate the auxiliary matrix of the tth iteration using the following formula

[0031]

[0032] Among them, I M represents the M×M-dimensional unit matrix;

[0033] a3) The matrix obtained in step a2) Decompose and get the auxiliary matrix of the tth iteration Satisfy in, represents an M×M-dimensional vector;

[0034] a4) Calculate the auxiliary vector in the tth iteration according to the following formula

[0035]

[0036] a5) Calculate the auxiliary variable λ in the tth iteration (t) ,

[0037]

[0038] a6) Use the following formula to calculate the auxiliary variable ρ (t) 、μ (t) Perform binary search and update the beamforming vector sent by the jth base station to its user after the tth iteration

[0039]

[0040] in,

[0041] In step 5, according to the calculated beamforming vector Calculate the intelligent metasurface reflection phase shift matrix Φ (t) , including the following sub-steps:

[0042] b1) Set the inner loop convergence threshold ξ, initialize the inner loop iteration number r = 1, and calculate the phase shift matrix Φ of the intelligent metasurface. (t-1) , the phase shift vector of the smart metasurface reflection Initialize so that The nth element of is Φ (t-1) The vector consisting of the nth diagonal elements of , where n=1,…,N;

[0043] b2) Calculate the objective function obtained by the r-1th iteration using the following formula:

[0044]

[0045] in, Re{·} means taking the real part;

[0046] b3) Calculate the objective function using the following formula The gradient ξ in Euclidean space (r-1) :

[0047]

[0048] in,

[0049] b4) Calculate the objective function according to the following formula: The Riemann gradient of :

[0050]

[0051] Where ⊙ represents the Hadamard product, and the superscript (·) * indicates conjugation;

[0052] b5) Calculation Where τ is the step size; it is adjusted according to the Armijo-Goldstein condition;

[0053] b6) Update the smart metasurface reflection phase shift in the rth iteration Among them, unit(·) means normalizing the modulus values ​​of all elements in the vector;

[0054] b7) Calculate the objective function in the rth iteration using the following formula

[0055]

[0056] b8) Judgment Is it true? If so, go to step b9); otherwise, set r = r + 1 and go to step b3);

[0057] b9) Update the smart metasurface reflection phase shift matrix obtained in the tth iteration

[0058] The present invention provides a design method for intelligent metasurface-assisted transmission with maximized energy efficiency, which has the following advantages:

[0059] (1) This paper proposes a power consumption model for intelligent metasurfaces based on actual measurements, and models and calculates the power consumption of intelligent metasurfaces with discrete phase shifts. This is the first study based on an actual RIS power consumption model.

[0060] (2) In the present invention, the beamforming vector sent by the base station and the intelligent metasurface reflection phase shift are jointly designed based on statistical channel state information, which not only reduces the power consumption of the intelligent metasurface controller, but also greatly reduces the computational complexity at the base station.

[0061] (3) The design of the beamforming vector sent by the base station and the intelligent metasurface reflection phase shift in the present invention has low complexity, is easy to implement, and has good performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a flow chart of a design method for intelligent metasurface-assisted transmission with maximized energy efficiency according to the present invention.

[0063] Figure 2 This is a simulation comparison diagram of an intelligent metasurface-assisted transmission design method for maximizing energy efficiency according to the present invention. DETAILED DESCRIPTION

[0064] In order to better understand the purpose, structure and function of the present invention, the following is a further detailed description of the energy efficiency maximizing intelligent metasurface assisted transmission design method of the present invention in conjunction with the accompanying drawings.

[0065] The present invention relates to a design method for intelligent metasurface-assisted transmission with maximum energy efficiency, which is characterized in that: the method is targeted at a system in which there are J cells in total, and each cell base station deploys a uniform antenna array containing M antenna elements; in each cell, there is a single-antenna user in a weak coverage or signal blind area at the cell edge, which needs to be set at the cell edge with N=N v ×N h The intelligent metasurface of N reflective units is used to assist user communication in the area. v Row N h The reflection units in the column are each implemented using a PIN diode. The phase shift accuracy of each reflection unit is 2 bits. The reflection phase shift value set is {0, π / 2, π, 3π / 2}, and the corresponding 2-bit codes are {00, 01, 11, 10}. First, the intelligent metasurface reflection phase shift is fixed and the beamforming vectors sent by each base station are designed. Then, the beamforming vectors sent by the base station are fixed and the intelligent metasurface reflection phase shift is optimized. The beamforming vectors sent by the base station and the intelligent metasurface reflection phase shift are alternately optimized until the ergodic energy efficiency of the system converges to the optimal value. The method specifically includes the following steps:

