CN115941010B - IRS auxiliary honeycomb removing large-scale MIMO system beam forming method based on branch definition - Google Patents
IRS auxiliary honeycomb removing large-scale MIMO system beam forming method based on branch definition Download PDFInfo
- Publication number
- CN115941010B CN115941010B CN202211396158.6A CN202211396158A CN115941010B CN 115941010 B CN115941010 B CN 115941010B CN 202211396158 A CN202211396158 A CN 202211396158A CN 115941010 B CN115941010 B CN 115941010B
- Authority
- CN
- China
- Prior art keywords
- irs
- node
- beam forming
- access point
- discrete
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 43
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 54
- 238000005457 optimization Methods 0.000 claims abstract description 40
- 238000006243 chemical reaction Methods 0.000 claims abstract description 16
- 238000013139 quantization Methods 0.000 claims abstract description 13
- 230000005540 biological transmission Effects 0.000 claims abstract description 12
- 230000009977 dual effect Effects 0.000 claims abstract description 11
- 230000010363 phase shift Effects 0.000 claims description 23
- 239000013598 vector Substances 0.000 claims description 23
- 239000011159 matrix material Substances 0.000 claims description 18
- 238000001210 attenuated total reflectance infrared spectroscopy Methods 0.000 claims description 16
- 230000001413 cellular effect Effects 0.000 claims description 7
- 230000002040 relaxant effect Effects 0.000 claims description 3
- 230000009466 transformation Effects 0.000 claims description 2
- 238000005265 energy consumption Methods 0.000 description 5
- 238000004088 simulation Methods 0.000 description 5
- 238000010586 diagram Methods 0.000 description 3
- 238000004891 communication Methods 0.000 description 2
- 230000021615 conjugation Effects 0.000 description 2
- 238000013461 design Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 238000010295 mobile communication Methods 0.000 description 2
- 238000007493 shaping process Methods 0.000 description 2
- NGHVIOIJCVXTGV-ALEPSDHESA-N 6-aminopenicillanic acid Chemical compound [O-]C(=O)[C@H]1C(C)(C)S[C@@H]2[C@H]([NH3+])C(=O)N21 NGHVIOIJCVXTGV-ALEPSDHESA-N 0.000 description 1
- 230000003321 amplification Effects 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 239000006185 dispersion Substances 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000003199 nucleic acid amplification method Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000000638 solvent extraction Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 238000012549 training Methods 0.000 description 1
- 238000011426 transformation method Methods 0.000 description 1
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
Abstract
The invention discloses an IRS auxiliary honeycomb removing large-scale MIMO system beam forming method based on branch definition, which is based on the WSR maximization problem of an IRS auxiliary CF-mMIMO system, and considers the condition that the IRS phase is more practical discrete, the constraint condition is that the maximum transmission power of an access point end and the IRS end phase are feasible, and the invention firstly decouples the original optimization problem into two sub-optimization problems through a Lagrangian dual conversion algorithm: an access terminal active beam forming problem and an IRS terminal passive beam forming problem. For the IRS end passive beam forming problem, a passive beam forming algorithm based on branch definition is provided, and then the original very challenging non-convex optimization problem is solved by alternately optimizing the two sub-problems. The passive beam forming algorithm based on the branch definition is obviously superior to the MM beam forming algorithm in a low quantization bit scene, and is more suitable for practical application scenes.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to an IRS (IRS assisted cellular removal) large-scale MIMO (multiple input multiple output) system beam forming method based on branch definition.
Background
The cellular large-scale multiple-in multiple-out (CF-mMIMO, cell Free massive Multiple Input Multiple Output) system introduces a network concept of centering on a user, so that the user can be served by a large number of surrounding Access Points (APs), the problem of serious intercell interference in the traditional cellular network is solved, and the method becomes one of key technologies in sixth generation (6G,Sixth Generation) mobile communication. With the increase of the number of APs, a great amount of energy consumption and backhaul network overhead are inevitably brought, and the energy efficiency of the system is reduced. In order to solve the problem of large energy consumption caused by the large-scale deployment of APs in CF-mMIMO, an intelligent reflection surface (IRS, intelligent Reflecting surface) is widely studied and applied as one of key technologies in 6G mobile communication. The IRS is different from the traditional amplification forwarding relay, has no receiving and transmitting functions, and only has the function of reflecting an incident signal, so that the energy consumption is low. On one hand, the IRS-assisted CF-mMIMO system can improve the energy efficiency of the system and reduce the energy consumption of the system; on the other hand, the system coverage can be increased, and reliable communication can be provided for users in a 'shadow area'.
In IRS assisted CF-mMIMO systems, how to design the phase shift parameters of the IRS so that the objective function, WSR, is at most a critical issue. Because the constraint condition of the to-be-solved optimization problem contains a non-convex Signal-to-Interference-plus-Noise Ratio (SINR) expression and a unit mode phase constraint expression, the above problem is difficult to obtain an optimal solution, and the solution has high complexity. Currently the dominant beamforming method, such as Semi-normal relaxation (SDR, semi-Definite Relaxation) beamforming, converts the original non-convex optimization problem into a Semi-normal programming (SDP, semi-Definite Programming) problem by introducing auxiliary variables, and then can be solved using a conventional convex optimization solver. Still other beamforming methods are approximated by constructing approximation sub-problems of the original problem, such as an optimization-Minimization (MM, majorization-Minimization) beamforming method, in each iteration, first constructing a surrogate objective function that satisfies the KKT (Karush-Kuhn-turner) condition, so that the upper bound of the original optimization problem can be obtained, then solving on the sub-problems, and finally converging the algorithm to obtain a sub-optimal solution of the original optimization problem.
