CN110445519B - Method and device for resisting inter-group interference based on signal-to-interference-and-noise ratio constraint - Google Patents
Method and device for resisting inter-group interference based on signal-to-interference-and-noise ratio constraint Download PDFInfo
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Abstract
An inter-group interference resisting method and device based on signal-to-interference-and-noise ratio constraint are disclosed, the method comprises the following steps: constructing a large-scale MIMO frequency division duplex downlink system based on channel statistics; based on the similarity of the geographic positions, carrying out user group division on the user terminals; according to long-term statistical characteristics, a first-stage pre-coding matrix is formed by selecting a characteristic wave beam and decomposing a characteristic value; and forming a second-stage precoding matrix based on the first-stage precoding matrix and the signal to interference plus noise ratio constraint. By the scheme, the problems of intra-group interference and inter-user-group interference existing in the user group can be solved when two-stage precoding design is carried out, and the total rate of the system is improved.
Description
Technical Field
The invention belongs to the technical field of communication, and particularly relates to an inter-group interference resisting method and device based on signal-to-interference-and-noise ratio constraint.
Background
Massive Multiple Input Multiple Output (MIMO) is considered to be very likely to become one of the main transmission techniques of 5G systems, and has received intense attention from both academic and industrial circles. Most of the existing mobile communication systems adopt a Frequency-Division Duplexing (FDD) mode of operation. In the frequency division duplex multiplexing mode, the time frequency resources required by uplink and downlink channel estimation are related to the number of base station antennas, and if a large-scale mimo system works in the frequency division duplex multiplexing mode, the channel estimation needs to be implemented by the uplink and downlink resources far larger than those of the traditional mimo system, so that a large amount of time frequency resources are occupied, and the effective throughput of the system is reduced. Since coherent time-frequency resources of the system are limited, the number of users simultaneously served in each cell in the massive mimo system is limited, but the number of antennas of the base station is not limited.
In a large-scale mimo system, a linear data processing method is usually adopted, and the influence of channel fast fading and noise on the system performance is reduced as the number of antennas increases. Inter-cell pilot pollution becomes a major factor affecting the performance of large-scale mimo systems. Since the length of the pilot frequency is limited in the channel estimation of the fdd mimo system, users in different cells need to use the multiplexed or correlated pilot frequency sequence, which causes inter-cell interference of the pilot frequency signal and degrades the performance of the channel estimation, i.e. so-called "pilot pollution".
In view of the important role of frequency division duplex multiplexing in the current communication system, it is necessary to study how to apply the large-scale mimo technology to the fdd multiplexing system, and the most central problem is how to reduce the overhead of acquiring downlink CSI by the base station. The codebook-based limited feedback technique widely used in the conventional mimo system is only applicable to small-scale antenna arrays, and thus it is necessary to develop a new channel estimation scheme according to characteristics of large-scale mimo channels. A two-stage limited feedback precoding scheme is provided by combining JSDM (Joint Spatial Division and Multiplexing) and utilizing the Spatial correlation of channels, and the scheme is particularly suitable for large-scale multiple-input multiple-output channels and can greatly reduce the cost of channel estimation. When the joint space division multiplexing scheme is used for carrying out two-stage precoding design, the problems of intra-group interference and inter-user group interference of user terminal grouping exist, and the improvement of the total rate of the system is severely limited.
Disclosure of Invention
The technical problem solved by the invention is how to solve the problems of the intra-group interference and the inter-user group interference existing in the user group when the two-stage precoding design is carried out, and the total rate of the system is improved.
In order to achieve the above object, the present invention provides an inter-group interference resisting method based on signal-to-interference-and-noise ratio constraints, the method comprising:
constructing a large-scale multi-input multi-output frequency division duplex downlink system based on channel statistics;
based on the similarity of the geographic positions, carrying out user group division on the user terminals;
according to the long-term statistical characteristics, a first-stage pre-coding matrix is formed by selecting eigen beams and decomposing eigenvalues;
and forming a second-stage precoding matrix based on the first-stage precoding matrix and the signal-to-interference-and-noise ratio constraint.
Optionally, the forming a first-stage precoding matrix by selecting eigen beams and eigenvalue decomposition according to the long-term statistical characteristics includes:
acquiring a channel covariance matrix of effective channel coherence time average of a user group;
performing eigenvalue decomposition on the channel covariance matrix to obtain an eigenvector and an eigenvalue of the channel covariance matrix;
and selecting a column vector which enables the value of a diagonal matrix formed by the eigenvalues to be maximum from the eigenvectors of the channel covariance matrix to form the first-stage precoding matrix.
