CN109257080B - Multi-user phase noise compensation suppression method in downlink of large-scale MIMO system - Google Patents

Multi-user phase noise compensation suppression method in downlink of large-scale MIMO system Download PDF

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CN109257080B
CN109257080B CN201811045599.5A CN201811045599A CN109257080B CN 109257080 B CN109257080 B CN 109257080B CN 201811045599 A CN201811045599 A CN 201811045599A CN 109257080 B CN109257080 B CN 109257080B
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成先涛
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • 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
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • H04L27/2689—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation
    • H04L27/2691—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation involving interference determination or cancellation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • H04L27/2689—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation
    • H04L27/2692—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation with preamble design, i.e. with negotiation of the synchronisation sequence with transmitter or sequence linked to the algorithm used at the receiver

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Abstract

The invention belongs to the technical field of wireless communication, and relates to a multi-user phase noise compensation suppression method in a downlink of a large-scale MIMO system. The invention mainly comprises the following steps: the method comprises the steps of firstly calculating a common phase error of phase noise by using a receiving symbol at a position corresponding to a pilot frequency, compensating, then judging a data symbol, taking a judgment result as an initial value of the following iteration, then iterating by a variational Bayesian algorithm, and finally converging an estimated value of the data symbol to a stable value under the condition of a known receiving signal. The method has the advantages that the judgment of the data symbols in a high-order modulation mode in a large-scale MIMO system can be realized, the adverse effect caused by phase noise is effectively inhibited, and the interference of multiple users is also effectively inhibited through a proper precoding technology, so that the system performance is obviously improved.

Description

Multi-user phase noise compensation suppression method in downlink of large-scale MIMO system
Technical Field
The invention belongs to the technical field of wireless communication, and relates to a multi-user phase noise compensation suppression method in a downlink of a large-scale MIMO system.
Background
In a wireless communication system, a massive MIMO system is widely considered as a core technology of next-generation mobile communication due to its high spectral efficiency and energy efficiency, and by deploying hundreds of antennas at a base station, massive MIMO can achieve simultaneous service for tens of users under the same time and frequency resources, thereby significantly improving spectral efficiency. As the number of base station antennas increases, the antenna gain of massive MIMO may reduce the power of a transmission signal per user by a certain ratio, thereby significantly improving energy efficiency.
However, the signals of the massive MIMO communication system are affected by the non-linear factors of the rf devices in addition to the fading of the channel during the transmission process, and these two factors degrade the performance of the receiving end system. The non-ideal part of the radio frequency front end in the communication system mainly comprises phase noise, IQ amplitude phase imbalance, nonlinear distortion of a power amplifier and the like, and the phase noise is actually a representation of the frequency stability of a frequency source. In general, frequency stability is divided into long-term frequency stability and short-term frequency stability. The short-term frequency stability refers to phase fluctuation or frequency fluctuation caused by random noise. As for the slow frequency drift due to temperature, aging, etc., it is called long-term frequency stability. The problem of short-term stability is usually mainly considered, and phase noise can be regarded as short-term frequency stability and is merely two different representations of a physical phenomenon. For an oscillator, frequency stability is a measure of how well it produces the same frequency over a specified time range. If there is a transient change in the signal frequency, which cannot be kept constant, then there is instability in the signal source, which is due to phase noise.
In a large-scale MIMO communication system, both the transmitting end and the receiving end need to generate corresponding carriers to complete the spectrum conversion between the corresponding radio frequency and the baseband. However, the crystal oscillator generating the carrier wave has a certain difference from the phase-locked loop, which causes a short-term random difference between the carrier frequency and the target frequency, and further causes a random phase jump of the generated sine wave signal, which is expressed as phase noise. For the modulation mode of orthogonal frequency division multiplexing, phase noise can generate common phase error and inter-carrier interference, and for the case of multiple users, the base station has multi-user interference when communicating with different users, which seriously affects the performance of communication.
Disclosure of Invention
The invention aims to provide a phase noise compensation suppression method for a multi-user downlink of a large-scale MIMO-OFDM system, which improves the reliability of signal transmission and reduces the error rate.