In a traditional intelligent reflection surface assisted honeycomb removal large-scale MIMO system, in order to obtain the maximum WSR gain, when an IRS phase model is considered, the phase is assumed to be continuous, i.e. the phase of the IRS can be arbitrarily valued in [0,2 pi ]. However, in practical hardware implementation, only discrete multi-bit phases can be made, and as the number of bits increases, the implementation difficulty and cost of hardware also increase, so it is of great importance to consider a more practical intelligent reflection surface-assisted cellular massive MIMO system model.
In order to solve the problem of optimization of non-convex WSR maximization, the main methods at present are as follows: the first is to obtain a convex problem by relaxing the original problem, and then solve the problem by using a traditional convex optimization solver; the second is to construct an approximation sub-problem, and in each iteration of the algorithm, construct a sub-problem meeting the KKT condition, so that the sub-problem is solved, and finally, the sub-problem converges to obtain a sub-optimal solution of the original optimization problem. However, the above beamforming method is only applicable to the case where the IRS phase is continuous, and even if some researches consider IRS phase dispersion, the phase is relaxed to be continuous first, and then the above beamforming method is used to solve the problem. Therefore, the existing beamforming method cannot obtain the optimal solution when the IRS phase is discrete, and a global optimal beamforming method needs to be designed.
Disclosure of Invention
The invention aims at the problems and provides a beam forming method of an IRS auxiliary honeycomb removing large-scale MIMO system based on branch definition, in an IRS auxiliary CF-mMIMO system, the problem of WSR maximization optimization is solved by designing the beam forming method, a more practical IRS auxiliary CF-mMIMO system model is considered, and particularly, the condition that IRS phases are discrete rather than continuous is considered. Aiming at the practical system model under consideration, the WSR maximization optimization problem is firstly provided, the objective function is WSR, the constraint condition is AP maximum transmission energy and IRS phase constraint, and a globally optimal beamforming algorithm is provided to solve the non-convex WSR maximization optimization problem.
The invention provides an IRS auxiliary honeycomb removing large-scale MIMO system beam forming method based on branch definition, which comprises the following steps:
constructing an IRS auxiliary honeycomb-removing large-scale MIMO system model, wherein the IRS auxiliary honeycomb-removing large-scale MIMO system model comprises M access points which are provided with N antennas, K single-antenna users and R IRS, phase shift parameters of the IRS are set to be discrete, and a discrete set with the phase shift of each unit of the IRS being advisable is obtained;
The WSR maximization problem P1 of the IRS auxiliary honeycomb removal large-scale MIMO system model is determined, and specifically comprises the following steps:
taking the precoding matrixes of all access points and the phase shift matrixes of all IRSs as decision variables, taking WSR maximization as an optimization target, and limiting a precoding vector absolute value threshold value, which is used as a WSR maximization problem P1, that the sum of the precoding vector absolute values from each access point to all users cannot exceed the access point;
the optimization problem P2 is obtained by sequentially carrying out Lagrangian dual conversion and secondary conversion on the WSR maximization problem P1;
The passive beamforming algorithm based on the branch definition solves to obtain a global optimal solution of an optimization problem P2, and the passive beamforming algorithm based on the branch definition specifically comprises the following steps:
Establishing a search tree , for each node associated with a feasible discrete set in/> , solving a lower bound and an upper bound of the node, wherein the feasible discrete set represents a set of discrete values that can be taken by all IRS units in algorithm iterations;
In each iteration, selecting a father node, branching the father node into two child nodes according to node branching rules, and respectively solving the lower bound and the upper bound of the two child nodes;
The upper limit of the search tree is updated using a boundary update rule, and as the number of iterations increases, when the difference between the upper and lower bounds is below the allowable error, then the solution is solved to obtain the globally optimal solution for the optimization problem P2.
Further, in the process of constructing the IRS-assisted cellular massive MIMO system model, the signal-to-interference-and-noise ratio SINR k of the kth user is determined according to the equivalent channel from the access point to the kth user and the precoding vector, where the specific expression is as follows:
Wherein represents an equivalent channel from M access points to the kth user, represents a precoding vector from M access points to the kth user, represents a precoding vector from M access points to the ith user, and σ 2 represents a variance of noise distribution.
Further, the specific expression of the WSR maximization problem P1 is:
P1:
Wherein decision variable represents the precoding matrix of all access points, decision variable represents the phase shift matrix of all IRSs,/> represents the weight of the kth user, SINR k represents the signal-to-interference-and-noise ratio of the kth user, w m,k represents precoding of the mth access point to the kth user,/> represents the set of access points, θ r,u represents the phase shift of the u-th element of the nth IRS,/> represents the set of IRSs,/> represents the set of elements of the IRSs, ρ max represents the maximum downlink transmission energy of each access point, and/> represents the discrete set that is desirable for θ r,u.
