CN108881078B - Millimeter wave system double-end phase noise suppression method based on variational Bayesian inference - Google Patents

Abstract

The invention belongs to the technical field of wireless communication, and relates to a millimeter wave system double-end phase noise suppression method based on variational Bayesian inference. 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 invention has the advantages that the accurate data symbol estimation can be realized in a millimeter wave communication system under the condition that phase noise exists at the transmitting end and the receiving end, and the bit error rate performance of the system is obviously improved.

Description

Millimeter wave system double-end phase noise suppression method based on variational Bayesian inference

Technical Field

The invention belongs to the technical field of wireless communication, and relates to phase noise suppression on a millimeter wave communication system by using a variational Bayesian inference algorithm under the condition of phase noise.

Background

In recent years, millimeter wave wireless communication systems have been regarded as being popular among many wireless communication transmission schemes due to their advantages of huge unlicensed bandwidth, ultra-high transmission rate, strong security, anti-interference capability, and the like, and become a hotspot for current wireless communication field research, and are more likely to become one of the most important technologies in future wireless communication.

However, millimeter wave communication systems still face a number of problems to be solved, one of which is phase noise. In addition to experiencing channel fading, the signal is also affected by non-linearity factors of the rf device during transmission, which both degrade performance at the receiving end. 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 millimeter wave communication system under the condition of phase noise, and the bit error rate performance of the system under the severe hardware condition is improved.

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 OFDM system with phase noise at both the transmitting end and the receiving end, the time domain channel vector of the transmitting end and the receiving end is recorded as h ═ h₁,h₂,…,h_L]^TWhere L is the length of the channel vector. For each OFDM symbol, the receiving end time domain signal is expressed as

r＝P_rHP_tF^Hd+n (1)

Wherein r ∈ C^N×1Is a time domain received signal, N is the number of OFDM subcarriers,

and

respectively representing the phase noise matrix at the receiving end and at the transmitting end, H being the Toeplitz channel matrix,its 1 st column is H (: 1) ═ H^T,0_1×(N-L)]^TWherein 0 is_1×(N-L)Representing a row vector of elements all 0 and length N-L. F is belonged to C^N×NIs a normalized FFT matrix whose ith row, jth element is

d＝[d₁,d₂,…,d_N]^TIs a transmitted data or pilot sequence. n is an element of C^N×1Is a complex white gaussian noise sequence in the time domain,

in the absence of phase noise, P_r＝P_tWhen I is defined, then (1) degenerates into

r＝HF^Hd+n (2)

Since H is a Toeplitz matrix, it can be decomposed into the following form:

H＝F^HH_fF (3)

wherein H_f＝diag{[H₁,H₂,…,H_N]^TTherein of

Substituting (3) into (2), and performing FFT to obtain a frequency domain received signal without phase noise

r_f＝H_fd+n (4)

In this case, a decision can be made on the data symbol:

wherein r is_f,nIs represented by r_fS represents a set of constellation points.

The use of the sequence c [ -Ga128, Gu512, Gv512, -Gb128 is contemplated]^TChannel estimation is performed where Ga128 and Gb128 are length-128 sequences, as defined in the IEEE 802.11ad standard. Gu512 [ -Gb128, -Ga128,Gb128,-Ga128]，Gv512＝[-Gb128,Ga128,-Gb128,-Ga128]. Sequence c has the following properties:

where c (k) denotes the kth element of sequence c, and Gu512(k) and Gv512(k) denote the kth elements of Gu512 and Gv 512. The received symbols corresponding to c (k) (129. ltoreq. k. ltoreq.1280) are

Wherein theta is_p,r,k，θ_p,t,kAnd n_p,kThe receiving end phase noise, the transmitting end phase noise and the white gaussian noise respectively corresponding to the symbols c (k), neglecting the influence of the noises, and the channel coefficient can be estimated by the following formula

On the other hand, since the value of the phase noise is small, the approximate relation e can be utilized^jθ1+ j θ, and rewriting the formula (1) to

r＝diag{1+jθ_r}Hdiag{1+jθ_t}F^Hd+n (9)

