Discrete Fourier transform method based on gain programmable metasurface

Abstract

The invention discloses a discrete Fourier transform method based on a gain programmable metasurface. Comprising the following steps: 1) generating discrete Fourier transform algorithm parameters; 2) further simplifying discrete Fourier transform algorithm parameters; 3) designing a gain programmable metasurface entity; 4) designing a post-processing scheme and a post-processing layer; and 5) constructing a computing system around the gain programmable metasurface. According to the method, input signals can be processed at a high speed by means of simplified operation and a high-parallelism computing system, and by means of the design based on the gain programmable metasurface, discrete Fourier transform operation can be carried out on the input signals more quickly only through a simple metamaterial system and extremely low time and energy expenditure. And the cost demand of a computing system is greatly reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing on programmable metasurfaces, and in particular to a discrete Fourier transform signal processing method based on gain programmable metasurfaces. Background Art

[0002] Fourier transform can express a specified function that meets certain conditions as a linear combination of trigonometric functions. Discrete Fourier transform is a basic method in the field of signal analysis. It can transform discrete signals from the time domain to the frequency domain. It is a discrete form of Fourier transform in the face of discrete time domain and frequency domain signals.

[0003] At present, with the rapid development of electromagnetic physics and information technology, researchers are exploring metamaterials (also known as metastructure materials) in full swing, and many researchers have made various achievements in the exploration of the unique physical properties of metamaterials. Della proposed the concept of digital metamaterials, and constructed "digital metamaterial bytes" by arranging "digital metamaterial bits" to obtain the required physical medium properties, introducing the concept of informatics into the field of metamaterials. However, "digital metamaterial bits" are still composed of material units with fixed physical medium properties, and have not been able to get rid of the category of equivalent medium metamaterials. In essence, they use digital bits to describe the properties of physical media. In order to abandon the backward and inconvenient equivalent medium method, Cui proposed the idea of ​​using digital coding to dynamically change the physical medium properties of metamaterials and designed programmable metamaterials. By changing the combination of digital coding units in spatial position, programmable metamaterials can achieve arbitrary control of the direction of electromagnetic waves; however, as a passive device, programmable metamaterials themselves will inevitably suffer losses during the operation of electromagnetic waves, which greatly limits the multi-layer combination of metamaterials. How to add active properties on the basis of programmable metamaterials is a development direction worthy of attention. Taravati tried to add an operational amplifier to the metamaterial to control the unidirectional conductivity of the metamaterial when electromagnetic waves passed through it. Based on Taravati's work, Chen considered operating the operational amplifier in the linear amplification region to achieve the attenuation and gain of the metamaterial when electromagnetic waves passed through it. We call this new metamaterial a gain-programmable metasurface. On this basis, researchers have designed many practical functions around metamaterials.

[0004] Liu first tried to arrange multiple gain-programmable metasurfaces in a straight line in space. This design showed certain deep learning characteristics, so it was named Programmable Artificial Intelligence Machine PAIM (Programmable Artificial Intelligence Machine, PAIM for short). However, the design of many functions only considers the native energy aggregation characteristics of programmable artificial intelligence machines. Although programmable artificial intelligence machines show good fitting ability for data, due to the black box effect of deep learning, it is impossible to determine whether the model uses the most correct strategy and is in the best state. In addition, multi-layer data processing will inevitably bring more time overhead. For Fourier transform, current methods focus on using digital signal processing to convert analog signals into digital signals, and then use processors for calculation and processing. Because this processing method requires powerful computing power, it often leads to complex systems and high costs when facing large bandwidth and high-frequency signals.

[0005] In view of the shortcoming of the current Fourier transform digital signal processing method that it is overly dependent on high-performance processors, it is necessary to study a discrete Fourier transform analog signal processing method that runs on a gain-programmable metasurface computing platform and implements it based on its light-speed processing capability for electromagnetic wave signals. Summary of the invention

[0006] The purpose of the present invention is to provide a discrete Fourier transform method based on a gain programmable metasurface in view of the deficiencies of the prior art. This method only requires a simple gain programmable metasurface and extremely low time and energy costs to achieve high-speed discrete Fourier transform operations on signals. The design of the gain programmable metasurface computing platform can complete the processing of input signals more quickly and greatly reduce the cost requirements of the computing system.

