CN108768480B - Method for estimating uplink data of large-scale MIMO system with phase noise - Google Patents

Method for estimating uplink data of large-scale MIMO system with phase noise Download PDF

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CN108768480B
CN108768480B CN201810748661.0A CN201810748661A CN108768480B CN 108768480 B CN108768480 B CN 108768480B CN 201810748661 A CN201810748661 A CN 201810748661A CN 108768480 B CN108768480 B CN 108768480B
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成先涛
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    • H—ELECTRICITY
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    • 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
    • H04B7/0452—Multi-user MIMO systems
    • 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
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/0848—Joint weighting
    • H04B7/0851—Joint weighting using training sequences or error signal
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    • H04L25/03891—Spatial equalizers
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    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/36—Modulator circuits; Transmitter circuits
    • H04L27/362—Modulation using more than one carrier, e.g. with quadrature carriers, separately amplitude modulated
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    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/38—Demodulator circuits; Receiver circuits
    • H—ELECTRICITY
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Abstract

The invention belongs to the technical field of wireless communication, and relates to a method for estimating uplink data of a large-scale MIMO system with phase noise. The invention adopts a variational Bayes inference algorithm, which is an algorithm for solving posterior distribution of unknown random variables, and obtains the mean and variance of hidden variables of a sample under known conditions through continuous iteration. The method has the advantages that the data symbol estimation of the uplink of the large-scale MIMO system can be realized under the condition of the existence of phase noise, and the bit error rate performance of the system is obviously improved.