The method adopts an expectation maximization algorithm, wherein the expectation maximization algorithm is an algorithm for solving posterior distribution of unknown random variables, and the mean and the variance of the hidden variables of the samples under the known conditions are obtained through continuous iteration.
In order to facilitate the understanding of the technical solution of the present invention by those skilled in the art, a system model adopted by the present invention will be described first.
Considering the model of the downlink of the MIMO OFDM system with phase noise, a transmitting end is provided with M antennas, a receiving end is provided with K users, each user is provided with 1 antenna, and the time domain channel vector between the mth antenna of the transmitting end and the kth antenna of the receiving end is recorded as
Figure BDA0001793216310000021
Where L is the length of the channel vector. For each OFDM symbol, the time domain signal expression of the kth user at the receiving end is as
Figure BDA0001793216310000022
Wherein the content of the first and second substances,
Figure BDA0001793216310000023
is the time domain received signal of the kth user, N is the number of OFDM subcarriers,
Figure BDA0001793216310000024
is the Toeplitz matrix of the channel from the mth transmitting antenna to the antenna of the kth user at the receiving end, whose column 1 is
Figure BDA0001793216310000025
Wherein 01×(N-L)Representing a row vector of elements all 0 and length N-L. P is belonged to CN×NRepresenting a phase noise matrix common across all transmit side antennas,
Figure BDA0001793216310000026
wherein theta isnRepresenting the phase noise sample value at the nth time instant in the OFDM symbol. F is belonged to CN×NIs a normalized FFT matrix whose ith row, jth element is
Figure BDA0001793216310000027
Figure BDA0001793216310000028
Is the precoding weight coefficient matrix of the mth antenna of the transmitting end to the kth user data,
Figure BDA0001793216310000029
dk'＝[dk',1,dk',2,…,dk',N]Tis a frequency domain transmit symbol sequence for the k' th user containing data and pilot.
Figure BDA00017932163100000210
Is a complex white gaussian noise sequence in the time domain,
Figure BDA00017932163100000211
Figure BDA00017932163100000212
can be decomposed into the following forms:
Figure BDA00017932163100000213
wherein Hm,k＝diag{[Hm,k,1,Hm,k,2,…,Hm,k,N]TAre multiplied by
Figure BDA00017932163100000214
Substituting (2) into (1) to obtain
Figure BDA00017932163100000215
When FFT is performed on the above formula, the received signal of the frequency domain of the kth user at the receiving end is
Figure BDA0001793216310000031
Wherein n isk∈CN×1Is a complex white gaussian noise sequence in the frequency domain,
Figure BDA0001793216310000032
Figure BDA0001793216310000033
for interference in the received signal, it is assumed that it also satisfies a complex Gaussian distribution
Figure BDA0001793216310000034
Here, a precoding scheme based on ZF is adopted, and s is noted for the nth subcarrier in the OFDM symboln＝[d1,n,d2,n,…,dK,n]TIndicating to each user on this sub-carrierThe transmitted frequency domain symbol is the precoding matrix
Figure BDA0001793216310000035
Wherein the content of the first and second substances,
Figure BDA0001793216310000036
to ensure the energy of the transmitted signal before and after precoding to remain unchanged, let
Figure BDA0001793216310000037
Wherein alpha isnIs a constant factor of the number of bits in the sample,
Figure BDA0001793216310000038
then
Figure BDA0001793216310000039
The elements in (1) represent weight coefficients for the transmitted frequency domain data of different users, i.e.
Figure BDA00017932163100000310
After precoding, the data symbols sent on each sending end antenna on the subcarrier are
Figure BDA00017932163100000311
From the preceding symbol definitions
Figure BDA00017932163100000312
For the case where phase noise is not present, i.e., P ═ I, the frequency domain received signal is
Figure BDA0001793216310000041
The data symbols may be decided by a maximum likelihood criterion and the nth data symbol for the kth user may be estimated by
Figure BDA0001793216310000042
Where S is the set of constellation points.
