CN115941010A - IRS (intelligent resilient system) assisted de-cellular large-scale MIMO (multiple input multiple output) system beam forming method based on branch definition - Google Patents
IRS (intelligent resilient system) assisted de-cellular large-scale MIMO (multiple input multiple output) system beam forming method based on branch definition Download PDFInfo
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Abstract
The invention discloses an IRS assisted de-cellular large-scale MIMO system beam forming method based on branch definition, which is based on the WSR maximization problem of an IRS assisted CF-mMIMO system, considers the condition that the IRS phase is more practical discrete, and takes the constraint conditions of the maximum transmission power of an access point end and the feasible solution of the IRS phase as constraint conditions, and firstly decouples the original optimization problem into two sub-optimization problems through a Lagrange dual transformation algorithm: the access end active beam forming problem and the IRS end passive beam forming problem. For the passive beam forming problem of the IRS terminal, a passive beam forming algorithm based on branch definition is provided, and then the original non-convex optimization problem which is very challenging is solved by alternately optimizing two sub-problems. The passive beam forming algorithm based on branch definition 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.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to an IRS (intelligent resilient station) assisted de-cellular large-scale MIMO (multiple input multiple output) system beam forming method based on branch definition.
Background
A Cell Free large Multiple Input Multiple Output (CF-mimo) system introduces a network concept of "centering on users", so that users can be served by a large number of Access Points (APs) around, the problem of serious intercell interference in the conventional cellular network is solved, and the system becomes one of key technologies in the sixth Generation (6 g, six Generation) mobile communication. As the number of APs increases, a large 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 a large number of AP deployed in CF-mMIMO, an Intelligent Reflection Surface (IRS) is widely researched and applied as one of key technologies in 6G mobile communication. The IRS is different from the traditional amplifying and forwarding relay, does not have receiving and transmitting functions, and only has the function of reflecting incident signals, so that the energy consumption is less. The CF-mMIMO system assisted by the IRS can improve the energy efficiency of the system and reduce the energy consumption of the system on one hand; on the other hand, the coverage area of the system can be increased, and reliable communication is provided for users in a 'shadow area'.
In an IRS-assisted CF-mimo system, how to design the phase shift parameters of the IRS such that the objective function, i.e. WSR, is maximized is a key issue. Because the constraint conditions of the optimization problem to be solved contain non-convex Signal-to-Interference-plus-noise ratio (SINR) expressions and unit modulus phase constraint expressions, the problem is difficult to obtain an optimal solution, and the complexity of the solution is high. Currently, the main beamforming method is, for example, semi-Definite Relaxation (SDR) beamforming, and by introducing additional variables, the method converts an original non-convex optimization problem into a Semi-Definite Programming (SDP) problem, and then can solve the problem by using a conventional convex optimization solver. Some beamforming methods are approximate solutions by constructing approximation subproblems of the original problem, such as an optimization-Minimization (MM) beamforming method, in each iteration, a substitute objective function satisfying KKT (Karush-Kuhn-Tucker) conditions is first constructed, so that an upper bound of the original optimization problem can be obtained, then solutions are performed on the subproblems, and finally algorithm convergence obtains a suboptimal solution of the original optimization problem.
In the traditional intelligent reflective surface assisted de-cellular massive MIMO system, much existing work is to obtain the maximum WSR gain, and when considering the IRS phase model, the phase is assumed to be continuous, that is, the IRS phase can be arbitrarily set within [0,2 pi ]. However, in actual hardware implementation, only discrete multi-bit phases can be achieved, and as the number of bits increases, the difficulty and cost of hardware implementation also increase, so that it is of great significance to consider a more practical intelligent reflective surface-assisted cellular massive MIMO system model.
To solve the non-convex WSR maximization optimization problem, there are two main methods at present: the first method is to obtain a convex problem by relaxing the original problem and then solve the convex problem by using a traditional convex optimization solver; and secondly, constructing an approximate subproblem, and constructing a subproblem meeting the KKT condition in each iteration of the algorithm, so that the subproblem is solved, and finally, convergence is carried out to obtain a suboptimal solution of the original optimization problem. However, the above beamforming method is only suitable for the case where the IRS phase is continuous, and even some studies consider the IRS phase dispersion, the case where 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 globally optimal beamforming method needs to be designed.
