Channel estimation and positioning method for massive MIMO systems under low-precision quantization

Abstract

The present invention belongs to the field of wireless communication technology, and specifically relates to a large-scale MIMO system channel estimation and positioning method under low-precision quantization. The present invention proposes an alternating iterative algorithm framework. In the first stage, channel parameters are extracted from it using GTurbo and sparse Bayesian learning. In the second stage, the Gauss-Newton method is used to restore the user terminal position through the obtained channel parameter estimation. Experimental results show that the millimeter wave communication system positioning method proposed by the present invention can still achieve accurate channel parameter estimation and user positioning when the number of quantization bits is low, and is close to the corresponding theoretical lower bound under high signal-to-noise ratio.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a large-scale MIMO system channel estimation and positioning method under low-precision quantization. Background Art

[0002] Massive Multiple-Input Multiple-Output (MIMO) millimeter wave communication achieves ultra-high data rate communication by utilizing the rich spectrum range of 30GHz to 300GHz. High-frequency band communication systems effectively solve the problem of tight spectrum resources, but face some new technical challenges such as hardware implementation problems. Millimeter wave communication has very high requirements for the sampling frequency of analog to digital converters (ADCs). When the sampling rate exceeds 100MSps, the power consumption of the ADC unit increases quadratically with the increase of the sampling frequency and increases exponentially with the increase of the number of quantization bits. Therefore, the application of high-speed and high-precision ADCs on millimeter wave receivers will lead to extremely high power consumption and system costs. This problem is one of the key bottlenecks in the implementation of millimeter wave systems. In this regard, the solution of using low-resolution ADCs to achieve low-power millimeter wave communication systems has attracted widespread attention. Since low-resolution ADCs introduce a lot of distortion in the original received signal, the performance of traditional signal processing algorithms may be greatly reduced. Summary of the invention

[0003] The purpose of the present invention is to propose a channel estimation and positioning method with better performance, so as to achieve efficient channel and position estimation with a lower number of quantization bits.

[0004] The present invention proposes an alternating iterative algorithm framework. In the first stage, GTurbo (generalizedTurbo, referred to as GTurbo) and sparse Bayesian Learning (Sparse Bayesian Learning, referred to as SBL) are used to obtain In the second stage, the Gauss-Newton method is used to recover the mobile station (MS) position through the obtained channel parameter estimation.

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

[0006] S1. Constructing a channel. Consider a MS equipped with Nr antennas communicating with a base station (BS) with Nt antennas. The total number of subcarriers is M. A low-precision ADC is used in the MS, and the quantization model is:

[0007]

[0008] Among them, the complex quantizer Two independent real quantizers composition, represents the received signal at the nrth antenna,

[0009]

[0010] in, is the normalized discrete Fourier transform matrix, whose i-th row and j-th column element is where n m,nr and h m,nr They are n m and h m The nrth element of . represents a mean of 0 and a variance of σ 2 Additive complex Gaussian noise. m is the frequency domain channel vector on the mth subcarrier.

[0011] S2, estimation of channel parameters. The algorithm block diagram is as follows Figure 2 As shown in the figure, the superscripts “pri”, “post” and “ext” represent the prior, a posteriori and external information respectively, and the subscripts “A” or “B” represent the module A or B. First, the parameters ω nr and∑ nr To initialize: ω nr =0, ∑ nr =10I.

[0012] Module A: Calculation of z nr The posterior mean and variance of .

[0013]

[0014] calculate The external mean and variance of

[0015]

[0016] Module B: Computing The posterior mean and variance of

[0017]

[0018] in

[0019]

[0020] in, express The (j,j)th element of .

[0021] Module A and module B are iteratively executed until convergence.

[0022] Module C: In the first cycle, first, θ Rx Create a dictionary to model the channel as:

[0023]

[0024] in, and Respectively and The mth element of m Each element in has a mean of 0 and a variance of β -1 The same complex Gaussian distribution of

[0025]

[0026] Among them, P r Indicates the angle of arrival The number of uniformly sampled grid points in [-1,1]. Subject to the same mean of 0 and variance of ρ -1 The complex Gaussian distribution of The posterior mean and variance of are:

[0027]

[0028] Among them, Υ=diag{ρ}.

[0029] The formula for updating ρ and β is:

[0030]

[0031] Iterate according to the update expressions shown in (9) and (10) to obtain After that, the angle value corresponding to the position of the K largest non-zero elements can be taken as θ Rx A rough estimate of the value of , based on which the dictionary is retained Corresponding columns, get the reduced dimension dictionary

[0032] Similarly, dictionaries are created for delay and emission angle respectively and Then, the update method of formulas (9) and (10) is used to obtain the rough estimates of the delay and the emission angle, as well as the reduced-dimensional dictionary and

[0033] In the second loop, the received signal is reconstructed as:

[0034]

[0035] in, and a'(f) represents the derivative of a(f) with respect to f. and and δ Tx ,δ Rx and δ τ Respectively represent θ Rx ,θ Rx and quantization error of τ.

