Millimeter wave communication system positioning method using low-precision quantization

Abstract

The present invention belongs to the field of wireless communication technology, and specifically relates to a positioning method for a millimeter wave communication system using low-precision quantization. The present invention proposes an alternating iterative algorithm framework in the channel estimation stage. First, the unquantized channel is restored by the generalized Turbo algorithm, and the channel is roughly estimated using multi-task sparse Bayesian learning. Subsequently, the channel is finely estimated based on expectation maximization, and the above process is iterated to complete the channel parameter estimation. In the position estimation stage, the residual between the channel parameters obtained from the position information and the channel parameters estimated by the algorithm is used as an optimization function, and the Newton method is used to solve the optimization problem. Experiments show that the millimeter wave communication system positioning method proposed in the present invention can still achieve accurate user positioning under low-precision quantization conditions and reach the corresponding theoretical lower bound.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a millimeter wave communication system positioning method using low-precision quantization. Background Art

[0002] Massive Multiple-Input Multiple-Output (MIMO) millimeter wave communication is an important potential technology for the next generation of wireless communication systems. It can achieve high data rate communication by utilizing the rich spectrum resources of the millimeter wave band. However, the use of large-scale array antennas seriously affects the cost and power consumption of the entire communication system. According to the Nyquist criterion, millimeter wave communication requires a very high sampling frequency on the analog to digital converter (ADC). The power consumption of the ADC is positively correlated with the number of quantization bits. In order to balance performance and cost and promote commercial use, researchers have proposed the use of low-precision ADCs combined with advanced signal processing techniques. Since low-precision ADCs can cause severe nonlinear distortion, existing work has explored a variety of advanced signal processing techniques, such as approximate message passing and sparse Bayesian learning. These solutions only consider solving the channel estimation problem in wireless communications, ignoring the potential advantages of low-precision broadband wireless communication systems in user position estimation. Summary of the Invention

[0003] The purpose of the present invention is to propose a position estimation method with better performance, which can achieve efficient position estimation with a lower number of quantization bits.

[0004] This paper proposes an alternating iterative algorithm framework for the channel estimation stage. First, the unquantized channel is recovered using the Gturbo algorithm, and a coarse channel estimate is performed using multi-task sparse Bayesian learning. Subsequently, a fine channel estimate is performed based on expectation maximization. This process is iterated to complete channel parameter estimation. In the position estimation stage, the residual between the channel parameters obtained from the position information and the channel parameters estimated by the algorithm is used as the optimization function, and the Levenberg-Marquarelt algorithm (LM algorithm) is used to solve this optimization problem.

[0005] The technical solution of the present invention is:

[0006] S1. Channel construction. Consider the uplink model in a massive MIMO OFDM system, where a single-antenna user terminal communicates with a base station equipped with a massive antenna array. The total number of subcarriers is M, and the number of antennas configured in the base station is N. The frequency domain channel on the mth subcarrier can be expressed as:

[0007]

[0008] Where L is the multipath number, cl and τ l is the complex gain and delay of the lth multipath, is the corresponding spatial direction, defined as

[0009] φ l,m =(1+f m / f c )d sinθ l / λ c (2)

[0010] 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 arrival angle of the lth path, d is the antenna spacing, set d = λ c / 2. a(φ l,m ) is the array response vector, considering a uniform linear array, we have

[0011]

[0012] At the BS end, the received signal of the mth subcarrier is as follows:

[0013] y m =h m s m +n m ,m=1,2,…,M (4)

[0014] where s m is the training symbol, means that the mean is 0 and the variance is σ 2 Without loss of generality, let s m Set to 1 and omitted below. Based on formula (4), the time domain signal received at the nth antenna is as follows:

[0015]

[0016] is the normalized discrete Fourier transform matrix, whose i-th row and j-th column element is where h m,n It is h m The nth element of . is the noise vector.

[0017] When low-precision ADC samples, it will Quantized into digital signal q n . Use and q n,p express and q n The pth element of

[0018]

[0019] in, and Respectively The real and imaginary parts of . Complex quantizer Two real quantizers Specifically, the quantization accuracy is Q b The ADC bit will and Map to One of the discrete values, as follows:

[0020]

[0021] Where -∞=u0 <u1<…<u B =∞ is the quantization threshold, v1 <v2<…<v B is the output level, for a medium-level uniform quantizer

[0022]

[0023] where Δ is the quantization interval.

