CN108768480B - Method for estimating uplink data of large-scale MIMO system with phase noise - Google Patents
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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
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 asWhere 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
Wherein,is the time domain received signal on the mth antenna, N is the number of OFDM subcarriers,is the phase noise matrix of the mth antenna of the receiving end,is a Toeplitz channel matrix from the kth user to the mth antenna of the receiving end, the 1 st column of which isWherein 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 isdk=[dk,1,dk,2,…,dk,N]TIs the data or pilot sequence transmitted by the kth user.Is a complex white gaussian noise sequence in the time domain,
wherein Hm,k=diag{[Hm,k,1,Hm,k,2,…,Hm,k,N]T},
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 antennasHas a prior probability density function of
The expression for the frequency domain received signal is
Wherein T ism=FPmFHIs a Toeplitz matrix with column 1 as Tm(:,1)=[Tm,1,Tm,2,…,Tm,N]T,
WhereinConsidering only TmThe element on the diagonal of (1), i.e. TmAssumed to be a diagonal matrix, Tm=Tm,1I, (8) can be approximated by
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 respectivelyThe pilot frequency is uniformly inserted into the frequency domain transmitting symbol sequence d of each userkIn, i.e.Considering that all the phase noise values of the G (G-1, 2, …, G) th group antenna are the same, thenThen for a particular pilot symbolReceived symbols for all antennas in the corresponding group may be utilizedTo pairMaking a rough estimate, i.e.
Average r to obtainIs estimated value ofThen for all of the antennas in the group,to pairAfter normalization, the received symbol r in frequency domain ismCompensation followed by ZF merging
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
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)
Given by (7), the received signal on the mth antenna is known for both phase noise and data symbolsComplex gaussian distribution obeying
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
S22, calculating the mean and variance of the posterior distribution of the data symbol vector:
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
S22, calculating the mean and variance of the posterior distribution of the data symbol vector:
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 asWherein 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
Wherein,is the time domain received signal on the mth antenna, N is the number of OFDM subcarriers,is the phase noise matrix of the mth antenna of the receiving end,is a Toeplitz channel matrix from the kth user to the mth antenna of the receiving end, the 1 st column of which isWherein 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 isdk=[dk,1,dk,2,…,dk,N]TIs the data or pilot sequence sent by the kth user;is a complex white gaussian noise sequence in the time domain,
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 Has a prior probability density function of
The expression for the frequency domain received signal is
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;
whereinConsidering only TmThe element on the diagonal of (1), i.e. TmAssumed to be a diagonal matrix, Tm=Tm,1I, (8) can be approximated by
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 respectivelyThe pilot frequency is uniformly inserted into the frequency domain transmitting symbol sequence d of each userkIn, i.e.Considering again that all the phase noise values on the G-th group of antennas are the same, G is 1,2, …, G, thenThen for a particular pilot symbolReceived symbols for all antennas in the corresponding group may be utilizedTo pairMaking a rough estimate, i.e.
Average r to obtainIs estimated value ofThen for all of the antennas in the group,to pairAfter normalization, the received symbol r in frequency domain ismCompensation followed by ZF merging
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
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)
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 antennaComplex gaussian distribution obeying
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
S22, calculating the mean and variance of the posterior distribution of the data symbol vector:
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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