[0036] Using the EM algorithm, we estimate {δ Tx ,δ Rx ,δ τ ,α,β}. In step E, the posterior mean and variance of γ are updated:

[0037]

[0038]

[0039] Where Λ=diag(α).

[0040] In the M step, the parameter set is updated.

[0041] The update formula of {α,β} is as follows:

[0042]

[0043]

[0044] δ Rx The update formula is as follows:

[0045]

[0046] in, And T(i,(i-1)×(K+1)+1)=1,i=1,...,K, and the rest of the elements are 0.

[0047]

[0048] in,

[0049]

[0050] δ τ The update formula is as follows:

[0051]

[0052] in

[0053]

[0054] in,

[0055]

[0056] δ Tx The update formula is as follows:

[0057]

[0058] in

[0059]

[0060] in, is a vector of all 1s.

[0061]

[0062] The E-step and M-step are iteratively updated until convergence. In each iteration, the parameters are updated as follows:

[0063]

[0064] The mean and variance of the recovered signal are sent back to Gturbo as h n The prior mean and variance of the channel are used for the next iteration. In order to reduce the complexity of the algorithm, the number of algorithm cycles is set to 2. After the cycle is completed, the estimated value of the channel parameter can be obtained.

[0065] S5. Estimation of location parameters.

[0066] According to the geometric relationship, the relationship between channel parameters and position parameters can be obtained:

[0067]

[0068] Note the position parameter vector where ζ1=[p x ,p y ] T , k =[s k,x ,s k,y ] T .p and s k The initialization is:

[0069]

[0070] Construct optimization function:

[0071]

[0072] in, Satisfy the following formula:

[0073]

[0074] Where f(ζ)=[f(p),…,f(s K-1 )] T The update formula of the position parameter is as follows

[0075]

[0076] The superscript t indicates the number of iterations, and J is the Jacobian matrix, whose (i, j)th element is

[0077] The beneficial effect of the present invention is that the channel parameter and position estimation algorithm proposed in the present invention can realize accurate user positioning in the case of low-precision multiple transmission and multiple reception, and provide reliable user position information for wireless communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 This is a diagram of the MIMO-OFDM uplink communication scenario using a low-precision ADC;

[0079] Figure 2 The block diagram of the algorithm for channel parameter estimation;

[0080] Figure 3 , 4 ,5 are the relationship between RMSE and signal-to-noise ratio of LOS path channel parameters under different bit numbers.

[0081] Figure 6 , 7 , 8 are the relationship between RMSE and signal-to-noise ratio of NLOS path channel parameters under different bit numbers.

[0082] Fig. 9 This is the relationship between RMSE of the position parameter and the signal-to-noise ratio under different bit numbers. DETAILED DESCRIPTION

[0083] The present invention will be described in detail below with reference to the accompanying drawings.

[0084] like Figure 1 As shown in Figure 1, consider the uplink model in a massive MIMO OFDM system, where a user terminal equipped with Nr antennas communicates with a base station terminal with Nt antennas. The total number of subcarriers is M, and the frequency domain channel vector on the mth subcarrier can be expressed as:

[0085]

[0086] in,

[0087]

[0088] Where L is the number of multipaths, θ Tx,l ,θ Rx,l , c l and τ l are the receiving angle, arrival angle, gain and delay of the lth path respectively, and is the array response vector, considering a uniform linear array, we have

[0089]

[0090] in, and is the corresponding spatial direction, defined as

[0091]

[0092] is the frequency of the mth subcarrier, W is the system bandwidth, f c is the carrier frequency, λ c is the carrier wavelength, d is the antenna spacing, set d = λ c / 2.

[0093] The signal arriving at the BS can be written as:

[0094] y m =h m s m +n m ,m=1,2,…,M (35)

[0095] Among them, s m is the training symbol, represents a mean of 0 and a variance of σ 2 Without loss of generality, let s m = 1. The time domain signal received at the nrth antenna is as follows:

[0096]

[0097] is the normalized discrete Fourier transform matrix, whose i-th row and j-th column element is where n m,nr and h m,nr They are n m and h m The nrth element of .

[0098] Using Complex Quantizer For receiving signal quantize each element of Two independent real quantizers Composition, namely:

[0099]

[0100] in, and express and q nr The pth element of . The quantization accuracy is Q b The bit ADC will Map to One of the discrete values, when the quantizer input is in the interval (u b-1 ,u b ], the output value is v b , i.e. the bth discrete value, where -∞=u0 <u1<…<u B =∞quantization threshold, v b For the interval (u b-1 ,u b ]’s center of mass.

