CN115604815A - Millimeter wave communication system positioning method adopting low-precision quantization - Google Patents

Millimeter wave communication system positioning method adopting low-precision quantization Download PDF

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CN115604815A
CN115604815A CN202211122290.8A CN202211122290A CN115604815A CN 115604815 A CN115604815 A CN 115604815A CN 202211122290 A CN202211122290 A CN 202211122290A CN 115604815 A CN115604815 A CN 115604815A
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关雅静
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
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
    • 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
    • H04B7/0413—MIMO systems
    • H04B7/0452—Multi-user MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/024—Channel estimation channel estimation algorithms

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Abstract

The invention belongs to the technical field of wireless communication, and particularly relates to a millimeter wave communication system positioning method adopting low-precision quantization. The invention provides an alternative iterative algorithm framework in a channel estimation stage. Firstly, recovering an unquantized channel through a generalized Turbo algorithm, performing channel rough estimation by utilizing multitask sparse Bayesian learning, then performing channel fine estimation based on expectation maximization, and iterating the above processes to complete channel parameter estimation. In the position estimation stage, the residual error between the channel parameter obtained by the position information and the channel parameter estimated by the algorithm is used as an optimization function, and the optimization problem is solved by utilizing a Newton method. Experiments show that the positioning method of the millimeter wave communication system provided by the invention can still realize accurate user positioning under the condition of low precision quantization and reach the corresponding lower theoretical bound.

Description

Millimeter wave communication system positioning method adopting low-precision quantization
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a millimeter wave communication system positioning method adopting low-precision quantization.
Background
Large-scale Multiple-Input Multiple-Output (MIMO) millimeter wave communication is an important potential technology of next-generation wireless communication systems, and high data rate communication can be realized by utilizing rich frequency spectrum resources of millimeter wave frequency bands. However, the use of large-scale array antennas severely impacts the cost and power consumption of the overall communication system. Millimeter wave communication requires very high sampling frequencies at Analog to Digital converters (ADCs) according to the nyquist criterion. The power consumption of the ADC is positively correlated with the number of quantization bits, and in order to balance performance and cost and promote commercialization, researchers have proposed using low-precision ADCs combined with advanced signal processing techniques. Since low-precision ADCs introduce severe nonlinear distortion, existing work explores a variety of advanced signal processing techniques, such as approximate message passing and sparse bayesian learning. These schemes only consider solving the channel estimation problem in wireless communication, neglecting the potential advantages of low-precision broadband wireless communication systems in user position estimation.
Disclosure of Invention
The invention aims to provide a position estimation method with better performance, and realize efficient position estimation with lower quantization bit number.
The invention provides an alternative iterative algorithm framework in a channel estimation stage. Firstly, recovering an unquantized channel through a Gturbo algorithm, performing channel rough estimation by utilizing multitask sparse Bayesian learning, then performing channel fine estimation based on expectation maximization, and iterating the above processes to complete channel parameter estimation. In the position estimation stage, the residual error between the channel parameters obtained by the position information and the channel parameters estimated by the algorithm is used as an optimization function, and the optimization problem is solved by using a Levenberg-Marquarelt algorithm (LM algorithm for short).
The technical scheme of the invention is as follows:
s1, constructing a channel. Considering an uplink model in a massive mimo ofdm system, a single-antenna ue communicates with a base station with massive antenna arrays. The total number of the sub-carriers is M, and the number of the base station configuration antennas is N. The frequency domain channel on the mth subcarrier may be represented as:
Figure BDA0003847662940000021
wherein L is the number of multipaths, c l And τ l Complex gain sum time for the l-th multipathAnd the time delay is carried out,
Figure BDA0003847662940000022
is a corresponding spatial direction, defined as
φ l,m ＝(1+f m /f c )d sinθ l /λ c (2)
Figure BDA0003847662940000023
Is the frequency of the mth subcarrier, W is the system bandwidth, f c Is the carrier frequency, λ c Is the carrier wavelength, θ l Is the angle of arrival of the l-th path, d is the antenna spacing, set d = λ c /2。a(φ l,m ) Is an array response vector, considering a uniform linear array, having
Figure BDA0003847662940000024
At the BS, the received signal of the mth subcarrier is as follows:
y m ＝h m s m +n m ,m＝1,2,…,M (4)
wherein s is m Is a training symbol that is a symbol of,
Figure BDA0003847662940000025
means mean 0 and variance σ 2 Additive complex gaussian noise. Without loss of generality, will s m Set to 1 and omitted hereinafter. Based on equation (4), the time domain signal received at the nth antenna is as follows:
Figure BDA0003847662940000026
Figure BDA0003847662940000027
is a normalized discrete Fourier transform matrix having the ith row and jth column elements of
Figure BDA0003847662940000028
Figure BDA0003847662940000029
Wherein h is m,n Is h m The nth element of (1).
