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CN111193534B - Low-complexity signal detection method in large-scale MIMO system - Google Patents

Low-complexity signal detection method in large-scale MIMO system Download PDF

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CN111193534B
CN111193534B CN202010017930.3A CN202010017930A CN111193534B CN 111193534 B CN111193534 B CN 111193534B CN 202010017930 A CN202010017930 A CN 202010017930A CN 111193534 B CN111193534 B CN 111193534B
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景小荣
文晶晶
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Nanjing Olay Technology Co ltd
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Abstract

The invention relates to a low-complexity signal detection method in a large-scale MIMO system, belonging to the technical field of wireless communication. Firstly, converting a signal detection problem in a large-scale MIMO system into a solution of a linear equation set; then solving a solution vector of a linear equation set based on the 2D-DSP; and finally, taking the solution vector after iteration for many times as an estimated value of the signal sent by the receiving end of the base station to each user. The invention breaks through the problem of high-dimensional matrix inversion related to the traditional linear detection method, uses 2D-DSP to iterate to realize solution vector solution, can quickly converge and approach the performance of the traditional linear detection algorithm through several iterations, and realizes compromise between performance and complexity; the method is simple in implementation process and wide in application range.

Description

Low-complexity signal detection method in large-scale MIMO system
Technical Field
The invention belongs to the technical field of wireless communication, and relates to a low-complexity signal detection method in a large-scale MIMO system.
Background
As one of key transmission technologies of a physical layer in a fifth-generation communication system, a large-scale Multiple Input Multiple Output (MIMO) technology provides services to Multiple users on the same time-frequency resource by configuring tens to hundreds of array antennas at a base station. The high diversity gain and the spatial resolution provided by the large-scale antenna array greatly improve the frequency spectrum efficiency and the energy efficiency of the system while realizing the transmission reliability. However, to fully utilize the advantages of massive MIMO technology, many bottleneck problems of wireless transmission are faced, one of which is the problem of uplink multi-user signal detection, and especially as the number of users increases, as the interference between users further increases, serious challenges are brought to high-quality signal recovery.
In a large-scale MIMO system, the optimal signal detector belongs to a Maximum Likelihood (ML) algorithm, but the algorithm needs to search all the transmitted signal combinations in a traversal manner, so that the required calculation amount increases exponentially with the product of the number of transmitting antennas and the modulation order. The huge computational complexity caused by the ML algorithm makes it difficult to apply in reality. In recent years, several approximately optimal detection algorithms have been proposed in succession for massive MIMO systems based on machine learning or artificial intelligence. The classical algorithms include a Likelihood Ascending Search (LAS) algorithm and a Reactive Tabu Search (RTS) algorithm. The two algorithms avoid the 'brute force' traversal search process of the ML algorithm, and the optimal estimated value of the transmitted signal vector can be obtained through multiple iterations only by giving the initial solutionThe computational complexity is O (K) respectively2)、ο(MK)+ο(K3) Where M denotes a QAM modulation order and K denotes the number of users (assuming that each user is provided with a single antenna). However, the performance of these two algorithms in the higher order modulation mode is not ideal. Wataru Fukuda combines with parallel interference cancellation to propose a Belief Propagation (BP) based algorithm. The Sheng Wu provides a random MCMC (random Markov Chain Monte Carlo, R-MCMC) signal detection algorithm, and the symbols in the current transmitted signal vector detection value are updated in a random mode, so that the flameout phenomenon of the traditional MCMC algorithm under the condition of high signal-to-noise ratio is effectively relieved, and the calculation complexity of the algorithm is about [ K ] (K)3). Based on a Factor Graph (FG) mathematical model, Tanumay Datta proposes an Approximate Message Propagation (AMP) based signal detection algorithm with a computational complexity of about omicron (KN). However, it should be noted that the above studies usually adopt a low-order modulation mode, and assume that the number of base station antennas is equal to the number of users, i.e., N is equal to K. In a practical system, due to the constraint of pilot pollution, the number of users K can only be much smaller than the number N of base station antennas, i.e., the system load factor K/N is 1. Research shows that, for a large-scale MIMO system, a base station can obtain performance close to ML even if a linear detection algorithm, such as Zero-Forcing (ZF) and Minimum Mean Square Error (MMSE) algorithms, is adopted, especially when the system load is small. However, these detection algorithms all involve a high-dimensional matrix inversion operation, which requires o (K), even if implemented using Cholesky decomposition3) The amount of calculation of (a) is large, and thus it is difficult to implement quickly and efficiently in practical use.
Disclosure of Invention
In view of this, the present invention provides an iterative signal detection method based on two-dimensional bi-continuous projection (2D-DSP) in a large-scale MIMO system, so as to solve the problem that the conventional linear detection algorithm involves high-dimensional matrix inversion, thereby obtaining a low-complexity fast signal detection method.
