DOA estimation method of spatiotemporal modulation metasurface based on non-uniform arrangement of units

Abstract

The present invention belongs to the technical field of metasurface signal processing, and in particular relates to a DOA estimation method for a spatiotemporal modulation metasurface based on non-uniform arrangement of units; the method comprises the following steps: S1 establishing a spatiotemporal modulation metasurface array model with non-uniform arrangement of units, designing a spatiotemporal coding matrix and using the model to spatiotemporally modulate an incident signal, S2 obtaining the harmonic components of a received signal, and S3 using the harmonic components of the received signal to perform DOA estimation; compared to a metasurface with uniformly arranged units, the present invention reduces the number of metasurface units through non-uniform arrangement of units, reduces hardware costs, and solves the problem of DOA estimation ambiguity when the unit spacing is greater than half a wavelength, thereby improving the DOA estimation accuracy under low signal-to-noise ratio conditions and having greater reliability.

Description

Technical Field

[0001] The present invention belongs to the technical field of metasurface signal processing, and in particular relates to a method for estimating the direction of arrival (DOA) of a spatiotemporal modulated metasurface based on non-uniform arrangement of units. Background Art

[0002] Direction of Arrival (DOA) estimation is widely used in radar detection, smart antennas, satellite communications, and other applications. He Chong et al. (C. He et al., "Direction Finding by Time-Modulated Linear Array," IEEE Transactions on Antennas and Propagation, vol. 66, no. 7, pp. 3642-3652, July 2018) proposed a DOA estimation method based on a time-modulated array. This method achieves high DOA accuracy but requires multiple antenna array receiving channels, resulting in high hardware costs.

[0003] In recent years, two-dimensional artificial electromagnetic materials, especially reconfigurable smart metasurfaces, have attracted widespread attention due to their simple design and low cost. By carefully designing its unit structure, the metasurface can achieve precise control of the amplitude and phase of electromagnetic waves. Therefore, many researchers have tried to combine the metasurface with array signal processing to achieve DOA estimation. Lin Mingtuan et al. (M.Lin et al.,"Single Sensor to Estimate DOAWith Programmable Metasurface,"inIEEE Internet of Things Journal,vol.8,no.12,pp.10187-10197,Jun.2021) spatially encoded the metasurface and used a single receiving channel to achieve DOA estimation. Compared with DOA estimation using multiple antenna channels, this method reduces hardware cost, but when the signal-to-noise ratio is low, the DOA estimation error is large; in addition, when the distance between units is close, a strong mutual coupling effect will be generated, resulting in the failure of the DOA estimation method. Summary of the Invention

[0004] In response to the above technical problems, the present invention proposes a DOA estimation method for a spatiotemporal modulation metasurface based on non-uniform arrangement of units. Compared with the metasurface with uniform arrangement of units, the present invention reduces the number of metasurface units through non-uniform arrangement of units, reduces hardware costs, and solves the problem of DOA estimation ambiguity when the unit spacing is greater than half a wavelength, improves the DOA estimation accuracy under low signal-to-noise ratio conditions, and has stronger reliability.

[0005] Specifically, the present invention is divided into the following steps:

[0006] S1 establishes a spatiotemporal modulation metasurface array model with non-uniformly arranged units, designs a spatiotemporal coding matrix, and uses the model to perform spatiotemporal modulation on the incident signal; the details are as follows:

[0007] S1.1 Design of a spatiotemporal metasurface array model with non-uniformly arranged units

[0008] The metasurface array model contains N×M units arranged into N rows and M columns. The units in each row are evenly arranged, and each column uses unit 1 as the reference unit. Only the distance between unit 2 and the reference unit does not exceed half the wavelength of the incident signal. The distance between unit 3 and unit 2 is twice the distance between units 1 and 2. The distance between unit 4 and unit 3 is twice the distance between units 2 and 3, and so on. The metasurface unit arrangement is as follows: Figure 2 As shown, the incident signal s modulated by the nth metasurface unit in each column is n (t) can be expressed as:

[0009]

