Signal Direction Finding System and Method Based on 1-bit Programmable Metasurface

Abstract

The present invention relates to a signal direction finding system and method based on a 1-bit programmable metasurface, belonging to the technical field of signal direction finding. In the present invention, the incident signal is received by the unit antennas on the 1-bit programmable metasurface, and a periodic modulation sequence is applied to each unit antenna by a controller, so as to apply a phase shift to the incident signal and then radiate it towards the receiving antenna; according to the designed periodic modulation sequence, the Fourier coefficients corresponding to the fundamental wave component and the first harmonic component of each unit antenna are calculated; the fundamental wave component and the first harmonic component at the receiving antenna are calculated; the functional relationship between the ratio of the first harmonic component to the fundamental wave component and the direction of the incident signal is obtained; according to the actually measured ratio of the first harmonic component to the fundamental wave component, the direction of the incident signal is calculated. The present invention realizes two-dimensional direction finding of signals, has a simple system structure and simple mathematical operations, and has the advantages of low cost and low complexity.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal direction finding, and relates to a signal direction finding system and method based on a 1-bit programmable metasurface. Background Art

[0002] Traditional direction finding methods can be divided into two categories: multi-radio frequency chain and single-radio frequency chain. Most of the multi-radio frequency chain direction finding methods need to obtain phase differences, amplitude differences, arrival time differences, etc. of multiple channels to estimate the signal direction, which makes the structure of the entire system very complex. Although the existing single-radio frequency chain direction finding methods simplify the structure, most of them have disadvantages such as high computational complexity and high stability requirements. In recent years, some direction finding methods based on time modulation arrays have emerged. This type of method belongs to single-radio frequency chain direction finding. Its principle is that through periodic switching or phase shift modulation, the output signal contains fundamental wave and harmonic components. Different signal incident directions will cause changes in the relative relationship between the components. Therefore, the angle can be calculated by analyzing the mathematical relationship between the components. It has simpler mathematical operation requirements compared with traditional single-radio frequency chain direction finding methods. However, the time modulation array itself also belongs to an antenna array. Its array elements need to be customized according to the working frequency band, and the size of the array elements is limited by the working wavelength and it is difficult to be lightweight and miniaturized. Therefore, there is currently a lack of methods with low complexity, low cost, easy deployment and certain accuracy requirements in the field of signal direction finding.

[0003] The programmable metasurface is a newly emerging artificial electromagnetic material. Its structure is a thin plate with several artificial units. Each artificial unit can apply a designed phase shift to the incident signal and then make it exit. Because of its low cost, smaller unit size than traditional array elements, and easy deployment, it is considered a potential solution for a new type of phased array. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a signal direction finding system and method based on a 1-bit programmable metasurface.

[0005] To achieve the above purpose, on the one hand, the present invention provides the following technical solutions:

[0006] A signal direction finding system based on a 1-bit programmable metasurface, comprising a 1-bit programmable metasurface. If the programmable metasurface is of the reflective type, M×N unit antennas are distributed on the side that receives signals. If it is of the transmissive type, M×N unit antennas are symmetrically distributed on both sides, where M is the number of rows of unit antennas and N is the number of columns of unit antennas; the programmable metasurface is further connected to a controller for applying a periodic modulation sequence to the unit antennas; a receiving antenna is provided at a certain distance from the geometric center of the programmable metasurface, the receiving antenna is connected to a receiver, and a signal processing module and an angle calculation module are provided in the receiver; the signal processing module is used to process the received signal through fast Fourier transform (FFT) or discrete Fourier transform (DFT); the angle calculation module is used to calculate the direction of the incident signal according to the periodic modulation sequence of each unit antenna and the result of the signal processing module.

[0007] On the other hand, the present invention provides a signal direction finding method based on a 1-bit programmable metasurface, comprising the following steps:

[0008] S1: Receive the incident signal through each unit antenna on the 1-bit programmable metasurface;

[0009] S2: Apply a periodic modulation sequence to each unit antenna;

[0010] S3: Each unit antenna applies a phase shift to the incident signal and then emits it, which is received by the receiving antenna;

[0011] S4: Calculate the Fourier coefficients corresponding to the fundamental wave component and the first harmonic component of each unit antenna according to the periodic modulation sequence;

[0012] S5: Calculate the fundamental wave component and the first harmonic component at the receiving antenna;

[0013] S6: Obtain the functional relationship between the ratio of the first harmonic component to the fundamental wave component and the direction of the incident signal;

[0014] S7: Calculate the direction of the incident signal according to the actually measured ratio of the first harmonic component to the fundamental wave component.