[0007] The technical solution to achieve the purpose of the present invention is:

[0008] Step 1: Determine the specific discrete Fourier transform algorithm and specific discrete Fourier transform algorithm parameters according to the characteristics of the signal to be transformed and the transformation requirements, especially the real number parameters simplified from its complex number parameters;

[0009] Step 2: Adapt and optimize according to the calculation characteristics and actual situation of the metasurface, and further simplify the specific real number operations of discrete Fourier transform; Step 3: Design the gain programmable metasurface entity according to the discrete Fourier transform algorithm parameters obtained in step 2. It is mainly responsible for the main part of the discrete Fourier transform operation;

[0010] Step 4: Set the post-processing layer after the hypersurface entity obtained in step 3. For the main calculation results, select the corresponding post-processing solution according to different calculation result requirements;

[0011] Step 5: Build a computing system around the gain programmable metasurface, use the gain programmable metasurface obtained in step 3 as the signal processing layer, set a signal input layer at the front to be responsible for signal input, and use the post-processing layer obtained in step 4 to post-process the signal according to needs.

[0012] Furthermore, after step 5, the overall computing system is fixed. If the target signal requirements for later calculations change, the system initialization operations from step 1 to step 4 need to be repeated. If it is necessary to switch the forward and inverse transforms of the discrete Fourier transform, such as adapting the forward transform calculation to the inverse transform, there is no need to repeat step 3, that is, to redesign the hypersurface entity. It is only necessary to repeat steps 1 and 2 to calculate the corresponding discrete Fourier transform algorithm parameters, and change to the corresponding post-processing scheme in step 5.

[0013] The discrete Fourier transform method based on gain programmable metasurface proposed in the present invention has the following advantages over the traditional discrete Fourier transform digital signal processing method:

[0014] (1) The present invention proposes to migrate the discrete Fourier transform algorithm to the gain programmable metasurface computing platform and simplify the algorithm according to the computing entity of the programmable metasurface. This not only realizes the calculation of discrete Fourier transform at a lower cost, but also improves the signal processing speed.

[0015] (2) The present invention proposes to utilize the characteristic of gain programmable metasurfaces that electromagnetic waves are used as data carriers. In theory, the signal processing speed of the system is only limited by the propagation speed of electromagnetic waves. At the same time, matrix operations are realized in the form of metasurface unit arrays, which increases the parallelism of the system. Both of these points greatly improve the signal processing speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a flow chart for implementing the signal processing method proposed in the present invention.

[0017] Figure 2 This is a schematic diagram of the signal processing unit proposed by the present invention.

[0018] Figure 3 This is a schematic diagram of the signal processing system proposed by the present invention. DETAILED DESCRIPTION

[0019] The method of the present invention is described in detail with reference to the accompanying drawings and embodiments.

[0020] Reference Figure 1, a discrete Fourier transform method based on gain programmable metasurface, implements the discrete Fourier transform algorithm on a programmable artificial intelligence computing platform, and uses the change in the amplitude of the electromagnetic wave during the propagation process to characterize the numerical change in the Fourier transform according to the gain programmable metasurface unit array, where:

[0021] The algorithm designed to run on the gain programmable metasurface is the discrete Fourier transform algorithm. According to the conversion requirements of the signal, the discrete Fourier transform forward transform or inverse transform is selected, that is, the discrete Fourier transform is selected when the signal is converted from the time domain to the frequency domain, and the discrete Fourier inverse transform is selected when the signal is converted from the frequency domain to the time domain. According to the bandwidth of the signal and the sampling theorem, the appropriate sampling rate is selected. The sampling rate should be at least twice the maximum frequency of the signal, and then the required calculation parameters are generated according to the definition of the discrete Fourier transform algorithm. Assuming a finite length sequence of length M and the number of samples is N, the discrete Fourier transform forward transform expression is shown in formula (1.1):

[0022]

[0023] Where x(n) represents the discrete signal vector in the time domain, X(ω) represents the discrete signal vector in the frequency domain, and the inverse discrete Fourier transform formula (2) is shown as follows:

[0024]

[0025] The discrete Fourier transform algorithm is expanded through the Euler formula, and the discrete Fourier transform forward transform is expanded into formula (2.1):

[0026]

[0027] The inverse discrete Fourier transform is expanded into formula (2.2):

[0028]

[0029] In this way, complex exponential operations are simplified to trigonometric functions.