Figure BDA00038476629400000210
Is a noise vector.
When the low-precision ADC is used for sampling, the low-precision ADC will
Figure BDA00038476629400000211
Quantized into digital signals q n . Are used separately
Figure BDA00038476629400000212
And q is n,p Represent
Figure BDA00038476629400000213
And q is n P element of (1), then
Figure BDA00038476629400000214
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00038476629400000215
and
Figure BDA00038476629400000216
respectively represent
Figure BDA00038476629400000217
Real and imaginary parts of (c). Complex number quantizer
Figure BDA00038476629400000218
By two real quantizers
Figure BDA00038476629400000219
And (4) forming. Specifically, the quantization precision is Q b ADC of bit
Figure BDA00038476629400000220
And
Figure BDA00038476629400000221
mapping to
Figure BDA00038476629400000222
One of the discrete values, as follows:
Figure BDA0003847662940000031
wherein- ∞ = u 0 <u 1 <…<u B = infinity is the quantization threshold, v 1 <v 2 <…<v B Is the output level, for the average equalizer
Figure BDA0003847662940000032
Where Δ is the quantization interval.
So the system model based on the low-precision ADC is
Figure BDA0003847662940000033
S2, recovering the unquantized frequency domain channel by using the Gturbo algorithm
Figure BDA0003847662940000034
The gcho algorithm includes two modules:
a module A: calculating z n A posterior mean and variance of (a) due to
Figure BDA0003847662940000035
The elements are calculated in the same manner, and the subscript n is omitted in the following calculation procedure.
Figure BDA0003847662940000036
Figure BDA0003847662940000037
Calculating out
Figure BDA0003847662940000038
External mean and variance of
Figure BDA0003847662940000039
Figure BDA00038476629400000310
Figure BDA00038476629400000311
And a module B: calculating out
Figure BDA00038476629400000312
A posteriori mean and variance of
Figure BDA00038476629400000313
Figure BDA00038476629400000314
Figure BDA0003847662940000041
Calculating z n External mean and variance of
Figure BDA0003847662940000042
Figure BDA0003847662940000043
Will be provided with
Figure BDA0003847662940000044
As
Figure BDA0003847662940000045
According to an estimated value of
Figure BDA0003847662940000046
Wherein
Figure BDA0003847662940000047
Is that
Figure BDA0003847662940000048
M, then h can be obtained m . These two modules are performed iteratively until convergence.
And S3, estimating channel parameters. This part is dedicated to the channel h after recovery from quantization m And acquiring channel parameter information. Will channel h m Represented as a dictionary
Figure BDA0003847662940000049
Linear combination of atoms in, P represents angle of arrival
Figure BDA00038476629400000410
In the range of [ -1,1]The number of grid points. Then (4) can be rewritten as:
y m ＝D m x m +n m ,m＝1,2,…,M. (20)
wherein x is m ∈C N×1 Is a sparse vector with only L non-zero elements.
Figure BDA00038476629400000411
Figure BDA00038476629400000412
θ p ＝-1+(2p-1)P
Let x m Obeying the same mean value of 0 and variance of α x -1 Complex Gaussian distribution of (a) x ＝[α x,1 ,α x,2 ,...,α x,P ] T Then, there are:
Figure BDA00038476629400000413
wherein Λ x ＝diag{α x N, noise n m Subject each element to a mean of 0 and a variance of β -1 The same complex gaussian distribution. Can deduce x m The posterior distribution of (a) is also a complex gaussian distribution with mean and variance:
Figure BDA00038476629400000414
Figure BDA00038476629400000415
updating alpha x And β is given by:
Figure BDA0003847662940000051
Figure BDA0003847662940000052
wherein V xm (p, p) denotes a matrix V xm The p-th diagonal element of (a). . Performing iterative update according to the update expressions shown in (24) and (25) to obtain mu xm Then, the positions of K maximum non-zero elements can be taken as the candidate paths for further estimation, and the dictionary D is reserved according to the positions m Corresponding column sum μ xm Corresponding lines in the Chinese character to obtain the dimension-reduced characterDian (Chinese character)
Figure BDA0003847662940000053
And x m Is estimated value of
Figure BDA0003847662940000054
And S4, fine estimation of channel parameters. Next, how to further obtain the channel parameter values of the fine estimation through the coarse estimation will be described. Quantization errors are introduced to the true unknown dictionary linear approximation. Theta k As candidate radial dictionary
Figure BDA0003847662940000055
The corresponding angle value, at this time, the received signal may be reconstructed as:
Figure BDA0003847662940000056
wherein
Figure BDA0003847662940000057
And is
Figure BDA0003847662940000058
To represent
Figure BDA0003847662940000059
To theta k Derivation, gamma and eta represent the complex gain and delay of the candidate path,
Figure BDA00038476629400000510
and delta k ∈[-1/P,1/P]。
Figure BDA00038476629400000511
Initial value
Figure BDA00038476629400000512
Is calculated as follows
Figure BDA00038476629400000513
Figure BDA00038476629400000514
To represent
Figure BDA00038476629400000515
The kth element of (1).