[0015] Further, in the step S1, the unit antenna spacing D of the 1-bit programmable metasurface is half a wavelength, the receiving antenna is located directly in front of the center of the metasurface, and the distance is F; there are M×N unit antennas on the 1-bit programmable metasurface, where M is the number of rows of unit antennas and N is the number of columns; in the Cartesian coordinate system, the coordinates of the (m,n) unit antenna are [(m-(M + 1) / 2)D, (n-(N + 1) / 2)D, 0], where m represents the row number where the unit antenna is located and n represents the column number where the unit antenna is located, and the coordinates of the receiving antenna are [0, 0, F], then the distance l between the (m,n) unit antenna and the receiving antennam,n is:

[0016]

[0017] Furthermore, the periodic modulation sequence described in step S2 includes:

[0018] introducing the periodic switching function U m,n (t) of the (m,n) unit, whose value range is {1, -1}, representing two phase shifts of 0 and π; within a time modulation period T p the periodic switching function U m,n (t) is expressed as

[0019]

[0020] Furthermore, in step S3, a sine signal with a frequency point of F c is incident from the direction, θ is the elevation angle, is the azimuth angle, θ ∈ (-π / 2, π / 2), the radiation pattern of each unit antenna is l m,n the resulting path loss is a(l m,n ), after introducing the periodic modulation sequence, the instantaneous radiation pattern function of the receiving system composed of the metasurface and the receiving antenna is:

[0021]

[0022]

[0023] where represents the gain of the signal from each unit antenna to the receiving antenna direction, d m,n represents the wave path difference of the signal arriving at each unit antenna, j represents the imaginary symbol, and λ represents the wavelength of the incident signal.

[0024] Furthermore, in step S4, U m,n (t) satisfies U m,n (t) = U m,n (t + nT p ), τ m,n,on and τ m,n,off respectively represent the turn-on time and turn-off time of the normalized phase shift π of the (m,n) unit; as a periodic function, U m,n (t) is expanded in the form of a Fourier series as:

[0025]

[0026] where α m,n,kis the Fourier coefficient of the k-th harmonic, calculated by the following formula:

[0027]

[0028] Furthermore, the fundamental wave component and the first harmonic component at the receiving antenna described in step S5 are:

[0029]

[0030]

[0031] Furthermore, the functional relationship between the ratio of the first harmonic component and the fundamental wave component described in step S6 and the incident signal direction is:

[0032]

[0033] Furthermore, let the actually measured ratio of the first harmonic to the fundamental wave be p + qj. When all unit antennas are divided into 4 sub-arrays according to the parity of m and n, the periodic modulation sequence U m,n (t) is expressed as:

[0034]

[0035]

[0036]

[0037]

[0038] Then the direction estimate value of the incident signal is calculated by the following formula:

[0039]

[0040] Where:

[0041]

[0042] The beneficial effects of the present invention are as follows: The present invention combines 1-bit programmable metasurface with time modulation technology to achieve two-dimensional direction finding of signals. The direction finding system proposed by the present invention has a simple structure, low cost, and is easy to deploy. It only requires FFT or DFT to process signals, and the mathematical operations are simple, having the advantages of low cost and low complexity.

[0043] Other advantages, objectives, and features of the present invention will be set forth to some extent in the following description, and to some extent, will be apparent to those skilled in the art based on the examination and research of the following text, or can be learned from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following description. Brief Description of the Drawings

[0044] Figure 1 It is a schematic structural diagram of the signal direction-finding system based on the 1-bit programmable metasurface of the present invention;

[0045] Figure 2 It is a schematic diagram of the positions of the programmable metasurface and the horn antenna of the present invention;

[0046] Figure 3 It is a schematic diagram of the periodic modulation sequence applied in this embodiment;

[0047] Figure 4 It is a result diagram obtained by performing FFT on the received signal in this embodiment;

[0048] Figure 5 It is the mean square error curve of SNR from 0 to 20 obtained through 1000 Monte Carlo simulations. Detailed Embodiment

[0049] The programmable metasurface itself is a passive device. When used in the receiving state, the incident signal is applied and changed, then exits and is received by the antenna. The programmable metasurface is generally equipped with a real-time controller (usually FPGA or DSP), and its units can achieve an extremely fast phase shift response switching speed. Therefore, time modulation technology can be introduced into the real-time control of the metasurface to achieve the direction-finding function. The 1-bit programmable metasurface is the simplest and lowest-cost programmable metasurface, and its units can apply a phase shift of 0 or π to the incident electromagnetic wave.

[0050] The present invention provides a low-complexity and low-cost signal direction-finding system based on the time modulation of a 1-bit programmable metasurface.

