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 PDF

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CN107086886B
CN107086886B CN201710243584.9A CN201710243584A CN107086886B CN 107086886 B CN107086886 B CN 107086886B CN 201710243584 A CN201710243584 A CN 201710243584A CN 107086886 B CN107086886 B CN 107086886B
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景小荣
李敏
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Wang Ping
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0619—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
    • H04B7/0621—Feedback content
    • H04B7/0626—Channel coefficients, e.g. channel state information [CSI]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L2025/0335—Arrangements for removing intersymbol interference characterised by the type of transmission
    • H04L2025/03426—Arrangements for removing intersymbol interference characterised by the type of transmission transmission using multiple-input and multiple-output channels
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L2025/03592—Adaptation methods
    • H04L2025/03598—Algorithms
    • H04L2025/03611—Iterative algorithms
    • H04L2025/03617—Time recursive algorithms
    • H04L2025/03624—Zero-forcing

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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

Double-layer precoding design for large-scale MIMO system fusion zero forcing and Taylor series expansion
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 value
Figure BDA0001269976390000021
To cancel interference IUI of users between groups and then to select the actual channel HgWith the optimal outer precoding matrix
Figure BDA0001269976390000022
Combine to form equivalent channels
Figure BDA0001269976390000023
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 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
Figure BDA0001269976390000031
Wherein h isgk∈CM×1Representing the channel estimation vectors between the base station to the kth user of the g group,
Figure BDA0001269976390000032
representing the small-scale fading vectors between the base station to the kth user of the g group,
Figure BDA0001269976390000033
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,
Figure BDA0001269976390000034
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 matrix
Figure BDA0001269976390000035
The k-th row and l-th column elements of (1) can be expressed as
Figure BDA0001269976390000036
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,
Figure BDA0001269976390000037
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)
Figure BDA0001269976390000038
Where α represents the trace ratio, Tr {. cndot. represents the trace operation of the matrix, max (·) represents the maximization operation,
Figure BDA0001269976390000039
an outer precoding matrix representing the g-th group with dimension of M × Mg，MgRepresenting a matrix with a trace ratio of α
Figure BDA00012699763900000310
The number of the main characteristic values is,
Figure BDA00012699763900000312
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,
Figure BDA00012699763900000311
representing background noise power, IMRepresenting an identity matrix of dimension M by M, superscriptHRepresents a conjugate transpose of the matrix; by solving an optimisation function
Figure BDA0001269976390000041
G-th group of optimal outer precoding matrices
Figure BDA0001269976390000042
Figure BDA0001269976390000043
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
Figure BDA0001269976390000044
Figure BDA0001269976390000045
Representing dimension Mg×MgThe identity matrix of (2).
Further, the actual channel HgWith the optimal outer precoding matrix
Figure BDA0001269976390000046
Combine to form equivalent channels
Figure BDA0001269976390000047
The formula of (1) is:
Figure BDA0001269976390000048
wherein
Figure BDA0001269976390000049
Figure BDA00012699763900000410
Representing the channel matrix, K, between the base station and the group g of usersgThe total number of users in the g-th group,
Figure BDA00012699763900000411
and the optimal precoding matrix is the g group.
Further, the design step of the outer layer pre-woven matrix comprises:
starting to input: initialization of Rg，
Figure BDA00012699763900000412
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;
Figure BDA00012699763900000413
wherein
Figure BDA00012699763900000414
Is an initialized matrix, satisfies
Figure BDA00012699763900000415
λ0Representing the trace ratio when the iteration times of the algorithm is 0;
the second step is that: : for matrix
Figure BDA00012699763900000416
Decomposing the characteristic value to obtain MgA maximum eigenvalue
Figure BDA00012699763900000417
The 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，
Figure BDA0001269976390000051
Through the method, the optimal outer precoding matrix of the g-th group is finally designed
Figure BDA0001269976390000052
Further, based on equivalent channels
Figure BDA0001269976390000053
And the inner layer precoding matrix of the g group of users is designed by applying ZF technology as follows:
Figure BDA0001269976390000054
wherein
Figure BDA0001269976390000055
Represents 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 channels
Figure BDA0001269976390000056
And (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 matrix
Figure BDA0001269976390000057
The 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 matrix
Figure BDA0001269976390000058
Combined as equivalent channel
Figure BDA0001269976390000059
Realizing the dimension reduction of the channel; and then applying ZF technology based on equivalent channel
Figure BDA00012699763900000510