Disclosure of Invention
Aiming at the problems, the invention provides an IRS-assisted de-cellular massive MIMO system beam forming method based on branch definition, in an IRS-assisted CF-mMIMO system, the WSR maximization optimization problem is solved by designing the beam forming method, a more practical IRS-assisted CF-mMIMO system model is considered, and particularly, the IRS phase is considered to be discrete rather than continuous. Aiming at a considered practical system model, firstly, a WSR (wireless sensor network) maximization optimization problem is provided, an objective function is WSR, constraint conditions are AP (access point) maximum transmission energy and IRS (infrared receiver station) phase constraint, and a globally optimal beam forming algorithm is provided to solve the non-convex WSR maximization optimization problem.
The invention provides an IRS-assisted de-cellular massive MIMO system beam forming method based on branch definition, which comprises the following steps:
constructing an IRS assisted de-cellular large-scale MIMO system model, wherein the model comprises M access points, K single-antenna users and R IRS, wherein the M access points are all provided with N antennas, and phase shift parameters of the IRS are set to be discrete and a desirable discrete set of phase shifts of all units of the IRS is obtained;
determining a WSR maximization problem P1 of an IRS assisted de-cellular large-scale MIMO system model, which 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 the sum of the absolute values of the precoding vectors from each access point to all users not to exceed the threshold of the absolute value of the precoding vector of the access point as a WSR maximization problem P1;
obtaining an optimization problem P2 by carrying out Lagrange dual conversion and quadratic conversion on the WSR maximization problem P1 in sequence;
solving a global optimal solution of an optimization problem P2 by a passive beam forming algorithm based on branch definition, wherein the passive beam forming algorithm based on branch definition specifically comprises the following steps:
building a search tree
For->
Solving the lower bound and the upper bound of each node in each node associated with the feasible discrete set, wherein the feasible discrete set represents a discrete value set which all IRS units can adopt in algorithm iteration;
in each iteration, selecting a father node, branching the father node into two child nodes according to a node branching rule, and respectively solving the lower bound and the upper bound of the two child nodes;
updating search trees using boundary update rules
When the difference between the upper bound and the lower bound is lower than the allowable error with the increase of the iteration number, the global optimal solution of the optimization problem P2 is obtained by solving.
Further, in the process of constructing the IRS-assisted de-cellular massive MIMO system model, the SINR of the kth user is determined according to the equivalent channel and the precoding vector from the access point to the kth user k The specific expression is as follows:
wherein, the first and the second end of the pipe are connected with each other,
representing the equivalent channels of the M access points to the k-th user,
representing the precoding vectors of the M access points to the k-th user,
representing the precoding vectors, σ, of the M access points to the ith user 2 Representing the variance of the noise distribution.
Further, the specific expression of the WSR maximization problem P1 is:
wherein the decision variables
Precoding matrix, decision variable representing all access points
A phase shift matrix representing all IRSs, <' >>
Weight, SINR, representing the kth user k Representing the signal-to-interference-and-noise ratio, w, of the kth user m,k Represents the precoding of the mth access point to the kth user, based on the measured values>
Representing a set of access points, theta r,u Represents the phase shift of the u-th unit of the r-th IRS>
Represents the IRS set, is selected>
Set of cells, p, representing IRS max Represents the maximum downlink transmission energy, <' > in each access point>
Denotes theta r,u A discrete set of preferences.
Further, the obtaining of the optimization problem P2 by sequentially performing lagrangian dual conversion and quadratic transformation on the WSR maximization problem P1 specifically includes:
p1 is decoupled into the following parts by a Lagrange dual conversion method:
wherein the objective function
γ＝[γ 1 ,γ 2 ,…,γ K ] T For an introduced K-dimensional auxiliary variable, <' >>
Represents an equivalent channel of M access points to the kth user, and->
Precoding vectors representing M access points to kth user, based on the precoding vector>
Representing precoding vectors of M access points to an ith user;
through secondary transformation, P1.1 is simplified to obtain
Wherein
ξ＝[ξ 1 ,…,ξ K ] T ，
q i,k (Θ)＝a i,k +θ H b i,k ，μ k ＝η k (1+γ k ) And theta denotes a diagonal element of the phase shift matrix theta,
F m indicating the channel between the mth access point and all IRSs, g k Represents the channel between all IRS and the kth user; />
Further simplifying P1.2, and finally obtaining an optimization problem P2 as follows:
wherein f is 3 (θ)＝θ H Λθ-2Re{θ H ν}，
Wherein b is k,k Is b i,k A value of mid i = k>
Is represented by i,k And (6) conjugation. .