[0010] Where n = 1, 2, ..., N, t is the time series, A0 represents the amplitude of the incident signal, F c is the frequency of the incident signal, φ0 represents the initial phase of the incident signal, K = 2π / λ is the spatial wave number of the incident signal, λ is the wavelength of the incident signal, θ is the pitch angle of the incident signal, w n (t) is the Gaussian white noise when the nth metasurface unit is modulated, D n is the distance between the nth metasurface unit and the first metasurface unit, so D1 = 0. When D2 = λ / 2, the arrangement characteristics of the metasurface unit array are as follows:

[0011] S1.2 Design a spatiotemporal coding matrix and use this model to perform spatiotemporal modulation on the incident signal

[0012] The size of the space-time coding matrix is ​​N×L, where L represents the number of modulation codes in a modulation period T0. The coding matrix is ​​as follows: Figure 3 As shown. In a modulation period T0, the modulation signal of the nth metasurface unit in the spatiotemporal modulation metasurface array can be expressed as:

[0013]

[0014] in, is the lth modulation code of the nth metasurface unit in a modulation cycle, It is a pulse function with a period of T0, and its specific expression is:

[0015]

[0016] In the formula, μ represents the modulation period number, which is a positive integer, and τ l,on The modulation code in a modulation cycle When τ is set to 1, l,off The modulation code in a modulation cycle When set to -1, l represents the modulation coding sequence number, l = 1, 2, ..., L.

[0017] For the periodic modulation signal Γ n (t), and expand it into a Fourier series:

[0018]

[0019] Where F0 = 2π / T0 represents Γ n The fundamental frequency of (t), ψ n,q represents the harmonic coefficient of the qth harmonic of the modulation signal of the nth metasurface unit, and its expression is:

[0020]

[0021] After being modulated by the metasurface array with non-uniformly arranged units, the signal modulated by each unit of the metasurface array is received by a receiving antenna located at a height h above the center of the metasurface array. h needs to meet the near-field distance condition. Usually, 0.4λ≤h≤0.6λ, and the received signal s a (t) can be expressed as:

[0022]

[0023] Substituting formulas (1) to (5) into formula (6), we can get the received signal s a The Fourier series expansion of (t) is as follows:

[0024]

[0025] S2 obtains the harmonic components of the received signal

[0026] Perform Fourier transform on the received signal, and its spectrum S a (f) can be expressed as:

[0027]

[0028] f represents the spectrum S a (f) frequency, the spectrum S of the received signal can be obtained by formula (8) a (f), such as Figure 4 As shown. Then the spectrum S aIn (f), the incident signal frequency F c As the center, the qth order harmonic component with the fundamental frequency F0 can be expressed as:

[0029]

[0030] S3 uses the harmonic components of the received signal to perform DOA estimation

[0031] S3.1 Using the received signal s a The analytical relationship of the Q-order harmonic component of (t) is constructed

[0032] Expand formula (7) and limit the range of the harmonic order q on the right side to between -Q and +Q. In formula (9), extract the -Q to +Q order harmonic components. Under this condition, combining formulas (7) to (9) yields:

[0033]

[0034] Where Ψ is the coefficient matrix composed of the harmonic coefficients of each order of the modulation signal of each unit:

[0035]

[0036] A is the hypersurface unit manifold vector:

[0037]

[0038] Γ is S a (f) With the incident signal frequency F c The coefficient vector of the qth order harmonic component with the fundamental frequency F0 as the center is:

[0039]

[0040] Through the matrix equation (10), we can get:

[0041]

[0042] Where n=2,3,...,N,Ψ -1 represents the inverse of the matrix Ψ, [Ψ -1 Γ] n Represents the vector Ψ -1 The nth element of Γ.

[0043] S3.2 Calculate the phase ambiguity value using the non-uniform arrangement characteristics of the metasurface units

[0044] When the distance between the metasurface units is greater than half the wavelength of the incident signal, the phase of the incident signal will be repeated with a period of 2π. Therefore, the incident signal s is calculated for each element of the metasurface unit manifold vector A. n (t) Phase:

[0045]

[0046] as a result Not the incident signal s n (t) is not the real phase, but the fuzzy phase. Combined with formula (1), the relationship between the two is expressed as:

[0047]

[0048] Where n=1,2,3,...,N,β n Represents the incident signal s n The phase ambiguity value of (t) is that the distances between units 1 and 2 and unit 1 do not exceed half a wavelength, so there is no ambiguity between these two units, and their ambiguity values ​​β1=β2=0.