Designing inner precoding matrix WgThus, the CSI it actually requires is greatly reduced, since it only requires an equivalent channel
Figure BDA00012699763900000511
Therefore, 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, an
Figure BDA0001269976390000061
G 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
Figure BDA0001269976390000071
Wherein
Figure BDA0001269976390000072
Representing the channel vector between the base station to the kth user of the g group,
Figure BDA0001269976390000073
representing the small-scale fading vectors between the base station to the kth user of the g group,
Figure BDA0001269976390000074
each element in (a) is independent of the other and follows a complex gaussian distribution with a mean of 0, a variance of 1,
Figure BDA0001269976390000075
represents the channel covariance matrix of the G-th group of users, and G is 1,2 …, G
Figure BDA0001269976390000076
The k-th row and l-th column elements of (1) can be expressed as
Figure BDA0001269976390000077
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
Wherein
Figure BDA0001269976390000078
Indicating that all users in the cell receive the signal vector,
Figure BDA0001269976390000079
represents the channel matrix from the base station to all users, and
Figure BDA00012699763900000710
the superscript H denotes the transpose conjugate operator of the matrix,
Figure BDA00012699763900000711
representing the channel matrix between the base station to all users in the g-th group,
Figure BDA00012699763900000712
the outer precoding matrix V of a cell is partitioned into G sub-matrices, e.g., V ═ V1V2…VG]，
Figure BDA00012699763900000713
Wherein the outer precoding matrix V of the g-th groupgSatisfy the requirement of
Figure BDA00012699763900000714
Figure BDA00012699763900000715
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])，
Figure BDA00012699763900000716
For the inner precoding matrix of the g-th group,
Figure BDA00012699763900000717
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.
Figure BDA00012699763900000718
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,
Figure BDA0001269976390000081
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
Figure BDA0001269976390000082
Wherein
Figure BDA0001269976390000083
Which represents a vector of the transmitted signal,
Figure BDA0001269976390000084
the superscript T denotes the transpose operator of the matrix,
Figure BDA0001269976390000085
indicating the base station to the Kth in the g-th groupgThe signals transmitted by the individual users are transmitted,
Figure BDA0001269976390000086
represents a background noise vector, and
Figure BDA0001269976390000087
the signal received by the kth user in the g group can be expressed as
Figure BDA0001269976390000088
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
Figure BDA0001269976390000089
Where | represents a modulo operation,
Figure BDA00012699763900000810
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
Figure BDA00012699763900000811
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
Figure BDA0001269976390000091
Figure BDA0001269976390000092
Representing dimension Mg×MgThe identity matrix of (2). By solving the above equation and optimizing the solved matrix
Figure BDA0001269976390000093
As an outer precoding matrix of the g-th group,
Figure BDA0001269976390000094
upper label ofoptRepresenting the first three letters of the English optimization. Because of the fact that
Figure BDA0001269976390000095
After formula derivation and operation simplification, the method is used for solving the problems of the prior art
Figure BDA0001269976390000096
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,
Figure BDA0001269976390000097
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)
Figure BDA0001269976390000098
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.
While
Figure BDA0001269976390000101
Figure BDA0001269976390000102
Representation matrix
Figure BDA0001269976390000103
And sorting the k characteristic values from large to small.
And v (α) is a matrix
Figure BDA0001269976390000104
The normalized feature vector corresponding to the feature value β (α), i.e., | | v (α) | 1, | | | · | | represents the vector-2 norm operation
Figure BDA0001269976390000105
β '(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:
starting to input: initialization of Rg，
Figure BDA0001269976390000106
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
Figure BDA0001269976390000107
Wherein
Figure BDA0001269976390000108
Is an initialized matrix, satisfies
Figure BDA0001269976390000109
λ0Represents the trace ratio value when the iteration number of the algorithm is 0.
The second step is that: for matrix
Figure BDA00012699763900001010
Decomposing the characteristic value to obtain MgA maximum eigenvalue
Figure BDA00012699763900001011
The corresponding characteristic vectors form a matrix Vg(λt)。βk(λt) Indicating a track ratio of λtTime matrix
Figure BDA00012699763900001012
The kth largest eigenvalue of (a).
The third step: updating the trace ratio λt+1。
Figure BDA00012699763900001013
Representation βk(α) at α ═ λtApproximate estimation of the Taylor series expansion of (A) can be expressed as
Figure BDA00012699763900001014
And characteristic value βk(λt) About lambdatFirst derivative β ofk'(λt) Can be expressed as
Figure BDA0001269976390000111
Wherein v isk(λt) Indicating a track ratio of λtTime matrix
Figure BDA0001269976390000112
The feature vector corresponding to the kth maximum feature value of (1) is
Figure BDA0001269976390000113
Upper 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
Figure BDA0001269976390000114
MgRepresenting a matrix with a trace ratio of α
Figure BDA0001269976390000115
The number of main eigenvalues of (c).