Further, the passive beamforming 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 The optimization problem P2 is converted into:
wherein g (theta ) = Tr (Lambda theta) -2Re { theta H ν}，
A set of discrete values that represent the units of each IRS, RU being the dimension of θ;
relaxing the constraint, P2.1 is converted to P2.2:
wherein the feasible region
The set of (a) is: />
Let theta t Is an optimal solution for P2.2, then the lower bound of P2.1->
The obtained solution theta t Is projected to
Get up->
unit is a function, x = for an N-dimensional vector[x 1 ,…x N ] T ，/>
Upper bound of P2.1->
Wherein->
Representing a discrete value set which all IRS units in the t-th algorithm iteration can adopt;
node division: in the t-th iteration, the ith with the smallest lower bound is selected ★ Dividing each node, and dividing a feasible region corresponding to the node with the minimum lower bound
Evenly divided into left and right parts, i.e. <' >>
And &>
Wherein:
and (3) updating the boundary: for two nodes obtained by node division, respectively solving to obtain the corresponding nodes
According to>
And &>
Smaller values of (A) update the upper bound, lower bound, and optimal solution scoreIs g (theta) corresponding to t ,θ t ) And &>
Further, the passive beamforming algorithm based on branch definition is implemented by the following steps:
Step 6, corresponding the nodes
Joining a search tree pick>
Performing the following steps;
step 7, letting t = t +1;
step 8, selecting search tree
Has a minimum lower bound->
A node of (2);
step 9, deleting the minimum lower bound
A node of (2);
Step 11, for
Solving for a P2.2 correspondence>
And &>
Step 12, if
Then it is updated->
The corresponding optimal solution is updated to £ or>
Step 13, for
Solving for a P2.2 correspondence>
And &>
Step 14, if
Then it is updated->
The corresponding optimal solution is updated to £ or>
Step 16, if
Returning to execution of step 6-step 15, if->
Outputting the optimal result theta ★ ＝θ t 。
The invention provides a branch definition-based beam forming method for an IRS-assisted de-cellular large-scale MIMO system, which establishes a WSR maximization problem of the IRS-assisted CF-mMIMO system, considers the more practical discrete condition of the IRS phase, and takes the constraint conditions of the maximum transmission power at the AP end and the feasible solution of the IRS phase. The method comprises the following steps of firstly decoupling an original optimization problem into two sub-optimization problems through a Lagrange dual transformation algorithm: the active beam forming problem of the AP end and the passive beam forming problem of the IRS end. For the passive beam forming problem of the IRS terminal, a passive beam forming algorithm based on branch definition is provided, and then the original non-convex optimization problem which is very challenging is solved by alternately optimizing 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 flowchart illustrating a beamforming method for an IRS-assisted de-cellular massive MIMO system based on branch definition according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an IRS-assisted CF-mMIMO system model structure according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of an IRS-assisted CF-mMIMO system channel in an embodiment of the present invention;
FIG. 4 is a graph of WSR as a function of the number of iterations of the algorithm in an embodiment of the present invention;
FIG. 5 is a graph of WSR as a function of the number of quantization bits in an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail 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 of the invention. It should be further noted that, for the convenience of description, only some of the structures related to the present invention are shown in the drawings, not all of the structures.