In order to achieve the purpose, the invention provides the following technical scheme:
a low-complexity signal detection method in a large-scale MIMO system specifically comprises the following steps:
s1: converting a signal detection problem in a large-scale MIMO system into a linear equation solving system;
s2: solving a linear equation set by using a Two-Dimensional Double continuous Projection (2D-DSP) iteration method;
s3: and the base station receiving end estimates the transmitted signal vector.
Further, in step S1, converting the signal detection problem in the massive MIMO system into a solution problem of a linear equation set, specifically including: in massive MIMO system, the base station end received signal vector y-Hx + n is filtered by Minimum Mean Square Error (MMSE), and the estimated value of x is expressed as
Figure GDA0002423342540000021
Deform it into
Figure GDA0002423342540000022
Wherein
Figure GDA0002423342540000023
A real-number domain channel matrix is represented,
Figure GDA0002423342540000024
representing a real-domain user transmitted signal vector,
Figure GDA0002423342540000025
representing a real-number domain noise vector,
Figure GDA0002423342540000026
representing a real-number domain MMSE filter matrix, G ═ HTH is a Graham matrix, I2KWhich represents an identity matrix of order 2K,
Figure GDA0002423342540000027
representing matched filtered signals, superscriptTIndicating transpose of matrix, superscript-1Representation matrix inversion, σ 22 represents the variance of elements in a real-number domain noise vectorN represents the number of base station antennas, and K represents the number of single-antenna users in a massive MIMO system.
Further, in step S2, the linear equation set is processed by using the 2D-DSP iterative method
Figure GDA0002423342540000028
Performing iterative solution, specifically: solution vector after i +1 th inner iteration in t-th outer iteration
Figure GDA0002423342540000029
Wherein
Figure GDA00024233425400000210
Represents the t-th outer iteration and the i + 1-th inner iteration solution vector, αt,iAnd betat,iRepresenting the iteration coefficient, gamma1And gamma2The unit vector is represented, T belongs to {1, 2.,. T }, i belongs to {1, 2.,. 2K }, T represents the maximum iteration number, and K represents the number of single-antenna users in the massive MIMO system.
Further, step S3 specifically includes: the solution vector after completing T iterations
Figure GDA00024233425400000211
As an estimate of the transmitted signal vector by the base station, wherein
Figure GDA0002423342540000031
And expressing the results of the T-th external iteration and the 2K-th internal iteration, wherein T expresses the maximum iteration number, and K expresses the number of single-antenna users in the large-scale MIMO system.
The invention has the beneficial effects that: the invention provides a low-complexity signal detection method by utilizing a two-dimensional double continuous projection (2D-DSP) iteration thought aiming at the signal detection problem in an uplink large-scale MIMO system. Compared with the traditional linear detection algorithm, the method solves the solution vector through a plurality of simple iterative operations, thereby avoiding the inversion operation of a high-dimensional matrix, greatly reducing the computational complexity and better realizing the compromise between the performance and the computational complexity.
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 model diagram of a massive MIMO communication system;
FIG. 2 is a general flowchart of a low complexity signal detection method in a massive MIMO system according to the present invention;
FIG. 3 is a flow chart of a specific implementation of the iterative signal detection method based on 2D-DSP according to the present invention;
fig. 4 is a graph comparing the change of the signal-to-noise ratio of the present invention with the existing MMSE signal detection algorithm.
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 4, a system environment of the present invention is a multi-user massive MIMO system as shown in fig. 1. Suppose that the system consists of a base station with N antennas and K single-antenna end users, and N > K is satisfied. K users form sending symbol vectors by respectively passing information bit streams to be transmitted through respective channel encoders and modulators
Figure GDA0002423342540000032
And transmitting from the transmitting antennas of the K users simultaneously. At the receiving end, the base station receives the signal
Figure GDA0002423342540000033
Signal recovery is performed. Order to
Figure GDA0002423342540000034
Representing the complex field channel matrix from K users to the base station, the base station receives the signal ycCan be expressed as:
yc＝Hcxc+nc
wherein n iscDenotes a mean of 0 and a covariance matrix of σ2INComplex gaussian background noise vector of, INRepresenting an identity matrix of order N.
In order to adapt to the 2D-DSP method, the signal model is first converted from the complex domain to the real domain for processing (in this embodiment, the variable without subscript c is a real variable).
