A multi-source excitation FDTD simulation field separation method based on code division multiplexing

Abstract

This invention discloses a method for field separation in multi-source excitation FDTD simulations based on code division multiplexing, belonging to the field of computational electromagnetics and electromagnetic field numerical simulation technology. To overcome the problems of low efficiency in source-by-source repetitive computation and difficulty in separating the independent responses of each source in mixed observations in multi-source FDTD simulations, this invention generates code division multiplexed broadband excitation signals with low cross-correlation characteristics for each excitation source, injects them simultaneously in a single FDTD simulation, and records the mixed field time-domain sequence by a monitor. After performing Fourier transforms on the mixed sequence and the excitation signals of each source, the non-correlation characteristics of the codes are used to decouple the mixed observation equations, extract the independent complex frequency domain field response coefficients of each source, and then reconstruct the independent field components contributed by each source. This invention can achieve accurate separation of multi-source field responses in a single simulation, significantly reducing computational costs and monitoring resource requirements, and is applicable to various FDTD simulation scenarios such as free space, complex dielectric structures, and multi-port devices.

Description

Technical Field

[0001] This invention relates to the field of computational electromagnetics and electromagnetic field numerical simulation technology, and in particular to a multi-source excitation FDTD simulation field separation method based on code division multiplexing. Background Technology

[0002] In full-wave FDTD simulations of electromagnetic fields, tasks such as port response analysis of multi-port devices, field response analysis of arrays or multiple feed sources simultaneously, and field response evaluation at a specified location or cross section when multiple sources are present often require obtaining the frequency domain amplitude and phase response of each excitation source at the target location to support structural evaluation, parameter scanning, and result comparison.

[0003] The Finite-Difference Time-Domain (FDTD) method solves Maxwell's equations in the time domain using discrete methods, allowing the time-domain field sequence at the target location to be recorded by a monitor in a single simulation. The monitor can be positioned in free space to record the time-domain sequence of electromagnetic field components, or it can be set as a monitoring section at a device port to record the time-domain data of the electric and magnetic fields at the port. By performing Discrete Fourier Transforms on the injected source excitation waveform and the time-domain field quantities recorded by the monitor, complex spectral values ​​at multiple discrete frequency points can be obtained within the effective bandwidth of the excitation. For the single-source case, the relationship between the monitor output spectrum and the excitation spectrum can be characterized by complex frequency domain response coefficients, for example, as follows: (1); in, Injecting the excitation spectrum into the source, The obtained spectrum is recorded by the monitor. Indicates the source-to-monitor location at frequency The complex frequency domain response at that point.

[0004] When multiple sources excite simultaneously, under electromagnetic linearity conditions, the frequency domain quantities recorded by the monitor satisfy a superposition relationship, that is, the spectrum recorded by the monitor is formed by the superposition of the responses of each source, which can be written as: (2); in, For the first The spectrum of the source-injected excitation This represents the complex frequency domain response corresponding to the source. At this point, the observation given by the monitor at each frequency point is a superposition and mixing result of the multi-source responses, while what needs to be determined is the complex frequency domain response corresponding to each of the multiple sources. When monitoring resources are limited and no additional constraints or distinguishing information are introduced, it is usually difficult to directly obtain the independent frequency domain response results corresponding to each source from the mixed observations after the simulation, thus making field separation processing difficult.

[0005] To obtain the frequency domain response for each source, a common engineering practice is to use source-by-source simulation: only one source is activated at a time, and the FDTD simulation is performed multiple times, then the response of that source is obtained as a single-source ratio. When the number of sources is At that time, at least one step is usually required. The overall simulation time and cycle increase significantly with the number of sources, especially when the grid size is large, the time step is small, or the simulation window is long. Repeated simulations will lead to high resource consumption and time costs.

[0006] On the other hand, if it is desired to enable multiple sources simultaneously in a single simulation to reduce the number of repeated simulations, the observations recorded by the monitor will include the superposition of the responses from each source. Existing solutions often rely on adding monitors / monitoring surfaces to obtain more independent observations in order to improve solvability. This approach leads to an increase in monitor configuration and data volume, and correspondingly increases post-processing complexity, while still not fundamentally solving the efficiency problem of obtaining independent responses from each source under the condition of "one simulation + limited monitoring resources".