The { gamma, delta, eta, alpha, beta } is estimated using the EM algorithm. In step E, the posterior mean and variance of γ are updated:
Figure BDA00038476629400000516
Figure BDA00038476629400000517
wherein the content of the first and second substances,
Figure BDA00038476629400000518
Λ = diag (α), and the posterior mean μ is taken as an estimate of γ.
In step M, the parameter set { δ, η, α, β } is updated. The log expectation of the full likelihood function can be written as
Figure BDA0003847662940000061
Wherein, V k,k Representing the kth diagonal element of the matrix V. tr (-) denotes the trace of the matrix, const stands for constant term. The update formula of the parameters is as follows
Figure BDA0003847662940000062
Figure BDA0003847662940000063
Figure BDA0003847662940000064
δ＝G -1 U
Wherein
Figure BDA0003847662940000065
Figure BDA0003847662940000066
Figure BDA0003847662940000067
Figure BDA0003847662940000068
Wherein
B m ＝Φ m diag{μ} (36)
Figure BDA0003847662940000069
Figure BDA00038476629400000610
And E, iteratively updating the step E and the step M until convergence. The angle theta is updated in a way of theta (t+1) ＝θ (t) +δ，θ (t) Indicating the angle at the time of the t-th update. The mean and variance of the recovered signal are transmitted back to Gturbo as h n Prior mean and variance.
And S5, estimating the position parameters. From the geometric relationship, one can obtain
Figure BDA0003847662940000071
Figure BDA0003847662940000072
Figure BDA0003847662940000073
Figure BDA0003847662940000074
The above formula can be regarded as a position parameter vector
Figure BDA0003847662940000075
To channel parameter vector
Figure BDA0003847662940000076
Is specifically mapped as
Figure BDA0003847662940000077
Wherein κ l ＝[τ l ,θ l ,c l ] T ，ζ 1 ＝[p x ,p y ] T ，ζ l ＝[s l,x ,s l,y ] T ，
Figure BDA0003847662940000078
According to the channel parameter vector
Figure BDA0003847662940000079
κ l ＝[τ l ,θ l ,c l ] T . Location parameter vector
Figure BDA00038476629400000710
Wherein ζ 1 ＝[p x ,p y ] T ，ζ l ＝[s l,x ,s l,y ] T . Constructing an optimization function
Figure BDA00038476629400000711
Wherein, J κ Is a weighting matrix and can be replaced by a unit matrix.
Figure BDA00038476629400000712
Satisfies the following formula:
Figure BDA00038476629400000713
the update formula of the position parameter is as follows
ζ new ＝ζ+h (43)
Wherein h is the step distance, the calculation formula is as follows
h＝-(H+μI) -1 g (44)
Figure BDA00038476629400000714
Figure BDA00038476629400000715
Wherein J jacobi Is a Jacobian matrix, and the calculation formula is as follows
Figure BDA0003847662940000081
Figure BDA0003847662940000082
Figure BDA0003847662940000083
Figure BDA0003847662940000084
Figure BDA0003847662940000085
Figure BDA0003847662940000086
Mu in the algorithm is a damping coefficient, the value is determined by a gain rho,
Figure BDA0003847662940000087
wherein
Figure BDA0003847662940000088
If ρ <0, the size of μ is increased, and vice versa, the size of μ is decreased. The iteration ends, so far a fine estimate of the position parameter is obtained.
The invention has the advantages that the channel parameter and position estimation algorithm provided by the invention can realize accurate user positioning under a lower quantization bit number, and provides reliable user position information for wireless communication.
Drawings
Fig. 1 shows RMSE of LOS path channel parameters as a function of snr, with experimental conditions L =2 and b =4;
fig. 2 shows RMSE of NLOS path channel parameters as a function of snr, with experimental conditions of L =2 and b =4;
fig. 3 shows the RMSE of the position parameter with respect to the signal-to-noise ratio for different bits, with L =2.