Further, the optimizing problem P2 is obtained by sequentially performing lagrangian dual conversion and secondary conversion on the WSR maximizing problem P1, which specifically includes:
p1 is decoupled by lagrangian dual conversion methods as:
P1.1:
wherein, the objective function is an introduced K-dimensional auxiliary variable,/> represents an equivalent channel from M access points to the kth user,/> represents a precoding vector from M access points to the kth user, and represents a precoding vector from M access points to the ith user;
by secondary transformation, P1.1 is simplified to obtain
P1.2:
Wherein qi,k(Θ)＝ai,k+θHbi,k,μk＝ηk(1+γk),θ denotes a diagonal element of the phase shift matrix Θ, Fm denotes channels between the mth access point and all IRSs, and g k denotes channels between all IRSs and kth users;
Further simplifying P1.2, the final optimization problem P2 is:
P2:
Wherein f 3(θ)＝θHΛθ-2Re{θHν}, wherein b k,k is the value of i=k in b i,k,/> denotes conjugated to a i,k. .
Further, the passive beam forming algorithm based on the branch definition comprises the following specific steps:
Determining the lower and upper bounds of the optimization problem P2:
let Θ=θ H, convert the optimization problem P2 into:
P2.1:
diag(Θ)＝1RU,
Θ＝θθH,
Where g (Θ, θ) =tr (ΛΘ) -2Re { θ Hν}, represents the set of discrete values that the unit of each IRS can take, RU is the dimension of θ;
relaxing the constraint, converting P2.1 to P2.2:
P2.2:
diag(Θ)＝1RU,
Θ≥θθH,
Wherein the set of feasible regions is: by/> let θ t be the optimal solution for P2.2, then the lower bound/> for P2.1
Projecting the obtained solution theta t onto to obtain/> unit as a function, wherein/> represents a set of discrete values that are desirable for all IRS units in the t-th algorithm iteration for an N-dimensional vector x= [ x 1,…xN]T,/> P2.1 upper bound/> ;
node division: in the t iteration, selecting the ith ＊ node with the smallest lower bound for division, and uniformly dividing a feasible region corresponding to the node with the smallest lower bound into a left part and a right part, namely/> and/> , wherein:
Updating the boundary: for two nodes obtained by node division, respectively solving to obtain the corresponding to update the upper bound according to the smaller values of/> and/> , wherein the lower bound and the optimal solution are the corresponding g (Θ t,θt) and/>, respectively
Further, the passive beam forming algorithm based on branch definition comprises the following specific implementation processes:
step 1, setting iteration times t=0, and threshold limiting parameters epsilon=10 -4;
step 2, assigning initial values to a discrete value set A t which can be taken by all IRS units in algorithm iteration;
step 3, calculating an initial solution { theta t,Θt } through P2.2;
step 4), obtaining a solution of P2.1 through theta t＝unit(θt);
Step 5, calculating the upper bound/>, of the lower bound of P2.1
Step 6, adding corresponding to the node into the search tree/> ;
step 7, let t=t+1;
Step 8, selecting a node with the smallest lower bound/> in the search tree ;
Step 9, deleting the node with the minimum lower bound ;
Step 10, dividing/> corresponding to the node with the smallest lower bound into two subsets/> and/>
Step 11, solving/> and/> corresponding to P2.2 for
Step 12, updating the optimal solution corresponding to/> to/>, if is present
Step 13, solving/> and/> corresponding to P2.2 for
Step 14, if is yes, updating the optimal solution corresponding to/> to be/>
Step 15, adding and/> corresponding to the two branch nodes into/>
Step 16, if returns to step 6-step 15, if/> outputs the optimal result θ ★＝θt.
The invention provides an IRS auxiliary honeycomb-removing large-scale MIMO system beam forming method based on branch definition, which establishes the WSR maximization problem of an IRS auxiliary CF-mMIMO system, considers the situation that the IRS phase is more practical discrete, and has the constraint condition that the maximum transmission power of an AP end and the IRS end phase are feasible. The method comprises the steps of firstly decoupling an original optimization problem into two sub-optimization problems through a Lagrangian dual conversion algorithm: an AP end active beam forming problem and an IRS end passive beam forming problem. For the IRS end passive beam forming problem, a passive beam forming algorithm based on branch definition is provided, and then the original very challenging non-convex optimization problem is solved by alternately optimizing the two sub-problems. Simulation results show that the passive beam forming algorithm provided by the invention is obviously superior to the MM beam forming algorithm in a low quantization bit scene, and is more suitable for practical application scenes.
Drawings
Fig. 1 is a schematic flow chart of an IRS-assisted cellular-removal massive MIMO system beamforming method based on branch definition in an embodiment of the present invention;
FIG. 2 is a schematic diagram of an IRS-assisted CF-mMIMO system model in an embodiment of the invention;
FIG. 3 is a schematic diagram of IRS-assisted CF-mMIMO system channels in an embodiment of the present invention;
FIG. 4 is a graph of WSR versus number of algorithm iterations in an embodiment of the present invention;
fig. 5 is a graph of WSR as a function of quantization bit number in an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting thereof. It should be further noted that, for convenience of description, only some, but not all of the structures related to the present invention are shown in the drawings.