[0007] Therefore, in order to achieve the separation and extraction of multi-source field responses under a single simulation, it is necessary to introduce a distinguishable mechanism at the excitation construction level and apply code division multiplexing to FDTD multi-source excitation: configure coded excitations with low cross-correlation characteristics for different excitation sources and inject them synchronously in a single simulation, so that the mixed observations are distinguishable in a coding sense, thereby further obtaining the frequency domain field responses corresponding to each source based on the output of a single simulation. Summary of the Invention

[0008] To address the aforementioned technical problems, this invention provides a multi-source excitation FDTD simulation field separation method based on code division multiplexing, aiming to accurately separate and extract the independent frequency domain field responses of each excitation source from the mixed observed field quantities under a single simulation condition.

[0009] To achieve the above objectives, the technical solution of the present invention is as follows:

[0010] A multi-source excitation FDTD simulation field separation method based on code division multiplexing includes the following steps: Step S1: Generate code division multiplexing broadband excitation signals with low cross-correlation characteristics for each of the K excitation sources in the FDTD simulation, where K≥2; Step S2: In a single FDTD simulation, K code division multiplexing broadband excitation signals are injected into the corresponding K excitation source positions to achieve simultaneous excitation of multiple sources, and the mixed field time domain sequence is recorded by a monitor set in the simulation space. Step S3: Perform Fourier transform on the hybrid field time-domain sequence and the K code division multiplexing broadband excitation signals respectively to obtain the hybrid observation spectrum and the excitation spectrum of each of the K excitation sources; Step S4: Based on the principle of linear superposition of electromagnetic fields, using the coding non-correlation characteristics of the excitation spectra of each of the K excitation sources, the hybrid observation equation composed of the hybrid observation spectrum is decoupled and parameters are extracted to obtain the independent complex frequency domain field response coefficients of the K excitation sources at the monitor. Step S5: Based on the independent complex frequency domain field response coefficients of the K excitation sources, reconstruct and output the independent field components contributed by each excitation source.

[0011] In the above scheme, step S1 specifically includes: Step S11: Generate a spreading code with good autocorrelation properties and low cross-correlation for each excitation source; Let the first The spreading code corresponding to each excitation source is: , Its approximate orthogonality is expressed as follows: ; in, The length of the spreading code; This is a discrete-time index, representing the chip number of the spreading code; For the first The first excitation source spreading code of the first excitation source spreading code Each chip can be used to obtain a value; For the first The first excitation source spreading code of the first excitation source spreading code Each chip can be used to obtain a value; and Indicates the sequence number of the excitation source, and ; Step S12: Repeat the chip of each spreading code a preset number of times to form a baseband spreading sequence; Spread code Each chip repeats This time, the length is obtained as single-bit waveform sequence Let the m-th bit symbol be... Then the baseband spread spectrum sequence in the m-th bit period satisfy: ; Step S13: Perform continuous phase modulation on the baseband spread spectrum sequence to generate a code division multiplexing broadband excitation signal with continuous phase and smooth energy. ; in, It is a code division multiplexing broadband excitation signal; The carrier frequency determines the position of the excitation signal's carrier center. For the first The physical time corresponding to each sampling point For the first The source in the first The instantaneous phase of each sampling point is expressed as follows: ; in, The time sampling interval is... It is a proportionality coefficient related to the modulation index and symbol rate.

[0012] In the above scheme, the continuous phase modulation adopts minimum frequency shift keying (MSK) modulation.

[0013] In the above scheme, in step S2, the spatial form of the K code division multiplexing broadband excitation signal injection regions includes point sources, line sources, or waveguide port surface sources.

[0014] In the above scheme, in step S2, when injecting with a point source, at each time step, the corresponding modulation excitation signal is superimposed and injected into the selected field component update term, so as to realize the simultaneous excitation of K sources in the same simulation process. The specific update form is as follows: ; in, For the injection location, For code division multiplexing broadband excitation signal, In the first Time step, location The field component update item at the location.