Detailed Description
The invention is described in detail below with reference to the drawings and simulation examples to prove the applicability of the invention.
Considering an uplink model in a massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system, a single-antenna user terminal communicates with a base station terminal having a massive antenna array. The total number of the sub-carriers is M, and the number of the base station configured antennas is N. The frequency domain channel on the mth subcarrier may be represented as:
Figure BDA0003847662940000091
wherein L is the number of multipaths, c l And τ l For the complex gain and delay of the l-th multipath,
Figure BDA0003847662940000092
is the corresponding spatial direction, defined as
φ l,m ＝(1+f m /f c )d sinθ l /λ c (51)
Figure BDA0003847662940000093
Is the frequency of the mth subcarrier, W is the system bandwidth, f c Is the carrier frequency, λ c Is the carrier wavelength, θ l Is the angle of arrival of the l-th path, d is the antenna spacing, set d = λ c /2。a(φ l,m ) Is an array response vector, considering a Uniform Linear Array (ULA), having
Figure BDA0003847662940000094
At the BS side, the received signal of the mth subcarrier is as follows:
y m ＝h m s m +n m ,m＝1,2,…,M (53)
wherein s is m Is a training symbol that is a symbol of,
Figure BDA0003847662940000095
means mean 0 and variance σ 2 Additive complex gaussian noise. Without loss of generality, will s m Set to 1 and therefore may be omitted hereinafter. Based on equation (53), the time domain signal received at the nth antenna is as follows:
Figure BDA0003847662940000096
Figure BDA0003847662940000097
is a normalized FFT matrix with the ith row and jth column elements of
Figure BDA0003847662940000098
Figure BDA0003847662940000099
Wherein h is m,n Is h m The nth element of (1).
Figure BDA00038476629400000910
Is a noise vector, and n m Have the same statistical properties.
When the low-precision ADC is used for sampling, the low-precision ADC will
Figure BDA00038476629400000911
Quantized to digital signals q n . Respectively using
Figure BDA00038476629400000912
And q is n,p To represent
Figure BDA00038476629400000913
And q is n The p-th element of (2), then
Figure BDA00038476629400000914
Wherein the content of the first and second substances,
Figure BDA0003847662940000101
and
Figure BDA0003847662940000102
respectively represent
Figure BDA0003847662940000103
Real and imaginary parts of (c). Complex number quantizer
Figure BDA0003847662940000104
By two real quantizers
Figure BDA0003847662940000105
And (4) forming. Specifically, the quantization precision is Q b ADC of bit
Figure BDA0003847662940000106
And
Figure BDA0003847662940000107
mapping to
Figure BDA0003847662940000108
One of the discrete values, as follows:
Figure BDA0003847662940000109
wherein- ∞ = u 0 <u 1 <…<u B = infinity is the quantization threshold, v 1 <v 2 <…<v B Is the output level, for the medium average quantizer
Figure BDA00038476629400001010
Where Δ is the quantization interval.
So the system model based on the low-precision ADC is
Figure BDA00038476629400001011
Consider the recovery of an unquantized frequency domain channel using Gturbo
Figure BDA00038476629400001012
The gcosh algorithm includes two modules: module A is based on the relationships in (54)
Figure BDA00038476629400001013
Generating
Figure BDA00038476629400001014
By taking into account the coarse estimate of
Figure BDA00038476629400001015
A priori variance a of h Sum mean u h To refine the estimate. These two modules are performed iteratively until convergence.
A module A: calculating z n A posterior mean and variance of (a) due to
Figure BDA00038476629400001016
The elements are calculated in the same manner, and the subscript n is omitted in the following calculation process.
Figure BDA00038476629400001017
Figure BDA00038476629400001018
Computing
Figure BDA00038476629400001019
Outer mean and variance of
Figure BDA00038476629400001020
Figure BDA00038476629400001021
Figure BDA0003847662940000111
And a module B: calculating out
Figure BDA0003847662940000112
A posteriori mean and variance of
Figure BDA0003847662940000113
Figure BDA0003847662940000114
Figure BDA0003847662940000115
Calculating z n External mean and variance of
Figure BDA0003847662940000116
Figure BDA0003847662940000117
Will be provided with
Figure BDA0003847662940000118
As
Figure BDA0003847662940000119
According to an estimated value of
Figure BDA00038476629400001110
Wherein
Figure BDA00038476629400001111
Is that
Figure BDA00038476629400001112
M, then h can be obtained m 。
Will channel h m Expressed as a dictionary
Figure BDA00038476629400001113
Linear combination of middle atoms, P denotes angle of arrival
Figure BDA00038476629400001114
In the range of [ -1,1]The number of grid points. Then (53) may be rewritten as:
y m ＝D m x m +n m ,m＝1,2,…,M. (69)
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00038476629400001115
is a sparse vector with only L non-zero elements.