[0049] Since the metasurface units are arranged linearly, when they modulate the far-field incident signal, the actual phase difference between each unit and the reference unit is proportional to the distance difference. Combined with formula (1), we have:

[0050]

[0051] n,k=2,3,4,...,N, fix the value of k to 2, use unit 2 to defuzzify units 3 to N, that is, combine formulas (16) to (17) to obtain:

[0052]

[0053] n=3,4,...,N。

[0054] S3.3 Calculate the exact solution for DOA estimation

[0055] By taking the phase on both sides of formula (14) at the same time, the DOA estimation value calculated by the (n-1)th unit and the nth unit of the metasurface array can be solved. A total of (N-1) estimation values ​​are solved and named as η1, η2, ..., η N-1 , combined with formulas (15) to (16), η n Expressed as:

[0056]

[0057] Where n=1,2,...,N-1, substitute formula (18) into formula (19) to achieve η n Deblurring.

[0058] The calculated (N-1) η n The values ​​are averaged:

[0059]

[0060] By using formula (20), we can get the exact solution for the incident signal DOA estimation:

[0061] Compared with the prior art, the present invention has the following technical effects:

[0062] 1. Using a metasurface with non-uniformly arranged units for DOA estimation reduces hardware costs and the mutual coupling effect between units.

[0063] 2. The harmonics generated by space-time coding can improve the DOA estimation accuracy under low signal-to-noise ratio. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 1 is a flow chart of a method for estimating DOA of a spatiotemporal modulation metasurface based on a non-uniform array provided by the present invention;

[0065] Figure 2 This is a schematic diagram of the structure of the spatiotemporal modulation metasurface for DOA estimation based on the non-uniform arrangement of units;

[0066] Figure 3 This is a schematic diagram of the space-time coded modulation sequence of the metasurface;

[0067] Figure 4 is the spectrum of the signal after metasurface modulation;

[0068] Figure 5 This is the root mean square error (RMSE) curve of the DOA estimation at different angles.

[0069] Figure 6 This is the Root Mean Square Error (RMSE) curve of the direction finding under different signal-to-noise ratios of this method; DETAILED DESCRIPTION

[0070] The present invention is further described below with reference to the accompanying drawings and examples.

[0071] The present invention comprises the following steps:

[0072] S1 establishes a spatiotemporal modulation metasurface array model with non-uniformly arranged units, designs a spatiotemporal coding matrix and uses the model to perform spatiotemporal modulation on the incident signal.

[0073] S1.1 Design of a spatiotemporal metasurface array model with non-uniformly arranged units

[0074] The number of non-uniform metasurface array units is 8, with unit No. 1 as the reference unit. The distance between unit No. 2 and the reference unit is half the wavelength of the incident signal. The distance between unit No. 3 and unit No. 2 is twice the distance between units No. 1 and 2. The distance between unit No. 4 and unit No. 3 is twice the distance between units No. 2 and 3, and so on. Unit No. 2 is used to deambiguate units No. 3, 4, ... 8.

[0075] S1.2 Design a spatiotemporal coding matrix and use this model to perform spatiotemporal modulation on the incident signal

[0076] Figure 3 This is the spatiotemporal modulation matrix of each 8×8 metasurface unit. Each row represents the modulation sequence of a unit, with a total of eight coding sequences. Yellow indicates a modulation coefficient of 1, i.e., a metasurface modulation phase of 0°, and blue indicates a modulation coefficient of -1, i.e., a metasurface modulation phase of 180°. Each column represents the modulation code of each unit, with a total of eight units modulated.

