CN107086886B - Double-layer precoding design for large-scale MIMO system fusion zero forcing and Taylor series expansion - Google Patents
Double-layer precoding design for large-scale MIMO system fusion zero forcing and Taylor series expansion Download PDFInfo
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Abstract
The invention discloses a double-layer precoding design method fusing zero forcing and Taylor series expansion in a large-scale multi-input multi-output system, and belongs to the technical field of wireless communication. The specific design process is as follows: firstly, a user obtains a downlink channel state information estimation value through a received pilot frequency sequence, and feeds back a CSI estimation value to a base station through a feedback link; the base station only needs to utilize the channel statistical information and adopts a Taylor series expansion mode to realize the design of an outer layer precoding matrix so as to eliminate the interference of users among groups; then, the actual channel and the outer layer pre-coding matrix are regarded as equivalent channels; and finally, the base station realizes the design of an inner layer precoding matrix based on the equivalent channel and by applying a zero forcing technology to eliminate the IUI in the group. The invention not only realizes the elimination of interference, improves the performance of the system, but also reduces the complexity of channel estimation, correspondingly reduces the information feedback quantity of CSI and saves frequency spectrum resources.
Description
Technical Field
The invention belongs to the technical field of future mobile communication, and particularly belongs to a precoding technology in a large-scale MIMO system.
Background
With the rapid development of wireless communication technology, people have an increasingly strong demand on communication efficiency, and a large number of antennas are configured at a transmitting end and a receiving end in a large-scale Multiple Input Multiple Output (MIMO) technology, so that the system performance is greatly improved under the condition that the system bandwidth and the transmitting power are not increased, and high-quality and high-rate transmission of information on limited spectrum resources is realized. On one hand, the large-scale MIMO technology brings more satisfactory User experience and more reliable voice service to people, and on the other hand, the large-scale MIMO system has more serious Inter-data stream Interference and Inter-User Interference (IUI), and some signal detection technologies with extremely high complexity are difficult to be applied to the MIMO system because the receiver has limited signal processing capability; aiming at the problem of interference in a large-scale MIMO system, a precoding technology in the large-scale MIMO system is generated. The precoding technique often requires that a transmitting end confirms current Channel State Information (CSI), and in an actual system, especially in a Frequency Division Duplex (FDD) system, downlink channel estimation is a very troublesome problem, the length of a pilot sequence used for downlink channel estimation is limited by coherence time, and in addition, in a large-scale MIMO system, a CSI estimation value is fed back to a base station through an uplink channel, so that a large amount of feedback overhead is inevitably generated, and a large amount of spectrum resources in the system are inevitably occupied.
In order to solve the existing problems, some scholars propose a double-layer precoding design scheme in a massive MIMO system adapted to the FDD mode of operation. The core idea is as follows: in a large-scale MIMO system, firstly, a user group served by a base station is divided into a plurality of user groups according to some characteristics of users, and then outer precoding matrixes of all groups are designed based on each group to eliminate IUIs among all groups; then, the actual channel and the outer layer precoding matrix are regarded as equivalent channels, and finally, the inner layer precoding matrix is designed based on the equivalent channels so as to eliminate IUI in the group. Other scholars propose: the outer precoding matrix of each user packet employs a Block Diagonalization (BD) precoding technique. Designing is carried out, so that an eigen matrix corresponding to a main eigenvalue of the channel covariance matrix of the expected user group is mapped to a Zero space of the channel covariance matrix of the unexpected user group, and then, the inner-layer precoding matrix is designed based on an equivalent channel by adopting a Regularized Zero-Forcing (RZF) technology. Although the inter-group IUI is eliminated to some extent by the outer precoding matrix designed based on the BD precoding technique, the improvement of the system performance is limited.