[0066] Step 1: Set the convergence threshold ε and the number of iterations t = 1; initialize the beamforming vector sent by the j-th base station to the users in the cell. where j = 1,…,J,1 M×1 represents an M×1 dimensional vector with all elements equal to 1; the initial value of the smart metasurface reflection phase shift matrix Randomization is performed, diag(·) represents a diagonal matrix generated with the elements in the brackets as diagonal elements, Indicates the phase shift value of the nth reflector unit during initialization;

[0067] Step 2: Calculate the smart metasurface reflection phase shift matrix obtained at the t-1th iteration Total power consumption of the smart metasurface And establish a continuous relationship between the total power consumption of the smart metasurface and the discrete phase shift, represents the phase shift value of the nth reflector unit at the t-1th iteration; after the t-1th iteration, the total power consumption of the smart metasurface Calculated by the following formula:

[0068]

[0069] Among them, P static and They are the static power consumption and dynamic power consumption of the intelligent metasurface respectively; the static power consumption is the power consumption of the control circuit; the dynamic power consumption is approximately calculated using the following formula

[0070]

[0071] in,

[0072] Step 3: Use the following formula to calculate the beamforming vector sent by the jth base station to the user in the cell after the t-1th iteration: And the smart metasurface reflection phase shift matrix is ​​Φ (t-1) The system ergodic energy efficiency evaluation value G (t-1) :

[0073]

[0074] in, is the equivalent channel from the j-th base station to the user in the j-th cell after the t-1-th iteration, represents the line-of-sight path component of the channel from the jth base station to the smart metasurface, represents the line-of-sight path component from the smart metasurface to the user channel in the jth cell, represents the line-of-sight path component of the channel from the qth base station to the smart metasurface, represents the line-of-sight path component from the smart metasurface to the user channel in the qth cell, with the superscript (·) H represents the conjugate transpose, represents the beamforming vector sent by the j-th base station to its user after the t-1-th iteration, represents the beamforming vector sent by the qth base station to its user after the t-1th iteration, represents the noise power at the user in the jth cell, ν represents the efficiency of the transmitting power amplifier, P BS and P user Represent the circuit power consumption of base station and user respectively, represents the Ricean factor of the channel from the qth base station to the smart metasurface, κ j represents the Ricean factor of the channel from the smart metasurface to the user in the jth cell;

[0075] Step 4: Use the smart metasurface reflection phase shift matrix Φ obtained in the t-1th iteration (t-1) and the beamforming vector sent by the jth base station to its user Calculate the beamforming vector sent by the jth base station to its user in the tth iteration The following sub-steps are included:

[0076] a1) Calculate the auxiliary variable in the tth iteration using the following formula

[0077]

[0078] a2) Calculate the auxiliary matrix of the tth iteration using the following formula

[0079]

[0080] Among them, I M represents the M×M-dimensional identity matrix.

[0081] a3) The matrix obtained in step a2) Decompose and get the auxiliary matrix of the tth iteration Satisfy

[0082] a4) Calculate the auxiliary vector in the tth iteration according to the following formula

[0083]

[0084] a5) Calculate the auxiliary variable λ in the tth iteration (t) ,

[0085]

[0086] a6) Use the following formula to calculate the auxiliary variable ρ (t) 、μ (t) Perform binary search and update the beamforming vector sent by the jth base station to its user after the tth iteration

[0087]

[0088] in,

[0089] Step 5: The beamforming vector calculated according to step 4 Calculate the smart metasurface reflection phase shift matrix Φ of the tth iteration (t ), including the following sub-steps:

[0090] b1) Set the inner loop convergence threshold ξ, initialize the inner loop iteration number r = 1, and calculate the phase shift matrix Φ of the intelligent metasurface. (t-1) , the phase shift vector of the smart metasurface reflection Initialize so that The nth element of is Φ (t-1) The vector consisting of the nth diagonal elements of , where n=1,…,N;

[0091] b2) Calculate the objective function obtained by the r-1th iteration using the following formula:

[0092]

[0093] in,

[0094] b3) Calculate the objective function using the following formula The gradient ξ in Euclidean space (r-1) :

[0095]

[0096] in,

[0097] b4) Calculate the objective function according to the following formula: The Riemann gradient of :

[0098]

[0099] Where ⊙ represents the Hadamard product, and the superscript (·) * indicates conjugation;

[0100] b5) Calculation Where τ is the step size; it is adjusted according to the Armijo-Goldstein condition;

[0101] b6) Update the smart metasurface reflection phase shift in the rth iteration Among them, unit(·) means normalizing the modulus values ​​of all elements in the vector;

[0102] b7) Calculate the objective function in the rth iteration using the following formula

[0103]

[0104] b8) Judgment Is it true? If so, go to step b9); otherwise, set r = r + 1 and go to step b3);