For the case of the presence of phase noise, firstly the symbol sequence d is usedkK is 1,2, …, the pilots in K make a rough estimate of the phase noise, in (4), the FPFHIs a Toeplitz matrix with column 1 as [ P1,P2,…,PN]TWherein
Figure BDA0001793216310000043
Considering only FPFHThe element on the diagonal of (1), i.e. FPFHAssuming a diagonal matrix, then (4) can be simplified to
Figure BDA0001793216310000044
Wherein
Figure BDA0001793216310000045
Is the common phase error. Let the number of pilot frequencies in one OFDM symbol be S, and the pilot frequencies in different user data sequences are all the same, and the pilot frequency symbols are respectively
Figure BDA0001793216310000046
The pilot frequency is uniformly inserted into the frequency domain transmitting symbol sequence d of each userkIn (1). Then for a particular pilot symbol
Figure BDA0001793216310000047
Can utilize corresponding received symbols
Figure BDA00017932163100000412
To P1Making a rough estimate, i.e.
Figure BDA0001793216310000048
Averaging s to obtain P1Is estimated value of
Figure BDA0001793216310000049
To pair
Figure BDA00017932163100000410
After normalization, the received symbol r in frequency domain iskPerforming compensation and using maximum likelihood detection to obtain initial decisions of data symbols, i.e.
Figure BDA00017932163100000411
On the other hand, equation (4) is modified as follows:
Figure BDA0001793216310000051
wherein the content of the first and second substances,
Figure BDA0001793216310000052
using approximate relationships due to the small value of phase noise
Figure BDA0001793216310000053
Can further deform (14) into
Figure BDA0001793216310000054
Wherein θ ═ θ1,θ2,…,θN]TThe phase noise vector is a real gaussian distribution, i.e., θ ═ N (0, Φ). 1 is an N-dimensional all-1-column vector.Since the covariance matrix Φ of θ is a real symmetric matrix, its eigenvalues are real numbers, and can be similarly diagonalized with an orthogonal matrix
Φ＝VΛVT (16)
Wherein Λ ═ diag { [ λ { [ lambda { ]1,λ2,…,λN]TIs a diagonal matrix having eigenvalues of Φ arranged in order from the largest to the smallest as diagonal elements, and V is an orthogonal matrix, each column of which is a unit eigenvector of the eigenvalue of the corresponding column of Λ. If the phase noise vector is linearly transformed
θ＝Vx (17)
From the nature of the gaussian distribution, x to N (0, Λ) are independent of each other because Λ is a diagonal matrix. Through calculation, it can be found that only the first few terms of diagonal elements in Λ are large in value, and other elements are small compared with the first few terms, so that only the first t term elements can be taken to approximate, and then Λ is a diagonal matrix of t × t, and corresponding V also takes the corresponding first t columns, so that the matrix becomes an N × t dimensional matrix. Substituting (17) into (15) can obtain
Figure BDA0001793216310000055
The EM algorithm is used below to pair x and dkAnd (6) estimating.
Since x is a real random vector, equation (18) is changed to a real form:
Figure BDA0001793216310000056
note the book
Figure BDA0001793216310000061
Figure BDA0001793216310000062
Then (19) can be written as
Figure BDA0001793216310000063
Receiving signals with known phase noise
Figure BDA0001793216310000064
Obeying a real Gaussian distribution, i.e.
Figure BDA0001793216310000065
Wherein the content of the first and second substances,
Figure BDA0001793216310000066
x has a prior probability density function of
Figure BDA0001793216310000067
Then x and
Figure BDA0001793216310000068
has a joint probability density function of
Figure BDA0001793216310000069
Taking logarithm of the above formula to obtain
Figure BDA00017932163100000610
The (24) is organized and can be written in the form of a gaussian probability density function plus a constant, which is the posterior probability density function of the phase noise expansion vector x. After the posterior probability density function of x is obtained, the expectation is obtained for the complex logarithm combined probability density function, and then the relation d is obtainedkAnd the result is made equal to zero, the data symbol d is obtainedkAn estimate of (d).