Optionally, the first-stage precoding matrix is:
B g ＝U g (S g )；
wherein, B g Representing the first-stage precoding matrix, U g An eigenvector representing the channel covariance matrix, S g And selecting a column vector which enables a diagonal matrix formed by the eigenvalues to have the maximum value from the eigenvectors of the channel covariance matrix.
Optionally, the forming a second-stage precoding matrix based on the first-stage precoding matrix and the signal-to-interference-and-noise ratio constraint includes:
acquiring the information of the signal to interference and noise ratio of each user terminal;
introducing an interference coefficient for limiting the user terminals of the adjacent user groups into the constraint denominator of the signal to interference and noise ratio of each user terminal, and converting the problem of solving the maximum sum rate of the system under the minimum interference into the problem of solving the inter-group interference constraint;
and converting the non-convex solving inter-group interference constraint problem into a corresponding near-vision convex set problem by adopting a continuous convex approximation method and solving to obtain the second precoding matrix.
The embodiment of the invention also provides an inter-group interference resisting device based on the signal-to-interference-and-noise ratio constraint, which comprises:
the building unit is suitable for building a large-scale MIMO frequency division duplex downlink system based on channel statistics;
the dividing unit is suitable for dividing the user group of the user terminal based on the similarity of the geographic position;
the first pre-coding unit is suitable for forming a first-stage pre-coding matrix by selecting the eigen-beams and decomposing the eigen-values according to long-term statistical characteristics;
and the second pre-coding unit is suitable for forming a second-stage pre-coding matrix based on the first-stage pre-coding matrix and the signal to interference plus noise ratio constraint.
Optionally, the first-stage precoding unit is adapted to obtain a channel covariance matrix of an effective channel coherence time average of a user group; performing eigenvalue decomposition on the channel covariance matrix to obtain an eigenvector and an eigenvalue of the channel covariance matrix; and selecting a column vector which enables the value of a diagonal matrix formed by the eigenvalues to be maximum from the eigenvectors of the channel covariance matrix to form the first-stage precoding matrix.
Optionally, the first-stage precoding matrix constructed by the first-stage precoding unit is:
B g ＝U g (S g )；
wherein, B g Representing the first-stage precoding matrix, U g An eigenvector representing the channel covariance matrix, S g And representing a column vector which is selected from the eigenvectors of the channel covariance matrix and enables the value of a diagonal matrix formed by the eigenvalues to be maximum.
Optionally, the second-stage precoding unit is adapted to obtain information of a signal-to-interference-and-noise ratio of each user equipment; introducing an interference coefficient for limiting the user terminals of the adjacent user groups into the constraint denominator of the signal to interference and noise ratio of each user terminal, and converting the problem of solving the maximum sum rate of the system under the minimum interference into the problem of solving the inter-group interference constraint; and converting the non-convex solving inter-group interference constraint problem into a corresponding near-vision convex set problem by adopting a continuous convex approximation method and solving to obtain the second precoding matrix.
Compared with the prior art, the invention has the following beneficial effects:
according to the scheme, a large-scale multi-input multi-output frequency division duplex downlink system based on channel statistics is constructed, user groups are divided for user terminals based on the similarity of geographical positions, according to long-term statistical characteristics, a first-stage precoding matrix is formed by selecting eigen beams and eigenvalues and decomposing the eigen beams and the eigenvalues, then a second-stage precoding matrix is formed based on the first-stage precoding matrix and signal to interference and noise ratio constraints, the intra-group interference and the inter-user group interference existing in the user groups can be eliminated, and the total rate of the system is improved.
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In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the description below are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a schematic flowchart of an inter-group interference rejection method based on signal-to-interference-and-noise ratio constraints according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating experimental results of system performance simulation under different encoding methods;
fig. 3 is a schematic structural diagram illustrating an inter-group interference rejection apparatus based on a signal-to-interference-and-noise ratio constraint according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present application will be described clearly and completely with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only some embodiments of the present application, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application. The directional indications (such as up, down, left, right, front, rear, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship between the components, the movement situation, etc. in a specific posture (as shown in the drawings), and if the specific posture is changed, the directional indication is changed accordingly.
As described in the background art, in the prior art, when a joint space division multiplexing scheme is used to perform two-stage precoding design, the problems of intra-group interference and inter-user group interference in user terminal grouping severely limit the increase of the total rate of the system.