[0024] Therefore, the system model based on low-precision ADC is

[0025]

[0026] S2, use the Gturbo algorithm to recover the unquantized frequency domain channel The Gturbo algorithm consists of two modules:

[0027] Module A: Calculating z n The posterior mean and variance of The calculation method for each element is the same, and the subscript n is omitted in the following calculation process.

[0028]

[0029]

[0030] calculate The external mean and variance of

[0031]

[0032]

[0033]

[0034] Module B: Computing The posterior mean and variance of

[0035]

[0036]

[0037]

[0038] Calculate z n The external mean and variance of

[0039]

[0040]

[0041] Will As The estimated value of in yes The mth element of , then we can get h m These two modules are iteratively executed until convergence.

[0042] S3, Estimation of channel parameters. This part is dedicated to the channel h after quantization recovery. m Get channel parameter information. m Represented as a dictionary The linear combination of atoms in, P represents the arrival angle The number of uniformly sampled grid points is [-1,1]. Then (4) can be rewritten as:

[0043] y m =D m x m +n m ,m=1,2,…,M. (20)

[0044] Among them, x m ∈C N×1 is a sparse vector with only L non-zero elements.

[0045]

[0046]

[0047] θ p =-1+(2p-1)P

[0048] Let x m Subject to the same mean of 0 and variance of α x -1 Complex Gaussian distribution, α x =[α x,1,α x,2 ,...,α x,P ] T , then: where Λ x =diag{α x}, noise n m Each element in has a mean of 0 and a variance of β -1 The same complex Gaussian distribution of . It can be derived that x m The posterior distribution of is also a complex Gaussian distribution with mean and variance:

[0049]

[0050]

[0051] Update α x The formulas for β and β are:

[0052]

[0053]

[0054] Where V xm (p,p) represents the matrix V xm The pth diagonal element of . . Iteratively update according to the update expressions shown in (24) and (25) to obtain μ xm After that, the positions of the K largest non-zero elements can be taken as candidate paths for further estimation, and the dictionary D is retained according to the position. m The corresponding columns and μ xm The corresponding rows in the , get the dimensionality reduction dictionary and x m Estimated value of

[0055] S4. Fine estimation of channel parameters. Next, we will introduce how to obtain fine estimated channel parameter values ​​through coarse estimation. The linear approximation of the true unknown dictionary introduces quantization error. k For candidate paths in the dictionary The corresponding angle value in , at this time, the received signal can be reconstructed as:

[0056]

[0057] in and express θ k Derivative, γ and η represent the complex gain and delay of the candidate path, And δ k ∈[-1 / P,1 / P]. Initial value The calculation is as follows

[0058]

[0059] express The kth element of .

[0060] Use the EM algorithm to estimate {γ,δ,η,α,β}. In the E step, update the posterior mean and variance of γ:

[0061]

[0062]

[0063] in, Λ=diag(α), and the posterior mean μ is used as the estimated value of γ.

[0064] In the M step, the parameter set {δ,η,α,β} is updated. The logarithmic expectation of the total likelihood function can be written as

[0065]

[0066] Among them, V k,k represents the kth diagonal element of the matrix V. tr(·) represents the trace of the matrix, and const represents the constant term. The parameter update formula is as follows

[0067]

[0068]

[0069]

[0070] δ=G -1 U

[0071] in

[0072]

[0073]

[0074]

[0075]

[0076] in

[0077] B m =Φ m diag{μ} (36)

[0078]

[0079]

[0080] The E-step and M-step iterative updates are performed until convergence. The angle θ is updated as θ (t+1) =θ (t) +δ,θ (t) The mean and variance of the recovered signal are returned to Gturbo as h n The prior mean and variance of .