The invention is realized by the following steps:
s1, calculating and compensating a common phase error of the phase noise by using the received symbols at the positions corresponding to the pilot frequency, then carrying out data symbol judgment, and taking the judgment result as the initial value of the following iteration;
s2, the iteration of the variational Bayes algorithm is realized through the following steps:
s21, calculating the mean and variance of the posterior distribution of x:
Figure BDA0001793216310000071
Figure BDA0001793216310000072
wherein, note
Figure BDA0001793216310000073
S22, calculating data symbol dkIs estimated value of
Figure BDA0001793216310000074
S23, looping through steps S21-S22, estimating value d of data symbol under condition of known received signalkWill converge to a stable value.
The method has the advantages that the judgment of the data symbols in a high-order modulation mode in a large-scale MIMO system can be realized, the adverse effect caused by phase noise is effectively inhibited, and the interference of multiple users is also effectively inhibited through a proper precoding technology, so that the system performance is obviously improved.
Drawings
FIG. 1 is a schematic downlink diagram of a massive MIMO system under the influence of phase noise for use in the present invention;
FIG. 2 is a flow chart of the present invention for implementing phase noise estimate compensation suppression;
FIG. 3 is a graph comparing the effect of the number of different eigenvalues and the number of iterations on the system performance BER curve under 64QAM modulation;
fig. 4 is a graph comparing the effect of different levels of phase noise on the system performance BER curve under 64QAM modulation.
Detailed Description
The practical effects of the present invention will be described below with reference to the drawings.
The invention mainly comprises the following steps:
s1, in an initial case, calculating and compensating a common phase error of the phase noise by using the received symbol at the position corresponding to the pilot, then performing data symbol decision, and taking a decision result as an initial value of the following iteration, specifically:
Figure BDA0001793216310000081
wherein the content of the first and second substances,
Figure BDA0001793216310000082
is the common phase error and S represents the set of constellation points.
S2, the iteration of the variational Bayes inference algorithm is realized through the following steps:
s21, calculating the mean and variance of the posterior distribution of x:
Figure BDA0001793216310000083
Figure BDA0001793216310000084
s22, calculating the estimated value of the data symbol d
Figure BDA0001793216310000085
S23, loop through steps S21-S22, the estimated values of the data symbols converge to a stable value under the condition of known received signals.
Fig. 3 is a graph comparing the influence of the expectation-maximization algorithm on the system performance BER curve under the condition of adopting the number of eigenvalues and the number of pilot frequencies of different phase noise covariance matrices, wherein t in the legend represents the number of eigenvalues, fig. 4 is a graph comparing the performance BER curve of the expectation-maximization algorithm for different phase noise levels, the simulation adopts a 64QAM modulation method, fig. 3 takes the phase noise level under the frequency offset of 1MHz as-90 dBc/Hz, and fig. 4 takes the phase noise level under the frequency offset of 1MHz as-90 dBc/Hz, -88dBc/Hz and-86 dBc/Hz. The channels all adopt multi-path fast fading channels with 4 sparsity, the number of taps is 64, the channel changes once every time an OFDM symbol is sent, the number of receiving antennas is 64, and the number of OFDM subcarriers is 512.
As can be seen from fig. 3, in the presence of phase noise, the system performance is greatly affected without using the phase noise suppression algorithm proposed by the present invention, and when using the algorithm proposed by the present invention, the system performance is very close to the ideal curve without phase noise. And it can be seen that the algorithm is already able to achieve good performance when the number of eigenvalues is 3 and the number of iterations is 2, which means that the required complexity of the algorithm is so small that it is negligible.
As can be seen from fig. 4, the compensation suppression algorithm of the present invention achieves good effect for different phase noise level systems. In engineering, the phase noise level at 1MHz frequency offset is generally no less than-90 dBc/Hz. The phase noise level under the frequency offset of 1MHz in the figure 4 is up to-86 dBc/Hz, which shows that the algorithm can resist the phase noise with wider horizontal range and has larger practical value.