[0105] b9) Update the smart metasurface reflection phase shift matrix obtained in the tth iteration

[0106] Step 6: Use the following formula to calculate the beamforming vector sent by the jth base station to the user in the cell after the tth iteration: And the smart metasurface reflection phase shift matrix is ​​Φ (t) The system ergodic energy efficiency evaluation value G (t) :

[0107]

[0108] in, represents the beamforming vector sent by the qth base station to its user after the tth iteration;

[0109] Step 7: Determine whether the following formula is true:

[0110]

[0111] If not, set t = t + 1 and go to step 4; otherwise, As the beamforming vector sent by the j-th base station to its user, Φ (t) As a smart metasurface reflective phase-shifting matrix.

[0112] Figure 2 The meanings of the abbreviations are as follows:

[0113] EEmax: Using the algorithm of the present invention, the transmit beamforming vector and the RIS reflection phase shift matrix at the base station are jointly optimized to maximize the system energy efficiency.

[0114] SEmax: Using the algorithm of the present invention, the transmit beamforming vector at the base station and the RIS reflection phase shift matrix are jointly optimized to maximize the system spectrum efficiency.

[0115] Random phase shift: The RIS phase shift is randomly generated, and the transmit beamforming vector at the base station still uses the algorithm of the present invention.

[0116] As can be seen from the figure above, the algorithm of the present invention significantly improves system energy efficiency compared to the random phase shift algorithm. Furthermore, compared to the SEmax algorithm, the system energy efficiency achieved by the SEmax algorithm drops sharply when the base station transmit power is too high. This is primarily because, when optimizing spectral efficiency, the base station allocates its power to signal transmission, ignoring the impact of system power consumption on overall system performance. Therefore, the research of the present invention, which optimizes system energy efficiency, is more practical.

[0117] In summary, the present invention maximizes the total energy efficiency of the system traversal by jointly designing the beamforming vector transmitted by the base station and the phase shift of the intelligent metasurface reflection, and surpasses the traditional transmission design method in terms of runtime complexity and system performance. The flow chart of a smart metasurface-assisted transmission design method with maximum energy efficiency is shown in the figure below. Figure 1 shown.

[0118] It will be understood that the present invention is described by way of some embodiments, and it will be appreciated by those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are intended to be protected by the present invention.

Claims

1. A design method for intelligent metasurface-assisted transmission with maximum energy efficiency, characterized in that: The method is targeted at a system with a total of J cells, and each cell base station deploys a uniform antenna array containing M antenna elements; in each cell, there is a single-antenna user in a weak coverage or signal blind area at the cell edge, which needs to be set at the cell edge with N=N v ×N h The intelligent metasurface with N reflective units is used to assist the user communication in the weak coverage or signal blind area at the edge of the cell. v Row N h The system consists of a series of reflection units, each of which is implemented using a PIN diode. The phase shift accuracy of each reflection unit is 2 bits, and the set of reflection phase shift values ​​is {0, π / 2, π, 3π / 2}, and the corresponding 2-bit codes are {00, 01, 11, 10}. First, the smart metasurface reflection phase shift matrix is ​​fixed, and the beamforming vectors sent by each base station are designed. Then, the beamforming vectors sent by the base station are fixed, and the smart metasurface reflection phase shift matrix is ​​optimized. The beamforming vectors sent by the base station and the smart metasurface reflection phase shift matrix are alternately optimized until the ergodic energy efficiency of the system converges to the optimal value. The method specifically comprises the following steps: Step 1: Set the convergence threshold ε and the number of iterations t = 1; initialize the beamforming vector sent by the j-th base station to the users in the cell. where j = 1,…,J,1 M×1 represents an M×1 dimensional vector with all elements equal to 1; the initial value of the smart metasurface reflection phase shift matrix Randomization is performed, diag(·) represents a diagonal matrix generated with the elements in the brackets as diagonal elements, Indicates the phase shift value of the nth reflector unit during initialization; Step 2: Calculate the smart metasurface reflection phase shift matrix obtained at the t-1th iteration Total power consumption of the smart metasurface And establish a continuous relationship between the total power consumption of the smart metasurface and the discrete phase shift, represents the phase shift value of the nth reflector unit at the t-1th iteration; Step 3: Use the following formula to calculate the beamforming vector sent by the jth base station to the user in the cell after the t-1th iteration: And the smart metasurface reflection phase shift matrix is ​​Φ (t-1) The system ergodic energy efficiency evaluation value G (t-1) : in, is the equivalent channel from the j-th base station to the user in the j-th cell after the t-1-th iteration, represents the line-of-sight path component of the channel from the jth base station to the smart metasurface, represents the line-of-sight path component from the smart metasurface to the user channel in the jth cell, represents the line-of-sight path component of the channel from the qth base station to the smart metasurface, represents the line-of-sight path component from the smart metasurface to the user channel in the qth cell, with the superscript (·) H represents the conjugate transpose, represents the beamforming vector sent by the j-th base station to its user after the t-1-th iteration, represents the beamforming vector sent by the qth base station to its user after the t-1th iteration, represents the noise power at the user in the jth cell, ν represents the efficiency of the transmitting power amplifier, P BS and P user Represent the circuit power consumption of base station and user respectively, represents the Ricean factor of the channel from the qth base station to the smart metasurface, κ j represents the Ricean factor of the channel from the smart metasurface to the user in the jth cell; Step 4: Use the smart metasurface reflection phase shift matrix Φ obtained in the t-1th iteration (t-1) and the beamforming vector sent by the jth base station to its user Calculate the beamforming vector sent by the jth base station to its user in the tth iteration Step 5: The beamforming vector calculated according to step 4 Calculate the smart metasurface reflection phase shift matrix Φ of the tth iteration (t) and the total power consumption of the smart metasurface Step 6: Use the following formula to calculate the beamforming vector sent by the jth base station to the user in the cell after the tth iteration: And the smart metasurface reflection phase shift matrix is ​​Φ (t) The system ergodic energy efficiency evaluation value G (t) : in, represents the beamforming vector sent by the qth base station to its user after the tth iteration; Step 7: Determine whether the following formula is true: If not, set t = t + 1 and go to step 4; otherwise, As the beamforming vector sent by the j-th base station to its user, Φ (t) as the smart metasurface reflection phase shift matrix; where ε represents the threshold.