Before discussing exemplary embodiments in more detail, it should be noted that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although a flowchart may describe the steps as a sequential process, many of the steps can be performed in parallel, concurrently or simultaneously. In addition, 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 figure. 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 in an embodiment includes the following steps:
constructing an IRS assisted de-cellular large-scale MIMO system model, wherein the model comprises M access points, K single-antenna users and R IRS, wherein the access points are all provided with N antennas, and phase shift parameters of the IRS are set to be discrete and a desirable discrete set of phase shifts of all units of the IRS is obtained;
determining a WSR maximization problem P1 of an IRS-assisted de-cellular massive MIMO system model, specifically:
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 the sum of the absolute values of the precoding vectors from each access point to all users not to exceed the threshold of the absolute value of the precoding vector of the access point as a WSR maximization problem P1;
obtaining an optimization problem P2 by sequentially carrying out Lagrange dual conversion and quadratic conversion on the WSR maximization problem P1;
solving a global optimal solution of an optimization problem P2 by a passive beam forming algorithm based on branch definition, wherein the passive beam forming algorithm based on branch definition specifically comprises the following steps:
building a search tree
For->
Solving the lower bound and the upper bound of each node in each node associated with the feasible discrete set, wherein the feasible discrete set represents a discrete value set which all IRS units can adopt in algorithm iteration;
in each iteration, selecting a father node, branching the father node into two child nodes according to a node branching rule, and respectively solving the lower bound and the upper bound of the two child nodes;
updating search trees using boundary update rules
When the difference between the upper bound and the lower bound is lower than the allowable error with the increase of the iteration number, the global optimal solution of the optimization problem P2 is obtained by solving.
The specific implementation process is as follows:
(1) Intelligent reflection surface assisted large-scale de-cellular MIMO system model
The system structure of the intelligent reflective surface aided large-scale cellular MIMO system model of the present embodiment is shown in fig. 2, and the system model includes M APs, where each AP has N antennas and K single-antenna users. In order to further increase the capacity of the system and reduce the energy consumption, R IRSs are introduced, wherein the number of units of each IRS is U, and each IRS is provided with a controller connected with the IRS to control the phase shift of each unit. Order to
Respectively representing AP, IRS unit, index set of user. 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 practical hardware limitations. Let L represent the number of bits per cell, then each cell can be configured with L =2 l The possible quantization levels. Order to
The phase shift matrix representing the r-th IRS can be expressed as:
Θ r ＝diag(θ r,1 ,…,θ r,U ) (1)
wherein theta is r,u Phase shift, θ, of the u-th element representing the r-th IRS r,u The preferred discrete set is:
in the IRS-assisted CF-mimo system, each AP needs to estimate channels of all users, specifically, a channel between the mth AP and the kth user is composed of a direct channel from the mth AP to the kth user and an rxu reflection channel, an equivalent channel diagram is shown in fig. 3, and an equivalent channel from the mth AP to the kth user may be given by the following formula:
wherein
Represents a direct channel from the mth AP to the kth user, in conjunction with a channel selection algorithm>
And &>
Representing the channel between the mth AP and the r-th IRS and the channel between the r-th IRS and the k-th user, respectively.
The embodiment mainly considers the downlink transmission scene, and during downlink transmission, the mth AP transmits a signal x to all users m Can be expressed as:
wherein
Representing the precoding vector, s, from the m-th AP to the i-th user i Representing the signal transmitted to the ith user. The signal received by the kth user can be expressed as:
wherein
Equivalent channels and precoding vectors representing all APs through kth user, respectively, <' > based on the channel condition>
Representing the noise energy received by the k-th user, where σ 2 Representing the variance of the noise distribution. And w i Should satisfy the energy limit of each AP, let ρ max Representing the maximum downlink transmission energy per AP, then:
the signal received by the user is re-expressed 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 assisted de-cellular massive MIMO system
The WSRs of all users can be expressed as:
wherein
Representing the weight of the kth user, the WSR maximum problem for all end users can be expressed as: />
Wherein the decision variables are
Respectively representing the precoding matrix of all APs and the phase shift matrix of all IRS. It can be observed that the objective function is non-convex and the two decision variables are coupled to each other, and by the lagrange dual conversion method, P1.1 can be decoupled as:
wherein the objective function f (Θ, W, γ) is:
wherein γ = [ γ = 1 ,γ 2 ,…,γ K ] T For the introduced K-dimensional auxiliary variable, f k (Θ, W) can be expressed as:
fix (theta, W), let
The calculation is as follows:
by fixing (W, γ), P1.2 can be expressed as:
wherein
μ k ＝η k (1+γ k ) Then, the method is further simplified by using a quadratic transformation method to obtain:
wherein:
in the formula (17), in order to correspond to the argument Θ of the function on the left side of the formula, (Θ) represents the right end
Contains theta.