In the invention, in a large-scale MIMO system based on an FDD working mode, firstly, a user group served by a base station is divided into a plurality of user groups according to some characteristics of users, then, a certain grouping outer layer precoding matrix is designed based on channel statistical information of each grouping user, then, an actual channel and the outer layer precoding matrix are combined into an equivalent channel, the dimension reduction of the channel is realized, and finally, the base station designs a certain grouping inner layer precoding matrix based on the Zero-Forcing (ZF) technology of the equivalent channel, thereby reducing the complexity and the feedback overhead of channel estimation.
Disclosure of Invention
The IUI problem has become a main factor that restricts the performance of a large-scale MIMO system, and in order to solve the IUI problem in the large-scale MIMO system, a double-layer precoding design method that realizes interference elimination, reduces the complexity of channel estimation and the feedback amount of CSI information, improves the system performance, and saves spectrum resources is provided in the MIMO system by fusing zero forcing and taylor series expansion. The technical scheme of the invention is as follows:
a double-layer precoding design method for fusing zero forcing and Taylor series expansion in an MIMO system comprises the following steps:
firstly, a user obtains a downlink Channel State Information (CSI) estimation value through a received pilot frequency sequence, and feeds the downlink Channel State Information (CSI) estimation value back to a base station through a feedback link; the base station obtains the optimal outer precoding matrix by applying a Taylor series expansion mode to the received CSI estimation valueTo cancel interference IUI of users between groups and then to select the actual channel HgWith the optimal outer precoding matrixCombine to form equivalent channelsWherein G represents the grouped group number, G is 1,2, …, G represents the total number of user groups in the cell, and the superscript isequThe first three initials of the English equivalence equivalent value are markedoptRepresenting the first three letters of the english optimization.
And finally, the base station realizes the design of an inner layer precoding matrix based on the equivalent channel and by applying a zero forcing technology to eliminate the IUI in the group.
Further, the CSI estimation value of the downlink channel state information may be expressed as
Wherein h isgk∈CM×1Representing the channel estimation vectors between the base station to the kth user of the g group,representing the small-scale fading vectors between the base station to the kth user of the g group,each element in (a) is independent of each other and follows a complex gaussian distribution with a mean value of 0, a variance of 1, M represents the total number of base station antennas,denotes a G-th group channel covariance matrix, and G is 1,2, …, G denotes a total number of user groups, the G-th group user channel covariance matrixThe k-th row and l-th column elements of (1) can be expressed as
Where ^ (·) denotes an integral operation, θ denotes a central angle of each group, Δ denotes an angle spread, λ denotescRepresenting carrier wavelength, d antenna spacing, k and l representing the g-th group of channel covariance matrix RgThe k-th row, the l-th column,upper label ofcThe first letter of the english word channel representing the channel.
Further, the obtaining, by the base station, the outer precoding matrix from the received CSI estimation value by using taylor series expansion specifically includes:
designing outer precoding matrix of g-th group by solving optimization function f (α)
Where α represents the trace ratio, Tr {. cndot. represents the trace operation of the matrix, max (·) represents the maximization operation,an outer precoding matrix representing the g-th group with dimension of M × Mg,MgRepresenting a matrix with a trace ratio of αThe number of the main characteristic values is,with a representation dimension of Mg×MgOf the identity matrix RfA channel covariance matrix representing the f-th group of users, f ≠ 1,2, …, G, and f ≠ G,representing background noise power, IMRepresenting an identity matrix of dimension M by M, superscriptHRepresents a conjugate transpose of the matrix; by solving an optimisation functionG-th group of optimal outer precoding matrices
Wherein argmax (·) represents the value of the argument when the function is maximized, and the outer precoding matrix V of the g-th group of usersgNeed to satisfy Representing dimension Mg×MgThe identity matrix of (2).
Further, the actual channel HgWith the optimal outer precoding matrixCombine to form equivalent channelsThe formula of (1) is:wherein Representing the channel matrix, K, between the base station and the group g of usersgThe total number of users in the g-th group,and the optimal precoding matrix is the g group.