Before discussing exemplary embodiments in more detail, it should be mentioned that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although a flowchart depicts steps as a sequential process, many of the steps may be implemented in parallel, concurrently, or with other steps. Furthermore, the order of the steps may be rearranged. The process may be terminated when its operations are completed, but may have additional steps not included in the figures. The processes may correspond to methods, functions, procedures, subroutines, and the like.
As shown in fig. 1, an IRS-assisted de-cellular massive MIMO system beamforming method based on branch definition according to an embodiment includes the following steps:
constructing an IRS auxiliary honeycomb-removing large-scale MIMO system model, wherein the IRS auxiliary honeycomb-removing large-scale MIMO system model comprises M access points which are provided with N antennas, K single-antenna users and R IRS, phase shift parameters of the IRS are set to be discrete, and a discrete set with the phase shift of each unit of the IRS being advisable is obtained;
The WSR maximization problem P1 of the IRS auxiliary honeycomb removal large-scale MIMO system model is determined, and specifically comprises the following steps:
taking the precoding matrixes of all access points and the phase shift matrixes of all IRSs as decision variables, taking WSR maximization as an optimization target, and limiting a precoding vector absolute value threshold value, which is used as a WSR maximization problem P1, that the sum of the precoding vector absolute values from each access point to all users cannot exceed the access point;
the optimization problem P2 is obtained by sequentially carrying out Lagrangian dual conversion and secondary conversion on the WSR maximization problem P1;
The passive beamforming algorithm based on the branch definition solves to obtain a global optimal solution of an optimization problem P2, and the passive beamforming algorithm based on the branch definition specifically comprises the following steps:
Establishing a search tree , for each node associated with a feasible discrete set in/> , solving a lower bound and an upper bound of the node, wherein the feasible discrete set represents a set of discrete values that can be taken by all IRS units in algorithm iterations;
In each iteration, selecting a father node, branching the father node into two child nodes according to node branching rules, and respectively solving the lower bound and the upper bound of the two child nodes;
The upper limit of the search tree is updated using a boundary update rule, and as the number of iterations increases, when the difference between the upper and lower bounds is below the allowable error, then the solution is solved to obtain the globally optimal solution for the optimization problem P2.
The specific implementation process is as follows:
(1) Intelligent reflection surface auxiliary honeycomb removing large-scale MIMO system model
The intelligent reflection surface of the embodiment assists in removing the honeycomb large-scale MIMO system model, the system structure is shown in figure 2, the system model comprises M APs, each AP has N antennas, and K single-antenna users. To further increase the capacity of the system and reduce the energy consumption, R IRSs are introduced, where the number of units of each IRS is U, each IRS having a controller connected to it to control the phase shift of each unit. Let represent the index set of the cell, user, of AP, IRS, IRS, respectively. In the embodiment, the system works in a time division duplex mode and comprises three stages: uplink training, downlink data transmission, uplink data transmission.
In a specific implementation, the phase shift parameter of the IRS is set to be discrete rather than continuous, taking into account the actual hardware limitations. Let L denote the number of bits per cell, then each cell may be configured to l=2 l possible quantization levels. Let represent the phase shift matrix of the r IRS and can be expressed as:
Θr＝diag(θr,1,…,θr,U) (1)
where θ r,u represents the phase shift of the u-th element of the r-th IRS, the discrete set that θ r,u would take is:
In the IRS assisted CF-mMIMO system, each AP needs to estimate the channels of all users, specifically, the channel between the mth AP and the kth user is composed of the direct channel from the mth AP to the kth user and the r×u reflection channel, and the equivalent channel diagram is shown in fig. 3, and the equivalent channel from the mth AP to the kth user can be given by the following formula:
Wherein represents a direct channel from the mth AP to the kth user,/> and/> represent a channel between the mth AP and the r IRS and a channel between the r IRS and the kth user, respectively.
The embodiment mainly considers the downlink transmission scenario, and during downlink transmission, the signal x m transmitted by the mth AP to all users can be expressed as:
Where represents a precoding vector from the mth AP to the ith user, and s i represents a signal transmitted to the ith user. The signal received by the kth user can be expressed as:
Wherein represents the equivalent channels and precoding vectors of all APs to the kth user, respectively,/> represents the noise energy received by the kth user, wherein σ 2 represents the variance of the noise distribution. And w i should satisfy the energy constraint of each AP, let ρ max represent the maximum downlink transmission energy per AP, then:
Re-express the signal received by the user as:
Then, the Signal-to-interference-plus-noise Ratio (SINR) of the kth user can be expressed as:
(2) WSR maximization problem of intelligent reflection surface auxiliary honeycomb removal large-scale MIMO system
The WSR for all users can be expressed as:
Where represents the weight of the kth user, the WSR maximum problem for all end users can be expressed as:
wherein decision variables represent the precoding matrix of all APs and the phase shift matrix of all IRSs, respectively. It can be observed that the objective function is non-convex and that the two decision variables are coupled to each other, P1.1 can be decoupled by the lagrangian dual conversion method as:
wherein the objective function f (Θ, W, γ) is:
Where γ= [ γ 1,γ2,…,γK]T is the introduced K-dimensional auxiliary variable, f k (Θ, W) can be expressed as:
fixed (Θ, W), let calculate as:
by fixing (W, γ), P1.2 can be expressed as:
μk＝ηk(1+γk) and then further simplified by using a secondary transformation method to obtain:
Wherein:
In the equation (17), the argument Θ for the function on the left side of the equation is expressed as Θ included in the right end .