According to the technical scheme, a large-scale MIMO-FDD downlink system based on channel statistics is constructed, user groups are divided for user terminals based on the similarity of geographical positions, according to long-term statistical characteristics, a first-stage precoding matrix is formed by selecting eigen beams and eigenvalues and decomposing the eigen beams and the eigenvalues, then a second-stage precoding matrix is formed based on the first-stage precoding matrix and signal to interference and noise ratio constraints, the intra-group interference and the inter-user group interference existing in the user groups can be eliminated, and the total rate of the system is improved.
In order to make the aforementioned objects, features and advantages of the present invention more comprehensible, embodiments accompanying figures are described in detail below.
Fig. 1 is a schematic flowchart of an inter-group interference rejection method based on signal-to-interference-and-noise-ratio constraints according to an embodiment of the present invention. Referring to fig. 1, a method for resisting inter-group interference based on signal-to-interference-and-noise ratio constraints may specifically include the following steps:
step S101: and constructing a large-scale MIMO frequency division duplex downlink system based on channel statistics.
In a specific implementation, the system comprises a single base station signal transmitting end with multiple antennas and a plurality of user terminals with single antennas. The sending end of the base station is provided with M antennas, and the base station simultaneously serves K single-antenna user terminals. To reduce the complexity of the analysis, in terms of transmit antenna correlation, a single loop model is used, the distance from the user terminal to the antenna is S, the azimuth angle is θ, the terminal is surrounded by a circular scatterer of radius r, and the Angular Spread (AS) Δ ≈ arctan (r/S).
Then, the downlink reception signal of the channel can be expressed as:
wherein Y represents a K-dimensional signal vector received by the Kth user terminal, x is an M-dimensional signal vector transmitted by the base station with M antennas, and z-CN (0, I) K ) Is Gaussian white noise, h k ～CN(0，R K ) Is the M-dimensional channel vector for user terminal K.
Next, the user terminal channel vector { h } can be transformed using the Karhunen-Loeve expression k Expressed as:
wherein w k ～CN(0，I)，R K Is a symmetric semi-positive definite channel covariance matrix, Λ K Is R K R x r dimensional diagonal matrix, U, formed by non-zero eigenvalues of K Is R K The high-order unitary matrix is formed by the eigenvectors corresponding to the nonzero eigenvalue.
The base station, using the M × N dimensional linear precoding matrix V, can express the transmission signal as:
X＝Vd (4)
where d is the S-dimensional data symbol vector that needs to be sent to the user terminal.
Step S102: and carrying out user group division on the user terminals based on the approximation of the geographic position.
In the specific implementation, assuming that the received power of plane waves from the base station antenna is uniformly distributed, although the user terminals are uniformly distributed around the base station, they may often be interworked in geographical locations, so as to form a natural user cluster, and the base station considers the cluster when designing the transmission strategy.
Step S103: and according to the long-term statistical characteristics, a first-stage precoding matrix is formed by selecting the eigenbeams and decomposing the eigenvalues.
In the specific implementation, the K user terminals are divided into G user groups, K g Indicates the number of user terminals, u, in the user group g g Representing the number of user terminals, S, in a user group g g Representing a statistical beam, B, directed to each user in a group g of users g For all the statistical beams corresponding to the ues in the ue group g, there is B ═ B 1 … B g ]，w k Is K g And the second-stage precoding matrix of the Kth user terminal. The data transmitted to the Kth user terminal is d K ，z k Is gaussian white noise. Therefore, the reception signal of the kth ue is:
in the above equation (5), the first term on the right side of the equation
Second term for the desired received signal of the user terminal
The signal transmitted by the BS to other UEs in the group is an interference signal in the group relative to the Kth UE in the group, and the third term
Fourth term z for inter-user group interference K Is gaussian white noise.
Therefore, the signal-to-interference-and-noise ratio of the kth user terminal can be expressed as:
then the sum rate of the system is:
wherein R represents the sum rate of the system, α K Indicating the weight determining the scheduling priority of user terminal K.
Assuming that the channel statistical characteristics of all user terminals remain unchanged for a period of time, in this case, the channel covariance matrix may be decomposed by an Eigenvalue (EVD) to obtain its eigenvector and its corresponding eigenvalue, so as to construct the first-stage precoding matrix.
By using
Representing the superposition of all channel matrices in the user group g,
by using
A channel covariance matrix representing an effective channel coherence time average. Channel covariance matrix R averaged over effective channel coherence time g By performing eigenvalue decomposition (EVD), one can obtain:
wherein,
as a channel covariance matrix R g Is used to generate a matrix of feature vectors,
as a channel covariance matrix R g The feature vectors of (a) form a diagonal matrix with corresponding feature values.