[0015] In the above scheme, in step S3, the mixed-field time-domain sequence output by the monitor is... And the known K code division multiplexing broadband excitation signals The excitation spectrum was obtained by performing discrete Fourier transforms on each. , ; At discrete frequency points Let the independent complex frequency domain field response coefficients corresponding to the k-th excitation source at a single monitor be denoted as . For the general case of K sources, the mixed observation spectrum satisfies a linear superposition relationship, as expressed below: ; in, This is the source number.

[0016] In the above scheme, step S4, which involves decoupling and extracting parameters from the hybrid observation equation, specifically includes: Step S41: Express the independent complex frequency domain field response coefficients of the k-th excitation source to be determined in polar coordinate form, including amplitude and phase terms; Step S42: Within a local frequency window near the target frequency point, expand the modulus square of the mixed observation spectrum into a combination of the squares of the amplitude terms of each source and the cross terms between the sources; Step S43: Based on the data of multiple frequency sampling points within the local frequency window, construct a set of fitting equations for the amplitude term and the cross term, and solve them using the least squares estimation method to obtain the amplitude estimates of each excitation source and the relative phase differences between each pair. Step S44: Select a reference source and use its unknown reference phase to uniformly characterize the absolute phase of all excitation sources, simplifying the hybrid observation equation into an expression containing only a single unknown reference phase; Step S45: Construct a residual objective function for the unknown reference phase, and minimize the residual objective function through phase optimization search to obtain an estimated value of the reference phase; Step S46: Based on the estimated value of the reference phase and the relative phase difference, the absolute phase of all K excitation sources is finally determined, thereby obtaining the complete complex frequency domain field response coefficients of each excitation source.

[0017] In the above scheme, the monitors are one or more, and their arrangement includes point monitors, line monitors, surface monitors, and monitoring sections of device ports in free space.

[0018] In the above scheme, the reconstruction of the independent field components contributed by each source in step S5 is specifically as follows: at each discrete frequency point in the target frequency band, the excitation spectrum of the k-th excitation source is multiplied by the independent complex frequency domain field response coefficient corresponding to the source to obtain the independent frequency domain field components contributed by the excitation source.

[0019] Through the above technical solution, the multi-source excitation FDTD simulation field separation method based on code division multiplexing provided by the present invention has the following beneficial effects:

[0020] 1. Significantly reduces the computational cost of multi-source simulation. Traditional source-by-source simulation methods require multiple FDTD simulations equal to the number of excitation sources, with the overall computation time increasing linearly with the number of sources. This invention, by simultaneously injecting multiple excitation sources encoded via code division multiplexing into a single FDTD simulation and utilizing the non-correlation characteristics of the encoding to separate the independent frequency domain responses of each source from the mixed observation field, avoids repetitive simulations. This shortens the overall simulation cycle to the duration of a single simulation, significantly reducing computational resource consumption and time costs, making it particularly suitable for scenarios with large grid sizes, long simulation windows, or a large number of sources.

[0021] 2. Reduce monitoring resource requirements and post-processing complexity Existing methods for improving the solvability of multi-source mixed observations often require adding multiple monitors or monitoring surfaces to obtain a sufficient number of independent observation equations, leading to a surge in data volume and complex post-processing. This invention introduces a code division multiplexing differentiation mechanism at the excitation construction level, achieving effective separation of multi-source responses with only a small number of monitors (e.g., a single point monitor or a single port monitoring section). This eliminates the need for additional observation points, time-division excitation, or frequency division, thereby reducing monitor configuration requirements and data storage and post-processing computation, making it suitable for computational scenarios with limited monitoring resources.