Further, the design step of the outer layer pre-woven matrix comprises:
The first step is as follows: t denotes the number of iterations, λtRepresenting a trace ratio obtained by iterative computation after the t iterative computation, making t equal to 0, and initializing the trace ratio;
whereinIs an initialized matrix, satisfiesλ0Representing the trace ratio when the iteration times of the algorithm is 0;
the second step is that: : for matrixDecomposing the characteristic value to obtain MgA maximum eigenvalueThe corresponding characteristic vectors form a matrix Vg(λt);
The third step: updating the trace ratio λt+1;
The fourth step: if λt+1-λtIf | < epsilon, executing a fifth step, wherein epsilon represents an algorithm ending threshold value; otherwise t is t +1, and executing the second step;
fifth step optimal trace ratio αopt=λt+1,Through the method, the optimal outer precoding matrix of the g-th group is finally designed
Further, based on equivalent channelsAnd the inner layer precoding matrix of the g group of users is designed by applying ZF technology as follows:
whereinRepresents the transmission power, P, of the base station transmitting information to each user in the g-th groupgkRepresents the transmission power of the base station when transmitting information to the kth user in the g group, and an inner precoding vector wgkThe conditions are required to be satisfied: i Wgk||21 because the g-th group inner precoding matrix WgBased on equivalent channelsAnd (5) designing.
The invention has the following advantages and beneficial effects:
the invention combines the ZF technology and Taylor series expansion, and provides a double-layer precoding design method fusing zero forcing and Taylor series expansion in a large-scale MIMO system. The invention eliminates IUI by means of user grouping, reduces the dimension of the channel, reduces the complexity of downlink channel estimation and the feedback quantity of CSI information, improves the system performance and saves the frequency spectrum resource. Because of the optimal outer precoding matrixThe design is carried out based on the channel covariance matrix of each group of users only, but not the actual channel H of each group of usersgOf the actual channel HgWith the optimal outer precoding matrixCombined as equivalent channelRealizing the dimension reduction of the channel; and then applying ZF technology based on equivalent channelDesigning inner precoding matrix WgThus, the CSI it actually requires is greatly reduced, since it only requires an equivalent channelTherefore, the complexity of downlink channel estimation and the information amount of CSI fed back by the user to the base station can be reduced, wherein G represents the grouped group number, G is 1,2, …, G represents the total number of user groups in the cell, and the superscript represents the total number of the user groups in the celloptFirst three letters representing the English optimization, superscriptequRepresents the first three initials of equivalence (equivalent value).
Drawings
FIG. 1 is a diagram of a dual-layer precoding design model in a massive MIMO downlink system based on user grouping according to a preferred embodiment of the present invention;
fig. 2 is a flow chart of a double-layer precoding design method fusing zero forcing and taylor series expansion in a large-scale MIMO system.
Detailed Description
The technical solutions in the embodiments of the present invention will be described in detail and clearly with reference to the accompanying drawings. The described embodiments are only some of the embodiments of the present invention.
The technical scheme for solving the technical problems is as follows:
the following describes in detail an embodiment of the present invention with reference to fig. 1 and 2.
The large-scale MIMO downlink system works in an FDD mode, firstly, a base station sends a pilot frequency sequence to a user for downlink channel estimation, the user obtains a downlink CSI estimation value through the received pilot frequency sequence and feeds the CSI estimation value back to the base station through a feedback link, and the base station only needs to realize the design of an outer layer precoding matrix based on channel statistical information of each group and by using a Taylor series expansion mode to eliminate IUI among the groups; then, the actual channel and the outer layer precoding matrix are regarded as equivalent channels, so that the dimension reduction of the channel is realized, the complexity of channel estimation is reduced, the information feedback quantity of CSI in an uplink channel is reduced, and the frequency spectrum resource is saved; and finally, the base station realizes the design of an inner layer precoding matrix based on the equivalent channel and by applying a ZF technology to eliminate the IUI in the group. The invention not only realizes the elimination of the interference among users based on the form of user grouping, but also reduces the complexity of channel estimation, improves the system performance, reduces the information feedback quantity of CSI and saves the frequency spectrum resource.