[0101] So the system model based on low-precision ADC is

[0102]

[0103] The channel parameter estimation algorithm is designed based on GTurbo and SBL.

[0104] Module A: Calculation of z nr The posterior mean and variance of .

[0105]

[0106] calculate The external mean and variance of

[0107]

[0108] Module B: Computing The posterior mean and variance of

[0109]

[0110] in,

[0111]

[0112] in, express Module A and module B are iteratively executed until convergence.

[0113] Module C: In the first cycle, use and h m The relationship can be obtained

[0114]

[0115] in, express The mth element of m Each element in has a mean of 0 and a variance of β -1 The same complex Gaussian distribution.

[0116] First, for θ Rx Create a dictionary to model the channel as:

[0117]

[0118] in

[0119]

[0120] Among them, P r Indicates the angle of arrival The number of uniformly sampled grid points in [-1,1]. Subject to the same mean of 0 and variance of ρ -1 The complex Gaussian distribution of Then we have: Where Υ=diag{ρ}, we can deduce The posterior distribution of is also a complex Gaussian distribution, with mean and variance as:

[0121]

[0122] The formula for updating ρ and β is:

[0123]

[0124] Perform iterative updates according to the update expressions shown in (46) and (47), and obtain After that, the angle value corresponding to the position of the K largest non-zero elements can be taken as θ Rx A rough estimate of the value of , based on which the dictionary is retained Corresponding columns, get the reduced dimension dictionary

[0125] The channel is modeled as:

[0126]

[0127] in, and is the range of delay values, Δ is the sampling interval of delay, and then the updating method (46)-(47) is used to select The delay values ​​corresponding to the positions of the K largest non-zero elements of the posterior mean are used as rough estimates of τ to obtain the reduced-dimensional dictionary Then the channel is modeled as:

[0128]

[0129] in,

[0130]

[0131] Among them, P t Indicates the sending angle The number of uniformly sampled grid points in [-1,1]. Using the update method of (46)-(47), select The posterior mean K largest non-zero position corresponding to the delay value is taken as θ Tx A rough estimate of the dimension reduction dictionary

[0132] In the second loop, the received signal is reconstructed as:

[0133]

[0134] in, and a'(f) represents the derivative of a(f) with respect to f. and and δ Tx ,δ Rx and δ τ Respectively represent θ Rx ,θ Rx and quantization error of τ.

[0135] Using the EM algorithm, we estimate {δ Tx ,δ Rx ,δ τ ,α,β}. In step E, the posterior mean and variance of γ are updated:

[0136]

[0137]

[0138] Where Λ=diag(α).

[0139] In the M step, the parameter set is updated. The logarithmic expectation of the total likelihood function can be written as

[0140]

[0141] 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 update formula for {α,β} is as follows:

[0142]

[0143]

[0144] δ Rx The update formula is as follows:

[0145]

[0146] in, And T(i,(i-1)×(K+1)+1)=1,i=1,...,K, and the rest of the elements are 0.

[0147]

[0148] in,

[0149]

[0150] δ τ The update formula is as follows:

[0151]

[0152] in,

[0153]

[0154] in,

[0155]

[0156] δ Tx The update formula is as follows:

[0157]

[0158] in,

[0159]

[0160] in, is a vector of all 1s.

[0161]

[0162] The E-step and M-step are iteratively updated until convergence. In each iteration, the parameters are updated as follows:

[0163]

[0164] The mean and variance of the recovered signal are sent back to Gturbo as h n The prior mean ω nr and variance Σ nr To carry out the next iteration. In order to reduce the complexity of the algorithm, the number of algorithm loops is set to 2. After the loop is completed, the estimated value of the channel parameter can be obtained.

[0165] According to the geometric relationship, we can get

[0166]

[0167] Note the position parameter vector where ζ1=[p x ,p y ] T , k =[s k,x ,s k,y ] T .p and s k The initialization is:

[0168]

[0169] Construct optimization function:

[0170]

[0171] in, Satisfy the following formula:

[0172]

[0173] Where f(ζ)=[f(p),…,f(s K-1 )] T The update formula of the position parameter is as follows

[0174]

[0175] where J is the Jacobian matrix, whose (i,j)th element is

[0176] In the simulation, the uplink broadband millimeter wave MIMO-OFDM system is considered, and Nr=16, Nt=16, f c =28GHz, W=100MHz, M=64, L=K=2. Path gain c l Obeys cyclic symmetric Gaussian distribution Where c = 3 × 10 8 m / s, d is the distance from the base station to the user end. Considering the indoor environment, the base station position q = [0,0] T, the user end position p = [p x ,p y ] T is random, where p x ~U[5,7],p y ~U[1,3], U[a,b] represents uniform distribution in the range [a,b]. 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 ,θ Rx,l and θ Tx,l The Cramer-Rao Lower Bounds (CRB) is used to provide a reference benchmark for algorithm performance.

