CN111510403A - Large-scale MIMO system iterative signal detection method based on symmetry L Q - Google Patents

Large-scale MIMO system iterative signal detection method based on symmetry L Q Download PDF

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CN111510403A
CN111510403A CN202010289666.9A CN202010289666A CN111510403A CN 111510403 A CN111510403 A CN 111510403A CN 202010289666 A CN202010289666 A CN 202010289666A CN 111510403 A CN111510403 A CN 111510403A
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CN111510403B (en
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景小荣
陈洪燕
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Chongqing University of Post and Telecommunications
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    • 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
    • H04L25/0264—Arrangements for coupling to transmission lines
    • H04L25/0292—Arrangements specific to the receiver end
    • 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
    • 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
    • H04L25/03891—Spatial equalizers
    • H04L25/03898—Spatial equalizers codebook-based design
    • 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
    • H04L25/03891—Spatial equalizers
    • H04L25/03898—Spatial equalizers codebook-based design
    • H04L25/0391—Spatial equalizers codebook-based design construction details of matrices
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention relates to a large-scale MIMO system iterative signal detection method based on symmetry L Q, belonging to the technical field of wireless communication, the method firstly converts a multi-user signal recovery problem in a large-scale MIMO system into a linear equation solving system, then adopts a symmetry L Q (symmetry L Q, S-L Q) method to iteratively solve the linear equation system, and takes a solution vector of the linear equation system as an estimated value of a transmitted signal vector after the maximum iteration times are completed.

Description

Large-scale MIMO system iterative signal detection method based on symmetry L Q
Technical Field
The invention belongs to the technical field of wireless communication, and relates to a large-scale MIMO system iterative signal detection method based on symmetry L Q.
Background
With the increasing number of users using the mobile internet and the internet of things, in order to meet future requirements, a fifth Generation mobile communication system (5st Generation, 5G) becomes a research hotspot, and a Multiple-Input Multiple-Output (MIMO) technology is one of the main 5G technologies.
Although the large-scale MIMO system has excellent performance, due to the large increase of the number of antennas, the application to the business still faces a great problem, such AS high computation complexity of signal detection, the maximum likelihood (M L) detection algorithm is the optimal detection algorithm, but the computation complexity of the algorithm shows an exponential growth rule with the number of users increasing, in order to reduce the computation complexity of the M L detection algorithm, the K-best detection algorithm and the SD decoding detection algorithm are proposed one after another, the K-best detection algorithm is implemented by using a breadth-first strategy, the SD decoding detection algorithm is based on a depth-first strategy, the computation complexity of the two algorithms is still very high, therefore, the objective of reducing the computation complexity can be achieved by using a local Search optimization algorithm, such AS likelihood-raising Search algorithm (L elihood-using Search, L AS) and active Tabu Search (Tabu Search, TS), the basic idea of the two algorithms is to determine the optimal vector according to the initial vector, determine the optimal AS-adjacent-receiving algorithm, the N-N.
To date, many papers have shown that when the number of base station antennas and the number of transmitting antennas satisfy the condition of N > K, N represents the number of receiving antennas at the base station, and K represents the number of users using a single antenna, the channels between users gradually tend to be orthogonal, so if the influence of additive white gaussian noise is not considered, the linear detection algorithm can also achieve the performance of M L detection algorithms, such as Zero-Forcing (ZF) detection algorithm and Minimum Mean-Square Error (MMSE) detection algorithmThe inversion operation results in a too high computational complexity of the linear detection algorithm. In order to reduce the computational complexity of the MMSE detection algorithm, Cholesky decomposition is adopted to avoid the operation of matrix inversion, but the computational complexity of the method is O (K)3) And the method is difficult to be applied to practice, so that the problem of high computational complexity of the traditional linear detection algorithm must be solved.
Disclosure of Invention
In view of this, the present invention provides a symmetric L Q-based iterative signal detection method for a large-scale MIMO system, which solves the problem of excessive computational complexity of the conventional linear detection algorithm due to the inversion operation of a high-dimensional matrix.
In order to achieve the purpose, the invention provides the following technical scheme:
a large-scale MIMO system iterative signal detection method based on symmetry L Q comprises the following steps:
s1: converting a multi-user signal recovery problem in a large-scale MIMO system into a linear equation solving system;
and S2, iteratively solving the linear equation set by adopting a Symmetric L Q (symmetry L Q, S-L Q) method, and taking a solution vector of the linear equation set as an estimated value of a transmission signal vector after the maximum iteration times are finished.