First, as shown in fig. 1, consider a single-cell massive MIMO downlink system, where a cell includes a Uniform Linear Array (ULA) base station configured with M antennas and K single-antenna users. The K users are averagely divided into G groups, anG represents the total number of packets in a cell, G represents the group number after grouping, KgIndicating the number of users in the g-th group. The channel model is expressed as
WhereinRepresenting the channel vector between the base station to the kth user of the g group,representing the small-scale fading vectors between the base station to the kth user of the g group,each element in (a) is independent of the other and follows a complex gaussian distribution with a mean of 0, a variance of 1,represents the channel covariance matrix of the G-th group of users, and G is 1,2 …, GThe k-th row and l-th column elements of (1) can be expressed as
Where ^ (·) denotes an integral operation, θ denotes a central angle of each group, Δ denotes an angle spread, λ denotescRepresenting carrier wavelength, d antenna spacing, k and l representing the g-th group of channel covariance matrix RgThe kth row and the l column.
So that the received signal vectors of all users in a cell can be expressed as
y=HVWs+n
WhereinIndicating that all users in the cell receive the signal vector,represents the channel matrix from the base station to all users, andthe superscript H denotes the transpose conjugate operator of the matrix,representing the channel matrix between the base station to all users in the g-th group,the outer precoding matrix V of a cell is partitioned into G sub-matrices, e.g., V ═ V1V2…VG],Wherein the outer precoding matrix V of the g-th groupgSatisfy the requirement of With a representation dimension of Mg×MgThe identity matrix of (2). MgRepresents VgWhere the inner layer precoding matrix of a cell may be represented as W ═ diag ([ W)1W2…WG]),For the inner precoding matrix of the g-th group,wgkinner layer precoding vector representing kth user of the g-th group, and K is 1,2, …, KgAnd | | | wgk||2Table 1, diag (·)A diagonal matrix is shown.Representing the transmitted signal vector, sgSignal vectors representing all users in the g-th group sent by the base station to the cell satisfy E { sg0, E { · } denotes the desired operation,representing the background noise vector, ngRepresenting the background noise of the g-th group of users, each element in n is independent of each other and follows a complex gaussian distribution with mean 0 and variance 1. In addition, the average transmission signal power of the base station needs to satisfy: tr { VWWHVH}≤PT,PTRepresents the total transmitted signal power of the base station, where Tr {. cndot.) represents the trace operation of the matrix.
In a large-scale MIMO system based on an FDD working mode, a double-layer precoding design mode is adopted, and the complexity of downlink channel estimation and the CSI feedback quantity of an uplink channel are reduced. Wherein, the outer layer precoding matrix is used for eliminating IUI among groups, and the inner layer precoding matrix is used for eliminating IUI in groups.
For further analysis, the received signal vectors of all users in the g-th group can be expressed as
WhereinWhich represents a vector of the transmitted signal,the superscript T denotes the transpose operator of the matrix,indicating the base station to the Kth in the g-th groupgThe signals transmitted by the individual users are transmitted,represents a background noise vector, andthe signal received by the kth user in the g group can be expressed as
Provided that the inner precoding matrix for each group of users is designed based on ZF technique, then the SLNR of the kth user in the g-th group can be expressed as
Where | represents a modulo operation,designing outer precoding matrix of the g-th group such as SLNR in a manner of maximizing the SLNR of the kth user of the g-th group by representing noise power
Wherein argmax (·) represents the value of the argument when the function is maximized, and the outer precoding matrix V of the g-th group of usersgNeed to satisfy Representing dimension Mg×MgThe identity matrix of (2). By solving the above equation and optimizing the solved matrixAs an outer precoding matrix of the g-th group,upper label ofoptRepresenting the first three letters of the English optimization. Because of the fact that
After formula derivation and operation simplification, the method is used for solving the problems of the prior art
Furthermore, the specific design process of the outer precoding matrix of the g-th group is as follows
RgIs a semi-positive definite Hermitian matrix,is a positive definite Hermitian matrix. Let E { SLNRgkα, and the optimization problem of the trace ratio can be equivalent to the zero point problem of the optimization function f (α)
The function f (α) is a monotonically decreasing function of α, and it is known that f (0) ≧ 0, and f (+ ∞) ≦ 0, so that f (α) has a zero point.