In a specific implementation, now through U g Selected column vector S g So that S is g Corresponding diagonal array Lambda g Is the maximum. Then, a first stage can be obtainedThe precoding matrix is:
B g ＝U g (S g ) (9)
wherein, B g Representing the first-stage precoding matrix, U g An eigenvector representing the channel covariance matrix, S g And representing a column vector which is selected from the eigenvectors of the channel covariance matrix and enables the value of a diagonal matrix formed by the eigenvalues to be maximum.
At the same time, a selected column vector S is obtained g Combined new matrix U g 。
Step S104: and forming a second-stage precoding matrix based on the first-stage precoding matrix and the signal to interference plus noise ratio constraint.
In a specific implementation, the main purpose of the second-stage precoding is to maximize the received power of the target ue, and at the same time minimize the interference to other ues in the same group and ues in other groups. But the limited number of transmit antennas M necessarily results in energy leakage to the adjacent groups due to the presence of statistical beam sidelobes. For this purpose, inter-group interference optimization is firstly performed to improve the system and speed.
To design a dimension-reduced pre-beamformer for each user group, the interference term of the constraint denominator of each user terminal in the above-cited SINR expression is represented as
Wherein,
in order to limit the adjacent user group f to be in the middle of G, f is not equal to G and is the interference coefficient to the user terminal, namely the interference coefficient is the second item corresponding to the right denominator of the equal sign in the formula (6).
By introducing new variablesζ f,k Then, specific groups are coordinated among user groups
Threshold values, the precoding matrix of the second stage can be designed for each user group. The problem is therefore represented by the maximum sum rate in the case of minimum interference shown in equation (12)
The method is converted into an intergroup interference constraint problem shown in an equation (13).
Because the above formula is a non-convex problem, a convergence solution cannot be solved, and therefore a continuous convex approximation technology is adopted, the non-convex problem is replaced by a near-sighted convex set problem, and iterative solution is carried out until convergence is achieved. The left equation of the above equation is convex, so some operating points are selected
A taylor approximation of a quadratic linear function is used nearby, and the following are provided:
solving the approximate convex equation using the above approximate equation is as follows:
wherein λ is k And
for each user terminal in the system, a constraint coefficient, p g For each power constraint factor, θ, of the user terminal group g,k To restrain
The interference coefficient at a fixed value. Karush-Kuhn-Tucker conditional constraint variable is assumed to be lambda k ,
θ g,k ，ρ g The lagrange expression is as follows, except for the constraint variables of the above inequality
Respectively to gamma k ,β k ,w k The derivation comprises:
the Karush-Kuhn-Tucker condition constraints are:
wherein by fixing λ k > 0 and
can solve gamma k And beta k To satisfy the IGI constraint, its bivariate θ g,i Solving for the second-stage precoding W by iterative solution, substituting (15), (16), (17) and (18) g 。
Fig. 2 shows a schematic diagram of system performance simulation experiment results under different encoding methods. Wherein, the simulation experiment adopts a uniform linear antenna array, and the base station is provided with 64 uniform arrays to simultaneously serve 16 independent single-antenna user terminals. These user terminals are randomly distributed within the base station sector. The user terminals are divided into 4 user groups,
and total power P sum 20 dB. From the results of fig. 2, the total rate of the method proposed by the present invention is similar to the total rate performance under ideal conditions, and the theoretical results are consistent with the simulation results.
The above detailed description is provided for the method for resisting inter-group interference based on the signal-to-interference-and-noise-ratio constraint in the embodiment of the present invention, and apparatuses corresponding to the above method will be described below.