Further, the step S1 specifically includes: in an uplink multi-user large-scale MIMO system, a base station is provided with N receiving antennas to serve K single-antenna users; the base station receives the signal vector y as Hx + n by minimum mean-Square Error (MMSE), and the user transmits the estimated value of the vector x
Figure BDA0002449906560000021
Wherein F ═ HHH+σ2IK)-1HHAn MMSE equalization matrix; g is HHH，W＝G+σ2IK，
Figure BDA0002449906560000022
Then satisfy
Figure BDA0002449906560000023
Then, the problem of signal detection is converted into the solution of a linear equation set; wherein y isN×1Is a received signal vector, xK×1Is a transmitted signal vector, HN×KIs a channel matrix; n is a noise vector, assumed to obey a mean of 0 and a covariance matrix of σ2INComplex Gaussian random variable of (I)NIs an N × N-dimensional unit matrix;
Figure BDA0002449906560000029
is an estimate of the transmitted signal vector, W is the MMSE filtering matrix,
Figure BDA00024499065600000210
is a matched filtered signal; (.)HIndicating the operation of conjugate transpose of the matrix, superscript (. cndot.)-1Representing the inversion of the matrix.
Further, the step S2 specifically includes iteratively solving the linear equation system by using a symmetric L Q method
Figure BDA0002449906560000024
In the t +1 th iteration, the solution vector is updated:
Figure BDA0002449906560000025
wherein, g(t+1)、c(t+1)And ζ(t+1)As an iteration coefficient, w(t)And v(t+1)For iterative vector, superscript (. cndot.)(t)Representing the T iteration, T ∈ 1,2, …, T, T representing the maximum iteration time, after finishing the T iterations, the linear equation set is
Figure BDA0002449906560000026
Solution vector of
Figure BDA00024499065600000211
As an estimate of the transmitted signal vector.
Further, a symmetric L Q method is used to iteratively solve the system of linear equations
Figure BDA0002449906560000028
The specific process comprises the following steps:
let w and v be two sets of linearly independent vectors, let Km＝span w，KmIs the right subspace, Lm＝span v，LmIs the left subspace; for linear system of equations
Figure BDA00024499065600000318
Iterative solution is carried out to seek a value belonging to KmApproximate solution of
Figure BDA0002449906560000032
The condition of Petorv-Galerkin is satisfied:
Figure BDA0002449906560000033
by using the dominant diagonal dominance characteristic of the matrix W, the initial solution of the S-L Q iterative method is set as
Figure BDA0002449906560000034
The process of solving the linear equation set by the S-L Q iterative method is as follows:
(1) according to
Figure BDA0002449906560000035
Calculating an initial residual r(0)；
Setting rho | | | r(0)||2、v(0)＝r(0)/ρ、w(0)＝v(0)Setting up an initial vector of
Figure BDA0002449906560000036
Initial parameter settings are β(0)＝0、
Figure BDA0002449906560000037
κ(0)＝、c＝-1、ζ(0)＝0、g (0)0 and
Figure BDA0002449906560000038
wherein | · | purple2Represents a 2-norm, 0K×1Is a K × 1-dimensional zero vector, superscript (·)(0)An initial value representing a setup iteration;
(2) the intermediate quantity is updated and the intermediate quantity is updated,
Figure BDA0002449906560000039
Figure BDA00024499065600000310
Figure BDA00024499065600000311
Figure BDA00024499065600000312
(3) updating a system of linear equations
Figure BDA00024499065600000313
The vector of the solution of (a) is,
Figure BDA00024499065600000314
(4) update the intermediate vector, w(t+1)＝ζ(t+1)w(t)-c(t+1)v(t+1)、
Figure BDA00024499065600000315
(5) Judging whether T is true or not, if so, finishing iteration and outputting
Figure BDA00024499065600000316
Otherwise, jumping to the step (2); after completing T iterations, the solution vector of the linear equation system
Figure BDA00024499065600000317
As an estimate of the transmitted signal vector.