Claims (1)

1. A multi-user phase noise compensation suppression method in a downlink of a large-scale MIMO system is characterized in that a transmitting end of the system is provided with M antennas, the number of OFDM subcarriers is N, a receiving end of the system is provided with K users, each user is provided with 1 antenna, and a time domain channel vector between an mth antenna of the transmitting end and an antenna of a kth user of the receiving end is recorded as
Figure FDA0002899387830000011
Wherein L is the length of the channel vector, and for each OFDM symbol, the time domain signal expression of the kth user at the receiving end is:
Figure FDA0002899387830000012
wherein the content of the first and second substances,
Figure FDA0002899387830000013
is the time domain received signal of the kth user, N is the number of OFDM subcarriers,
Figure FDA0002899387830000014
is the Toeplitz matrix of the channel from the mth transmitting antenna to the antenna of the kth user at the receiving end, whose column 1 is
Figure FDA0002899387830000015
Wherein 01×(N-L)Representing row vectors with elements of 0 and length N-L; p is belonged to CN×NRepresenting a phase noise matrix common across all transmit side antennas,
Figure FDA0002899387830000016
wherein theta isnRepresenting a phase noise sampling value of the nth time in the OFDM symbol; f is belonged to CN×NIs a normalized FFT matrix whose ith row, jth element is
Figure FDA0002899387830000017
Figure FDA0002899387830000018
Is the precoding weight coefficient matrix of the mth antenna of the transmitting end to the kth user data,
Figure FDA0002899387830000019
dk'＝[dk',1,dk',2,…,dk',N]Tis a frequency domain transmission symbol sequence of the kth user containing data and pilot;
Figure FDA00028993878300000110
is a complex white gaussian noise sequence in the time domain,
Figure FDA00028993878300000111
Figure FDA00028993878300000112
can be decomposed into the following forms:
Figure FDA00028993878300000113
wherein Hm,k＝diag{[Hm,k,1,Hm,k,2,…,Hm,k,N]TAre multiplied by
Figure FDA00028993878300000114
Substituting (2) into (1) to obtain
Figure FDA00028993878300000115
When FFT is performed on the above formula, the received signal of the frequency domain of the kth user at the receiving end is
Figure FDA0002899387830000021
Wherein n isk∈CN×1Is a complex white gaussian noise sequence in the frequency domain,
Figure FDA0002899387830000022
Figure FDA0002899387830000023
for interference in the received signal, it is assumed that it also satisfies a complex Gaussian distribution
Figure FDA0002899387830000024
Adopting a precoding mode based on ZF, and recording s for the nth subcarrier in the OFDM symboln＝[d1,n,d2,n,…,dK,n]TRepresenting the frequency domain symbols transmitted to each user on this subcarrier, the precoding matrix is
Figure FDA0002899387830000025
Wherein the content of the first and second substances,
Figure FDA0002899387830000026
to ensure the energy of the transmitted signal before and after precoding to remain unchanged, let
Figure FDA0002899387830000027
Wherein alpha isnIs a constant factor of the number of bits in the sample,
Figure FDA0002899387830000028
then
Figure FDA0002899387830000029
The elements in (1) represent weight coefficients for the transmitted frequency domain data of different users, i.e.
Figure FDA00028993878300000210
After precoding, the data symbols sent on each sending end antenna on the subcarrier are
Figure FDA00028993878300000211
From the preceding symbol definitions
Figure FDA00028993878300000212
For the case where phase noise is not present, i.e., P ═ I, the frequency domain received signal is
Figure FDA0002899387830000031
The data symbol is judged through the maximum likelihood criterion, and the nth data symbol of the kth user can be estimated through the following formula
Figure FDA0002899387830000032
Where S is a set of constellation points;
for the case of the presence of phase noise, firstly the symbol sequence d is usedkK is 1,2, …, the pilots in K make a rough estimate of the phase noise, in (4), the FPFHIs a Toeplitz matrix with column 1 as [ P1,P2,…,PN]TWherein
Figure FDA0002899387830000033
Considering only FPFHThe element on the diagonal of (1), i.e. FPFHAssuming a diagonal matrix, then (4) can be simplified to
Figure FDA0002899387830000034
Wherein
Figure FDA0002899387830000035
Is a common phase error, the number of pilot frequencies in an OFDM symbol is set as S, the pilot frequencies in different user data sequences are the same, and the pilot frequency symbols are respectively
Figure FDA0002899387830000036
The pilot frequency is uniformly inserted into the frequency domain transmitting symbol sequence d of each userkPerforming the following steps; then for a particular pilot symbol
Figure FDA0002899387830000037
Using corresponding received symbols
Figure FDA0002899387830000038
To P1Making a rough estimate, i.e.