[0022] 3. Excellent versatility and adaptability to various scenarios This invention is designed for full-wave FDTD electromagnetic field numerical simulation tasks, without special limitations on the electromagnetic environment and structure type. The code division encoding method, modulation method, and source injection form can all be flexibly selected. Experimental verification shows that this invention is applicable to simple propagation environments such as free space and homogeneous media, as well as multipath interference scenarios involving complex structures such as dielectric blocks and scatterers. It can also be extended to tasks such as port response analysis of multi-port devices (such as waveguide-coupled structures) and spatial field synthesis of multi-feed arrays, demonstrating a wide range of applicability and good engineering practicality. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0024] Figure 1 This is a schematic diagram of a multi-source excitation FDTD simulation field separation method based on code division multiplexing disclosed in an embodiment of the present invention; Figure 2 A schematic diagram showing the positional relationship between source A, source B, and the monitor, and the propagation path; Figure 3 The amplitude and phase curves of the field response coefficients of a single-source reference complex frequency domain (free space). Figure 4 Comparison of field response coefficient extraction results under dual-source hybrid observation with single-source reference (free space). Figure 5 A comparison diagram of the real and imaginary parts of the frequency domain field components separated by two sources (free space). Figure 6 This is a cross-sectional view of the device structure and port monitoring. Figure 7 Comparison of field response coefficient extraction results under dual-source hybrid observation with single-source reference (device port); Figure 8 This is a comparison diagram of the real and imaginary parts of the frequency domain field components separated by dual sources (device ports). Detailed Implementation

[0025] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0026] This invention provides a multi-source excitation FDTD simulation field separation method based on code division multiplexing, such as... Figure 1 As shown, it includes the following steps:

[0027] Step S1: Code Division Excitation Construction Generate code division multiplexing broadband excitation signals with low cross-correlation characteristics for each of the K excitation sources in the FDTD simulation, where K≥2.

[0028] Specifically, it includes: Step S11: Based on the code division multiplexing principle, generate a spreading code with good autocorrelation characteristics and low cross-correlation for each excitation source.

[0029] Let the first The spreading code corresponding to each excitation source is: , Its approximate orthogonality is expressed as follows: (3); in, The length of the spreading code; This is a discrete-time index, representing the chip number of the spreading code; For the first The first excitation source spreading code of the first excitation source spreading code Each chip can be used to obtain a value; For the first The first excitation source spreading code of the first excitation source spreading code Each chip can be used to obtain a value; and Indicates the sequence number of the excitation source, and ;

[0030] Step S12: Repeat the chip of each spreading code a preset number of times to form a baseband spreading sequence.

[0031] Spread code Each chip repeats This time, the length is obtained as single-bit waveform sequence Let the m-th bit symbol be... Then the baseband spread spectrum sequence in the m-th bit period satisfy: (4);

[0032] Step S13: To obtain a broadband excitation with continuous phase, smooth energy, and suitable for FDTD injection, continuous phase modulation is performed on the baseband spread spectrum sequence, with minimum frequency shift keying (MSK) selected as a typical modulation method. By mapping the spread spectrum baseband sequence to phase increments and performing discrete integration, the continuous phase trajectory is obtained as follows: (5); in, The time sampling interval is... It is a proportionality coefficient related to the modulation index and symbol rate.

[0033] The final result is a phase-continuous and energy-smooth code-division multiplexed broadband excitation signal injected into the actual FDTD mesh; (6); in, It is a code division multiplexing broadband excitation signal; The carrier frequency determines the position of the excitation signal's carrier center. For the first The physical time corresponding to each sampling point.

[0034] Step S2: Single-run concurrent simulation In a single FDTD simulation, K code division multiplexed broadband excitation signals are injected into the corresponding K excitation source positions to achieve simultaneous excitation from multiple sources, and the mixed field time-domain sequence is recorded by a monitor set in the simulation space.

[0035] In the FDTD simulation space, K independent source injection positions are set for each of the K excitation sources. The spatial form of the source injection region can be selected according to the simulation object, including but not limited to point source, line source, waveguide port surface source, etc.

[0036] When injecting from a point source, at each time step, the corresponding modulation excitation signal is superimposed and injected into the update term of the selected field component, so as to achieve simultaneous excitation of K sources in the same simulation process. The specific update form is as follows: (7); in, For the injection location, For code division multiplexing broadband excitation signal, In the first Time step, location The field component update item at the location.

[0037] Throughout the simulation, the time-domain sequence of electromagnetic field components is completed by a single monitor located at the monitoring position. The acquisition and recording are performed using one or more monitors, which can be arranged as point monitors, line monitors, surface monitors, and monitoring sections at device ports in free space.