[0081] S5. Estimation of position parameters. According to the geometric relationship, we can obtain

[0082]

[0083]

[0084]

[0085]

[0086] The above formula can be regarded as a position parameter vector To the channel parameter vector The specific mapping relationship is where κ l =[τ l ,θ l ,c l ] T ,ζ1=[p x ,p y ] T ,ζ l =[s l,x ,s l,y ] T ,

[0087]

[0088] According to the channel parameter vector κ l =[τ l ,θ l ,c l ] T . Position parameter vector where ζ1=[p x ,p y ] T ,ζ l =[s l,x ,s l,y ] T . Construct optimization function

[0089]

[0090] Among them, J κ is a weighted matrix and can be replaced by an identity matrix. Satisfy the following formula:

[0091]

[0092] The update formula of the position parameter is as follows

[0093] ζ new =ζ+h (43)

[0094] Where h is the step distance, calculated as follows

[0095] h=-(H+μI) -1 g (44)

[0096]

[0097]

[0098] Among them J jacobi is the Jacobian matrix, and the calculation formula is as follows

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] The μ in the algorithm is the damping coefficient, and its value is determined by the gain ρ.

[0106]

[0107] in

[0108]

[0109] If ρ < 0, increase μ, otherwise, decrease μ. The iteration ends and a fine estimate of the position parameter is obtained.

[0110] The beneficial effect of the present invention is that the channel parameter and position estimation algorithm proposed in the present invention can achieve accurate user positioning with a lower quantization bit number, providing reliable user position information for wireless communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0111] Figure 1 The relationship between RMSE and signal-to-noise ratio of LOS path channel parameters, the experimental conditions are L = 2, B = 4;

[0112] Figure 2 The relationship between RMSE and signal-to-noise ratio of NLOS path channel parameters is shown in the experimental conditions: L = 2, B = 4;

[0113] Figure 3 Figure 2 is the relationship between the RMSE of the position parameter and the signal-to-noise ratio under different numbers of bits. The experimental condition is L=2. DETAILED DESCRIPTION

[0114] The present invention is described in detail below with reference to the accompanying drawings and simulation examples to demonstrate the practicability of the present invention.

[0115] Consider the uplink model in a massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system, where a single-antenna user terminal communicates with a base station equipped with a massive antenna array. The total number of subcarriers is M, and the number of antennas configured in the base station is N. The frequency domain channel on the mth subcarrier can be expressed as:

[0116]

[0117] Where L is the multipath number, c l and τ l is the complex gain and delay of the lth multipath, is the corresponding spatial direction, defined as

[0118] φ l,m =(1+f m / f c )d sinθ l / λ c (51)

[0119] 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 arrival angle of the lth path, d is the antenna spacing, set d = λ c / 2. a(φ l,m ) is the array response vector, considering the uniform linear array (ULA), there is

[0120]

[0121] At the BS end, the received signal of the mth subcarrier is as follows:

[0122] y m =h m sm +n m ,m=1,2,…,M (53)

[0123] where s m is the training symbol, means that the mean is 0 and the variance is σ 2 Without loss of generality, let s m It is set to 1, so it can be omitted below. Based on formula (53), the time domain signal received at the nth antenna is as follows:

[0124]

[0125] is the normalized FFT matrix, whose i-th row and j-th column element is where h m,n It is h m The nth element of . is the noise vector, and n m have the same statistical properties.

[0126] When low-precision ADC samples, it will Quantized into digital signal q n . Use and q n,p express and q n The pth element of

[0127]

[0128] in, and Respectively The real and imaginary parts of . Complex quantizer Two real quantizers Specifically, the quantization accuracy is Q b The ADC bit will and Map to One of the discrete values, as follows:

[0129]

[0130] Where -∞=u0 <u1<…<u B =∞ is the quantization threshold, v1 <v2<…<v B is the output level, for a medium-level uniform quantizer

[0131]

[0132] where Δ is the quantization interval.

[0133] Therefore, the system model based on low-precision ADC is

[0134]

[0135] Consider using Gturbo to recover the unquantized frequency domain channel The Gturbo algorithm consists of two modules: Module A is based on the relationship in (54) produce A rough estimate of The prior variance α h and mean u h To refine the estimate, these two modules are iteratively executed until convergence.

[0136] Module A: Calculating z n The posterior mean and variance of The calculation method for each element is the same, and the subscript n is omitted in the following calculation process.