Where 1 represents a full 1-column vector of length N, θ_r＝[θ_r,1,θ_r,2,…,θ_r,N]^TAnd theta_t＝[θ_t,1,θ_t,2,…,θ_r,N]^TThe phase noise vector being a real Gaussian distribution, i.e. p (theta)_r)＝p(θ_t) N (0, Φ). Due to theta_rAnd theta_tThe 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＝UΛU^T(10)

wherein Λ ═ diag { [ λ { [ lambda { ]₁,λ₂,…,λ_N]^TIs a diagonal matrix with diagonal elements of phi's descending eigenvalues, U is positiveAnd each column of the intersection matrix is an eigenvector of eigenvalues of 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≈VΓV^T(11)

Γ＝diag{[λ₁,λ₂,…,λ_I]^TIs a diagonal matrix with the first I eigenvalues in Λ as diagonal elements, V ∈ C^N×IIs a matrix consisting of the first I columns of the first U. For phase noise vector theta_rAnd theta_tMaking a linear transformation

From the nature of the Gaussian distribution, p (x)_r)＝p(x_t) N (0, Γ), x is a diagonal matrix, so x_rAnd x_tAre independent of each other. Substituting (12) into (9) to obtain

r＝diag{1+jVx_r}Hdiag{1+jVx_t}F^Hd+n (13)

x_rAnd x_tHas a prior probability density function of

The symbol sequence d is assumed to obey an a priori complex gaussian distribution as follows

p(d)＝CN(0,I)＝π^-Nexp{-||d||²} (15)

The received signal r follows a complex gaussian distribution with known phase noise and known data symbols

The invention is realized by the following steps:

s1, carrying out channel estimation by using a sequence correlation method;

s2, calculating a public phase error of the phase noise, compensating the received signal, and roughly judging the data symbol to be used as an initial value of 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 the phase noise spreading vector of the receiving end

S22, calculating the mean and variance of the posterior distribution of the phase noise spreading vector of the transmitting end

S23, calculating the mean and variance of the posterior distribution of the data symbol vector

S24, loop through steps S21-S23, the data symbol vector will converge to a stable value under known received signal conditions.

The invention has the advantages that the accurate data symbol estimation can be realized in a millimeter wave communication system under the condition that phase noise exists at the transmitting end and the receiving end, and the bit error rate performance of the system is obviously improved.

Drawings

FIG. 1 is a schematic diagram of a millimeter wave communication system model for use with the present invention;

FIG. 2 is a flow chart of an implementation of the phase noise suppression and data symbol estimation algorithm of the present invention;

FIG. 3 is a graph of BER performance of the algorithm of the present invention at different phase noise levels for a 16QAM modulation scheme over a LOS channel;

FIG. 4 is a graph of BER performance of the algorithm of the present invention at different phase noise levels for NLOS channel 16QAM modulation

Detailed Description

The invention is described in detail below with reference to the attached drawing figures:

s1, using sequence correlation method to estimate channel, the concrete method is

S2, calculating a public phase error of the phase noise, compensating the received signal, and then roughly judging the data symbol to be used as an initial value of 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 the phase noise spreading vector of the receiving end

S22, calculating the mean and variance of the posterior distribution of the phase noise spreading vector of the transmitting end

S23, calculating the mean and variance of the posterior distribution of the data symbol vector

S24, loop through steps S21-S23, the data symbol vector will converge to a stable value under known received signal conditions.

FIG. 3 shows the BER performance curve of the system under different phase noise levels of LOS channel, the modulation mode is 16QAM, the number of OFDM subcarriers is 512, the phase noise levels are respectively-90 dBc/Hz @1MHz, -88dBc/Hz @1MHz, -86dBc/Hz @1MHz, the characteristic value of the phase noise covariance matrix is 5, and the number of iterations is 2.

Fig. 4 is a system BER performance curve under different phase noise levels of an NLOS channel, the simulation setup is the same as fig. 3, and the overall performance has a larger gap compared with an LOS channel due to severe multipath fading of the NLOS channel, but the system performance can still approach an ideal curve by using the algorithm of the present invention, which shows that the algorithm of the present invention has strong universality.