Order to
Further mixing q with i,k (Θ) reduces to:
q i,k (Θ)＝a i,k +θ H b i,k (18)
wherein
Diagonal element, 1, representing the phase shift matrix Θ RU Is a full 1 vector of RU length, greater than or equal to>
Present in formula (17->
b i,k Indicates that for the kth user (K also takes the value from 1-K), i is any of 1-K, b k,k That is, for the k-th user i = k, a i,k And a k,k As well. Fixing theta can obtain optimal xi = [ xi ] 1 ,…,ξ K ] T Wherein xi is k Comprises the following steps:
fixed ξ, one can get:
further, the last term of equation (17) may be simplified to:
bringing (21) into (20) yields:
f 2 (Θ)＝-θ H Λθ+2Re{θ H ν}-δ (22)
wherein:
wherein [ ·] * Represents conjugation, i.e.
Is represented by a i,k Conjugation, then, P2.2 can be converted to:
wherein f is 3 (θ)＝θ H Λθ-2Re{θ H ν}。
(3) Global optimal beamforming algorithm
In order to solve the problem of P2.3, a globally optimal passive beamforming algorithm based on Branch and Bound (BnB) is provided to solve the problem, and the algorithm can obtain a globally optimal solution of the passive beamforming problem.
In the concrete implementation process, the
Sets of discrete values desirable for a unit representing each IRS>
Represents the set of discrete values that all IRS units may assume in the t-th iteration of the algorithm. The core idea of the BnB algorithm is to establish a search tree @>
For->
Neutralization feasible discrete set->
For each associated node, the lower bound and upper bound of the node may be determined. In each iteration, a parent node is selected and branched into two child nodes according to a node branching rule. Then, the lower and upper bounds of the two child nodes are solved separately. Next, the search tree is updated using boundary update rules>
The upper limit of (2). As the number of iterations increases, the difference between the upper and lower bounds becomes lower than the allowed error e. The details of the BnB algorithm are as follows:
(1) lower and upper bounds for optimization problem
P2.3 was first converted to:
where RU is the dimension of θ, θ i Is the ith dimension thereof, let Θ = θ H Then P2.4 is equivalent to:
wherein g (Θ, θ) = Tr (Λ Θ) -2Re { θ { (θ) } H V, in order to get the lower bound of P2.5, relaxing the constraint, P2.5 can be converted into:
where Tr is the trace operation of the matrix,
representing the matrix theta-theta H Is a semi-positive decision matrix in which row fields @>
The set of (a) is:
and for all of the j's,
let theta t Is an optimal solution for P2.6, then P2.5Lower bound of (2)
Then the obtained solution theta is t Projected to->
Get up->
A unit is defined as a function, for an N-dimensional vector x = [ x ] 1 ,…x N ] T ，/>
The function of this function is to unitize the size of each dimension of the vector x.
Then, the upper bound of P2.5
(2) Node partitioning
In the t-th iteration, the ith with the smallest lower bound is selected ★ Dividing each node, and dividing the feasible region corresponding to the node
Evenly divided into left and right parts, i.e. <' >>
And &>
Wherein:
(3) updating boundaries
For the two nodes obtained by the division in the last step, the corresponding nodes can be obtained by respectively solving
Then according to >>
And &>
The smaller value of (c) updates the upper bound, the lower bound and the corresponding optimal solution to be g (theta) respectively t ,θ t ) And &>
The global optimal beamforming algorithm based on the branch definition algorithm is summarized in the following algorithm 1:
in order to better embody the effect of the present invention, the embodiment verifies the proposed beamforming algorithm based on branch definition through simulation to solve the WSR maximization problem. Suppose that there are 6 APs in a scene, each AP has 4 antennas, 2 IRS, and the number of each IRS unit is 120,4 users. The channel model takes into account the direct path component and the non-direct path component, assuming that the maximum transmission power per AP is 5dbm. Consider the actual case where the IRS phase is discrete 4 bits and assume that all users have a weight of 1. In simulation, the active beam forming of the AP end is realized by using a Weighted Minimum Mean Square Error (WMMSE) algorithm; for passive beamforming at the IRS end, a proposed branch definition-based algorithm and an MM algorithm as a comparison are considered; and the IRS is considered to be closed, and only the situation of active beam forming at the AP end is taken as reference. Fig. 4 shows the variation of WSR with the number of iterations of the joint beamforming algorithm. For the case of IRS closure, WSR is a straight line. Both curves of the joint beamforming can converge quickly and the WSR is significantly higher than the case of IRS off, which illustrates the effectiveness of the IRS-side passive beamforming. In addition, the beam forming algorithm based on branch definition provided by the invention has obvious WSR gain compared with the MM beam forming algorithm, and the global optimality of the beam forming algorithm based on branch definition is verified in performance.