The invention has the beneficial effects that: compared with the traditional linear detection algorithm, the iterative signal detection algorithm of the large-scale MIMO system avoids the operation of matrix inversion, greatly reduces the computational complexity, and can obtain the performance close to the MMSE detection algorithm after a plurality of iterative operations.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
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For the purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a diagram of a model of a MIMO communication system;
FIG. 2 is a general flowchart of a signal detection method in a low-complexity large-scale MIMO system according to the present invention;
fig. 3 is a flowchart of a specific implementation of the iterative signal detection algorithm of the massive MIMO system based on S-L Q provided in the present invention.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Referring to fig. 1 to fig. 3, a system environment according to an embodiment of the present invention is a multi-user massive MIMO system, as shown in fig. 1. Suppose a massive MIMO system is configured with N antennas and K (K < N) single-antenna user equipments at the base station end. At the transmitting end, K users transmit respective signals to be transmitted simultaneously through respective transmitting antennas. At the receiving end, the base station performs signal detection according to the received combined signal, thereby recovering the transmitted signal. Therefore, the base station received signal in the massive MIMO system can be expressed as:
y＝Hx+n
wherein y isN×1Is a received signal vector, xK×1Is a vector of transmitted signals, HN×KIs a Channel matrix, and each element is independent from each other, obeys complex gaussian random variable distribution with mean value of 0 and variance of 1, and assumes the known Channel State Information (CSI) of the base station; n is a noise vector, assumed to obey a mean of 0 and a covariance matrix of σ2INComplex Gaussian random variable of (I)NIs an N × N dimensional identity matrix.
Based on the system and with reference to fig. 2 and fig. 3, each step of the iterative multi-user signal detection algorithm of the large-scale MIMO system based on the symmetric L Q method specifically includes:
(1) converting the multi-user signal recovery problem into solving a system of linear equations
At the receiving end, the base station end knows the received signal vector y and the channel matrix H, and can recover the signals of multiple users by using the equalizing filter matrix of MMSE. G is HHH，W＝G+σ2IK，
Figure BDA0002449906560000041
The MMSE equalization filter matrix can therefore be equivalent to: f ═ HHH+σ2IK)-1HHWhereby the user transmit vector has an estimated value of
Figure BDA0002449906560000042
Based on this, the target problem is converted into a solution of a system of linear equations. y isN×1Is a received signal vector, HN×KIs a channel matrix, n is a noise vector;
Figure BDA0002449906560000043
is an estimate of the transmitted signal vector, W is the MMSE filtering matrix,
Figure BDA0002449906560000044
is a matched filtered signal; (.)HIndicating the operation of conjugate transpose of the matrix, superscript (. cndot.)-1Representing the inversion of the matrix.
(2) Algorithm for iterative solution by adopting S-L Q method
Let w and v be two sets of linearly independent vectors, let Km＝span w，KmIs the right subspace, Lm＝span v，LmIs the left subspace. For linear system of equations
Figure BDA0002449906560000051
Iterative solution is carried out to seek a value belonging to KmApproximate solution of
Figure BDA0002449906560000052
The condition of Petorv-Galerkin is satisfied:
Figure BDA0002449906560000053
firstly, in order to accelerate the convergence rate of the S-L Q iterative method, the initial solution of the S-L Q iterative method can be set as
Figure BDA0002449906560000054
The S-L Q iterative method solves the linear equation set as follows:
a. according to
Figure BDA0002449906560000055
Calculating an initial residual r(0). Setting rho | | | r(0)||2、v(0)＝r(0)/ρ、w(0)＝v(0)Setting up an initial vector of
Figure BDA0002449906560000056
Initial parameter settings are β(0)＝0、
Figure BDA0002449906560000057
κ(0)＝、c＝-1、ζ(0)＝0、g (0)0 and
Figure BDA0002449906560000058
wherein | · | purple2Represents a 2-norm, 0K×1Is a K × 1-dimensional zero vector, superscript (·)(0)An initial value representing a setup iteration;
b. the intermediate quantity is updated and the intermediate quantity is updated,
Figure BDA0002449906560000059
Figure BDA00024499065600000510
Figure BDA00024499065600000511
Figure BDA00024499065600000512
c. the solution vector of the system of linear equations is updated,
Figure BDA00024499065600000513
the upper label (·)(t)Represents the T-th iteration, T ∈ 1,2, …, T;
d. update the intermediate vector, w(t+1)＝ζ(t+1)w(t)+c(t+1)v(t+1)、
Figure BDA00024499065600000514
e. Judging whether T is true or not, if so, finishing iteration and outputting
Figure BDA00024499065600000515
Otherwise, jumping to the step (2). After completing T iterations, the solution vector of the linear equation system
Figure BDA00024499065600000516
As an estimate of the transmitted signal vector.
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.