Claims (1)

1. A millimeter wave system double-end phase noise suppression method based on variational Bayes inference sets the time domain channel vectors of a transmitting end and a receiving end as h ═ h in an OFDM system with phase noise at the transmitting end and the receiving end₁,h₂,…,h_L]^TWherein L is the length of the channel vector; for each OFDM symbol, the receiving end time domain signal is expressed as

r＝P_rHP_tF^Hd+n (1)

Wherein r ∈ C^N×1Is a time domain received signal, N is the number of OFDM subcarriers,

and

respectively representing the phase noise matrix of the receiving end and the transmitting end, and H is a Toeplitz channel matrix, and the 1 st column of the Toeplitz channel matrix is H (: 1) ═ H^T,0_1×(N-L)]^TWherein 0 is_1×(N-L)Representing row vectors with elements of 0 and length N-L; f is belonged to C^N×NIs a normalized FFT matrix whose ith row, jth element is

d＝[d₁,d₂,…,d_N]^TIs the transmitted data or pilot sequence; n is an element of C^N×1Is a complex white gaussian noise sequence in the time domain;

in the absence of phase noise, P_r＝P_tWhen I is defined, then (1) degenerates into

r＝HF^Hd+n (2)

Since H is a Toeplitz matrix, the decomposition is of the form:

H＝F^HH_fF (3)

wherein H_f＝diag{[H₁,H₂,…,H_N]^TTherein of

Substituting (3) into (2), and performing FFT to obtain a frequency domain received signal without phase noise

r_f＝H_fd+n (4)

And (3) judging the data symbols:

wherein r is_f,nIs represented by r_fS represents a set of constellation points;

using the sequence c [ -Ga128, Gu512, Gv512, -Gb128]^TPerforming channel estimation, wherein Ga128 and Gb128 are length-128 sequences, defined in the IEEE 802.11ad standard; gu512 [ -Gb128, -Ga128, Gb128, -Ga128]，Gv512＝[-Gb128,Ga128,-Gb128,-Ga128](ii) a Sequence c has the following properties:

wherein c (k) denotes the kth element of sequence c, Gu512(k) and Gv512(k) denote the kth elements of Gu512 and Gv 512; the received symbols corresponding to c (k) (129. ltoreq. k. ltoreq.1280) are

Wherein theta is_p,r,k，θ_p,t,kAnd n_p,kReceiving end phase noise, transmitting end phase noise and white Gaussian noise respectively corresponding to symbols c (k), neglecting the influence of the noises, and obtaining the channel coefficient by the following formula estimation

Using an approximate relation e^jθ1+ j θ, and rewriting the formula (1) to

r＝diag{1+jθ_r}Hdiag{1+jθ_t}F^Hd+n (9)

Where 1 represents a full 1-column vector of length N, θ_r＝[θ_r,1,θ_r,2,…,θ_r,N]^TAnd theta_t＝[θ_t,1,θ_t,2,…,θ_r,N]^TThe phase noise vector being a real Gaussian distribution, i.e. p (theta)_r)＝p(θ_t) N (0, Φ); due to theta_rAnd theta_tThe 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＝UΛU^T(10)

wherein Λ ═ diag { [ λ { [ lambda { ]₁,λ₂,…,λ_N]^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; setting the values of a plurality of terms of diagonal elements in Lambda to be larger than other elements, and only taking the first I term to carry out approximate calculation, namely

Φ≈VΓV^T(11)

Γ＝diag{[λ₁,λ₂,…,λ_I]^TIs a diagonal matrix with the first I eigenvalues in Λ as diagonal elements, V ∈ C^N×IIs a matrix consisting of the first I columns of the first U; for phase noise vector theta_rAnd theta_tMaking a linear transformation

From the nature of the Gaussian distribution, p (x)_r)＝p(x_t) N (0, Γ), x is a diagonal matrix, so x_rAnd x_tAre independent of each other; substituting (12) into (9) to obtain

r＝diag{1+jVx_r}Hdiag{1+jVx_t}F^Hd+n (13)

x_rAnd x_tHas a prior probability density function of

The symbol sequence d is assumed to obey an a priori complex gaussian distribution as follows

p(d)＝CN(0,I)＝π^-Nexp{-||d||²} (15)

The received signal r follows a complex gaussian distribution with known phase noise and known data symbols

Characterized in that the method comprises the following steps:

s1, carrying out channel estimation by using a sequence correlation method;

s2, calculating a public phase error of the phase noise, compensating the received signal, and roughly judging the data symbol to be used as an initial value of 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 the phase noise spreading vector of the receiving end

S22, calculating the mean and variance of the posterior distribution of the phase noise spreading vector of the transmitting end

S23, calculating the mean and variance of the posterior distribution of the data symbol vector

S24, loop through steps S21-S23, the data symbol vector will converge to a stable value under known received signal conditions.

Images