[0030] The discrete Fourier transform algorithm applied on the gain programmable metasurface is adapted and optimized according to the actual situation of the metasurface calculation and the application signal. First, the complex number operation is processed, and the real part and imaginary part of the complex number are separated and operated separately, as shown in formula (3.1) and formula (3.2):

[0031]

[0032] In the forward transform process of discrete Fourier transform, the input signal is a real signal. Therefore, after the inverse transform of discrete Fourier transform, the expected output is also a real signal, which leads to the imaginary part of the output result, that is, x im(n) is always 0, and the calculation of the imaginary part is simplified and deleted, so that the positive and negative discrete Fourier transforms can be performed simultaneously without changing the structure of the metasurface unit array.

[0033] Reference Figure 2 , a gain-programmable metasurface signal processing unit, as a computing entity of the discrete Fourier transform algorithm, uses electromagnetic wave changes to perform equivalent digital operations. The gain-programmable metasurface can process the input signal e in The gain is adjusted, and the gain coefficient is t. When the electromagnetic wave signal passes through the gain programmable metasurface, the gain is adjusted by the internal circuit of the gain programmable metasurface. Finally, the output electromagnetic wave e is obtained. out =e in t. Then the propagation formula of the single-layer gain programmable metasurface is shown in formula (4):

[0034] E out =E in ⊙T (4)

[0035] Where E out is the output electromagnetic wave matrix, E in is the input electromagnetic wave matrix, T is the electromagnetic wave gain coefficient matrix of the gain programmable metasurface, and ⊙ represents the Hadamard product of the matrix. If the metasurface array is composed of N rows and M columns of gain programmable metasurface units, then the dimensions of the matrix mentioned above are all N×M, that is, E out , E in , T∈R N×M . Then the calculation form of the hypersurface of the discrete Fourier transform forward transform is shown in formula (4.1):

[0036]

[0037] in The length of the time domain signal to be transformed is M, and the number of discrete Fourier transform sampling, that is, the length of the frequency domain signal, is N. The calculation form of the hypersurface of the inverse discrete Fourier transform is as described in formula (4.2):

[0038]

[0039] We select the corresponding gain programmable metasurface unit according to the operating frequency. The Fourier transform parameters are determined according to the signal conversion requirements and formulas (4.1) and (4.2). Taking the forward Fourier transform of converting a time domain signal of length M to a frequency domain signal of length N as an example, the required Fourier transform parameters are the C matrix and S matrix of size M×N. Two gain programmable metasurfaces of size M×N are used as operation carriers to operate the main part of the algorithm, namely the two Hadamard products in formulas (4.1) and (4.2).

[0040] The rest of the discrete Fourier transform, i.e. the summation part, is completed through the post-processing layer. The receiving antenna and adder are set up in the post-processing layer to complete the summation operation of the rest of the parts. Furthermore, the output results can be processed again. For example, the results that the discrete Fourier transform forward transform conventionally hopes to obtain are the amplitude and phase of the frequency domain signal, which can be obtained through different post-processing schemes in the post-processing layer. Among them, the amplitude of the frequency domain signal is The phase of the frequency domain signal is These are easily achieved through traditional signal processing methods such as adding circuits.