Fig. 3 is a schematic structural diagram illustrating an inter-group interference rejection apparatus based on a signal-to-interference-and-noise ratio constraint according to an embodiment of the present invention. Referring to fig. 3, an inter-group interference rejection apparatus 30 based on the signal-to-interference-and-noise ratio constraint may include a constructing unit 301, a dividing unit 302, a first precoding unit 303, and a second precoding unit 304, where:
the constructing unit 301 is adapted to construct a large-scale mimo-fdd downlink system based on channel statistics;
the dividing unit 302 is adapted to divide the user group of the user terminals based on the proximity of the geographic location;
the first precoding unit 303 is adapted to form a first-stage precoding matrix by selecting a eigen beam and decomposing an eigenvalue according to long-term statistical characteristics; in an embodiment of the present invention, the first-stage precoding unit 303 is adapted to obtain a channel covariance matrix of an effective channel coherence time average of a user group; performing eigenvalue decomposition on the channel covariance matrix to obtain an eigenvector and an eigenvalue of the channel covariance matrix; and selecting a column vector which enables the value of a diagonal matrix formed by the eigenvalues to be maximum from the eigenvectors of the channel covariance matrix to form the first-stage precoding matrix. Wherein the first-stage precoding matrix constructed by the first-stage precoding unit is: b is g ＝U g (S g ) (ii) a Wherein, B g Representing the first-stage precoding matrix, U g An eigenvector, S, representing the channel covariance matrix g And selecting a column vector which enables a diagonal matrix formed by the eigenvalues to have the maximum value from the eigenvectors of the channel covariance matrix.
The second precoding unit 304 is adapted to form a second-stage precoding matrix based on the first-stage precoding matrix and the signal-to-interference-and-noise ratio constraint.
In an embodiment of the present invention, the second-stage precoding unit 304 is adapted to obtain information of a signal to interference plus noise ratio of each ue; introducing an interference coefficient for limiting the user terminals of the adjacent user groups into the constraint denominator of the signal to interference and noise ratio of each user terminal, and converting the problem of solving the maximum sum rate of the system under the minimum interference into the problem of solving the inter-group interference constraint; and converting the non-convex solving inter-group interference constraint problem into a corresponding near-vision convex set problem by adopting a continuous convex approximation method and solving to obtain the second precoding matrix.
According to the scheme in the embodiment of the invention, a large-scale MIMO-FDD downlink system based on channel statistics is constructed, the user terminals are divided into user groups based on the similarity of geographic positions, a first-stage precoding matrix is formed by selecting eigen beams and eigenvalues according to long-term statistical characteristics and is decomposed based on the long-term statistical characteristics, and a second-stage precoding matrix is formed based on the first-stage precoding matrix and signal-to-interference-plus-noise ratio constraints, so that the intra-group interference and inter-user-group interference existing in the user groups can be eliminated, and the total rate of the system is improved.
The foregoing shows and describes the general principles, principal features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the foregoing description only for the purpose of illustrating the principles of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the invention as defined by the appended claims, specification, and equivalents thereof.
Claims (6)
1. An inter-group interference immunity method based on signal-to-interference-and-noise ratio constraints is characterized by comprising the following steps:
constructing a large-scale MIMO frequency division duplex downlink system based on channel statistics;
based on the similarity of the geographic position, dividing user groups of the user terminals;
according to the long-term statistical characteristics, a first-stage pre-coding matrix is formed by selecting eigen beams and decomposing eigenvalues;
forming a second-stage precoding matrix based on the first-stage precoding matrix and the signal-to-interference-and-noise ratio constraint, specifically comprising: acquiring the information of the signal-to-interference-and-noise ratio of each user terminal; by approximation of the signal to interference and noise ratio at said each user terminalIntroducing an interference coefficient for limiting user terminals of adjacent user groups into the bundle denominator, and converting the maximum sum rate problem of the system under the minimum interference into the problem of solving the inter-group interference constraint:
wherein h is k M-dimensional channel vector, B, representing user terminal k g Represents all statistical beams, w, corresponding to user terminals in the user group g k Second stage precoding matrix, u, representing the kth user terminal in the user group Kg g Representing the number of user terminals in a user group G, wherein G represents the number of user groups obtained by dividing K user terminals; converting the non-convex solving inter-group interference constraint problem into a corresponding near-vision convex set problem by adopting a continuous convex approximation method and solving to obtain the second-stage precoding matrix, specifically:
the left equation for solving the interclass interference constraint problem is convex, so some operating points are chosen
If a section of Taylor approximation of a quadratic linear function is adopted nearby, an approximate formula with an inter-group interference constraint problem is as follows:
solving an approximate convex formula using the approximate formula:
wherein, B f Representing the first-stage precoding matrix, λ, of a group of users f k And
for each user terminal in the system, a constraint coefficient, p g For each power constraint factor, θ, of the user terminal group g,k To restrain
Interference coefficient at fixed value;
Karush-Kuhn-Tucker conditional constraint variable is assumed to be lambda k 、
θ g,k 、ρ g The constraint variables are respectively approximate convex formulas, so that the Lagrange expression is as follows:
respectively to gamma k ,β k ,w k The derivation comprises:
the Karush-Kuhn-Tucker condition constraints are:
wherein by fixing λ k > 0 and
can solve gamma k And beta k To satisfy the IGI constraint, its bivariate θ g,i Substituting the iterative solution into the approximate convex formula to obtain the second-stage precoding w g 。
2. The method of claim 1, wherein the forming a first-stage precoding matrix by selecting eigenbeams and eigenvalue decomposition according to long-term statistical characteristics comprises:
acquiring a channel covariance matrix of effective channel coherence time average of a user group;
performing eigenvalue decomposition on the channel covariance matrix to obtain an eigenvector and an eigenvalue of the channel covariance matrix;
and selecting a column vector which enables the value of a diagonal matrix formed by the eigenvalues to be maximum from the eigenvectors of the channel covariance matrix to form the first-stage precoding matrix.