Claims (4)

1. A large-scale MIMO system iterative signal detection method based on symmetry L Q is characterized by comprising the following steps:
s1: converting a multi-user signal recovery problem in a large-scale MIMO system into a linear equation solving system;
and S2, iteratively solving the linear equation set by adopting a Symmetric L Q (symmetry L Q, S-L Q) method, and taking a solution vector of the linear equation set as an estimated value of a transmission signal vector after the maximum iteration times are finished.
2. The iterative signal detection method for the symmetric L Q-based massive MIMO system according to claim 1, wherein the step S1 specifically comprises assuming that a base station is equipped with N receiving antennas to serve K single-antenna users in the uplink multiuser massive MIMO system, receiving a signal vector y ═ Hx + N by the base station, receiving with Minimum Mean-Square Error (MMSE), and transmitting an estimated value of the vector x by the user
Figure FDA0002449906550000011
Wherein F ═ HHH+σ2IK)-1HHAn MMSE equalization matrix; g is HHH，W＝G+σ2IK，
Figure FDA0002449906550000012
Then satisfy
Figure FDA0002449906550000013
Then, the problem of signal detection is converted into the solution of a linear equation set; wherein y isN×1Is receivingSignal vector, xK×1Is a transmitted signal vector, HN×KIs a channel matrix; n is a noise vector, assumed to obey a mean of 0 and a covariance matrix of σ2INComplex Gaussian random variable of (I)NIs an N × N-dimensional unit matrix;
Figure FDA0002449906550000014
is an estimate of the transmitted signal vector, W is the MMSE filtering matrix,
Figure FDA0002449906550000015
is a matched filtered signal; (.)HIndicating the operation of conjugate transpose of the matrix, superscript (. cndot.)-1Representing the inversion of the matrix.
3. The iterative signal detection method for massive MIMO system based on symmetry L Q of claim 1, wherein the step S2 comprises applying a symmetry L Q method to solve the linear system of equations iteratively
Figure FDA0002449906550000016
In the t +1 th iteration, the solution vector is updated:
Figure FDA0002449906550000017
wherein, g(t+1)、c(t+1)And ζ(t+1)As an iteration coefficient, w(t)And v(t+1)For iterative vector, superscript (. cndot.)(t)Representing the T iteration, T ∈ 1,2, the
Figure FDA0002449906550000018
Solution vector of
Figure FDA0002449906550000019
As an estimate of the transmitted signal vector.
4. The symmetrical L Q-based large-scale MIMO system iterative signal detection method of claim 3, wherein a symmetrical L Q method is adopted to solve the linear equation system iteratively
Figure FDA00024499065500000110
The specific process comprises the following steps:
let w and v be two sets of linearly independent vectors, let Km＝span w，KmIs the right subspace, Lm＝span v，LmIs the left subspace; for linear system of equations
Figure FDA00024499065500000111
Iterative solution is carried out to seek a value belonging to KmApproximate solution of
Figure FDA00024499065500000112
The condition of Petorv-Galerkin is satisfied:
Figure FDA00024499065500000113
by using the dominant diagonal dominance characteristic of the matrix W, the initial solution of the S-L Q iterative method is set as
Figure FDA0002449906550000021
The process of solving the linear equation set by the S-L Q iterative method is as follows:
(1) according to
Figure FDA0002449906550000022
Calculating an initial residual r(0)；
Setting rho | | | r(0)||2、v(0)＝r(0)/ρ、w(0)＝v(0)Setting up an initial vector of
Figure FDA0002449906550000023
Initial parameter settings are β(0)＝0、
Figure FDA0002449906550000024
κ(0)＝ρ、c＝-1、ζ(0)＝0、g(0)0 and
Figure FDA0002449906550000025
wherein | · | purple2Represents a 2-norm, 0K×1Is a K × 1-dimensional zero vector, superscript (·)(0)An initial value representing a setup iteration;
(2) the intermediate quantity is updated and the intermediate quantity is updated,
Figure FDA0002449906550000026
Figure FDA0002449906550000027
Figure FDA0002449906550000028
Figure FDA0002449906550000029
(3) updating a system of linear equations
Figure FDA00024499065500000210
The vector of the solution of (a) is,
Figure FDA00024499065500000211
(4) update the intermediate vector, w(t+1)＝ζ(t+1)w(t)+c(t+1)v(t+1)、
Figure FDA00024499065500000212
(5) Judging whether T is true or not, if so, finishing iteration and outputting
Figure FDA00024499065500000213
Otherwise, jumping to the step (2); after completing T iterations, the solution vector of the linear equation system
Figure FDA00024499065500000214
As an estimate of the transmitted signal vector.
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