Figure BDA00038476629400001117
Due to the fact that
Figure BDA00038476629400001118
Has shared sparsity, and can directly utilize joint sparse Bayesian learning to estimate
Figure BDA00038476629400001119
Let x m Obey the same mean of 0 and variance of α x -1 Complex Gaussian distribution of (a) x ＝[α x,1 ,α x,2 ,...,α x,P ] T Then, there are:
Figure BDA0003847662940000121
wherein Λ x ＝diag{α x N, noise n m Subject each element to a mean of 0 and a variance of β -1 Same complex height ofA gaussian distribution. The likelihood function is:
Figure BDA0003847662940000122
can deduce x m The posterior distribution of (a) is also a complex gaussian distribution with mean and variance:
Figure BDA0003847662940000123
Figure BDA0003847662940000124
updating alpha x And β is given by:
Figure BDA0003847662940000125
Figure BDA0003847662940000126
performing iterative update according to the update expressions shown in (74) and (75) to obtain mu xm Then, the positions of K maximum non-zero elements can be taken as the candidate paths for further estimation, and the dictionary D is reserved according to the positions m Corresponding column sum μ xm Obtaining a dimension-reduced dictionary from corresponding lines
Figure BDA0003847662940000127
And x m Is estimated value of
Figure BDA0003847662940000128
The true angle of arrival may not be exactly at the sample point, thus introducing quantization errors to the true unknown dictionary linear approximation. Theta k As candidate radial dictionary
Figure BDA0003847662940000129
In which case the received signal may be reconstructed to the corresponding angle value
Figure BDA00038476629400001210
Wherein
Figure BDA00038476629400001211
And is
Figure BDA00038476629400001212
To represent
Figure BDA00038476629400001213
To theta k Derivation, where γ and η represent the complex gain and delay of the candidate path,
Figure BDA00038476629400001214
and delta k ∈[-1/P,1/P]。
Figure BDA00038476629400001215
Initial value
Figure BDA00038476629400001216
Is calculated as follows
Figure BDA00038476629400001217
Figure BDA00038476629400001218
To represent
Figure BDA00038476629400001219
The kth element of (1).
Let us obey the following a priori distribution
Figure BDA0003847662940000131
Wherein α = [ α = 1 ,...α K ] T ，
Figure BDA0003847662940000132
Represents a mean of 0 and a variance of
Figure BDA0003847662940000133
Complex gaussian distribution.
And (4) estimating the gamma, delta, eta, alpha and beta by using an EM algorithm. In step E, the posterior mean and variance of γ are updated. According to (76), y is obtained m A posterior distribution of
Figure BDA0003847662940000134
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003847662940000135
according to Bayesian theory, the posterior distribution of gamma is
Figure BDA0003847662940000136
q (γ) is a complex Gaussian distribution with a mean and variance of
Figure BDA0003847662940000137
Figure BDA0003847662940000138
Where Λ = diag (α), the posterior mean μ is taken as the estimated value of γ.
In step M, the parameter set { δ, η, α, β } is updated. The log expectation of the full likelihood function can be written as
Figure BDA0003847662940000139
Wherein, V k,k Representing the kth diagonal element of matrix V. tr (-) denotes the trace of the matrix. By making
Figure BDA00038476629400001310
And
Figure BDA00038476629400001311
to 0, the update formula for the available parameters is as follows
Figure BDA0003847662940000142
Wherein
Figure BDA0003847662940000144
Figure BDA0003847662940000145
Figure BDA0003847662940000146
Figure BDA0003847662940000147
Wherein
B m ＝Φ m diag{μ} (89)
Figure BDA0003847662940000148
Figure BDA0003847662940000149
And E, iteratively updating the step E and the step M until convergence. In the process of each update,
Figure BDA00038476629400001410
angle theta of (1) k To be updated, i.e. theta (t+1) ＝θ (t) +δ，θ (t) Indicating the angle at the time of the t-th update. The mean and variance of the recovered signal are transmitted back to Gturbo as h n The prior mean and variance.