Let further reduce q i,k (Θ) to:
qi,k(Θ)＝ai,k+θHbi,k (18)
Where represents the diagonal elements of the phase shift matrix Θ,1 RU is an all 1 vector of length RU, and/> bi,k appearing in equation (17) represents the case where i is any one of 1-K for the kth user (K also being a value from 1-K), b k,k is the case where i=k for the kth user, a i,k is the same as a k,k. Fixing Θ, the optimal ζ= [ ζ 1,…,ξK]T ] can be obtained, where ζ k is:
fixing xi, can obtain:
further, the last term of equation (17) can be reduced to:
Bringing (21) into (20) can be achieved:
f2(Θ)＝-θHΛθ+2Re{θHν}-δ (22)
Wherein:
Where [. Cndot. * represents conjugation, i.e. represents conjugation with a i,k, then P2.2 can be converted into:
Where f 3(θ)＝θHΛθ-2Re{θH v }.
(3) Global optimal beamforming algorithm
In order to solve P2.3, a global optimal passive beamforming algorithm based on Branch definition (BnB, branch and Bound) is proposed to solve the problem, and the algorithm can obtain a global optimal solution of the passive beamforming problem.
In a specific implementation, represents a set of discrete values that are desirable for each IRS unit, and/() represents a set of discrete values that are desirable for all IRS units in the t-th algorithm iteration. The core idea of the BnB algorithm builds a search tree/> for each node associated with a feasible discrete set/> in/> , and can find the lower bound and the upper bound of the node. In each iteration, a parent node is selected and is branched into two child nodes according to node branching rules. Then, the lower bound and the upper bound of the two child nodes are solved separately. Next, the upper bound of the search tree/> is updated using the boundary update rules. As the number of iterations increases, the difference between the upper and lower bounds is progressively lower than the allowable error e. The details of the BnB algorithm are as follows:
① Lower and upper bounds of optimization problem
First, P2.3 is converted into:
P2.4:
Where RU is the dimension of θ, θ i is the i-th dimension therein, let θ=θ H, then P2.4 is equivalent to:
Where g (Θ, θ) =tr (ΛΘ) -2re { θ H v }, to get the lower bound of P2.5, the constraint is relaxed, P2.5 can be converted into:
Where Tr is the trace operation of the matrix, Θ++θθ H represents that the matrix Θ - θ H is a semi-positive definite matrix, where the set of feasible domains is:
And for all j let θ t be the optimal solution for P2.6, then the lower bound for P2.5 then projects the resulting solution θ t onto/> to get/> unit defined as a function that is unitary in size for each dimension of vector x for an N-dimensional vector x= [ x 1,…xN]T,/>.
Then the upper bound of P2.5
② Node partitioning
In the t iteration, selecting the ith ＊ node with the smallest lower bound for division, and uniformly dividing a feasible region corresponding to the node into a left part and a right part, namely/> and/> , wherein:
③ Updating boundaries
For the two nodes obtained in the last step, the corresponding can be respectively solved to obtain the lower bound and the corresponding optimal solution of the upper bound and the lower bound are respectively corresponding g (Θ t,θt) and/>, and then the upper bound is updated according to the smaller values of/> and/>
The global optimal beamforming algorithm based on the branch definition algorithm is summarized in algorithm 1 as follows:
in order to better embody the effect of the invention, the embodiment verifies the proposed beam forming algorithm based on branch definition through simulation and simulation to solve the WSR maximization problem. Assuming that there are 6 APs in the scene, each AP has 4 antennas, 2 IRSs, and each IRS unit number is 120,4 users. The channel model considers direct path components and indirect path components assuming a maximum transmission power of 5dbm per AP. Consider the practical case where the IRS phase is discrete 4 bits and assume that the weights of all users are 1. In the simulation, the realization of active beam shaping at the AP end by using a weighted minimum mean square error (WMMSE, weighted Minimum Mean Square Error) algorithm is considered; for passive beam forming of the IRS end, a proposed algorithm based on branch definition and a MM algorithm for comparison are considered; and the IRS is considered to be closed, and only the situation of active beam shaping at the AP end is taken as a reference. Fig. 4 shows the variation of WSR with the number of iterations of the joint beamforming algorithm. For the case of IRS off, WSR is a straight line. Both curves of the joint beamforming can converge quickly, and the WSR is significantly higher than the IRS closed condition, which illustrates the effectiveness of the IRS end passive beamforming. In addition, the beam forming algorithm based on the branch definition has obvious WSR gain compared with the MM beam forming algorithm, and the global optimality of the beam forming algorithm based on the branch definition is verified in terms of performance.