Figure GDA0002423342540000041
Then the corresponding real number domain signal model is
y＝Hx+n
Where H represents the corresponding 2N x 2K dimensional real number domain channel matrix,
Figure GDA0002423342540000042
wherein
Figure GDA0002423342540000043
And
Figure GDA0002423342540000044
respectively representing the real part of the fetch vector/matrix andan imaginary part. Based on the above system and with reference to fig. 2 and fig. 3, the low-complexity signal detection method in the massive MIMO system provided by the present invention is described in detail.
(1) Converting signal detection problems in large-scale MIMO system into solving linear equation set
In massive MIMO systems, the bs-end received signal vector y-Hx + n is filtered by Minimum Mean Square Error (MMSE), and the estimated value of x can be expressed as
Figure GDA0002423342540000045
Deform it into
Figure GDA0002423342540000046
The signal detection problem in the large-scale MIMO system is then transformed into a solution problem of a linear system of equations.
Figure GDA0002423342540000047
A real-number domain channel matrix is represented,
Figure GDA0002423342540000048
representing a real-domain user transmitted signal vector,
Figure GDA0002423342540000049
representing a real-number domain noise vector,
Figure GDA00024233425400000410
representing a real-number domain MMSE filter matrix, G ═ HTH is a Graham matrix, I2KWhich represents an identity matrix of order 2K,
Figure GDA00024233425400000411
representing matched filtered signals, superscriptTIndicating transpose of matrix, superscript-1Representing the matrix inversion. Sigma2And 2, N respectively represents the variance of elements in the real number domain noise vector and the number of base station antennas, and K represents the number of single-antenna users in the massive MIMO system.
(2) Solving linear equation set by using two-dimensional dual continuous projection (2D-DSP) iteration method
The 2D-DSP method upwards xi ═ span { gamma } to the two-dimensional search subspace by imposing a Petrov-Galerkin condition1,γ2Project and require a two-dimensional constraint subspace η ═ span { γ }1,γ2Orthogonal to find solutions to the system of linear equations
Figure GDA00024233425400000412
Specifically, the Petrov-Galerkin condition requires that each internal iteration be in the two-dimensional subspace ξ ═ span { γ ═ span { (γ) }1,γ2Find an approximate solution in
Figure GDA00024233425400000413
At the same time, require the corresponding residual amount
Figure GDA00024233425400000414
And two-dimensional subspace η ═ span { γ ═1,γ2Are orthogonal, i.e.
Figure GDA00024233425400000415
And is
Figure GDA00024233425400000416
I.e. at the setting of the initial solution
Figure GDA00024233425400000417
The process of iteratively solving the system of linear equations by the 2D-DSP method can be analyzed as follows.
According to the 2D-DSP method, the result of the i +1 th internal iteration in the t-th external iteration process
Figure GDA00024233425400000418
Can be expressed as a number of times,
Figure GDA0002423342540000051
where T ∈ {1, 2.. multidata, T } represents an outer iterationThe number of times, T, represents the maximum number of external iterations; i ∈ {1, 2., 2K } represents the number of inner iterations, K represents the number of single-antenna users in a massive MIMO system. After executing the internal iteration for 2K times, the value of the external iteration time t is increased by 1; meanwhile, the value of i is increased by 1 every time the internal iteration is executed; alpha is alphat,iAnd betat,iCoefficients representing the i-th inner iteration in the t-th outer iteration. According to
Figure GDA0002423342540000052
Is provided with
Figure GDA0002423342540000053
By simplification, the coefficient αt,iAnd betat,iCan be expressed as:
Figure GDA0002423342540000054
wherein
Figure GDA0002423342540000055
l＝<Wγ1,γ1>ν＝<Wγ1,γ2>＝<Wγ2,γ1>，τ＝<Wγ2,γ2>Let gamma be1＝ei，γ2＝ej，eiAnd ejRespectively represent unit matrices I2KThe ith and jth columns of (1). K denotes the number of single antenna users in a massive MIMO system.
(3) Estimation of transmitted signal vectors by a base station receiving end
The solution vector after completing T iterations
Figure GDA0002423342540000056
As an estimate of the transmitted signal vector by the base station, wherein
Figure GDA0002423342540000057
Denotes the T th timeAnd the result of the outer iteration and the 2K-th inner iteration is shown, T represents the maximum iteration number, and K represents the number of users in the large-scale MIMO system.