[0038] Step S3: Frequency Domain Transformation Processing Fourier transforms are performed on the mixed field time-domain sequence and the K code-division multiplexed broadband excitation signals to obtain the mixed observation spectrum and the excitation spectrum of each of the K excitation sources.

[0039] Mixed field time-domain sequence output to monitor And the known K code division multiplexing broadband excitation signals The excitation spectrum was obtained by performing discrete Fourier transforms on each. , ;

[0040] At discrete frequency points Let the independent complex frequency domain field response coefficients corresponding to the k-th excitation source at a single monitor be denoted as . For the general case of K sources, the mixed observation spectrum satisfies a linear superposition relationship, as expressed below: (8); in, This is the source number.

[0041] Step S4: Decoupling and Parameter Extraction Based on the principle of linear superposition of electromagnetic fields, the hybrid observation equation composed of hybrid observation spectra is decoupled and parameters are extracted by utilizing the coding non-correlation characteristics of the excitation spectra of each of the K excitation sources, so as to obtain the independent complex frequency domain field response coefficients of the K excitation sources at the monitor.

[0042] The hybrid observation equations are decoupled and parameters are extracted, specifically including: Step S41: Express the independent complex frequency domain field response coefficients of the k-th excitation source in polar coordinate form, including amplitude and phase terms: (9); in, For the first An excitation source at a frequency point The amplitude term at the location, For the first An excitation source at a frequency point Phase term at; It can be directly obtained from the simulation output. and the excitation spectrum of K sources The independent complex frequency domain field response coefficients corresponding to each excitation source in equation (9) The quantity to be determined.

[0043] Step S42: To improve the solution stability, within a local window composed of frequency sampling points near the target frequency point, expand the modulus square of the mixed observation spectrum into a combined form including the squares of the amplitudes of each source and the cross terms between each source; (10); where, is the field response amplitude of the th excitation source at the frequency point , is the field response amplitude of the th excitation source at the frequency point ; is the field response phase of the th excitation source at the frequency point , is the field response phase of the th excitation source at the frequency point ;

[0044] Step S43: Based on the data of multiple frequency sampling points within the local frequency window, construct a fitting equation system for the amplitude terms and cross terms, and solve it by the least squares estimation method to obtain the amplitude estimation values of each excitation source and the relative phase differences between each pair.

[0045] Since the field response amplitude term of the excitation source and the phase term vary relatively smoothly within the local frequency range near the target frequency point, they can be approximately regarded as constants within this local window. At this time, based on the non-correlation characteristics of the code division multiplexing excitation signal in the frequency domain, the <00003​​​​​​​​​​​​​​​​

[0047] Step S44: Obtain amplitude estimates for all sources through the above steps. With independent phase difference Subsequently, in order to further determine the absolute phase of each source response, a reference source is selected, and its unknown reference phase is used to uniformly characterize the absolute phase of all excitation sources, simplifying the hybrid observation equation into an expression containing only a single unknown reference phase.

[0048] In this embodiment, source 1 is selected as the reference source, and the absolute phase of all sources is uniformly represented as the sum of the reference phase and the known relative phase difference: ; Among them, the reference phase The variable is the only unknown. Substituting the above relationship back into equation (8), the original multivariate equation can be simplified to an expression containing only a single unknown: (11);

[0049] Step S45: Based on this relationship, construct a residual objective function for the unknown reference phase, and minimize the residual objective function through phase optimization search to obtain an estimate of the reference phase.

[0050] The objective function is as follows:

[0051] (12);

[0052] Step S46: Based on the estimated value of the reference phase and the relative phase difference, the absolute phase of all K excitation sources is finally determined, thereby obtaining the complete complex frequency domain field response coefficients of each excitation source.

[0053] For the objective function Perform a search within the phase domain and take the value that minimizes the residual as the reference phase. The estimated value, and then used The absolute phase of each of the K excitation sources can be derived from the relation. .

[0054] At this point, the K excitation sources are at the current frequency Complex frequency domain field response coefficients ,..., It is uniquely determined.