[0137]

[0138]

[0139] calculate The external mean and variance of

[0140]

[0141]

[0142]

[0143] Module B: Computing The posterior mean and variance of

[0144]

[0145]

[0146]

[0147] Calculate z n The external mean and variance of

[0148]

[0149]

[0150] Will As The estimated value of in yes The mth element of , then we can get h m .

[0151] Channel h m Represented as a dictionary The linear combination of atoms in, P represents the arrival angle The number of uniformly sampled grid points is [-1,1]. Then (53) can be rewritten as:

[0152] y m =D m x m +n m ,m=1,2,…,M. (69)

[0153] in, is a sparse vector with only L non-zero elements.

[0154]

[0155] because With shared sparsity, joint sparse Bayesian learning can be used to estimate Let x m Subject to the same mean of 0 and variance of α x -1 Complex Gaussian distribution, α x =[α x,1 ,α x,2 ,...,α x,P ] T , then: where Λ x =diag{α x}, noise n m Each element in has a mean of 0 and a variance of β -1 The likelihood function is:

[0156]

[0157] It can be deduced that x m The posterior distribution of is also a complex Gaussian distribution with mean and variance:

[0158]

[0159]

[0160] Update α x The formulas for β and β are:

[0161]

[0162]

[0163] Perform iterative updates according to the update expressions shown in (74) and (75) to obtain μ xm After that, the positions of the K largest non-zero elements can be taken as candidate paths for further estimation, and the dictionary D is retained according to the position. m The corresponding columns and μ xm The corresponding rows in the , get the dimensionality reduction dictionary and x m Estimated value of

[0164] The true arrival angle cannot be exactly located at the sampling point, so the linear approximation of the true unknown dictionary introduces quantization error. k For candidate paths in the dictionary The corresponding angle value in , at this time, the received signal can be reconstructed as

[0165]

[0166] in and express θ k Derivative, γ and η represent the complex gain and delay of the candidate path, And δ k ∈[-1 / P,1 / P]. Initial value The calculation is as follows

[0167]

[0168] express The kth element of .

[0169] Assume that γ follows the following prior distribution

[0170]

[0171] where α=[α1,...α K ] T , The mean is 0 and the variance is The complex Gaussian distribution of .

[0172] Use the EM algorithm to estimate {γ,δ,η,α,β}. In the E step, update the posterior mean and variance of γ. According to (76), we can get y m The posterior distribution of

[0173]

[0174] in,

[0175] According to Bayesian theory, the posterior distribution of γ is

[0176]

[0177] q(γ) is a complex Gaussian distribution with mean and variance

[0178]

[0179]

[0180] Where Λ = diag(α), and the posterior mean μ is used as the estimated value of γ.

[0181] In the M step, the parameter set {δ,η,α,β} is updated. The logarithmic expectation of the total likelihood function can be written as

[0182]

[0183] Among them, V k,k represents the kth diagonal element of the matrix V. tr(·) represents the trace of the matrix. By letting and Is 0, the parameter update formula can be obtained as follows

[0184]

[0185] in

[0186]

[0187]

[0188]

[0189]

[0190] in

[0191] B m =Φ m diag{μ} (89)

[0192]

[0193]

[0194] E-step and M-step iterative updates until convergence. During each update, The corresponding angle θ k To update, θ (t+1) =θ (t) +δ,θ(t) The mean and variance of the recovered signal are returned to Gturbo as h n The prior mean and variance of .

[0195] According to the geometric relationship, we can get

[0196]

[0197] The above formula can be regarded as a position parameter vector To the channel parameter vector The specific mapping relationship is where κ l =[τ l ,θ l ,c l ] T ,ζ1=[p x ,p y ] T ,ζ l =[s l,x ,s l,y ] T ,

[0198]

[0199] Channel parameter vector κ l =[τ l ,θ l ,c l ] T . Position parameter vector where ζ1=[p x ,p y ] T ,ζ l =[s l,x ,s l,y ] T . Construct optimization function

[0200]

[0201] Among them, J k is a weighted matrix and can be replaced by an identity matrix.

