Space-time modulation metasurface DOA estimation method based on unit non-uniform arrangement

Abstract

The invention belongs to the technical field of metasurface signal processing, and particularly relates to a space-time modulation metasurface DOA estimation method based on unit non-uniform arrangement. Comprising the following steps: S1, establishing a space-time modulation metasurface array model with non-uniformly arranged units, designing a space-time coding matrix and carrying out space-time modulation on an incident signal by using the model, S2, obtaining a harmonic component of a received signal, and S3, carrying out DOA estimation by using the harmonic component of the received signal. Compared with a metasurface with uniformly arranged units, the number of the metasurface units is reduced through non-uniform arrangement of the units, the hardware cost is reduced, meanwhile, the problem that DOA estimation is fuzzy under the condition that the unit spacing is larger than half-wavelength is solved, the DOA estimation precision under the condition of low signal-to-noise ratio is improved, and higher reliability is achieved.

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] DOA estimation is widely used in radar detection, smart antennas, satellite communications, etc. 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, Jul. 2018) proposed a DOA estimation method based on a time-modulated array. This method estimates DOA with high accuracy, but requires multiple antenna array receiving channels, which results in high hardware costs.

[0003] In recent years, two-dimensional artificial electromagnetic materials, especially reconfigurable intelligent 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 DOA With Programmable Metasurface," in IEEE Internet of Things Journal, vol. 8, no. 12, pp. 10187-10197, Jun. 2021) spatially encodes the metasurface and uses a single receiving channel to achieve DOA estimation. Compared with DOA estimation using multiple antenna channels, this method reduces the 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 a 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-uniform arrangement of design units

[0008] The metasurface array model includes a metasurface array with N×M units arranged in N rows and M columns. The units in each row are evenly arranged, and each column takes unit No. 1 as the reference unit. Only the distance between unit No. 2 and the reference unit does not exceed 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. The arrangement of metasurface units 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 elevation angle of the incident signal, and w n (t) is the Gaussian white noise when the nth metasurface unit is modulated, D n is the distance between the nth supersurface unit and the first supersurface unit, therefore, D1 = 0. When D2 = λ / 2 is set, according to the arrangement characteristics of the supersurface unit array,

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

[0012] The size of the space-time coding matrix is ​​N×L, where L means there are L modulation codes in one modulation period T0. The coding matrix is ​​as follows: Figure 3 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, 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 it is set to -1, l represents the modulation coding number, l=1, 2,…, L.

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

[0018]

[0019] Among them, 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-uniform arrangement of units, the signal modulated by each unit of the metasurface array is received by the 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. 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 The frequency of the received signal can be obtained by using formula (8) a (f) If Figure 4 As shown. Then the spectrum S a(f) The incident signal frequency F c Centered at , the qth order harmonic component with fundamental frequency F0 can be expressed as:

[0029]

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

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

[0032] Expand formula (7) and limit the range of the harmonic number 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 each unit modulation signal:

[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 base 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 period 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 (t), the distances between units 1 and 2 and unit 1 are all less than half a wavelength, so there is no ambiguity in 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), and we can get:

[0052]

[0053] n=3,4,...,N.

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

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

[0056]

[0057] Where n = 1, 2, ..., N-1, substituting formula (18) into formula (19) can 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. The DOA estimation is performed using a metasurface with non-uniformly arranged units, which reduces the hardware cost and the mutual coupling effect between units.