[0055] The aforementioned local frequency window fitting and phase search are examples of solution methods. Without deviating from the premise that "code division multiplexing is used for FDTD multi-source excitation and a single simulation mixed observation can separate and recover the independent responses of each source", field separation solution can also be achieved by correlation decoding, solving linear equations, regularized least squares or other equivalent estimation methods.

[0056] Step S5: Field Reconstruction and Output Based on the independent complex frequency domain field response coefficients of the K excitation sources, the independent field components contributed by each excitation source are reconstructed and output.

[0057] Within the preset target frequency band, the above amplitude fitting and phase search process is performed point by point for each discrete frequency point to obtain the complete amplitude and phase response curves of the two K sources in the entire target frequency band.

[0058] Finally, based on the successfully decoupled independent field response coefficients, the independent field response components corresponding to the K sources at the monitor are reconstructed in the frequency domain using Equation (13), thereby completing the physical separation of the multi-source field.

[0059] (13);

[0060] To verify the universality and separation effect of the multi-source excitation FDTD simulation field separation method based on code division multiplexing of the present invention, the technical solution of the present invention will be further described in detail below with reference to specific embodiments. These embodiments are all carried out under the premise of satisfying the above-mentioned general technical solution, and only K=2 dual-source excitation is used as a typical scenario for simulation verification. The free space propagation scenario and the device port response analysis scenario are used for illustration, as detailed below: 1. Free Space Dual-Source Implementation A two-dimensional free-space dual-source FDTD simulation model was constructed. The simulation region was discretized into 500×250 grid cells, with a spatial step size of [missing information]. The time step satisfies the CFL stability condition, and the absorption boundary uses a 16-layer PML. The excitation carrier wavelength is set to... ,exist The analysis is performed within the wavelength range. Let source A and source B represent the two sources, and their positions relative to the monitor and propagation paths are as follows: Figure 2 As shown.

[0061] To obtain reference data, single-source FDTD simulations were first performed separately for each of the excitation sources A and B. The field quantities were recorded by the monitor and processed to obtain the complex frequency domain field response coefficients under single-source conditions. The results are as follows: Figure 3 As shown. The field response coefficients in the complex frequency domain are complex values ​​and can be expressed as a combination of amplitude and phase: Therefore, the amplitude response curve and phase response curve can be extracted separately. In Figure 3, (a) and (c) are the amplitude response curves of source A and source B, respectively. It can be seen that the changes of both are relatively smooth within the operating frequency band, without obvious resonance abrupt changes. In Figure 3, (b) and (d) are the phase response curves of source A and source B, respectively. It can be seen that the phase changes approximately linearly with frequency, which is in line with the propagation law of electromagnetic waves and can be used as a comparison benchmark for subsequent separation results.

[0062] Subsequently, while keeping the mesh environment unchanged, sources A and B were simultaneously activated in the same FDTD simulation, and the aforementioned code division multiplexing broadband excitation signals were injected into them respectively. At this time, a single monitor recorded the field superimposed by the two sources. Using the decoupling algorithm based on local frequency windows proposed in this invention, the complex frequency domain field response coefficients corresponding to sources A and B were separated and extracted from this mixed spectrum. , Compare the extracted results with... Figure 3 The baseline curves in the data are overlapped for comparison, and the results are as follows: Figure 4 As shown in Figure 4. Figure 4(a) and (c) are comparisons of the amplitude separation results of source A and source B, respectively. Figure 4(b) and (d) are comparisons of the phase separation results of source A and source B, respectively. It can be seen that the separation curves are highly coincident with the reference reference, indicating that this method can achieve high-precision amplitude and phase recovery.

[0063] After obtaining the response coefficients, the independent frequency domain field components contributed by source A and source B at the monitor are further reconstructed using equation (13). , Figure 5(a) and (c) show the comparison of the real parts of the field components of source A and source B, respectively, while Figure 5(b) and (d) show the comparison of the imaginary parts. It can be seen that all curves are consistent with the reference height, which intuitively verifies the accuracy of the field separation results.

[0064] To quantitatively assess the accuracy, the average relative error of the amplitude and the average absolute error of the phase of the separation results within the target frequency band relative to the reference results were statistically analyzed, and the data are shown in Table 1. The results show that the error magnitude is extremely low, fully demonstrating that the proposed method has excellent separation accuracy under mixed observation conditions in free space.