Summarizing the analysis, the signal detection method in the low-complexity large-scale MIMO system is finally obtained. With reference to fig. 3, the detailed implementation steps of the specific implementation flow are summarized as follows:
1) initializing MMSE filter matrix W, matching filter output
Figure GDA0002423342540000058
Diagonal matrix D, the initial solution vector, of the MMSE filter matrix
Figure GDA0002423342540000059
And setting the parameter f to 3;
2) setting a loop variable initial value t-1 and i-1;
3) judging that i is less than or equal to f, if so, j is i-f +2K, otherwise, j is i-f;
4) obtaining iteration parameters of a 2D-DSP method and executing a two-dimensional bicontinuous projection iteration algorithm: and (3) calculating iteration method parameters:
λi＝Wi,iWi,j-Wi,j 2，
Figure GDA00024233425400000510
Figure GDA00024233425400000511
executing a two-dimensional bicontinuous projection iterative algorithm:
Figure GDA00024233425400000512
5) internal for loop variable ramp: i is i + 1;
6) judging whether the internal for loop variable i is smaller than 2K, if so, jumping to the step 3), otherwise, executing the step 7);
7) external for loop variable auto-increment: t is t + 1;
8) and judging whether the external for loop variable T is smaller than T, if so, jumping to the step 3), and if not, ending the program.
And (3) experimental verification: monte Carlo simulation is adopted to verify the performance of the MMSE signal detection algorithm based on the 2D-DSP. In the simulation, assuming that a transmission channel is subject to random Rayleigh fading, the code rate adopted by channel coding is 1/2, and the generated code word is [133 ]o171o](subscript o denotes octal) standard convolutional code, the modulation mode is 64-QAM and the user average transmit power is set to 1. The receiving end of the base station adopts a Viterbi decoding mode. The number N of base station antennas is 128, and the number K of users is 16. FIG. 4 shows a comparison graph of Bit Error Rate (BER) performance with Signal Noise Ratio (SNR) variation of MMSE Signal detection algorithm based on 2D-DSP, MMSE Signal detection algorithm based on Neumann series expansion and MMSE Signal detection algorithm based on Cholesky decomposition (MMSE Signal detection algorithm based on Neumann series expansion and MMSE Signal detection algorithm based on Cholesky decomposition both from "Large-scale MIMO detection for 3GPP LTE: algorithm and FPGA optimization, IEEE Journal of Selected bits in Signal Processing"). As can be seen from fig. 4, as the SNR increases, the BER of each algorithm gradually decreases; meanwhile, with the increase of the iteration times, the performance of the MMSE signal detection algorithm based on the 2D-DSP and the performance of the MMSE signal detection algorithm based on Neumann series expansion gradually approach the performance of the MMSE signal detection algorithm based on Cholesky decomposition. However, under the same iteration number, the performance of the MMSE signal detection algorithm based on the 2D-DSP is better than that of the MMSE signal detection algorithm based on Neumann series expansion.
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 (1)

1. A low-complexity signal detection method in a large-scale MIMO system is characterized by specifically comprising the following steps:
s1: converting a signal detection problem in a large-scale MIMO system into a linear equation solving system;
the method specifically comprises the following steps: in massive MIMO systems, the base station receive signal vector y ═ Hx + n is filtered by Minimum Mean Square Error (MMSE), and the estimated value of x is expressed as
Figure FDA0002840313240000011
Deform it into
Figure FDA0002840313240000012
Wherein
Figure FDA0002840313240000013
A real-number domain channel matrix is represented,
Figure FDA0002840313240000014
representing a real-domain user transmitted signal vector,
Figure FDA0002840313240000015
representing a real-number domain noise vector,
Figure FDA0002840313240000016
representing a real-number domain MMSE filter matrix, G ═ HTH is a Graham matrix, I2KWhich represents an identity matrix of order 2K,
Figure FDA0002840313240000017
representing matched filtered signals, superscriptTIndicating transpose of matrix, superscript-1Representation matrix inversion, σ2The/2 represents the variance of elements in the noise vector of the real number domain, N represents the number of base station antennas, and K represents the number of single-antenna users in the massive MIMO system;
s2: using Two-Dimensional Double sequential projection (Two-Dimensional Double sequential projection)ive Projection,2D-DSP) iterative method to solve a linear equation set; the method specifically comprises the following steps: solution vector after i +1 th inner iteration in t-th outer iteration
Figure FDA0002840313240000018
Wherein
Figure FDA0002840313240000019
Represents the t-th outer iteration and the i + 1-th inner iteration solution vector, αt,iAnd betat,iRepresenting the iteration coefficient, gamma1And gamma2The method comprises the steps of representing a unit vector, wherein T belongs to {1, 2., T }, i belongs to {1, 2., 2K }, T represents the maximum iteration number, and K represents the number of single-antenna users in a large-scale MIMO system;
s3: the estimation of the base station receiving end on the transmitted signal vector specifically comprises the following steps: the solution vector after completing T iterations
Figure FDA00028403132400000110
As an estimate of the transmitted signal vector by the base station, wherein
Figure FDA00028403132400000111
And expressing the results of the T-th external iteration and the 2K-th internal iteration, wherein T expresses the maximum iteration number, and K expresses the number of single-antenna users in the large-scale MIMO system.
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