From the geometric relationship, one can obtain
Figure BDA0003847662940000153
The above equation can be regarded as a position parameter vector
Figure BDA0003847662940000155
To channel parameter vector
Figure BDA0003847662940000156
The specific mapping relationship is
Figure BDA0003847662940000157
Wherein κ l ＝[τ l ,θ l ,c l ] T ，ζ 1 ＝[p x ,p y ] T ，ζ l ＝[s l,x ,s l,y ] T ，
Figure BDA0003847662940000158
Channel parameter vector
Figure BDA0003847662940000159
κ l ＝[τ l ,θ l ,c l ] T . Location parameter vector
Figure BDA00038476629400001510
Wherein ζ 1 ＝[p x ,p y ] T ，ζ l ＝[s l,x ,s l,y ] T . Constructing an optimization function
Figure BDA00038476629400001511
Wherein, J k Is a weighting matrix and can be replaced by a unit matrix.
Figure BDA00038476629400001512
The update formula of the position parameter is as follows
ζ new ＝ζ+h (96)
Wherein h is the step distance, the calculation formula is as follows
h＝-(H+μI) -1 g (97)
Figure BDA00038476629400001513
Figure BDA00038476629400001514
Wherein J jacobi Is a Jacobian matrix, and the calculation formula is as follows:
Figure BDA0003847662940000161
Figure BDA0003847662940000162
Figure BDA0003847662940000163
Figure BDA0003847662940000164
Figure BDA0003847662940000165
Figure BDA0003847662940000166
mu in the algorithm is a damping coefficient, the value is determined by a gain rho,
Figure BDA0003847662940000167
wherein
Figure BDA0003847662940000168
If ρ<0, increasing the size of μ, and conversely, decreasing the size of μ. Finally, the iteration is finished, and the fine estimation value of the position parameter p can be obtained
Figure BDA0003847662940000169
In the simulation, an uplink broadband millimeter wave MIMO-OFDM system is considered, where the number of base station configured antennas is N =64, and the number of mobile user side configured antennas is 1. The system center carrier frequency is f c =28GHz and bandwidth W =200MHz, and the total number of subcarriers is set to M =16. Angle of arrival { theta }at the same time l Are randomly distributed in
Figure BDA00038476629400001610
Then there is sin (theta) l )∈[-1,+1]And sin (theta) l )∈[-1,+1]. Path gain c l Obeying a circularly symmetric Gaussian distribution
Figure BDA00038476629400001611
Where c represents the speed of light and d is the distance from the base station to the subscriber end. Considering an indoor environment, the base station location is q = [0,0 =] T . User end position p = [ p ] x ,p y ] T Random, wherein p is x ～U[5,7]，p y ～U[1,3]Wherein U [ a, b]Represents the range [ a, b]Are uniformly distributed. Position s of refraction point l ＝[s l,x ,s l,y ] T Random, wherein s l,x ～U[3,4]，s l,y ～U[3,5]. According to q, p and s l τ can be determined l And theta l 。
In performance analysis, the invention first checks the channel parameters
Figure BDA0003847662940000171
Wherein the Cramer-Rao Lower bound (CRB) provides a reference for the performance of the algorithm. The adopted index is a minimum Root Mean Square Error (RMSE), which is defined as:
Figure BDA0003847662940000172
FIG. 1 depicts the relationship between RMSE and Signal-to-noise Ratio (SNR) for LOS path with experimental conditions set to Q b =4,l =2. It can be observed from the figure that the proposed scheme can obtain accurate estimation of angle and time delay parameters, and the estimation error of the angle and time delay parameters is close to the theoretical lower limit.
Fig. 2 illustrates the relationship between RMSE and Signal-to-noise Ratio (SNR) for NLOS paths. Comparing fig. 1 and 2, it can be seen that the estimation of the LOS path-related parameter has the best performance of all paths.
FIG. 3 depicts the quantization precision Q b In relation to RMSE, the proposed algorithm can provide accurate position estimation even with a small number of quantized bits.
In conclusion, the invention develops a positioning method of a millimeter wave communication system by adopting low-precision quantization. In order to solve the problem of nonlinear distortion caused by quantization, a Gturbo algorithm is used for recovering an unquantized channel, and on the basis of times, expectation maximization and an LM algorithm are used for respectively estimating the channel and the position. Simulation results show that the proposed method can effectively estimate position information even in the case of adopting a low-resolution ADC.