[0065] Table 1. Statistics on frequency domain field component separation errors in free space scenes

[0066] 2. Device Port Scenarios and Examples A two-dimensional FDTD device model with a straight waveguide and semi-ring coupling structure was constructed, and dual-source field separation verification was performed in a device port scenario. A single monitor in the device port scenario was set as the port monitoring section to record the time-domain data of the electric and magnetic fields at the port. Considering that the field quantities at the port are distributed cross-sectionally, to extract the response characteristics of a specified transmission mode, the port field recorded by the port monitoring section needs to be projected onto the mode field distribution of the target mode, thereby obtaining the equivalent time-domain sequence and its spectrum under the target mode. Subsequent complex response coefficient extraction and field separation solutions are based on the equivalent quantities of the target mode. A schematic diagram of the device structure and port monitoring section is shown below. Figure 6As shown, the horizontal axis represents the dimension in the x-direction and the vertical axis represents the dimension in the y-direction, which intuitively illustrates the device structure and port location.

[0067] In this scenario, source A and source B are injected via ports a and b, respectively, while port c is the sole observation port. To obtain a unified port response physical quantity, projection processing targeting the same target mode is performed on the inputs of ports a and b and the output of port c, resulting in the corresponding single-mode equivalent excitation, single-mode equivalent output, and their spectra.

[0068] Based on the above port single-mode equivalent input / output, the field separation solution steps follow the aforementioned process, recovering the independent responses corresponding to the two sources within the target frequency band. , . Figure 7 A comparison between the recovery results and the single-source control results is given. Figure 7(a) and (c) show the amplitude response comparison between port A and port B, respectively, and Figure 7(b) and (d) show the phase response comparison, respectively. It can be seen that good consistency is maintained even under multipath interference conditions.

[0069] Based on this, utilize the recovered , Reconstruct the independent port field components contributed by the two sources respectively. Figure 8 A comparison between the reconstructed port field components and the reference port field components is presented. Figure 8(a) and (c) show the comparison of the real parts of the field components of port A and port B, respectively, while Figure 8(b) and (d) show the comparison of the imaginary parts. It can be seen that the reconstruction result is in good agreement with the reference height, thus further proving that the present invention can achieve effective separation and correct reconstruction of the mixed field of the port output in the device port scenario.

[0070] To further quantitatively evaluate the field separation accuracy in the device port scenario, the aforementioned error statistics methodology was adopted, and the average relative amplitude error and average phase error within the target frequency band were statistically analyzed. The statistical results are shown in Table 2. The present invention maintains a small and stable error with frequency variation even in the device port scenario, thus verifying the effectiveness and stability of the method for device port response analysis and mixed field separation of port output.

[0071] Table 2. Statistics on frequency domain field component separation error in device port scenarios

[0072] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-source excitation FDTD simulation field separation method based on code division multiplexing, characterized in that, Includes the following steps: Step S1: Generate code division multiplexing broadband excitation signals with low cross-correlation characteristics for each of the K excitation sources in the FDTD simulation, where K≥2; Step S2: In a single FDTD simulation, K code division multiplexing broadband excitation signals are injected into the corresponding K excitation source positions to achieve simultaneous excitation of multiple sources, and the mixed field time domain sequence is recorded by a monitor set in the simulation space. Step S3: Perform Fourier transform on the hybrid field time-domain sequence and the K code division multiplexing broadband excitation signals respectively to obtain the hybrid observation spectrum and the excitation spectrum of each of the K excitation sources; Step S4: Based on the principle of linear superposition of electromagnetic fields, using the coding non-correlation characteristics of the excitation spectra of each of the K excitation sources, the hybrid observation equation composed of the hybrid observation spectrum is decoupled and parameters are extracted to obtain the independent complex frequency domain field response coefficients of the K excitation sources at the monitor. Step S5: Based on the independent complex frequency domain field response coefficients of the K excitation sources, reconstruct and output the independent field components contributed by each excitation source.

