A wave domain reasoning method based on sim-based multi-harmonic modulation and frequency domain mixing

Abstract

This invention belongs to the field of signal processing and wireless communication technology, specifically relating to a wave domain inference method based on SIM multi-harmonic modulation and frequency domain mixing. The method first constructs complex modulation coefficients at the source coding layer through multi-scale sliding window fusion of images. Then, a time-varying modulation function formed by the superposition of multiple single-frequency components is applied to each layer of superatoms to generate discrete harmonics in the electromagnetic wave domain and achieve convolutional frequency domain mixing. Next, at the receiving end, frequency selection is performed on specified harmonic components to construct energy features of "antenna index - harmonic index," and a trainable temperature parameter is introduced to complete energy-based softmax prediction and end-to-end cross-entropy training. Simultaneously, passive normalization constraints ensure that the modulation coefficients meet physical realizability conditions. This invention achieves better recognition accuracy and stable inference performance under different superatomic array sizes and different layer and harmonic number configurations, improving the expressive power and trainability of SIM wave domain inference under passive constraints.

Description

Technical Field

[0001] This invention belongs to the field of signal processing and wireless communication technology, specifically relating to a wave domain inference method based on multi-harmonic modulation and frequency domain mixing of a reconfigurable stacked intelligent metasurface (SIM). Background Technology

[0002] Semantic communication (SemCom) aims to directly transmit semantic information useful for tasks, thereby improving spectral efficiency and end-to-end task performance. However, existing SemCom schemes typically rely on deep neural networks (DNNs) for feature extraction and inference, which have high computational complexity and energy consumption, limiting their deployment on resource-constrained platforms.

[0003] In recent years, Simulation-based Inference (SIM) has been used as a physical layer platform to directly process semantic features in the electromagnetic domain, thereby migrating some task inference to the wave domain and reducing the processing burden on the baseband side. However, traditional SIMs mostly rely on static phase modulation, which limits frequency response, degrees of freedom, and nonlinear expression capabilities under hardware constraints, making it difficult to support richer task mappings. To overcome these limitations, time-varying metasurfaces can be used to achieve harmonic generation and frequency domain mixing, thereby expanding the SIM's representation capabilities in the frequency domain while maintaining its advantages of low latency and energy efficiency. Therefore, there is an urgent need for a SIM-oriented implementation method that can achieve multi-harmonic modulation and frequency domain mixing under passive constraints and can be used for end-to-end wave domain inference. Summary of the Invention

[0004] This invention proposes a wave domain reasoning method based on SIM multi-harmonic modulation and frequency domain mixing. By applying multi-single-frequency time-varying modulation to each superatom of the SIM layer, harmonic expansion of the incident spectrum and convolutional frequency domain mixing are achieved. At the receiving end, semantic category reasoning is completed by "antenna-frequency" energy decision, thereby improving the expressive power and trainability of wave domain reasoning under passive constraints. The method of this invention is used to complete task-oriented reasoning and classification in the electromagnetic wave domain.

[0005] The technical solution adopted in this invention is:

[0006] A wave domain inference method based on SIM multi-harmonic modulation and frequency domain mixing, the system includes a transmitter and a receiver. The transmitter includes a transmitting antenna and a SIM disposed in front of the transmitting antenna. The SIM includes... The first metasurface layer, of which the second... The first layer is the source coding layer, and the rest are semantic coding layers. Each layer consists of... An array of passive superatoms This represents the number of superatoms arranged along the horizontal direction of the array. This represents the number of superatoms arranged vertically along the array. The receiver includes... An array of receiving antennas is formed. The transmitting antenna is used to radiate narrowband electromagnetic waves as the incident field. The SIM is positioned in front of the transmitting antenna and within its forward radiation region, so that the incident field is sequentially incident on the SIM's 0th source coding layer and layers 1 through 2. The semantic coding layer consists of layers arranged sequentially along the main propagation direction and coupled between layers through free space propagation. Each layer's superatoms applies time-varying and phase modulation to the incident carrier, thereby generating a spectral response in the output field containing the carrier frequency and its harmonic mixing components; the receiving end... A receiving antenna constitutes a receiving array, arranged in front of and facing the last layer of the SIM, for receiving the emitted electromagnetic field processed by the SIM. The wave domain inference method is characterized by the following steps:

[0007] S1. Image multi-scale sliding window fusion and source coding coefficient construction:

[0008] Setting the input image A sliding window scale is used, and fusion weights are set. At each scale, sliding window segmentation and resampling are performed to obtain image patches; for the source coding layer... Each superatomic structure uses pixel values ​​as complex modulation coefficients with real parts and imaginary parts of 0. ,in Indicates harmonic index, Indicates a superatomic index. This represents the scale index. A passive normalization constraint is applied to the coefficients at each scale.