As shown in fig. 5, which shows the WSR as a function of the quantization bit number of IRS, it can be observed that the slopes of the two curves become gradually smaller as the quantization bit number increases, because the WSR gain due to 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 equivalent bit number is 1, the passive beamforming algorithm based on branch definition has significant gain compared with the passive beamforming algorithm based on MM, which shows that the passive beamforming algorithm based on branch definition provided by the invention is more applicable in a low-quantization bit scene, and the low-quantization bit is also beneficial to reducing the difficulty of actual hardware design and the calculation time of the beamforming algorithm.
It can be seen from the embodiments that the beam forming method for the IRS-assisted de-cellular large-scale MIMO system based on branch definition provided by the present invention establishes the WSR maximization problem of the IRS-assisted CF-MIMO system, considers the case that the IRS phase is more practical discrete, and has the constraint conditions of the maximum transmission power at the AP end and the feasible solution at the IRS end. The method comprises the following steps of firstly decoupling an original optimization problem into two sub-optimization problems through a Lagrange dual transformation algorithm: the active beam forming problem of the AP end and the passive beam forming problem of the IRS end. For the IRS-end passive beam forming problem, a passive beam forming algorithm based on branch definition is provided, and then the original non-convex optimization problem which is very challenging is solved by alternately optimizing 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 or method 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 or method.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
Claims (6)
1. An IRS-assisted de-cellular massive MIMO system beam forming method based on branch definition is characterized by comprising the following steps:
constructing an IRS assisted de-cellular large-scale MIMO system model, wherein the model comprises M access points, K single-antenna users and R IRS, wherein the M access points are all provided with N antennas, and phase shift parameters of the IRS are set to be discrete and a desirable discrete set of phase shifts of all units of the IRS is obtained;
determining a WSR maximization problem P1 of an IRS-assisted de-cellular massive MIMO system model, specifically:
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 the sum of the absolute values of the precoding vectors from each access point to all users not to exceed the threshold of the absolute value of the precoding vector of the access point as a WSR maximization problem P1;
obtaining an optimization problem P2 by sequentially carrying out Lagrange dual conversion and quadratic conversion on the WSR maximization problem P1;
solving a global optimal solution of an optimization problem P2 by a passive beam forming algorithm based on branch definition, wherein the passive beam forming algorithm based on branch definition specifically comprises the following steps:
building a search tree
For->
Solving the lower bound and the upper bound of each node in each node associated with the feasible discrete set, wherein the feasible discrete set represents a discrete value set which all IRS units can adopt in algorithm iteration;
in each iteration, selecting a father node, branching the father node into two child nodes according to a node branching rule, and respectively solving the lower bound and the upper bound of the two child nodes;
updating search trees using boundary update rules
When the difference between the upper bound and the lower bound is lower than the allowable error with the increase of the iteration number, the global optimal solution of the optimization problem P2 is obtained by solving.
2. The method of claim 1, wherein in the process of constructing the IRS-assisted de-cellular massive MIMO system model, the SINR of the kth user is determined according to an equivalent channel and a precoding vector from an access point to the kth user k The specific expression is as follows:
wherein, the first and the second end of the pipe are connected with each other,
representing the equivalent channels of the M access points to the k-th user,
representing the precoding vectors of the M access points to the k-th user,
representing the precoding vectors, σ, of the M access points to the ith user 2 Representing the variance of the noise distribution.
3. The method of claim 1, wherein the WSR maximization problem P1 is expressed as follows:
wherein the decision variables are
Precoding matrix, decision variable representing all access points
A phase shift matrix representing all IRSs, <' >>
Weight, SINR, representing the kth user k Representing the signal-to-interference-and-noise ratio, w, of the kth user m,k Represents the precoding of the mth access point to the kth user, based on the measured values>
Representing a set of access points, theta r,u Represents the phase shift of the u-th unit of the r-th IRS>
Represents the IRS set, is selected>
Set of cells, p, representing IRS max Represents the maximum downlink transmission energy in each access point, in conjunction with the maximum downlink transmission energy in each access point>
Denotes theta r,u A discrete set of values is desirable.