2. The method according to claim 1, characterized in that, Step S1 specifically includes: Step S11: Generate a spreading code with good autocorrelation properties and low cross-correlation for each excitation source; Let the first The spreading code corresponding to each excitation source is: , Its approximate orthogonality is expressed as follows: ； in, The length of the spreading code; This is a discrete-time index, representing the chip number of the spreading code; For the first The first excitation source spreading code of the first excitation source spreading code Each chip can be used to obtain a value; For the first The first excitation source spreading code of the first excitation source spreading code Each chip can be used to obtain a value; and Indicates the sequence number of the excitation source, and ; Step S12: Repeat the chip of each spreading code a preset number of times to form a baseband spreading sequence; Spread code Each chip repeats This time, the length is obtained as single-bit waveform sequence Let the m-th bit symbol be... Then the baseband spread spectrum sequence in the m-th bit period satisfy: ； Step S13: Perform continuous phase modulation on the baseband spread spectrum sequence to generate a code division multiplexing broadband excitation signal with continuous phase and smooth energy. ； in, It is a code division multiplexing broadband excitation signal; The carrier frequency determines the position of the excitation signal's carrier center. For the first The physical time corresponding to each sampling point For the first The source in the first The instantaneous phase of each sampling point is expressed as follows: ； in, The time sampling interval is... It is a proportionality coefficient related to the modulation index and symbol rate.

3. The method according to claim 2, characterized in that, The continuous phase modulation employs minimum frequency shift keying (MSK) modulation.

4. The method according to claim 1, characterized in that, In step S2, the spatial form of the K code division multiplexing broadband excitation signal injection regions includes point sources, line sources, or waveguide port surface sources.

5. The method according to claim 4, characterized in that, In step S2, when injecting from a point source, at each time step, the corresponding modulation excitation signal is superimposed and injected into the selected field component update term, so as to achieve simultaneous excitation of K sources in the same simulation process. The specific update form is as follows: ； in, For the injection location, For code division multiplexing broadband excitation signal, In the first Time step, location The field component update item at the location.

6. The method according to claim 1, characterized in that, In step S3, the mixed-field time-domain sequence output by the monitor... And the known K code division multiplexing broadband excitation signals The excitation spectrum was obtained by performing discrete Fourier transforms on each. , ; At discrete frequency points Let the independent complex frequency domain field response coefficients corresponding to the k-th excitation source at a single monitor be denoted as . For the general case of K sources, the mixed observation spectrum satisfies a linear superposition relationship, as expressed below: ； in, This is the source number.

7. The method according to claim 6, characterized in that, Step S4 involves decoupling and extracting parameters from the hybrid observation equations, specifically including: Step S41: Express the independent complex frequency domain field response coefficients of the k-th excitation source to be determined in polar coordinate form, including amplitude and phase terms; Step S42: Within a local frequency window near the target frequency point, expand the modulus square of the mixed observation spectrum into a combination of the squares of the amplitude terms of each source and the cross terms between the sources; Step S43: Based on the data of multiple frequency sampling points within the local frequency window, construct a set of fitting equations for the amplitude term and the cross term, and solve them using the least squares estimation method to obtain the amplitude estimates of each excitation source and the relative phase differences between each pair. Step S44: Select a reference source and use its unknown reference phase to uniformly characterize the absolute phase of all excitation sources, simplifying the hybrid observation equation into an expression containing only a single unknown reference phase; Step S45: Construct a residual objective function for the unknown reference phase, and minimize the residual objective function through phase optimization search to obtain an estimated value of the reference phase; Step S46: Based on the estimated value of the reference phase and the relative phase difference, the absolute phase of all K excitation sources is finally determined, thereby obtaining the complete complex frequency domain field response coefficients of each excitation source.

8. The method according to claim 1, characterized in that, The monitors may be one or more, and their arrangement may include point monitors, line monitors, surface monitors, and monitoring sections of device ports in free space.

9. The method according to claim 1, characterized in that, In step S5, the independent field components contributed by each source are reconstructed as follows: at each discrete frequency point within the target frequency band, the excitation spectrum of the k-th excitation source is multiplied by the independent complex frequency domain field response coefficient corresponding to that source to obtain the independent frequency domain field components contributed by that excitation source.

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