[0009] ,

[0010] Scale fusion is then performed to obtain the final coefficients of the source coding layer.

[0011] ,

[0012] S2, Source coding layer multi-frequency superposition modulation and generation of multi-harmonic output:

[0013] For the Layer A time-varying modulation function consisting of the superposition of multiple single-frequency signals is applied to each superatom.

[0014] ,

[0015] The set of modulation frequencies satisfies the equal-interval frequency grid constraint. For the preset frequency interval, Indicates harmonic index, Indicates a superatomic index. This represents the number of harmonics in the 0th harmonic layer. Let... Then the output of layer 0 is:

[0016] ,

[0017] in For the incident carrier, For transmission power, The fixed propagation coefficient vector from the transmitting antenna to layer 0.

[0018] S3, Semantic coding layer layer-by-layer propagation and frequency domain mixing coding:

[0019] For the Layer A time-varying modulation function is applied to each superatom.

[0020] in For trainable complex modulation coefficients, No. Number of layer harmonics; let Then the output of this layer satisfies

[0021] ,

[0022] in This is the inter-layer propagation matrix. Passive amplitude constraints are applied to the modulation coefficients of each semantic coding layer to ensure they satisfy... After completing the first After layer-by-layer propagation and frequency-domain mixing coding, the stacked metasurface at the 1st... The emitted wave domain vector signal of the layer can be expressed as:

[0023] ,

[0024] in It is a continuous-time complex electromagnetic field vector signal with each superatom position as a sampling point.

[0025] S4. Receive and process signals (frequency selection, energy characteristic construction, and loss optimization):

[0026] The receiving channel adopts the Riesling fading model, and the received signal is... ,in For the received channel moment. (The rest of the text appears to be incomplete and requires further context.) The execution frequency selection yields the selected result. One harmonic component ( , ), and construct energy feature vectors Introducing a trainable temperature parameter ,make Construct classification probabilities

[0027] ,

[0028] one-hot label Construct cross-entropy loss and update it jointly based on mini-batch gradient descent. , and Furthermore, the passive constraint normalization is performed on the modulation coefficients after each parameter update.

[0029] S5, Category Mapping and Inference Output

[0030] The receiver uses a uniform linear array (ULA) and establishes a correspondence between semantic categories and the "receive antenna index – harmonic index" to ensure that the number of categories meets the requirements. During the inference phase, the category is output based on the maximum energy criterion.

[0031] The beneficial effects of this invention are as follows: under different superatomic array sizes and different layer and harmonic configurations, this invention can achieve better recognition accuracy and stable inference performance, and can improve the expressive power and trainability of SIM wave domain inference under passive constraints. Attached Figure Description

[0032] Figure 1 This is a flowchart of the method of the present invention;

[0033] Figure 2 For different superatomic array sizes Below is a comparison chart of the recognition accuracy of the method of the present invention and various control methods;

[0034] Figure 3 For different SIM layers and the number of single-frequency modulation components per layer Under certain configurations, the recognition accuracy varies with the size of the superatomic array. A comparison chart of the changes. Detailed Implementation

[0035] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings and embodiments:

[0036] This invention provides a wave domain inference method based on SIM multi-harmonic modulation and frequency domain mixing. The system includes a transmitter and a receiver. The transmitter includes a transmitting antenna and a SIM disposed in front of the transmitting antenna. The SIM includes... The first metasurface layer, of which the second... The first layer is the source coding layer, and the rest are semantic coding layers. Each layer consists of... An array of passive superatoms This represents the number of superatoms arranged along the horizontal direction of the array. This represents the number of superatoms arranged vertically along the array. The receiver includes... An array of receiving antennas is formed. The transmitting antenna is used to radiate narrowband electromagnetic waves with a carrier frequency of 10 GHz as the incident field. The SIM is positioned in front of the transmitting antenna and within its forward radiation region, so that the incident field is sequentially incident on the SIM's 0th source coding layer and layers 1 to 2... The semantic coding layer consists of layers arranged sequentially along the main propagation direction and coupled between layers through free space propagation. Each layer's superatoms applies time-varying and phase modulation to the incident carrier, thereby generating a spectral response in the output field containing the carrier frequency and its harmonic mixing components; the receiving end... A receiving array composed of several receiving antennas is arranged in front of and facing the last layer of the SIM, for receiving the emitted electromagnetic field processed by the SIM. Figure 1 As shown, the method includes the following steps:

[0037] S1. Image multi-scale sliding window fusion and source coding coefficient construction

[0038] Setting the input image A sliding window scale is used, and fusion weights are set. ,satisfy At each scale Perform sliding window segmentation and resampling to To obtain image patches , This represents the index of the image patch obtained by the sliding window. Indicates the scale index. For the source coding layer... Each superatomic structure uses pixel values ​​as complex modulation coefficients with real parts and imaginary parts of 0. , Indicates harmonic index, This represents a superatomic index.