Let fest(α) when equal to 0, then
Figure BDA0001269976390000116
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，
Figure BDA0001269976390000117
Through the method, the optimal outer precoding matrix of the g-th group is finally designed
Figure BDA0001269976390000118
Then, the actual channel HgOptimal outer precoding matrix with the g-th group of users
Figure BDA0001269976390000119
Viewed as equivalent channels
Figure BDA00012699763900001110
Such as
Figure BDA00012699763900001111
Wherein
Figure BDA00012699763900001112
The equivalent channel representing the g-th group of users,
Figure BDA00012699763900001113
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 channels
Figure BDA0001269976390000121
And applying ZF technology to carry out inner layer precoding matrix calculation on the g group of usersIs designed as
Figure BDA0001269976390000122
Wherein
Figure BDA0001269976390000123
Indicates the transmission power of the base station when transmitting information to each user in the g-th group,
Figure BDA0001269976390000124
indicating the transmission power of the base station when transmitting information to the kth user in the g group. And inner layer precoding vectors
Figure BDA0001269976390000125
The conditions are required to be satisfied:
Figure BDA0001269976390000126
because the g-th group inner precoding matrix WgBased on equivalent channels
Figure BDA0001269976390000127
Through 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 matrix
Figure FDA0002373181700000011
To cancel interference IUI of users between groups and then to select the actual channel HgWith the optimal outer precoding matrix
Figure FDA0002373181700000012
Combine to form equivalent channels
Figure FDA0002373181700000013
Wherein 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
Figure FDA0002373181700000014
Wherein h isgk∈CM×1Representing the channel estimation vectors between the base station to the kth user of the g group,
Figure FDA0002373181700000015
representing the small-scale fading vectors between the base station to the kth user of the g group,
Figure FDA0002373181700000016
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,
Figure FDA0002373181700000017
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 matrices
Figure FDA0002373181700000018
The k-th row and l-th column elements of (1) can be expressed as
Figure FDA0002373181700000019
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,
Figure FDA00023731817000000110
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)
Figure FDA0002373181700000021
Where α represents the trace ratio, Tr {. cndot. represents the trace operation of the matrix, max (·) represents the maximization operation,
Figure FDA0002373181700000022
an outer precoding matrix representing the g-th group with dimension of M × Mg，MgRepresenting a matrix with a trace ratio of α
Figure FDA0002373181700000023
The number of the main characteristic values is,
Figure FDA0002373181700000024
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,
Figure FDA0002373181700000025
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 function
Figure FDA0002373181700000026
G-th group of optimal outer precoding matrices
Figure FDA0002373181700000027
Figure FDA0002373181700000028
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
Figure FDA0002373181700000029
Figure FDA00023731817000000210
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 matrix
Figure FDA00023731817000000211
Combine to form equivalent channels
Figure FDA00023731817000000212
The formula of (1) is:
Figure FDA00023731817000000213
wherein
Figure FDA00023731817000000214
Figure FDA00023731817000000215
Representing the channel matrix, K, between the base station and the group g of usersgThe total number of users in the g-th group,
Figure FDA00023731817000000216
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，
Figure FDA00023731817000000217
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;
Figure FDA0002373181700000031
wherein
Figure FDA0002373181700000032
Is an initialized matrix, satisfies
Figure FDA0002373181700000033
λ0Representing the trace ratio when the iteration times of the algorithm is 0;
the second step is that: for matrix
Figure FDA0002373181700000034
Decomposing the characteristic value to obtain MgA maximum eigenvalue
Figure FDA0002373181700000035
The 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，
Figure FDA0002373181700000036
Through the method, the optimal outer precoding matrix of the g-th group is finally designed
Figure FDA0002373181700000037
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 channel
Figure FDA0002373181700000038
And the inner layer precoding matrix of the g group of users is designed by applying ZF technology as follows:
Figure FDA0002373181700000039
wherein
Figure FDA00023731817000000310
Indicating when the base station transmits information to each user in the g-th groupThe transmission power of the transmitter,
Figure FDA00023731817000000311
represents the transmission power of the base station when transmitting information to the kth user in the g group, and includes an inner precoding vector
Figure FDA00023731817000000312
The conditions are required to be satisfied:
Figure FDA00023731817000000313
because the g-th group inner precoding matrix WgBased on equivalent channels
Figure FDA00023731817000000314
And (5) designing.
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