As shown in fig. 5, which shows the change of WSR with the IRS quantization bit number, it can be observed that the slopes of the two curves gradually decrease with the increase of the quantization bit number, because the WSR gain brought by the increase of the quantization bit number gradually approaches the case where the IRS phase is continuous (i.e., the quantization bit number is infinite). In addition, when the number of the quantization bits is 1, the passive beamforming algorithm based on the branch definition has remarkable gain relative to the passive beamforming algorithm based on the MM, which proves that the passive beamforming algorithm based on the branch definition provided by the invention is more applicable in a low quantization bit scene, and the low quantization bits are also helpful for reducing the difficulty of actual hardware design and the calculation time of the beamforming algorithm.
According to the IRS auxiliary honeycomb-removing large-scale MIMO system beam forming method based on branch definition, the WSR maximization problem of the IRS auxiliary CF-mMIMO system is established, the situation that the IRS phase is more practical discrete is considered, and constraint conditions are that the maximum transmission power of an AP end and the IRS end phase are feasible. The method comprises the steps of firstly decoupling an original optimization problem into two sub-optimization problems through a Lagrangian dual conversion algorithm: an AP end active beam forming problem and an IRS end passive beam forming problem. For the IRS end passive beam forming problem, a passive beam forming algorithm based on branch definition is provided, and then the original very challenging non-convex optimization problem is solved by alternately optimizing the two sub-problems. Simulation results show that the passive beam forming algorithm provided by the invention is obviously superior to the MM beam forming algorithm in a low quantization bit scene, and is more suitable for practical application scenes.
In this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, or apparatus.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.
Claims (2)
1. The IRS assisted cellular removal large-scale MIMO system beam forming method based on branch definition is characterized by comprising the following steps:
constructing an IRS auxiliary honeycomb-removing large-scale MIMO system model, wherein the IRS auxiliary honeycomb-removing large-scale MIMO system model comprises M access points which are provided with N antennas, K single-antenna users and R IRS, phase shift parameters of the IRS are set to be discrete, and a discrete set with the phase shift of each unit of the IRS being advisable is obtained;
The WSR maximization problem P1 of the IRS auxiliary honeycomb removal large-scale MIMO system model is determined, and specifically comprises the following steps:
Taking the precoding matrixes of all access points and the phase shift matrixes of all IRSs as decision variables, taking WSR maximization as an optimization target, and limiting a precoding vector absolute value threshold value, which is used as a WSR maximization problem P1, that the sum of the precoding vector absolute values from each access point to all users cannot exceed the access point, wherein WSR represents the weighted sum rate;
the optimization problem P2 is obtained by sequentially carrying out Lagrangian dual conversion and secondary conversion on the WSR maximization problem P1;
The passive beamforming algorithm based on the branch definition solves to obtain a global optimal solution of an optimization problem P2, and the passive beamforming algorithm based on the branch definition specifically comprises the following steps:
Establishing a search tree , for each node associated with a feasible discrete set in/> , solving a lower bound and an upper bound of the node, wherein the feasible discrete set represents a set of discrete values that can be taken by all IRS units in algorithm iterations;
In each iteration, selecting a father node, branching the father node into two child nodes according to node branching rules, and respectively solving the lower bound and the upper bound of the two child nodes;
Updating the upper limit of the search tree by using a boundary updating rule, and solving to obtain a global optimal solution of the optimization problem P2 when the difference between the upper limit and the lower limit is lower than an allowable error along with the increase of iteration times;
In the process of constructing the IRS auxiliary honeycomb-removing large-scale MIMO system model, the SINR k of the kth user is determined according to the equivalent channel from the access point to the kth user and the precoding vector, and the specific expression is as follows:
wherein represents the equivalent channel from the M access points to the kth user, wherein/> represents the direct channel from the mth access point to the kth user; f m,r denotes a channel between an mth access point and an mth IRS, Θ r denotes a phase shift matrix of the mth IRS, g r,k denotes a channel between the mth IRS and a kth user,/> denotes a precoding vector from the M access point to the kth user, w m,k denotes a precoding vector between the mth access point and the kth user, and σ 2 denotes a variance of noise distribution;
The specific expression of the WSR maximization problem P1 is as follows:
P1:
Wherein decision variable represents the precoding matrix of all access points, decision variable represents the phase shift matrix of all IRSs,/> represents the weight of the kth user, SINR k represents the signal-to-interference-and-noise ratio of the kth user, w m,k represents precoding of the mth access point to the kth user,/> represents the set of access points, θ r,u represents the phase shift of the u-th element of the nth IRS,/> represents the set of IRSs,/> represents the set of elements of the IRSs, ρ max represents the maximum downlink transmission energy of each access point,/> represents the discrete set that is desirable for θ r,u;
The optimization problem P2 is obtained by sequentially carrying out Lagrangian dual conversion and secondary conversion on the WSR maximization problem P1, and specifically comprises the following steps:
p1 is decoupled by lagrangian dual conversion methods as:
P1.1:
Wherein, the objective function γ＝[γ1,γ2,…,γK]T is an introduced K-dimensional auxiliary variable,/> represents precoding vectors from M access points to the ith user;
by secondary transformation, P1.1 is simplified to obtain
P1.2:
Wherein ξ＝[ξ1,…,ξK]T of the above-mentioned components are combined,
qi,k(Θ)＝ai,k+θHbi,k,μk＝ηk(1+γk),qk,k(Θ) Q i,k (Θ) where i=k, θ represents a diagonal element of the phase shift matrix Θ,/> Fm represents channels between the mth access point and all IRSs, g k represents channels between all IRSs and the kth user, and w i,m represents a precoding vector between the ith access point and the mth user;
Further simplifying P1.2, the final optimization problem P2 is:
P2:
Wherein f 3(θ)＝θHΛθ-2Re{θHν}, wherein b k,k is the value of i=k in b i,k,/> denotes conjugated to a i,k;
The passive beam forming algorithm based on branch definition specifically comprises the following steps:
Determining the lower and upper bounds of the optimization problem P2:
let Θ=θ H, convert the optimization problem P2 into:
P2.1:
diag(Θ)＝1RU,
Θ＝θθH,
Where g (Θ, θ) =tr (ΛΘ) -2Re { θ Hν}, represents a set of discrete values that are desirable for each unit of IRS, RU is a dimension of θ, L represents a quantization level that each unit of IRS can configure, and θ i represents a phase angle of an i-th unit of IRS;
relaxing the constraint, converting P2.1 to P2.2:
P2.2:
diag(Θ)＝1RU,
Θ≥θθH,
Wherein the set of feasible regions is: the/> Tr represents the trace operation of the matrix, the Θ is larger than or equal to the θ H, the matrix Θ - θ H is a semi-positive definite matrix, and the θ t is the optimal solution of P2.2, so that the lower bound/>, of P2.1
Projecting the obtained solution theta t onto to obtain/> unit as a function, wherein/> represents a set of discrete values that are desirable for all IRS units in the t-th algorithm iteration for an N-dimensional vector x= [ x 1,…xN]T,/> P2.1 upper bound/> ;
Node division: in the t iteration, selecting the ith ★ node with the smallest lower bound for division, and uniformly dividing a feasible region corresponding to the node with the smallest lower bound into a left part and a right part, namely/> and/> , wherein: /(I)
Updating the boundary: for two nodes obtained by node division, respectively solving to obtain the corresponding updating upper bounds according to the smaller values of/> and/> , wherein the lower bounds and the optimal solutions are the corresponding g (Θ t,θt) and/> Θt respectively, the updating values of the matrix Θ at the t-th iteration are respectively obtained, the/> and/> respectively represent the θ left boundary, the θ left boundary and the θ right boundary of the current node, and t represents the number of times of the current iteration.
2. The branch definition-based IRS auxiliary cellular massive MIMO system beamforming method according to claim 1, wherein the specific implementation procedure of the branch definition-based passive beamforming algorithm is as follows:
step 1, setting iteration times t=0, and threshold limiting parameters epsilon=10 -4;
Step 2, assigning initial values to a discrete value set which can be taken by all IRS units in algorithm iteration;
step 3, calculating an initial solution { theta t,Θt } through P2.2;
step 4, obtaining a solution of P2.1 through ;
Step 5, calculating the upper bound/>, of the lower bound of P2.1
Step 6, adding corresponding to the node into the search tree/> ;
step 7, let t=t+1;
Step 8, selecting a node with the smallest lower bound/> in the search tree ;
step 9, deleting the node with the minimum lower bound ;
Step 10, dividing/> corresponding to the node with the smallest lower bound into two subsets/> and/>
Step 11, solving/> and/> corresponding to P2.2 for
Step 12, updating the optimal solution corresponding to/> to/>, if is present
Step 13, solving/> and/> corresponding to P2.2 for
Step 14, if is yes, updating the optimal solution corresponding to/> to be/>
Step 15, adding and/> corresponding to the two branch nodes into/>
Step 16, if returns to step 6-step 15, if/> outputs the optimal result θ ★＝θt.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211396158.6A CN115941010B (en) | 2022-11-09 | 2022-11-09 | IRS auxiliary honeycomb removing large-scale MIMO system beam forming method based on branch definition |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211396158.6A CN115941010B (en) | 2022-11-09 | 2022-11-09 | IRS auxiliary honeycomb removing large-scale MIMO system beam forming method based on branch definition |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN115941010A CN115941010A (en) | 2023-04-07 |
| CN115941010B true CN115941010B (en) | 2024-04-16 |
Family
ID=86651827
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211396158.6A Active CN115941010B (en) | 2022-11-09 | 2022-11-09 | IRS auxiliary honeycomb removing large-scale MIMO system beam forming method based on branch definition |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115941010B (en) |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112073107A (en) * | 2020-09-17 | 2020-12-11 | 南通大学 | Multi-group and multicast combined beam forming algorithm design based on intelligent reflecting surface |