[0177] The simulation conclusions are as follows:

[0178] Figure 3 , 4 , 5 describe the relationship between the minimum root mean square error (RMSE) and signal-to-noise ratio (SNR) of the LOS path parameters. It can be observed from the figure that the proposed scheme can obtain accurate estimates of the angle and delay parameters, and its estimation error is close to the theoretical lower limit.

[0179] Figure 6 , 7 8 depicts the relationship between RMSE and SNR of NLOS path parameters. It can be observed from the figure that the estimation performance of NLOS path channel parameters is much lower than that of LOS channel, but the algorithm of the present invention can still make the system performance close to the ideal curve.

[0180] Fig. 9 Describes the quantization accuracy Q b Relationship with the RMSE of location estimation, the proposed algorithm can provide accurate location estimation even when the number of quantization bits is small.

Claims

1. A method for channel estimation and positioning of a large-scale MIMO system under low-precision quantization, characterized in that: The following steps are involved: S1. Channel construction: Define that an MS equipped with Nr antennas communicates with a BS with Nt antennas. The total number of subcarriers is M. A low-precision ADC is used at the MS, and the quantization model is: Among them, the complex quantizer Two independent real quantizers composition, represents the received signal at the nrth antenna, in, is the normalized discrete Fourier transform matrix, whose i-th row and j-th column element is where n m,nr and h m,nr They are n m and h m The nrth element of ; represents a mean of 0 and a variance of σ 2 Additive complex Gaussian noise, h m is the frequency domain channel vector on the mth subcarrier; S2. Estimation of channel parameters: ω nr and∑ nr To initialize: ω nr =0, ∑ nr =10I; In the first calculation module A, the following is calculated: z nr The posterior mean and variance of The external mean and variance of The superscripts pri, post, and ext represent prior information, posterior information, and external information, respectively; In the second calculation module B, calculate: The posterior mean and variance of in in, express the (j,j)th element of ; Iteratively execute the first calculation module A and the second calculation module B until convergence; In the third calculation module C: In the first cycle, first, the arrival angle θ Rx Create a dictionary to model the channel as: in, and Respectively and The mth element of m Each element in has a mean of 0 and a variance of β -1 The same complex Gaussian distribution of Among them, P r Indicates the angle of arrival The number of uniformly sampled grid points in [-1,1], f m is the frequency of the mth subcarrier, f c is the carrier frequency, λ c is the carrier wavelength; let Subject to the same mean of 0 and variance of ρ -1 Complex Gaussian distribution The posterior mean and variance of are: Where, γ = diag{ρ}; The formula for updating ρ and β is: According to the update expressions shown in formula (9) and formula (10), iterative update is performed to obtain After that, the angle value corresponding to the position of the K largest non-zero elements can be taken as θ Rx A rough estimate of the value of , based on which the dictionary is retained Corresponding columns, get the reduced dimension dictionary Similarly, dictionaries are created for delay and emission angle respectively and Then use the update method of (9) and (10) to obtain the rough estimate of the delay and the emission angle, as well as the reduced dimensionality dictionary and In the second loop, the received signal is reconstructed as: in, and a'(φ) represents the derivative of a(φ) with respect to φ, and and δ Tx ,δ Rx and δ τ Respectively represent θ Rx ,θ Rx and quantization error of τ; Using the EM algorithm to estimate {δ Tx ,δ Rx ,δ τ ,α,β}: In the E step, update the posterior mean and variance of γ: Where, Λ = diag(α); In the M step, the parameter set is updated; The update formula of {α,β} is as follows: δ Rx The update formula is as follows: in, And Τ(i,(i-1)×(K+1)+1)=1,i=1,...,K, and the rest of the elements are 0; in, δ τ The update formula is as follows: in in, δ Tx The update formula is as follows: in in, is a vector of all 1s; The E-step and M-step are iteratively updated until convergence; in each iteration, the parameters are updated as follows: The mean and variance of the recovered signal are sent back to the second calculation module B as h n The prior mean and variance of the channel are used for the next iteration; in order to reduce the complexity of the algorithm, the number of algorithm cycles is set to 2. After the cycle is completed, the estimated value of the channel parameter is obtained. S5. Estimation of location parameters: According to the geometric relationship, the relationship between the channel parameters and the position parameters is obtained: Among them, p represents the user terminal location, q represents the base station location, and s l Indicates the position of the refraction point; Note the position parameter vector where ζ1=[p x ,p y ] T , k =[s k,x ,s k,y ] T ; p and s k The initialization is: Construct optimization function: in, Satisfy the following formula: Where f(ζ)=[f(p),…,f(s K-1 )] T ; The update formula of position parameters is as follows The superscript t indicates the number of iterations, and J is the Jacobian matrix, whose (i, j)th element is

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