4. The method as claimed in claim 3, wherein the optimization problem P2 is obtained by sequentially performing lagrangian dual transformation and quadratic transformation on the WSR maximization problem P1, and the method specifically includes:
p1 is decoupled into the following parts by a Lagrange dual conversion method:
wherein the objective function
γ＝[γ 1 ,γ 2 ,…,γ K ] T For an introduced K-dimensional auxiliary variable, <' >>
Represents an equivalent channel of M access points to the kth user, and->
Represents the precoding vectors from the M access points to the k-th user, based on the precoding vectors>
Representing precoding vectors of M access points to an ith user;
through secondary transformation, P1.1 is simplified to obtain
Wherein
further simplifying P1.2, and finally obtaining an optimization problem P2 as follows:
wherein f is 3 (θ)＝θ H Λθ-2Re{θ H ν}，
Wherein b is k,k Is b i,k Value of mid i = k>
Is represented by i,k And (6) conjugation. />
5. The method as claimed in claim 4, wherein the passive beamforming algorithm based on finger definitions specifically comprises:
determining a lower bound and an upper bound of the optimization problem P2:
let Θ = θ H The optimization problem P2 is converted into:
diag(Θ)＝1 RU ,
Θ＝θθ H ,
wherein g (theta ) = Tr (Lambda theta) -2Re { theta H ν}，
A set of discrete values that represent the units of each IRS, RU being the dimension of θ;
relaxing the constraint, P2.1 is converted to P2.2:
diag(Θ)＝1 RU ,
Θ≥θθ H ,
in which the feasible region
The set of (a) is: />
Tr represents the trace operation of matrix, theta is not less than theta H Representing the matrix theta-theta H Is a semi-positive definite matrix, let θ t Is an optimal solution for P2.2, then the lower bound of P2.1->
The obtained solution theta t Is projected to
Get up->
unit is a function, x = [ x ] for an N-dimensional vector 1 ,…x N ] T ，/>
Upper bound of P2.1->
Wherein +>
Representing a discrete value set which all IRS units in the t-th algorithm iteration can adopt;
node division: in the t-th iteration, the ith with the smallest lower bound is selected ★ Dividing each node, and dividing a feasible domain corresponding to the node with the minimum lower bound
Divided evenly into two parts, i.e. [ right ] and left>
And &>
Wherein: />
And (3) updating the boundary: for two nodes obtained by node division, respectively solving to obtain the corresponding nodes
According to>
And &>
The smaller value of (c) updates the upper bound, the lower bound and the optimal solution to be g (theta) respectively t ,θ t ) And &>
6. The method of claim 5, wherein the passive beamforming algorithm based on finger definitions is implemented by:
step 1, setting the iteration times t =0, and setting a threshold limiting parameter epsilon =10 -4 ；
Step 2, a discrete value set A which is advisable for all IRS units in algorithm iteration t Assigning an initial value;
step 3, calculating an initial solution { theta ] through P2.2 t ,Θ t }；
Step 4, by
Obtaining a solution of P2.1; />
Step 5, calculating the lower bound of P2.1
Upper bound->
Step 6, corresponding the nodes
Joining a search tree pick>
Performing the following steps;
step 7, letting t = t +1;
step 8, selecting search tree
Has a minimum lower bound>
A node of (2);
step 9, delete has minimumLower bound
A node of (2);
step 10, will have a minimum lower bound
In response to a node of->
Divided into two sub-sets->
And &>
Step 11, for
Solving for a P2.2 correspondence>
And &>
Step 12, if
Then update a->
The corresponding optimal solution is updated to £ or>
Step 13, for
Solving for P2.2 corresponding +>
And &>
Step 14, if
Then it is updated->
The corresponding optimal solution is updated to &>
Step 15, corresponding two branch nodes
And &>
Add or>
Step 16, if
Returning to execution of step 6-step 15, if->
Outputting the optimal result theta ★ ＝θ t 。/>
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