Description

Method for estimating uplink data of large-scale MIMO system with phase noise
Technical Field
The invention belongs to the technical field of wireless communication, and relates to data estimation and demodulation of a large-scale MIMO system uplink by using a variational Bayesian inference algorithm under the condition of phase noise.
Background
In modern wireless communication systems, massive MIMO systems are widely considered as core technologies of next-generation mobile communication due to their high spectral efficiency and energy efficiency, and in general, a base station has hundreds of antennas and can serve tens of users under the condition of simultaneous same frequency, thereby significantly improving spectral efficiency. As the number of base station antennas increases, the antenna gain of massive MIMO can significantly reduce the power of a transmission signal of each user, thereby improving energy efficiency.
However, massive MIMO systems still face a number of problems to be solved, one of which is phase noise. In addition to experiencing channel fading, signals of the massive MIMO communication system are affected by nonlinear factors of radio frequency devices during transmission, 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 method of orthogonal frequency division, the phase noise can generate common phase error and inter-carrier interference, which will seriously affect the performance of the system.
Disclosure of Invention
The invention aims to provide a data estimation and demodulation method aiming at an uplink of a large-scale MIMO-OFDM system under the condition of phase noise, and improve the bit error rate performance of the system under the severe hardware condition.
The invention adopts a variational Bayes inference algorithm, which is an algorithm for solving posterior distribution of unknown random variables, and obtains the mean and variance of hidden variables of a sample under known conditions 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 uplink of the MIMO OFDM system with phase noise, a transmitting end is provided with K users, each user is provided with 1 antenna, a receiving end base station is provided with M antennas, and a time domain channel vector between the kth user of the transmitting end and the mth antenna of the receiving end is recorded as
Figure GDA0002683145150000021
Where L is the length of the channel vector. For each OFDM symbol, the time domain signal expression of the mth antenna at the receiving end is as follows
Figure GDA0002683145150000022
Wherein,
Figure GDA0002683145150000023
is the time domain received signal on the mth antenna, N is the number of OFDM subcarriers,
Figure GDA0002683145150000024
is the phase noise matrix of the mth antenna of the receiving end,
Figure GDA0002683145150000025
is a Toeplitz channel matrix from the kth user to the mth antenna of the receiving end, the 1 st column of which is
Figure GDA0002683145150000026
Wherein 01×(N-L)Representing a row vector of elements all 0 and length N-L. F is belonged to CN×NIs a normalized FFT matrix whose ith row, jth element is
Figure GDA0002683145150000027
dk＝[dk,1,dk,2,…,dk,N]TIs the data or pilot sequence transmitted by the kth user.
Figure GDA0002683145150000028
Is a complex white gaussian noise sequence in the time domain,
Figure GDA0002683145150000029
Figure GDA00026831451500000210
can be decomposed into the following formsFormula (II):
Figure GDA00026831451500000211
wherein Hm,k＝diag{[Hm,k,1,Hm,k,2,…,Hm,k,N]T}，
And is
Figure GDA00026831451500000212
Substituting (2) into (1) to obtain
Figure GDA00026831451500000213
θm＝[θm,1,θm,2,…,θm,N]TThe phase noise vector being a real Gaussian distribution, i.e. thetamN (0, Φ). Due to thetamThe covariance matrix Φ of (c) is a real symmetric matrix whose eigenvalues are real numbers, and can be similarly diagonalized with an orthogonal matrix:
Φ＝UΛUT (4)
wherein Λ ═ diag { [ λ { [ lambda { ]1,λ2,…,λN]TIs a diagonal matrix with the diagonal elements being eigenvalues in descending order of Φ, and U is an orthogonal matrix with each column being an eigenvector of eigenvalues for the corresponding column of Λ. It can be found by calculation that the diagonal elements in Λ have only the first terms with larger values, and the other elements have smaller values than the first terms, and therefore can be approximated by taking only the first I term, i.e.
Φ≈VΓVT (5)
Γ＝diag{[λ1,λ2,…,λI]TIs a diagonal matrix with the first I eigenvalues in Λ as diagonal elements, V ∈ CN×IIs a matrix consisting of the first I columns of the first U. For phase noise vector thetamMaking a linear transformation
θm＝Uxm≈Vxm (6)
From the nature of the Gaussian distribution, xm＝N(0,Γ)，X is a diagonal matrix due to gammamAre independent of each other.
Now, when the receiving-end antennas are divided into G groups, each group has M/G ═ S antennas, and the S antennas in each group use the same oscillator, the values of the phase noise on the antennas in the group are the same, that is, for the antennas in the G-th (G ═ 1,2, …, G) group, there are antennas
Figure GDA0002683145150000031
Has a prior probability density function of
Figure GDA0002683145150000032
The expression for the frequency domain received signal is
Figure GDA0002683145150000033
Wherein T ism＝FPmFHIs a Toeplitz matrix with column 1 as Tm(:,1)＝[Tm,1,Tm,2,…,Tm,N]T，
Wherein
Figure GDA0002683145150000034
Considering only TmThe element on the diagonal of (1), i.e. TmAssumed to be a diagonal matrix, Tm＝Tm,1I, (8) can be approximated by
Figure GDA0002683145150000035