[0202]

[0203] The update formula of the position parameter is as follows

[0204] ζ new =ζ+h (96)

[0205] Where h is the step distance, calculated as follows

[0206] h=-(H+μI) -1 g (97)

[0207]

[0208]

[0209] Among them J jacobi is the Jacobian matrix, which is calculated as follows:

[0210]

[0211]

[0212]

[0213]

[0214]

[0215]

[0216] The μ in the algorithm is the damping coefficient, and its value is determined by the gain ρ.

[0217]

[0218] in

[0219]

[0220] If ρ<0, increase μ, otherwise, reduce μ. At the end of the final iteration, a detailed estimate of the position parameter p is obtained.

[0221] In the simulation, an uplink broadband millimeter wave MIMO-OFDM system is considered, with the number of antennas configured at the base station being N=64 and the number of antennas configured at the mobile user end being 1. The system center carrier frequency is f c = 28 GHz and bandwidth is W = 200 MHz, the total number of subcarriers is set to M = 16. l Randomly distributed in Then we have sin(θ l )∈[-1,+1] and sin(θ l )∈[-1,+1]. Path gain c l Obeys cyclic symmetric Gaussian distribution Where c represents the speed of light, and d is the distance from the base station to the user end. Considering the indoor environment, the base station position is q = [0,0] T The user terminal position p = [p x ,py ] T Random, where p x ~U[5,7],p y ~U[1,3], where U[a,b] represents a uniform distribution over the range [a,b]. The refraction point position s l =[s l,x ,s l,y ] T Random, where s l,x ~U[3,4],s l,y ~U[3,5]. According to q, p and s l , we can determine τ l and θ l .

[0222] In the performance analysis, the present invention first checks the channel parameters The Cramer-Rao Lower Bounds (CRB) provides a reference benchmark for algorithm performance. The metric used is the minimum root mean square error (RMSE), which is defined as:

[0223]

[0224] Figure 1 Describes the relationship between the RMSE of the LOS path and the signal-to-noise ratio (SNR). The experimental conditions are set to Q b = 4, L = 2. As can be observed from the figure, the proposed scheme can obtain accurate estimation of angle and delay parameters, and its estimation error is close to the theoretical lower limit.

[0225] Figure 2 Describes the relationship between the RMSE of the NLOS path and the signal-to-noise ratio (SNR). Figure 1 and Figure 2 , it can be found that the estimation of LOS path related parameters has the best performance among all paths.

[0226] Figure 3 Describes the quantization accuracy Q b Relationship with RMSE, the proposed algorithm can provide accurate position estimation even when the number of quantization bits is small.

[0227] In summary, this paper develops a positioning method for millimeter-wave communication systems using low-precision quantization. To address the nonlinear distortion caused by quantization, the Gturbo algorithm is used to recover the unquantized channel. Based on this, the expectation-maximization algorithm and the LM algorithm are used for channel and position estimation, respectively. Simulation results demonstrate that the proposed method can effectively estimate position information even when using a low-resolution ADC.