And v (α) is a matrixThe normalized feature vector corresponding to the feature value β (α), i.e., | | v (α) | 1, | | | · | | represents the vector-2 norm operationβ '(α) denotes the first derivative of β (α) with respect to α, and superscript' denotes the derivation operation.
Based on the above analysis, the algorithm design steps of the outer layer pre-programmed matrix of the invention are summarized as follows:
The first step is as follows: t denotes the number of iterations, λtRepresenting the trace ratio obtained by iterative computation after the t iterative computation, making t equal to 0, and initializing the trace ratio
WhereinIs an initialized matrix, satisfiesλ0Represents the trace ratio value when the iteration number of the algorithm is 0.
The second step is that: for matrixDecomposing the characteristic value to obtain MgA maximum eigenvalueThe corresponding characteristic vectors form a matrix Vg(λt)。βk(λt) Indicating a track ratio of λtTime matrixThe kth largest eigenvalue of (a).
The third step: updating the trace ratio λt+1。
Representation βk(α) at α ═ λtApproximate estimation of the Taylor series expansion of (A) can be expressed as
And characteristic value βk(λt) About lambdatFirst derivative β ofk'(λt) Can be expressed as
Wherein v isk(λt) Indicating a track ratio of λtTime matrixThe feature vector corresponding to the kth maximum feature value of (1) isUpper label ofestRepresenting the first three letters of the english animation.
And an approximate estimate f of the optimization function f (α)est(α) can be expressed as
Let fest(α) when equal to 0, then
λt+1Denotes λtThe value after 1 iteration update is let λt+1=α。
The fourth step: if λt+1-λtIf | < epsilon, executing a fifth step, wherein epsilon represents an algorithm ending threshold value; otherwise t is t +1 and the second step is performed.
Fifth step optimal trace ratio αopt=λt+1,Through the method, the optimal outer precoding matrix of the g-th group is finally designed
Then, the actual channel HgOptimal outer precoding matrix with the g-th group of usersViewed as equivalent channelsSuch as
WhereinThe equivalent channel representing the g-th group of users,upper label ofequRepresenting the first three letters of the english equival.
Finally, the specific design process of the inner layer precoding matrix of the g group of users is as follows:
based on equivalent channelsAnd applying ZF technology to carry out inner layer precoding matrix calculation on the g group of usersIs designed as
WhereinIndicates the transmission power of the base station when transmitting information to each user in the g-th group,indicating the transmission power of the base station when transmitting information to the kth user in the g group. And inner layer precoding vectorsThe conditions are required to be satisfied:because the g-th group inner precoding matrix WgBased on equivalent channelsThrough the design, the complexity of the downlink channel estimation of the g-th group and the channel feedback information quantity are greatly reduced.
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.