Claims (1)

1. A positioning method of a millimeter wave communication system adopting low precision quantization is used for a large-scale multiple-input multiple-output orthogonal frequency division multiplexing system, a definition system comprises a user terminal with a single antenna and a base station terminal with N antennas, and the positioning method is characterized by comprising the following steps:
s1, in a system uplink, the total number of subcarriers is M, and a frequency domain channel on an M-th subcarrier is represented as:
Figure FDA0003847662930000011
wherein L is the number of multipaths, c l And τ l Complex gain and delay for the ith multipath, phi l,m Is a corresponding spatial direction, defined as
φ l,m ＝(1+f m /f c )dsinθ l /λ c (2)
Figure FDA0003847662930000012
Is the frequency of the mth subcarrier, W is the system bandwidth, f c Is the carrier frequency, λ c Is the carrier wavelength, θ l Is the angle of arrival of the l-th path, d is the antenna spacing, set d = λ c /2；a(φ l,m ) Is an array response vector, considering a uniform linear array, having
Figure FDA0003847662930000013
At the base station, the received signal of the mth subcarrier is as follows:
y m ＝h m s m +n m (4)
wherein s is m Is a training symbol that is a symbol of,
Figure FDA0003847662930000014
means mean 0 and variance σ 2 Of additive complex Gaussian noise, will s m Set to 1, based on equation (4), the time domain signal received at the nth antenna is:
Figure FDA0003847662930000015
Figure FDA0003847662930000016
is a normalized discrete Fourier transform matrix with the ith row and jth column elements of
Figure FDA0003847662930000017
Figure FDA0003847662930000018
Wherein h is m,n Is h m The (n) th element of (a),
Figure FDA0003847662930000019
is a noise vector;
sampling by a low-precision ADC
Figure FDA00038476629300000110
Quantized into digital signals q n Respectively using
Figure FDA00038476629300000111
And q is n,p To represent
Figure FDA00038476629300000112
And q is n The p-th element of (a) can be obtained:
Figure FDA00038476629300000113
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003847662930000021
and
Figure FDA0003847662930000022
respectively represent
Figure FDA0003847662930000023
Real and imaginary, complex quantizer of
Figure FDA0003847662930000024
By two real quantizers
Figure FDA0003847662930000025
Composition by quantization precision of Q b ADC of bit
Figure FDA0003847662930000026
And
Figure FDA0003847662930000027
mapping to
Figure FDA0003847662930000028
One of the discrete values:
Figure FDA0003847662930000029
wherein- ∞ = u 0 <u 1 <…<u B = infinity is the quantization threshold, v 1 <v 2 <…<v B Is the output level, for the medium average quantizer:
Figure FDA00038476629300000210
wherein Δ is a quantization interval;
the system model based on the low-precision ADC is obtained as follows:
Figure FDA00038476629300000211
s2, recovering the unquantized frequency domain channel by using the Gturbo algorithm
Figure FDA00038476629300000212
The gcho algorithm includes two modules:
a module A: calculating z n A posterior mean and variance of (a) due to
Figure FDA00038476629300000213
The elements are calculated in the same manner, and the subscript n is omitted in the following calculation:
Figure FDA00038476629300000214
Figure FDA00038476629300000215
calculating out
Figure FDA00038476629300000216
External mean and variance of (c):
Figure FDA00038476629300000217
Figure FDA00038476629300000218
Figure FDA00038476629300000219
and a module B: computing
Figure FDA0003847662930000031
Posterior mean and variance of (a):
Figure FDA0003847662930000032
Figure FDA0003847662930000033
Figure FDA0003847662930000034
calculating z n External mean and variance of (c):
Figure FDA0003847662930000035
Figure FDA0003847662930000036
will be provided with
Figure FDA0003847662930000037
As
Figure FDA0003847662930000038
Is based on an estimated value of
Figure FDA0003847662930000039
Wherein
Figure FDA00038476629300000310
Is that
Figure FDA00038476629300000311
M, then h can be obtained m ；
Performing module A and module B iteratively until convergence;
s3, channel parameter estimation: will channel h m Expressed as a dictionary
Figure FDA00038476629300000312
Linear combination of middle atoms, P denotes angle of arrival
Figure FDA00038476629300000313
In the range of [ -1,1]The number of uniform sampling grid points, rewrite equation (4) as:
y m ＝D m x m +n m (20)
wherein x is m ∈C N×1 Is a sparse vector with only L non-zero elements,
Figure FDA00038476629300000314
let x be m Obeying the same mean value of 0 and variance of α x -1 Complex Gaussian distribution of (a) x ＝[α x,1 ,α x,2 ,...,α x,P ] T Then, there are:
Figure FDA00038476629300000315