[0077] S2 obtains the harmonic components of the received signal

[0078] The receiving antenna receives all incident signals modulated by the metasurface and performs fast Fourier transform on the received signals to obtain the amplitude spectrum and phase spectrum of the total received signal. Figure 3 The figure shows the corresponding spectrum in the simulation experiment when the signal-to-noise ratio is -10 dB and the incident signal DOA is 35.55°.

[0079] S3 uses the harmonic components of the received signal to perform DOA estimation

[0080] S3.1 Constructing an analytical relationship using the Q-order harmonic components of the received signal

[0081] S3.2 Calculate the phase ambiguity value using the non-uniform arrangement characteristics of the metasurface units

[0082] According to the non-uniform arrangement characteristics of the metasurface unit array, the unambiguous unit No. 2 is used to deambiguate the signals received by each unit to obtain the precise value of DOA.

[0083] S3.3 Calculate the exact solution for DOA estimation

[0084] Figure 5 The figure below shows the calculated DOA root mean square error as the signal-to-noise ratio changes after 1000 Monte Carlo iterations when the incident angle is 35.55°. It can be seen that the DOA direction finding error gradually decreases with the increase of the signal-to-noise ratio, and this trend slows down with the increase of the signal-to-noise ratio.

[0085] Figure 6This is a schematic diagram showing how the root mean square error of the DOA estimation calculated after 1000 Monte Carlo iterations changes with the incident angle when the signal-to-noise ratio is -10dB. It can be seen that when the signal is facing the metasurface, the power of the harmonic component is the highest. As the incident angle deviates from the facing direction, the power of the harmonic component decreases. Therefore, despite the same signal-to-noise ratio, the DOA measurement accuracy will still decrease with the increase of the incident angle.