[0041] Reference Figure 3 , a signal processing system is built around the gain programmable metasurface. The core is the gain programmable metasurface as the signal processing layer, the front part is the signal input layer responsible for the signal input, and the rear part is the post-processing layer used to post-process the signal according to the needs. Both the positive and negative discrete Fourier transforms use the same gain programmable metasurface computing system. The discrete Fourier transform algorithm parameters obtained above are loaded into the signal processing layer. The specific operation is to use the control circuit to assign the obtained C matrix and S matrix to the gain coefficient matrix T of the corresponding unit of the metasurface. In the discrete Fourier transform method based on gain programmable metasurface described in the present invention, the forward propagation process of the electromagnetic wave signal is as follows: First, the electromagnetic wave E is input in the signal input layer according to the algorithm formula. in After the electromagnetic wave passes through the signal processing layer, the electromagnetic wave E is initially transformed. out , and finally received and processed in the post-processing layer to obtain the final result. Because electromagnetic waves are used as carriers for discrete Fourier transform forward or inverse transform, the speed of data processing is only limited by the propagation speed of electromagnetic waves.

Claims

1. A discrete Fourier transform method based on gain programmable metasurface, characterized in that: The discrete Fourier transform algorithm is implemented on the gain programmable metasurface computing platform. Based on the gain programmable metasurface unit array, the numerical changes in the Fourier transform are represented by the changes in the amplitude of the electromagnetic wave during the propagation process, where: 1) Determine the specific discrete Fourier transform algorithm and algorithm parameters according to the characteristics of the signal to be transformed and the transformation requirements; 2) Further simplify the discrete Fourier transform algorithm according to the calculation characteristics of the metasurface and the actual situation; 3) Designing a gain programmable metasurface entity based on discrete Fourier transform algorithm parameters; 4) Design the corresponding post-processing scheme and set the post-processing layer according to the required calculation results; 5) A computing platform is built around the gain programmable metasurface. The core of the gain programmable metasurface computing platform is the gain programmable metasurface as the computing layer, with the front part being the signal input layer and the back part being the signal post-processing layer.

2. The discrete Fourier transform method of the gain programmable metasurface according to claim 1, characterized in that: The specific discrete Fourier transform algorithm and algorithm parameters are determined according to the characteristics of the signal to be transformed and the transformation requirements. The algorithm designed to run on the gain programmable metasurface is a discrete Fourier transform algorithm. The discrete Fourier transform algorithm is expanded using the Euler formula, and the exponential operation of complex numbers is simplified to operations between real numbers.

3. The discrete Fourier transform method of the gain programmable metasurface according to claim 1, characterized in that: According to the actual situation of metasurface calculation and application signal, the discrete Fourier transform algorithm applied on the gain programmable metasurface is further simplified. Specifically, the calculation of the imaginary part is deleted. In the process of discrete Fourier transform forward transformation, the input signal is a real signal, so after the discrete Fourier transform inverse transformation, the expected output is also a real signal, which means that the imaginary part of the output result is always 0. Simplifying the calculation of the imaginary part can perform both the positive and negative discrete Fourier transforms without changing the metasurface unit array structure.

4. The discrete Fourier transform method of the gain programmable metasurface according to claim 1, characterized in that: A gain-programmable metasurface that can adjust the gain of the input signal is used as a computing entity for discrete Fourier transform, and the change of electromagnetic waves is used for equivalent digital calculations. The design of the metasurface needs to be based on the optimized discrete Fourier transform algorithm parameters described in claim 3, that is, the corresponding gain-programmable metasurface unit is selected according to the actual situation such as the frequency of the carrier signal, which is specifically manifested in selecting the corresponding metasurface unit array size according to the discrete Fourier transform algorithm parameters.

5. The discrete Fourier transform method of the gain programmable metasurface according to claim 1, characterized in that: The preliminary calculation results of the gain programmable metasurface computing platform are processed through the corresponding post-processing scheme to obtain the required results. The results generally expected from the discrete Fourier transform forward transform are the amplitude and phase of the frequency domain signal, and the result generally expected from the inverse transform is the amplitude of the time domain signal. After preliminary calculations in the signal processing layer, they are obtained in the post-processing layer through the corresponding traditional signal processing means.

6. The discrete Fourier transform method of the gain programmable metasurface according to claim 1, characterized in that: A computing system is constructed around a gain programmable metasurface, wherein the core is the gain programmable metasurface described in claim 4 as a signal processing layer, the front part is a signal input layer responsible for signal input, and the rear part is a post-processing layer described in claim 5 for post-processing the signal as required, and both the positive and negative discrete Fourier transforms use the same gain programmable metasurface computing system.

Images