Figure FDA0002899387830000039
Averaging s to obtain P1Is estimated value of
Figure FDA00028993878300000310
To pair
Figure FDA00028993878300000311
After normalization, the received symbol r in frequency domain iskPerforming compensation and using maximum likelihood detection to obtain initial decisions of data symbols, i.e.
Figure FDA00028993878300000312
On the other hand, equation (4) is modified as follows:
Figure FDA0002899387830000041
wherein the content of the first and second substances,
Figure FDA0002899387830000042
using approximate relationships due to the small value of phase noise
Figure FDA0002899387830000043
Further deform (14) into
Figure FDA0002899387830000044
Wherein θ ═ θ1,θ2,…,θN]TA phase noise vector that is a real gaussian distribution, i.e., θ ═ N (0, Φ), with 1 being an N-dimensional all-1-column vector; since the covariance matrix phi of theta is a real symmetric matrix, and its eigenvalues are real numbers, the orthonormal matrix can be used for similarity diagonalization
Φ＝VΛVT (16)
Wherein Λ ═ diag { [ λ { [ lambda { ]1,λ2,…,λN]TA diagonal matrix in which eigenvalues of Φ arranged in order from the largest to the smallest are diagonal elements, V is an orthogonal matrix, and each column thereof is a unit eigenvector of the eigenvalue of the corresponding column of Λ; linear transformation of phase noise vectors
θ＝Vx (17)
According to the nature of Gaussian distribution, x to N (0, Λ) are independent from each other because Λ is a diagonal matrix; through calculation, the diagonal elements in the Λ have larger values of only the first items, and other elements are smaller than the first items, so that only the first t items are taken for approximation, the Λ is a diagonal matrix of t × t, and the corresponding V also takes the corresponding first t columns, so that the matrix becomes an N × t dimensional matrix; substituting (17) into (15) can obtain
Figure FDA0002899387830000045
Using EM algorithm to x and dkAnd (3) estimating:
since x is a real random vector, equation (18) is changed to a real form:
Figure FDA0002899387830000046
note the book
Figure FDA0002899387830000051
Figure FDA0002899387830000052
Then (19) is
Figure FDA0002899387830000053
Receiving signals with known phase noise
Figure FDA0002899387830000054
Obeying a real Gaussian distribution, i.e.
Figure FDA0002899387830000055
Wherein the content of the first and second substances,
Figure FDA0002899387830000056
x has a prior probability density function of
Figure FDA0002899387830000057
Then x and
Figure FDA0002899387830000058
has a joint probability density function of
Figure FDA0002899387830000059
Taking logarithm of the above formula to obtain
Figure FDA00028993878300000510
Sorting (24), writing the result into a form of adding a constant to a Gaussian distribution probability density function, wherein the Gaussian probability density function is a posterior probability density function of a phase noise expansion vector x;
the method is characterized by comprising the following steps:
s1, calculating and compensating a common phase error of the phase noise by using the received symbols at the positions corresponding to the pilot frequency, then carrying out data symbol judgment, and taking a judgment result as an initial value of subsequent iteration;
s2, iteration is carried out by adopting a variational Bayes inference algorithm:
s21, calculating the mean and variance of the posterior distribution of x:
Figure FDA0002899387830000061
Figure FDA0002899387830000062
wherein, note
Figure FDA0002899387830000063
S22, calculating the estimated value of the data symbol d
Figure FDA0002899387830000064
S23, loop through steps S21-S22, the estimated values of the data symbols converge to a stable value under the condition of known received signals.
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