Let the number of pilot frequencies in one OFDM symbol be R, pilot frequencies in different user data sequences are all the same, and the pilot frequency symbols are respectively
Figure GDA0002683145150000036
The pilot frequency is uniformly inserted into the frequency domain transmitting symbol sequence d of each userkIn, i.e.
Figure GDA0002683145150000037
Considering that all the phase noise values of the G (G-1, 2, …, G) th group antenna are the same, then
Figure GDA0002683145150000041
Then for a particular pilot symbol
Figure GDA0002683145150000042
Received symbols for all antennas in the corresponding group may be utilized
Figure GDA0002683145150000043
To pair
Figure GDA0002683145150000044
Making a rough estimate, i.e.
Figure GDA0002683145150000045
Average r to obtain
Figure GDA0002683145150000046
Is estimated value of
Figure GDA0002683145150000047
Then for all of the antennas in the group,
Figure GDA0002683145150000048
to pair
Figure GDA0002683145150000049
After normalization, the received symbol r in frequency domain ismCompensation followed by ZF merging
Figure GDA00026831451500000410
Further, the decision of the data symbol can be made by (11), and the decided data symbol is used as an initial value of the algorithm iteration.
On the other hand, rewrite (3) to
Figure GDA00026831451500000411
Now assume a symbol sequence dkObey a prior complex Gaussian distribution as follows, and the data between different users are statistically independent of each other
p(dk)＝CN(0,I)＝π-Nexp{-||dk||2}, k＝1,2,…,K (8)
Figure GDA00026831451500000412
Given by (7), the received signal on the mth antenna is known for both phase noise and data symbols
Figure GDA00026831451500000413
Complex gaussian distribution obeying
Figure GDA00026831451500000414
The invention is realized by the following steps:
s1, calculating common phase error of phase noise at initial stage, ZF combining received signals on each antenna after compensation to obtain initial value of data symbol
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 the phase noise expansion vector
Figure GDA0002683145150000051
Figure GDA0002683145150000052
S22, calculating the mean and variance of the posterior distribution of the data symbol vector:
Figure GDA0002683145150000053
Figure GDA0002683145150000054
s23, loop through steps S21-S22, the data symbol vector will converge to a stable value under known received signal conditions.
The method has the advantages that the data symbol estimation of the uplink of the large-scale MIMO system can be realized under the condition of the existence of phase noise, and the bit error rate performance of the system is obviously improved.
Drawings
FIG. 1 is a schematic uplink 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 an implementation of the data estimation algorithm of the present invention;
FIG. 3 is a graph of BER performance using the algorithm of the present invention under different antenna groupings;
FIG. 4 is a graph of BER performance curves using the algorithm of the present invention at different phase noise levels;
Detailed Description
The invention is described in detail below with reference to the attached drawing figures:
s1, calculating common phase error of phase noise at initial stage, ZF combining received signals on each antenna after compensation to obtain initial value of data symbol
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 the phase noise expansion vector
Figure GDA0002683145150000061
Figure GDA0002683145150000062
S22, calculating the mean and variance of the posterior distribution of the data symbol vector:
Figure GDA0002683145150000063
Figure GDA0002683145150000064
s23, loop through steps S21-S22, the data symbol vector will converge to a stable value under known received signal conditions.
Fig. 3 is a bit error rate performance curve under different antenna grouping conditions, in simulation, the modulation mode is 64QAM, the channel length is 64, the number of base station antennas is 64, the number of users is 5, the number of OFDM subcarriers is 512, the phase noise level is-85 dBc/Hz @1MHz, the number of antenna groupings is 1, 8, and 64, the number of eigenvalues of the covariance matrix of the phase noise is 3, and the number of iterations of the algorithm is 1. As can be seen from the simulation curve, when the number of antenna groups is 64, that is, each antenna is regarded as 1 group, the system performance is the best, the performance gradually deteriorates as the number of groups decreases, and when all antennas are regarded as 1 group, satisfactory performance cannot be achieved, and at this time, the eigenvalue of the covariance matrix of the phase noise is selected to be 5, and the number of iteration times of the algorithm is selected to be 2, so that still better performance can be achieved.
FIG. 4 is a performance curve of bit error rate under different antenna grouping conditions, the number of the antenna grouping is fixed to 8, the phase noise level is respectively-90 dBc/Hz @1MHz, -85dBc/Hz @1MHz, -80dBc/Hz @1MHz, and other simulation parameters are the same as those in FIG. 3. It can be seen from the simulation result that the system performance gradually deteriorates with the improvement of the phase noise, but the algorithm of the present invention can achieve better phase noise suppression and obtain satisfactory BER performance, when the phase noise level is-80 dBc/Hz @1MHz, similar to the case of fig. 3 where the number of simulated antenna packets is 1, the eigenvalue of the covariance matrix of the phase noise is selected to be 5, and the iteration number of the algorithm is selected to be 2, so that better performance can still be achieved.