[0051] The 1-bit M×N programmable metasurface can be transmissive or reflective. The spacing between adjacent units of the metasurface is generally half-wavelength λ / 2. According to the type of the metasurface, the receiving antenna is placed directly in front (corresponding to the reflective metasurface) or directly behind (corresponding to the transmissive metasurface) the geometric center of the metasurface and is connected to the receiver through a feeder. A controller is used to apply a periodic modulation sequence, and the received signal is processed by fast Fourier transform (FFT) or discrete Fourier transform (DFT) to analyze the incident direction of the signal. In this embodiment, the unit antenna is a patch antenna and the receiving antenna is a horn antenna.

[0052] The element spacing of a 1-bit M×N reflective programmable metasurface is D = λ / 2, i.e., half wavelength. The receiving antenna is located directly in front of the center of the metasurface at a distance of F. As Figure 2 shown, in the Cartesian coordinate system, the coordinates of the (m,n)th element are [(m - (M + 1) / 2)D, (n - (N + 1) / 2)D, 0], and the coordinates of the receiving antenna are [0, 0, F]. Then the distance between the (m,n)th element and the receiving antenna is

[0053]

[0054] The incident signal is received by each element, phase-shifted by the 1-bit element and then emitted, and finally received by the receiving antenna. Assume the radiation pattern of each element is Due to l m,n resulting in a path loss of a(l m,n ), then the instantaneous radiation pattern function of the receiving system composed of this metasurface and the receiving antenna can be obtained

[0055]

[0056] where, w m,n is the weight of the phase shifter on the (m,n) th element, with two values of 0 and 1, corresponding to phase shifts of 0 and π respectively.

[0057]

[0058] A sinusoidal signal with a frequency of F c is incident from the direction, θ is the elevation angle, is the azimuth angle, θ ∈ (-π / 2, π / 2),

[0059] By applying a periodic modulation sequence to each element through an FPGA or DSP device, the periodic switching function U m,n (t) of the (m,n)th element is introduced here. Its value range is {1, -1}, representing two phase shifts of 0 and π. Then, after introducing the time dimension into formula (2), a new radiation pattern function can be obtained

[0060]

[0061] Within a time modulation period T p , the function U m,n (t) can be expressed as

[0062]

[0063] U m,n (t) satisfies U m,n (t) = Um,n (t + nT p ), τ m,n,on and τ m,n,off represent the turn-on time and turn-off time of the normalized phase shift π of the (m, n) unit, respectively. As a periodic function, U m,n (t) can be expanded in the form of a Fourier series as

[0064]

[0065] α m,n,k is the Fourier coefficient of the k-th harmonic and can be calculated by the following formula:

[0066]

[0067] At this time, substituting the Fourier coefficients of the fundamental wave and the first harmonic components into formula (4) respectively can represent the fundamental wave and the first harmonic at the receiving antenna:

[0068]

[0069]

[0070] Then the ratio of the first harmonic to the fundamental wave component can be calculated

[0071]

[0072] If the measured ratio of the first harmonic to the fundamental wave is p + qj, we can obtain the equation

[0073]

[0074] Design the modulation function U m,n (t) of each unit, and the direction of the incident signal can be estimated by solving (11)

[0075] Example 1:

[0076] In this example, the structure of the direction finding system is as Figure 1 to Figure 2 shown. The received signal is a single-tone signal with a frequency of 29 GHz. The element spacing D of the 1-bit 20×20 reflective programmable metasurface is equal to half the wavelength λ / 2 at this frequency. The receiving antenna is located directly in front of the center of the metasurface, at a distance of 5λ. The artificial elements of the programmable metasurface are numbered according to the row and column numbers (m, n). According to the parity of m and n, many elements are divided into 4 sub-arrays, as Figure 3 shown. The periodic modulation sequence U m,n (t) applied by the controller to each unit of the 1-bit 20×20 reflective programmable metasurface is expressed as

[0077]

[0078]

[0079]

[0080]

[0081] The Fourier coefficients corresponding to the fundamental wave component and the first harmonic component of each unit can be calculated according to formula (6).

[0082]

[0083]

[0084] Substituting into formula (9), the ratio of the first harmonic component to the fundamental wave component can be calculated.

[0085]

[0086] Let

[0087]

[0088] There is

[0089]

[0090] If the ratio of the actually measured first harmonic to the fundamental wave is p + qj, according to formula (11), we can get

[0091]

[0092] From (15) and (17), the values of x and y can be solved, and the estimated value of the incident wave direction Can be calculated by the following formula

[0093]

[0094] This embodiment verifies the effect of the present invention based on MATLAB simulation. Let the signal be incident from the direction of (30°, -40°), the time modulation frequency is set to T p = 1 MHz, add additive white Gaussian noise (AWGN) according to the signal-to-noise ratio of SNR = 10, and the result obtained by performing FFT on the received signal is as Figure 4 Shown. Through the ratio of the first harmonic and the fundamental wave in the FFT result, calculate according to formulas (16) and (17) Table 1 shows the results of 10 independent direction measurements in this parameter scenario.