Claims

1. A method for DOA estimation based on a spatiotemporal modulation metasurface with non-uniform arrangement of units, characterized by: The method is divided into the following steps: S1 establishes a spatiotemporal modulation metasurface array model with non-uniformly arranged units, designs a spatiotemporal coding matrix, and uses the model to perform spatiotemporal modulation on the incident signal; the details are as follows: S1.1 Design of a spatiotemporal metasurface array model with non-uniformly arranged units The metasurface array model contains N×M units arranged into N rows and M columns. The units in each row are evenly arranged, and each column uses unit 1 as the reference unit. Only the distance between unit 2 and the reference unit does not exceed half the wavelength of the incident signal. The distance between unit 3 and unit 2 is twice the distance between units 1 and 2. The distance between unit 4 and unit 3 is twice the distance between units 2 and 3, and so on. The incident signal s modulated by the nth metasurface unit in each column is n (t) is expressed as: Where n = 1, 2, ..., N, t is the time series, A0 represents the amplitude of the incident signal, F c is the frequency of the incident signal, Φ0 represents the initial phase of the incident signal, K = 2π / λ is the spatial wave number of the incident signal, λ is the wavelength of the incident signal, θ is the pitch angle of the incident signal, w n (t) is the Gaussian white noise when the nth metasurface unit is modulated, D n is the distance between the nth hypersurface unit and the first hypersurface unit, therefore, D1=0; S1.2 Design a spatiotemporal coding matrix and use this model to perform spatiotemporal modulation on the incident signal The size of the spatiotemporal coding matrix is ​​N×L, where L represents L modulation codes in one modulation period T0. Within one modulation period T0, the modulation signal of the nth metasurface unit in the spatiotemporal modulation metasurface array is expressed as: in, is the lth modulation code of the nth metasurface unit in a modulation cycle, It is a pulse function with a period of T0, and its specific expression is: In the formula, μ represents the modulation period number, which is a positive integer, and τ l,on The modulation code in a modulation cycle When τ is set to 1, l,off The modulation code in a modulation cycle When set to -1, l represents the modulation code number, l = 1, 2, ..., L; For the periodic modulation signal Γ n (t), and expand it into a Fourier series: Where F0 = 2π / T0 represents Γ n The fundamental frequency of (t), ψ n,q represents the harmonic coefficient of the qth harmonic of the modulation signal of the nth metasurface unit, and its expression is: After being modulated by the metasurface array with non-uniformly arranged units, the receiving antenna located at a height h above the center of the metasurface array is used to receive the signal modulated by each unit of the metasurface array. The received signal s a (t) can be expressed as: Substituting formulas (1) to (5) into formula (6), we can get the received signal s a The Fourier series expansion of (t) is as follows: S2 obtains the harmonic components of the received signal Perform Fourier transform on the received signal, and its spectrum S a (f) can be expressed as: f represents the spectrum S a (f) frequency, the spectrum S of the received signal can be obtained by formula (8) a (f), then the spectrum S a (f) The incident signal frequency F c As the center, the qth order harmonic component with the fundamental frequency F0 can be expressed as: S3 uses the harmonic components of the received signal to perform DOA estimation S3.1 Using the received signal s a The analytical relationship of the Q-order harmonic component of (t) is constructed Expand formula (7) and limit the range of the harmonic order q on the right side to between -Q and +Q. In formula (9), extract the -Q to +Q order harmonic components. Under this condition, combining formulas (7) to (9) yields: Where Ψ is the coefficient matrix composed of the harmonic coefficients of each order of the modulation signal of each unit: A is the hypersurface unit manifold vector: Γ is S a (f) With the incident signal frequency F c The coefficient vector of the qth order harmonic component with the fundamental frequency F0 as the center is: Through the matrix equation (10), we can get: Where n=2,3,...,N,Ψ -1 represents the inverse of the matrix Ψ, [Ψ -1 Γ] n Represents the vector Ψ -1 The nth element of Γ; S3.2 Calculate the phase ambiguity value using the non-uniform arrangement characteristics of the metasurface units When the distance between the metasurface units is greater than half the wavelength of the incident signal, the phase of the incident signal will be repeated with a period of 2π. Therefore, the incident signal s is calculated for each element of the metasurface unit manifold vector A. n (t) Phase: as a result Not the incident signal s n (t) is not the real phase, but the fuzzy phase. Combined with formula (1), the relationship between the two is expressed as: Where n=1,2,3,...,N,β n Represents the incident signal s n Phase ambiguity value of (t), the distance between unit 1 and unit 2 and unit 1 does not exceed half a wavelength, so these two units are not ambiguous, and their ambiguity values ​​β1 = β2 = 0; Since the metasurface units are arranged linearly, when they modulate the far-field incident signal, the actual phase difference between each unit and the reference unit is proportional to the distance difference. Combined with formula (1), we have: n,k=2,3,4,...,N, fix the value of k to 2, use unit 2 to defuzzify units 3 to N, that is, combine formulas (16) to (17) to obtain: n=3,4,...,N; S3.3 Calculate the exact solution for DOA estimation By taking the phase on both sides of formula (14) at the same time, the DOA estimation value calculated by the (n-1)th unit and the nth unit of the metasurface array can be solved. A total of (N-1) estimation values ​​are solved and named as η1, η2, ..., η N-1 , combined with formulas (15) to (16), η n Expressed as: or n =arcsin[(arg([Ψ -1 C] n+1 )-arg([Ψ -1 C] n )+2(b n+1 -b n )π) / (-K(D n+1 -D n ))] (19) Where n=1,2,...,N-1, substitute formula (18) into formula (19) to achieve η n Deblurring; The calculated (N-1) η n The values ​​are averaged: By using formula (20), we can get the exact solution for the incident signal DOA estimation:

2. The method for DOA estimation based on a spatiotemporal modulation metasurface with non-uniform arrangement of units according to claim 1, wherein: When D2 = λ / 2, D3 = λ according to the arrangement characteristics of the metasurface unit array. D5=2λ,..., 3. The DOA estimation method based on the spatiotemporal modulation metasurface with non-uniform arrangement of units according to claim 1, characterized in that: In S1.2, the height h needs to meet the near-field distance condition.

4. The method for DOA estimation based on a spatiotemporal modulation metasurface with non-uniform arrangement of units according to claim 3, wherein: 0.4λ≤h≤0.6λ.

5. The DOA estimation method based on a spatiotemporal modulation metasurface with non-uniform arrangement of units according to any one of claims 1 to 4, characterized in that: The metasurface array model contains 8×1 units.

Images