Claims (1)

1. A method for estimating uplink data of a large-scale MIMO system with phase noise sets the uplink of an MIMO OFDM system with phase noise, a transmitting end is provided with K users, each user is provided with 1 antenna, a receiving end base station is provided with M antennas, and a time domain channel vector between the kth user of the transmitting end and the mth antenna of the receiving end is recorded as
Figure FDA0002683145140000011
Wherein L is the length of the channel vector, and for each OFDM symbol, the time domain signal expression of the m-th antenna at the receiving end is
Figure FDA0002683145140000012
Wherein,
Figure FDA0002683145140000013
is the time domain received signal on the mth antenna, N is the number of OFDM subcarriers,
Figure FDA0002683145140000014
is the phase noise matrix of the mth antenna of the receiving end,
Figure FDA0002683145140000015
is a Toeplitz channel matrix from the kth user to the mth antenna of the receiving end, the 1 st column of which is
Figure FDA0002683145140000016
Wherein 01×(N-L)Representing row vectors with elements of 0 and length N-L; f is belonged to CN×NIs a normalized FFT matrix whose ith row, jth element is
Figure FDA0002683145140000017
dk＝[dk,1,dk,2,…,dk,N]TIs the data or pilot sequence sent by the kth user;
Figure FDA0002683145140000018
is a complex white gaussian noise sequence in the time domain,
Figure FDA0002683145140000019
Figure FDA00026831451400000113
the decomposition is in the form:
Figure FDA00026831451400000110
wherein Hm,k＝diag{[Hm,k,1,Hm,k,2,…,Hm,k,N]TAre multiplied by
Figure FDA00026831451400000111
Substituting (2) into (1) to obtain
Figure FDA00026831451400000112
θm＝[θm,1,θm,2,…,θm,N]TThe phase noise vector being a real Gaussian distribution, i.e. thetamN (0, Φ); setting thetamThe covariance matrix Φ of (a) is a real symmetric matrix whose eigenvalues are real numbers, and the orthogonal matrix is used for similarity diagonalization:
Φ＝UΛUT (4)
wherein Λ ═ diag { [ λ { [ lambda { ]1,λ2,…,λN]TThe matrix is a diagonal matrix, the diagonal elements are eigenvalues of phi in descending order, U is an orthogonal matrix, and each column of the orthogonal matrix is an eigenvector of the eigenvalue of the corresponding column of lambda; the diagonal elements in the lambda are set to have larger values of only the first terms, other elements are smaller than the first terms, and only the first I term is taken as an approximation, namely
Φ≈VΓVT (5)
Γ＝diag{[λ1,λ2,…,λI]TIs a diagonal matrix with the first I eigenvalues in Λ as diagonal elements, V ∈ CN×IIs a matrix consisting of the first I columns of the first U; for phase noise vector thetamMaking a linear transformation
θm＝Uxm≈Vxm (6)
From the nature of the Gaussian distribution, xmN (0, Γ), x is a diagonal matrix, so xmAre independent of each other;
when the receiving antennas are divided into G groups, each group has M/G-S antennas, and the S antennas in each group use the same oscillator, the values of phase noise on the antennas in the group are the same, that is, for the antennas in the G-th (G-1, 2, …, G) group, there are antennas
Figure FDA0002683145140000021
Figure FDA0002683145140000022
Has a prior probability density function of
Figure FDA0002683145140000023
The expression for the frequency domain received signal is
Figure FDA0002683145140000024
Wherein T ism＝FPmFHIs a matrix of Toeplitz,its 1 st column is Tm(:,1)＝[Tm,1,Tm,2,…,Tm,N]T，nmIs white gaussian noise;
wherein
Figure FDA0002683145140000025
Considering only TmThe element on the diagonal of (1), i.e. TmAssumed to be a diagonal matrix, Tm＝Tm,1I, (8) can be approximated by
Figure FDA0002683145140000026
Let the number of pilot frequencies in one OFDM symbol be R, pilot frequencies in different user data sequences are all the same, and the pilot frequency symbols are respectively
Figure FDA0002683145140000027
The pilot frequency is uniformly inserted into the frequency domain transmitting symbol sequence d of each userkIn, i.e.
Figure FDA0002683145140000028
Considering again that all the phase noise values on the G-th group of antennas are the same, G is 1,2, …, G, then
Figure FDA0002683145140000031
Then for a particular pilot symbol
Figure FDA0002683145140000032
Received symbols for all antennas in the corresponding group may be utilized
Figure FDA0002683145140000033
To pair
Figure FDA0002683145140000034
Making a rough estimate, i.e.
Figure FDA0002683145140000035
Average r to obtain
Figure FDA0002683145140000036
Is estimated value of
Figure FDA0002683145140000037
Then for all of the antennas in the group,
Figure FDA0002683145140000038
to pair
Figure FDA0002683145140000039
After normalization, the received symbol r in frequency domain ismCompensation followed by ZF merging
Figure FDA00026831451400000310
The decision of the data symbol can be carried out by the aid of the decision device (11), and the decided data symbol is used as an initial value of algorithm iteration;
rewriting (3) into
Figure FDA00026831451400000311
Setting a symbol sequence dkObey a prior complex Gaussian distribution as follows, and the data between different users are statistically independent of each other
p(dk)＝CN(0,I)＝π-Nexp{-||dk||2},k＝1,2,…,K (8)
Figure FDA00026831451400000312
Given by (7), the sum of the phase noise and the sumAccording to the condition that the symbols are known, the received signal on the m-th antenna
Figure FDA00026831451400000313
Complex gaussian distribution obeying
Figure FDA00026831451400000314
Characterized in that the data estimation method comprises the following steps:
s1, calculating common phase error of phase noise at initial stage, ZF combining received signals on each antenna after compensation to obtain initial value of data symbol
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 the phase noise expansion vector
Figure FDA0002683145140000041
Figure FDA0002683145140000042
S22, calculating the mean and variance of the posterior distribution of the data symbol vector:
Figure FDA0002683145140000043
Figure FDA0002683145140000044
s23, loop through steps S21-S22, the data symbol vector will converge to a stable value under known received signal conditions.
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