| CN113179109A (en) * | 2021-04-26 | 2021-07-27 | 南京盛航海运股份有限公司 | Honeycomb-removing large-scale MIMO uplink spectrum efficiency optimization method |
| CN113225108A (en) * | 2021-03-18 | 2021-08-06 | 北京邮电大学 | Robust beam forming method for assisting multi-cell coordinated multi-point transmission by intelligent reflector |
| CN113315547A (en) * | 2021-05-28 | 2021-08-27 | 北京邮电大学 | Robust joint transmission beam optimization method for intelligent reflecting surface assisted multiple cells |
| CN114268350A (en) * | 2021-11-10 | 2022-04-01 | 华南理工大学 | Robust beam forming design method under non-ideal channel in intelligent reflector auxiliary communication |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111355520B (en) * | 2020-03-10 | 2022-03-08 | 电子科技大学 | Design method of intelligent reflection surface assisted terahertz safety communication system |
-
2022
- 2022-11-09 CN CN202211396158.6A patent/CN115941010B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112073107A (en) * | 2020-09-17 | 2020-12-11 | 南通大学 | Multi-group and multicast combined beam forming algorithm design based on intelligent reflecting surface |
| CN113225108A (en) * | 2021-03-18 | 2021-08-06 | 北京邮电大学 | Robust beam forming method for assisting multi-cell coordinated multi-point transmission by intelligent reflector |
| CN113179109A (en) * | 2021-04-26 | 2021-07-27 | 南京盛航海运股份有限公司 | Honeycomb-removing large-scale MIMO uplink spectrum efficiency optimization method |
| CN113315547A (en) * | 2021-05-28 | 2021-08-27 | 北京邮电大学 | Robust joint transmission beam optimization method for intelligent reflecting surface assisted multiple cells |
| CN114268350A (en) * | 2021-11-10 | 2022-04-01 | 华南理工大学 | Robust beam forming design method under non-ideal channel in intelligent reflector auxiliary communication |
Also Published As
| Publication number | Publication date |
|---|---|
| CN115941010A (en) | 2023-04-07 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN113225108B (en) | Robust beam forming method for intelligent reflector-assisted multi-cell coordinated multi-point transmission | |
| CN111865387A (en) | Beam forming design method of intelligent reflector assisted wireless communication system | |
| CN113873575B (en) | Intelligent reflector assisted non-orthogonal multiple access unmanned aerial vehicle air-ground communication network energy-saving optimization method | |
| CN113193894A (en) | Reconfigurable intelligent surface-assisted multi-user MISO downlink wireless communication spectrum efficiency joint optimization method | |
| Liu et al. | Two-timescale hybrid compression and forward for massive MIMO aided C-RAN | |
| CN114070365B (en) | Intelligent reflection surface assisted low-radio-frequency-complexity multi-user MIMO uplink spectrum efficiency optimization method | |
| CN111726156A (en) | NOMA-based resource allocation method and device | |
| CN113949607B (en) | Robust wave beam design method for intelligent reflection surface cell-free system | |
| Tang et al. | User selection and power minimization in full-duplex cloud radio access networks | |
| CN113949427B (en) | Multi-user wireless network security energy efficiency optimization design method and system | |
| CN115941010B (en) | IRS auxiliary honeycomb removing large-scale MIMO system beam forming method based on branch definition | |
| CN111740766A (en) | Codebook-based beam design method and device | |
| CN114785387B (en) | Intelligent omnidirectional plane-assisted multi-user MISO downlink weighting and rate optimization method | |
| CN112584403B (en) | Joint optimization method for maximum rate and minimum power of NOMA small cell | |
| CN111726157B (en) | Adaptive beam forming method for aviation communication | |
| CN115733533B (en) | IRS auxiliary honeycomb removing large-scale MIMO system beam forming method based on manifold | |
| Yang et al. | RIS-aided constant-envelope beamforming for multiuser wireless power transfer: A max-min approach | |
| Wang et al. | Beamforming Design for RIS-Aided AF Relay Networks | |
| CN114826833B (en) | Communication optimization method and terminal for CF-mMIMO in IRS auxiliary MEC | |
| CN114025368B (en) | Distributed intelligent reflection surface assisted D2D communication method and system | |
| CN117793758B (en) | Multi-variable joint optimization method in RIS-assisted NOMA system | |
| CN117062148A (en) | Interference processing method based on intelligent reflection surface auxiliary multi-cellular heterogeneous network | |
| CN117375683A (en) | Communication-centric RIS-assisted non-cellular ISAC network joint beam forming method | |
| CN114172763B (en) | Pilot frequency optimization design method and device for hybrid large-scale MIMO system | |
| CN116470938B (en) | IRS auxiliary communication service quality fairness combined beam forming optimization method and device |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| CB02 | Change of applicant information | ||
| CB02 | Change of applicant information |
Address after: 518000 Taoyuan Street, Nanshan District, Shenzhen City, Guangdong Province Applicant after: Harbin University of Technology (Shenzhen) (Shenzhen Institute of science and technology innovation Harbin University of Technology) Address before: 518000 Taoyuan Street, Nanshan District, Shenzhen City, Guangdong Province Applicant before: HARBIN INSTITUTE OF TECHNOLOGY (SHENZHEN) |
|
| GR01 | Patent grant | ||
| GR01 | Patent grant |