wherein Λ x ＝diag{α x H, noise n m Subject to a mean of 0 and a variance of β for each element in the sequence -1 Of the same complex Gaussian distribution, then x m The posterior distribution of (A) is also complexGaussian distribution with mean and variance:
Figure FDA0003847662930000041
Figure FDA0003847662930000042
updating alpha x And β is given by:
Figure FDA0003847662930000043
Figure FDA0003847662930000044
wherein V xm (p, p) represents a matrix V xm The p-th diagonal element of (2) is iteratively updated according to the updating expressions shown in the formula (24) and the formula (25), and mu is obtained xm Then, the positions of K maximum non-zero elements can be taken as the candidate paths for further estimation, and the dictionary D is reserved according to the positions m Corresponding column sum μ xm Obtaining a dimension-reduced dictionary from corresponding lines
Figure FDA0003847662930000045
And x m Is estimated value of
Figure FDA0003847662930000046
S4, fine estimation of channel parameters: introducing quantization error to real unknown dictionary linear approximation and defining theta k As candidate radial dictionary
Figure FDA0003847662930000047
And (3) reconstructing the received signal into:
Figure FDA0003847662930000048
wherein
Figure FDA0003847662930000049
And is
Figure FDA00038476629300000410
Figure FDA00038476629300000411
To represent
Figure FDA00038476629300000412
To theta k Derivation, gamma and eta represent the complex gain and delay of the candidate path,
Figure FDA00038476629300000413
and delta k ∈[-1/P,1/P]。
Figure FDA00038476629300000414
Initial value
Figure FDA00038476629300000415
Is calculated as follows
Figure FDA00038476629300000416
Figure FDA00038476629300000417
To represent
Figure FDA00038476629300000418
The kth element of (1);
estimating { gamma, delta, eta, alpha, beta } by using an EM algorithm, and updating the posterior mean and variance of gamma in the E step of the EM algorithm:
Figure FDA0003847662930000051
Figure FDA0003847662930000052
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003847662930000053
Λ = diag (α), with the posterior mean μ as the estimate of γ;
in the M step of the EM algorithm, the parameter set { δ, η, α, β } is updated, the log expectation of the full likelihood function is:
Figure FDA0003847662930000054
wherein, V k,k The k diagonal element of the matrix V is represented, tr (-) represents the trace of the matrix, const represents a constant term, and the updating formula of the parameter is as follows
Figure FDA0003847662930000055
Wherein
Figure FDA0003847662930000056
Figure FDA0003847662930000057
Figure FDA0003847662930000058
Figure FDA0003847662930000059
Wherein
B m ＝Φ m diag{μ} (36)
Figure FDA0003847662930000061
Figure FDA0003847662930000062
E, iteratively updating the step E and the step M until convergence; the angle theta is updated in a way of theta (t+1) ＝θ (t) +δ，θ (t) Representing the angle at the time of the t-th update, and transmitting the mean and variance of the recovered signal back to Gturbo as h n Prior mean and variance of;
s5, estimating the position parameters, and obtaining the following result according to the geometrical relationship:
Figure FDA0003847662930000063
the above formula is a position parameter vector
Figure FDA0003847662930000064
To channel parameter vector
Figure FDA0003847662930000065
Is specifically mapped as
Figure FDA0003847662930000066
Wherein κ l ＝[τ l ,θ l ,c l ] T ，ζ 1 ＝[p x ,p y ] T ，ζ l ＝[s l,x ,s l,y ] T ，
Figure FDA0003847662930000067
According to the channel parameter vector
Figure FDA0003847662930000068
κ l ＝[τ l ,θ l ,c l ] T Position parameter vector
Figure FDA0003847662930000069
Wherein ζ 1 ＝[p x ,p y ] T ，ζ l ＝[s l,x ,s l,y ] T And constructing an optimization function:
Figure FDA00038476629300000610
wherein, J κ Is a weighting matrix, which is replaced by a unit matrix,
Figure FDA00038476629300000611
satisfies the following formula:
Figure FDA0003847662930000071
the update formula of the position parameter is as follows
ζ new =ζ+h (43)
Wherein h is the step distance, the calculation formula is as follows
h＝-(H+μI) -1 g (44)
Figure FDA0003847662930000073
Figure FDA0003847662930000074
Wherein J jacobi Is a Jacobian matrix, and the calculation formula is as follows
Figure FDA0003847662930000075
Figure FDA0003847662930000076
Figure FDA0003847662930000077
Figure FDA0003847662930000078
Figure FDA0003847662930000079
Figure FDA00038476629300000710
Mu in the algorithm is a damping coefficient, the value is determined by a gain rho,
Figure FDA00038476629300000711
wherein
Figure FDA0003847662930000081
Increasing the size of μ if ρ <0, and decreasing the size of μ otherwise; the iteration is ended, so far, an estimated value of the position parameter is obtained.
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