[0095] Table 1

[0096]

[0097] Figure 5 The mean square error (MSE) curve of the signal-to-noise ratio (SNR) from 0 to 20 obtained through 1000 Monte Carlo simulations when the SNR varies from 0 to 20. It can be seen that as the SNR increases, θ and the estimated mean square error approaches 0, and the estimation accuracy improves.

[0098] This embodiment verifies the effectiveness of a signal direction finding system and method based on a 1-bit programmable metasurface provided by the present invention.

[0099] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the present technical solution, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A signal direction finding method based on a 1-bit programmable metasurface, characterized in that: A signal direction finding system based on a 1-bit programmable metasurface, including a 1-bit programmable metasurface. If the programmable metasurface is reflective, M×N unit antennas are distributed on the side that receives signals. If it is transmissive, M×N unit antennas are symmetrically distributed on both sides, where M is the number of rows of unit antennas and N is the number of columns of unit antennas; the programmable metasurface is also connected to a controller for applying a periodic modulation sequence to the unit antennas; at a certain distance from the geometric center of the programmable metasurface, there is a receiving antenna, the receiving antenna is connected to a receiver, and the receiver is provided with a signal processing module and an angle calculation module; the signal processing module is used to process the received signal through fast Fourier transform (FFT) or discrete Fourier transform (DFT); The angle calculation module is used to calculate the direction of the incident signal according to the periodic modulation sequence of each unit antenna and the result of the receiving signal processing module. The method includes the following steps: S1: Receive the incident signal through each unit antenna on the 1-bit programmable metasurface; the unit antenna spacing D of the 1-bit programmable metasurface is half-wavelength, the receiving antenna is located directly in front of the center of the metasurface, and the distance is F; there are M×N unit antennas on the 1-bit programmable metasurface, where M is the number of rows of unit antennas and N is the number of columns of unit antennas; in the Cartesian coordinate system, the coordinates of the (m, n) unit antenna are [(m - (M + 1) / 2)D, (n - (N + 1) / 2)D, 0], where m represents the row number where the unit antenna is located and n represents the column number where the unit antenna is located, and the coordinates of the receiving antenna are [0, 0, F], then the distance l between the (m, n) unit antenna and the receiving antenna m，n is: S2: Apply a periodic modulation sequence to each unit antenna; the periodic modulation sequence includes: Introduce the periodic switching function U of the (m, n) - th unit m，n (t), whose value range is {1, - 1}, representing two phase shifts of 0 and π; within a time - modulation period T p The periodic switching function U m，n (t) is expressed as S3: Each unit antenna emits the incident signal after applying an upward phase shift and is received by the receiving antenna; a sine signal with a frequency point of F c is incident from direction, θ is the elevation angle, is the azimuth angle, θ ∈ (-π / 2, π / 2), the radiation pattern of each unit antenna is l m，n The path loss caused by is a(l m，n ). After introducing the periodic modulation sequence, the instantaneous radiation pattern function of the receiving system composed of the metasurface and the receiving antenna is:[[]] Among them, represents the gain of the signal emitted from each unit antenna in the direction of the receiving antenna, and d m，n represents the path difference of the signal arriving at each unit antenna, j represents the imaginary symbol, and λ represents the wavelength of the incident signal; S4: Calculate the Fourier coefficients corresponding to the fundamental wave component and the first harmonic component of each unit antenna according to the periodic modulation sequence; U m，n U(t) satisfies U m，n U(t) = U m，n (t + nT p ), where τ m，n，on and τ m，n，off respectively represent the turn-on time and turn-off time of the normalized phase shift π of the (m, n) unit; as a periodic function, U m，n (t) is expanded in the form of a Fourier series as: where α m，n，k is the Fourier coefficient of the k-th harmonic and is calculated by the following formula: S5: Calculate the fundamental wave component and the first harmonic component at the receiving antenna; the fundamental wave component and the first harmonic component at the receiving antenna are: S6: Obtain the functional relationship between the ratio of the first harmonic component to the fundamental wave component and the direction of the incident signal; the functional relationship between the ratio of the first harmonic component to the fundamental wave component and the direction of the incident signal is: S7: Calculate the direction of the incident signal according to the ratio of the actually measured fundamental harmonic component to the fundamental wave component; let the ratio of the actually measured fundamental harmonic to the fundamental wave be p + qj. When all the unit antennas are divided into 4 sub-arrays according to the parity of m and n, the periodic modulation sequence U m，n (t) is expressed as: Then the estimated direction of the incident signal is calculated by the following formula: Where:

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