Claims (5)
1. A double-layer precoding design method for a large-scale MIMO system fusing zero forcing and Taylor series expansion is characterized by comprising the following steps:
firstly, a user obtains a downlink Channel State Information (CSI) estimation value through a received pilot frequency sequence, and feeds the downlink Channel State Information (CSI) estimation value back to a base station through a feedback link; the base station obtains the received CSI estimation value by applying Taylor series expansion modeTo an optimal outer precoding matrixTo cancel interference IUI of users between groups and then to select the actual channel HgWith the optimal outer precoding matrixCombine to form equivalent channelsWherein G represents the group serial number after grouping, G is 1,2, …, G represents the total number of user groups in the cell, the superscript equ represents the first three initials of the equivalent value of the English equality, and the superscript opt represents the first three letters of the English optimization;
finally, the base station realizes the design of an inner layer precoding matrix based on an equivalent channel and by applying a zero forcing technology to eliminate the IUI in the group;
the downlink Channel State Information (CSI) estimated value can be expressed as
Wherein h isgk∈CM×1Representing the channel estimation vectors between the base station to the kth user of the g group,representing the small-scale fading vectors between the base station to the kth user of the g group,each element in (a) is independent of each other and follows a complex gaussian distribution with a mean value of 0, a variance of 1, M represents the total number of base station antennas,denotes a channel covariance matrix of the G-th group, and G is 1,2, …, G denotes a total number of user groupsThe g-th group of user channel covariance matricesThe k-th row and l-th column elements of (1) can be expressed as
Where ^ (·) denotes an integral operation, θ denotes a central angle of each group, Δ denotes an angle spread, λ denotescRepresenting carrier wavelength, d antenna spacing, k and l representing the g-th group of channel covariance matrix RgThe k-th row, the l-th column,the superscript c of (a) indicates the first letter of the channel's english word channel.
2. The method of claim 1, wherein the step of obtaining the outer precoding matrix from the CSI estimation value by the base station using taylor series expansion includes:
designing outer precoding matrix of g-th group by solving optimization function f (α)
Where α represents the trace ratio, Tr {. cndot. represents the trace operation of the matrix, max (·) represents the maximization operation,an outer precoding matrix representing the g-th group with dimension of M × Mg,MgRepresenting a matrix with a trace ratio of αThe number of the main characteristic values is,with a representation dimension of Mg×MgOf the identity matrix RfA channel covariance matrix representing the f-th group of users, f ≠ 1,2, …, G, and f ≠ G,representing background noise power, IMRepresenting an identity matrix with dimension of M multiplied by M, and superscript H represents the conjugate transpose of the matrix; by solving an optimisation functionG-th group of optimal outer precoding matrices Wherein argmax (·) represents the value of the argument when the function is maximized, and the outer precoding matrix V of the g-th group of usersgNeed to satisfy Representing dimension Mg×MgThe identity matrix of (2).
3. The massive MIMO system zero forcing and Taylor series expansion fused double-layer precoding design method as claimed in claim 2, wherein the actual channel H isgWith the optimal outer precoding matrixCombine to form equivalent channelsThe formula of (1) is:wherein Representing the channel matrix, K, between the base station and the group g of usersgThe total number of users in the g-th group,and the optimal precoding matrix is the g group.
4. The massive MIMO system zero forcing and Taylor series expansion fused double-layer precoding design method as claimed in claim 3, wherein the design step of the outer pre-coding matrix comprises:
starting to input: initialization of Rg,The first step is as follows: t denotes the number of iterations, λtRepresenting a trace ratio obtained by iterative computation after the t iterative computation, making t equal to 0, and initializing the trace ratio;
whereinIs an initialized matrix, satisfiesλ0Representing the trace ratio when the iteration times of the algorithm is 0;
the second step is that: for matrixDecomposing the characteristic value to obtain MgA maximum eigenvalueThe corresponding characteristic vectors form a matrix Vg(λt);
The third step: updating the trace ratio λt+1;
The fourth step: if λt+1-λtIf | < epsilon, executing a fifth step, wherein epsilon represents an algorithm ending threshold value; otherwise t is t +1, and executing the second step;
5. The massive MIMO system zero forcing and Taylor series expansion fused double-layer precoding design method as claimed in claim 3, wherein the design method is based on equivalent channelAnd the inner layer precoding matrix of the g group of users is designed by applying ZF technology as follows:
whereinIndicating when the base station transmits information to each user in the g-th groupThe transmission power of the transmitter,represents the transmission power of the base station when transmitting information to the kth user in the g group, and includes an inner precoding vectorThe conditions are required to be satisfied:because the g-th group inner precoding matrix WgBased on equivalent channelsAnd (5) designing.
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