2. The energy-efficient intelligent metasurface-assisted transmission design method according to claim 1 is characterized in that: In the step 2, after the t-1th iteration, the intelligent metasurface reflection phase shift matrix Total power consumption of smart metasurface under Calculated by the following formula: Among them, P static and They are the static power consumption and dynamic power consumption of the intelligent metasurface respectively; the static power consumption is the power consumption of the control circuit; the dynamic power consumption is approximately calculated using the following formula in, represents the phase shift vector of the smart metasurface reflection after the t-1th iteration, P PIN Indicates the power consumption when the PIN tube is turned on, 1 N×1 Represents an N×1-dimensional vector of all ones.

3. The energy-efficient intelligent metasurface-assisted transmission design method according to claim 1 is characterized in that: In the step 4, the smart metasurface reflection phase shift matrix Φ obtained by the t-1th iteration is used. (t-1) and the beamforming vector sent by the jth base station to its user Calculate the beamforming vector sent by the jth base station to its user in the tth iteration The following sub-steps are included: a1) Calculate the auxiliary variable in the tth iteration using the following formula a2) Calculate the auxiliary matrix of the tth iteration using the following formula Among them, I M represents the M×M-dimensional unit matrix; a3) The matrix obtained in step a2) Decompose and get the auxiliary matrix of the tth iteration Satisfy in, represents an M×M-dimensional vector; a4) Calculate the auxiliary vector in the tth iteration according to the following formula a5) Calculate the auxiliary variable λ in the tth iteration (t) , a6) Use the following formula to calculate the auxiliary variable ρ (t) 、μ (t) Perform binary search and update the beamforming vector sent by the jth base station to its user after the tth iteration in, 4. The energy-efficient intelligent metasurface-assisted transmission design method according to claim 1, characterized in that: In step 5, according to the calculated beamforming vector Calculate the intelligent metasurface reflection phase shift matrix Φ (t) , including the following sub-steps: b1) Set the inner loop convergence threshold ξ, initialize the inner loop iteration number r = 1, and calculate the phase shift matrix Φ of the intelligent metasurface. (t-1) , the phase shift vector of the smart metasurface reflection Initialize so that The nth element of is Φ (t-1) The vector consisting of the nth diagonal elements of , where n=1,…,N; b2) Calculate the objective function obtained by the r-1th iteration using the following formula: in, Re{·} means taking the real part; b3) Calculate the objective function using the following formula The gradient ξ in Euclidean space (r-1) : in, b4) Calculate the objective function according to the following formula: The Riemann gradient of : Where ⊙ represents the Hadamard product, and the superscript (·) * indicates conjugation; b5) Calculation Where τ is the step size; b6) Update the smart metasurface reflection phase shift in the rth iteration Among them, unit(·) means normalizing the modulus values ​​of all elements in the vector; b7) Calculate the objective function in the rth iteration using the following formula b8) Judgment Is it true? If so, go to step b9); otherwise, set r = r + 1 and go to step b3); b9) Update the smart metasurface reflection phase shift matrix obtained in the tth iteration

Images