Claims

1. A low-precision quantized millimeter-wave communication system positioning method is used for a large-scale multiple-input multiple-output orthogonal frequency division multiplexing system. The system is defined as comprising a user end with a single antenna and a base station end with N antennas. The method is characterized by: The positioning method includes the following steps: S1. In the system uplink, the total number of subcarriers is M, and the frequency domain channel on the mth subcarrier is expressed as: Where L is the multipath number, c l and τ l is the complex gain and delay of the lth multipath, φ l,m is the corresponding spatial direction, defined as f l,m =(1+f m / f c )dsinθ l / l c (2) 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 arrival angle of the lth path, d is the antenna spacing, set d = λ c / 2; a(φ l,m ) is the array response vector, considering a uniform linear array, we have At the base station, the received signal of the mth subcarrier is as follows: y m =h m s m +n m (4) where s m is the training symbol, means that the mean is 0 and the variance is σ 2 The additive complex Gaussian noise of s m Set to 1, based on formula (4), the time domain signal received at the nth antenna is: is the normalized discrete Fourier transform matrix, and the element in row i and column j is where h m,n It is h m The nth element of is the noise vector; Sampling is done by a low-precision ADC. Quantized into digital signal q n , respectively and q n,p express and q n The pth element of , we can get: in, and Respectively The real and imaginary parts of the complex quantizer Two real quantizers Composition, through quantization precision Q b The ADC bit will and Map to One of the discrete values: where -∞=u0 <u1<…<u B =∞ is the quantization threshold, v1 <v2<…<v B is the output level, for a medium-level uniform quantizer: Where Δ is the quantization interval; The system model based on low-precision ADC is obtained as follows: S2, use the Gturbo algorithm to recover the unquantized frequency domain channel The Gturbo algorithm consists of two modules: Module A: Calculating z n The posterior mean and variance of The calculation method for each element is the same, and the subscript n is omitted in the following calculation process: calculate The external mean and variance of : Module B: Computing The posterior mean and variance of : Calculate z n The external mean and variance of : Will As The estimated value of in yes The mth element of , then we can get h m ; Iterate module A and module B until convergence; S3. Estimation of channel parameters: Estimation of channel h m Represented as a dictionary The linear combination of atoms in, P represents the arrival angle With uniform sampling grid points in [-1,1], formula (4) can be rewritten as: y m =D m x m +n m (20) Among them, x m ∈C N×1 is a sparse vector with only L non-zero elements, Let x m Subject to the same mean of 0 and variance of α x -1 Complex Gaussian distribution, α x =[α x,1 ,α x,2 ,...,α x,P ] T , then: where Λ x =diag{α x }, noise n m Each element in has a mean of 0 and a variance of β -1 The same complex Gaussian distribution, then x m The posterior distribution of is also a complex Gaussian distribution with mean and variance: Update α x The formulas for β and β are: Where V xm (p,p) represents the matrix V xm The p-th diagonal element of is iteratively updated according to the update expressions shown in formula (24) and formula (25) to obtain μ xm After that, the positions of the K largest non-zero elements can be taken as candidate paths for further estimation, and the dictionary D is retained according to the position. m The corresponding columns and μ xm The corresponding rows in the , get the dimensionality reduction dictionary and x m Estimated value of S4. Fine estimation of channel parameters: Introduce quantization error to the linear approximation of the true unknown dictionary and define θ k For candidate paths in the dictionary The corresponding angle value in , reconstructs the received signal as: in and express θ k Derivative, γ and η represent the complex gain and delay of the candidate path, And δ k ∈[-1 / P,1 / P], Initial value The calculation is as follows express The kth element of ; Use the EM algorithm to estimate {γ,δ,η,α,β}. In the E step of the EM algorithm, update the posterior mean and variance of γ: in, Λ=diag(α), taking the posterior mean μ as the estimated value of γ; In the M step of the EM algorithm, the parameter set {δ,η,α,β} is updated, and the logarithmic expectation of the complete likelihood function is: Among them, V k,k represents the kth diagonal element of the matrix V, tr(·) represents the trace of the matrix, const represents the constant term, and the parameter update formula is as follows in in B m =Φ m diag{μ} (36) The E-step and M-step iterative updates until convergence; the angle θ is updated as θ (t+1) =θ (t) +δ,θ (t) represents the angle at the tth update, and the mean and variance of the recovered signal are returned to Gturbo as h n The prior mean and variance of ; S5. Estimation of position parameters: According to geometric relationship: The above formula is a position parameter vector To the channel parameter vector The specific mapping relationship is where κ l =[τ l ,θ l ,c l ] T ,ζ1=[p x ,p y ] T ,ζ l =[s l,x ,s l,y ] T , According to the channel parameter vector κ l =[τ l ,θ l ,c l ] T , the position parameter vector where ζ1=[p x ,p y ] T ,ζ l =[s l,x ,s l,y ] T , construct the optimization function: Among them, J κ Is a weighted matrix, replaced by the identity matrix, Satisfy the following formula: The update formula of the position parameter is as follows g new =ζ+h (43) Where h is the step distance, calculated as follows h=-(H+μI) -1 g (44) Among them J jacobi is the Jacobian matrix, and the calculation formula is as follows The μ in the algorithm is the damping coefficient, and its value is determined by the gain ρ. in If ρ<0, increase the size of μ, otherwise, reduce the size of μ; the iteration ends, and the estimated value of the position parameter is obtained.

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