3. The method of claim 2, wherein the first-stage precoding matrix is:
B g ＝U g (S g )；
wherein, B g Representing the first-stage precoding matrix, U g An eigenvector representing the channel covariance matrix, S g And selecting a column vector which enables a diagonal matrix formed by the eigenvalues to have the maximum value from the eigenvectors of the channel covariance matrix.
4. An apparatus for resisting inter-group interference based on signal-to-interference-and-noise ratio (SINR) constraint, comprising:
the building unit is suitable for building a large-scale multi-input multi-output frequency division duplex downlink system based on channel statistics;
the dividing unit is suitable for dividing the user group of the user terminal based on the similarity of the geographic position;
the first pre-coding unit is suitable for forming a first-stage pre-coding matrix by selecting a characteristic wave beam and decomposing a characteristic value according to long-term statistical characteristics;
the second precoding unit is adapted to form a second-stage precoding matrix based on the first-stage precoding matrix and the signal-to-interference-and-noise ratio constraint, and specifically includes: acquiring the information of the signal-to-interference-and-noise ratio of each user terminal; and introducing an interference coefficient for limiting the user terminals of the adjacent user groups into the constraint denominator of the signal to interference and noise ratio of each user terminal, and converting the maximum sum rate problem of the system under the minimum interference to the problem of solving the intergroup interference constraint problem:
wherein h is k M-dimensional channel vector, B, representing user terminal k g Represents all statistical beams, w, corresponding to the user terminals in the user group g k Second stage precoding matrix, u, representing the kth user terminal in user group Kg g The number of the user terminals in the user group G is represented, and G represents the number of the user groups obtained by dividing K user terminals; converting the non-convex solving inter-group interference constraint problem into a corresponding near-vision convex set problem by adopting a continuous convex approximation method and solving to obtain the second-stage precoding matrix, specifically:
the left equation for solving the interclass interference constraint problem is convex, so some operating points are chosen
And if a Taylor approximation of a quadratic linear function is adopted nearby, an approximate formula with an intergroup interference constraint problem is as follows:
solving an approximate convex formula using the approximate formula:
wherein, B f Representing the first-stage precoding matrix lambda of the user group f k And
constraint coefficient, p, for each user terminal in the system g For each power constraint factor, θ, of the user terminal group g,k To restrain
Interference coefficient at fixed value;
Karush-Kuhn-Tucker conditional constraint variable is assumed to be lambda k 、
θ g,k 、ρ g The constraint variables are respectively approximate convex formulas, so that the Lagrange expression is as follows:
respectively to gamma k ,β k ,w k The derivation is as follows:
the Karush-Kuhn-Tucker condition constraints are:
wherein by fixing λ k > 0 and
can solve gamma k And beta k To be made ofSatisfies the IGI constraint condition, and the bivariate theta thereof g,i Substituting the iterative solution into the approximate convex formula to obtain the second-stage precoding w g 。
5. The apparatus according to claim 4, wherein the first precoding unit is adapted to obtain a channel covariance matrix of an effective channel coherence time average of a user group; performing eigenvalue decomposition on the channel covariance matrix to obtain an eigenvector and an eigenvalue of the channel covariance matrix; and selecting a column vector which enables the value of a diagonal matrix formed by the eigenvalues to be maximum from the eigenvectors of the channel covariance matrix to form the first-stage precoding matrix.
6. The apparatus according to claim 5, wherein the first-stage precoding matrix constructed by the first precoding unit is:
B g ＝U g (S g )；
wherein, B g Representing the first-stage precoding matrix, U g An eigenvector representing the channel covariance matrix, S g And selecting a column vector which enables a diagonal matrix formed by the eigenvalues to have the maximum value from the eigenvectors of the channel covariance matrix.
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