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

[0064] Figure 1 It is a schematic 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 It is a schematic diagram of the structure of DOA estimation based on the spatiotemporal modulation metasurface with non-uniform arrangement of units;

[0066] Figure 3 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 It is the root mean square error (RMSE) curve of DOA estimation at different angles of this method;

[0069] Figure 6 This is the root mean square error (RMSE) curve of the direction finding of this method under different signal-to-noise ratios; 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-uniform arrangement of 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-uniform arrangement of design units

[0074] The number of the non-uniform metasurface array units is 8, with unit No. 1 being the reference unit, the distance between unit No. 2 and the reference unit being half the wavelength of the incident signal, the distance between unit No. 3 and unit No. 2 being twice the distance between units No. 1 and 2, the distance between unit No. 4 and unit No. 3 being 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 the spatiotemporal coding matrix and use the model to perform spatiotemporal modulation on the incident signal

[0076] Figure 3 It is the spatiotemporal modulation matrix of each metasurface unit of 8×8, where each row represents the modulation sequence of a unit, and there are 8 coding sequences in total. Yellow indicates that the modulation coefficient is 1, that is, the metasurface modulation phase is 0°, and blue indicates that the modulation coefficient is -1, that is, the metasurface modulation phase is 180°. Each column represents the modulation coding of each unit, and there are 8 units modulated in total.

[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 -10dB and the incident signal DOA is 35.55°.

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

[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 signal received by each unit is deambiguated by the unambiguous unit No. 2 to obtain the precise value of DOA.

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

[0084] Figure 5 This is a schematic diagram of the change of the DOA root mean square error with the signal-to-noise ratio after 1000 Monte Carlo iterations when the incident angle is 35.55°. It can be seen that with the increase of the signal-to-noise ratio, the DOA direction finding error gradually decreases, and this trend slows down with the increase of the signal-to-noise ratio.

[0085] Figure 6This is a schematic diagram of the change of the root mean square error of the DOA estimation with the incident angle after 1000 Monte Carlo iterations 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 estimating DOA of a spatiotemporal modulation metasurface based on non-uniform arrangement of units, characterized in that: 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-uniform arrangement of design units The metasurface array model contains a metasurface array with N×M units arranged in N rows and M columns. The units in each row are evenly arranged, and each column takes unit No. 1 as the reference unit. Only the distance between unit No. 2 and the reference unit does not exceed 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. 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 elevation angle of the incident signal, and 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 the spatiotemporal coding matrix and use the model to perform spatiotemporal modulation on the incident signal The size of the space-time coding matrix is ​​N×L, where L means there are L modulation codes in one modulation period T0. In one modulation period T0, the modulation signal of the nth metasurface unit in the space-time modulation metasurface array is expressed as: in, is the lth modulation code of the nth metasurface unit in a modulation cycle, 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: Among them, 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 The frequency of the received signal can be obtained by using formula (8) a (f), then the spectrum S a (f) The incident signal frequency F c Centered at , the qth order harmonic component with fundamental frequency F0 can be expressed as: S3 uses the harmonic components of the received signal to estimate DOA S3.1 Using the received signal s a The Q-order harmonic component of (t) is constructed into an analytical relationship Expand formula (7) and limit the range of the harmonic number 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 each unit modulation signal: 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 base 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 period 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 (t) Phase ambiguity value, the distance between unit 1 and unit 2 and unit 1 is no more than 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), and we can get: n=3,4,...,N; S3.3 Calculate the exact solution for DOA estimation By taking the phases on both sides of formula (14) at the same time, the DOA estimation values ​​calculated by the (n-1)th unit and the nth unit of the metasurface array can be obtained. A total of (N-1) estimation values ​​are solved and named η1, η2, ..., η N-1 , combined with formulas (15) to (16), η n It is 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, substituting formula (18) into formula (19) can 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 estimating DOA of a spatiotemporal modulation metasurface based on non-uniform arrangement of units according to claim 1, characterized in that: When D2 = λ / 2, D3 = λ according to the arrangement characteristics of the metasurface unit array. D5=2λ,..., 3. The method for estimating DOA of a spatiotemporal modulation metasurface based on non-uniform arrangement of units according to claim 1, characterized in that: In S1.2, the height h needs to satisfy the near-field distance condition.

4. The method for estimating DOA of a spatiotemporal modulation metasurface based on non-uniform arrangement of units as claimed in claim 3, characterized in that: 0.4λ≤h≤0.6λ.

5. The method for DOA estimation of a spatiotemporal modulation metasurface based on 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.

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