[0039] And for each scale The coefficients are subject to passive normalization constraints:

[0040]

[0041] Scale fusion is then performed to obtain the final coefficients of the source coding layer.

[0042]

[0043] S2, Source coding layer multi-frequency superposition modulation and generation of multi-harmonic output.

[0044] Let the incident carrier be The transmission power is For the first Layer A time-varying modulation function consisting of the superposition of multiple single-frequency signals is applied to each superatom.

[0045]

[0046] The set of modulation frequencies satisfies the equal-interval frequency grid constraint. For the preset frequency interval, Indicates harmonic index, Indicates a superatomic index. This represents the number of harmonics in the 0th harmonic layer. Let... ,make Let represent the fixed propagation coefficient vector from the transmitting antenna to layer 0. Then the output of layer 0 is...

[0047]

[0048] S3, Semantic coding layer layer-by-layer propagation and frequency domain mixing coding

[0049] For any semantic coding layer Establish inter-layer propagation matrix Its elements satisfy

[0050]

[0051] in The distance between adjacent layers. For the superatomic area, For wavelength, For the first Layer The superatoms up to the first Layer The geometric distance of the first superatom; for the first Layer A time-varying modulation function is applied to each superatom.

[0052]

[0053] in Let be the trainable complex modulation coefficients. Then the output of this layer satisfies

[0054]

[0055] Passive amplitude constraints are applied to the modulation coefficients of each semantic coding layer to ensure that they meet the following conditions.

[0056]

[0057] After completing the first After layer-by-layer propagation and frequency-domain mixing coding, the stacked metasurface at the 1st... The emitted wave domain vector signal of the layer can be expressed as:

[0058]

[0059] in It is a continuous-time complex electromagnetic field vector signal with each superatom position as a sampling point.

[0060] S4, Reception, Frequency Selection, Energy Characteristic Construction and Loss Optimization

[0061] Let the receive channel matrix be... ,noise The received signal is

[0062]

[0063] The receiving channel adopts the Ries fading model.

[0064]

[0065] in For the Ries factor, It is a zero-mean circularly symmetric complex Gaussian random matrix. Determined by geometric distance, This is the path loss coefficient. For The execution frequency selection yields the selected result. One harmonic component ( , ), and construct energy feature vectors Introducing a trainable temperature parameter ,make Construct classification probabilities

[0066]

[0067] one-hot label Constructing cross-entropy loss

[0068]

[0069] And based on mini-batch gradient descent joint update , and Furthermore, the passive constraint normalization is performed on the modulation coefficients after each parameter update.

[0070] S5, Category Mapping and Inference Output

[0071] The receiver uses a uniform linear array (ULA) and establishes a correspondence between semantic categories and the "receive antenna index – harmonic index" to ensure that the number of categories meets the requirements. During the inference phase, the category is output based on the maximum energy criterion.

[0072] Example 1

[0073] This example verifies different superatomic array sizes. Below is a comparison of the recognition accuracy of the method of the present invention with that of various control methods, such as... Figure 2 As shown.

[0074] Simulation conditions and parameters:

[0075] This embodiment uses the MNIST handwritten digit dataset for task-oriented semantic recognition verification, with a number of categories. The system carrier frequency is set to... SIM thickness set to The superatoms are arranged in a uniform planar array, with the spacing between adjacent superatoms set to... The area of ​​a single superatom is set to The receiver is a uniform linear array, and the distance between the receiver array and the output layer is set to... The number of receiving antennas is set to Antenna spacing set to The channel adopts the Riesling fading model, and the Riesling factor is set to... Large-scale path loss adopts ,in , The transmit power is set to... Additive white Gaussian noise power set to Image patch resampling to the aperture grid employs interpolation: area interpolation for downsampling and bilinear interpolation for upsampling. Training uses the Adam optimizer with an initial learning rate of... Superatomic array size Take different values ​​according to the horizontal axis in the diagram. The configuration is scanned, and the remaining parameters remain unchanged.

[0076] Example 2

[0077] This example verifies different SIM layers. and the number of single-frequency modulation components per layer Under certain configurations, the recognition accuracy varies with the size of the superatomic array. Changes, such as Figure 3 As shown.

[0078] Simulation conditions and parameters:

[0079] This embodiment uses the MNIST handwritten digit dataset for task-oriented semantic recognition verification, with a number of categories. The system carrier frequency is set to... SIM thickness set to The superatoms are arranged in a uniform planar array, with the spacing between adjacent superatoms set to... The area of ​​a single superatom is set to The receiver is a uniform linear array, and the distance between the receiver array and the output layer is set to... The number of receiving antennas is set to Antenna spacing set to The channel adopts the Riesling fading model, and the Riesling factor is set to... Large-scale path loss adopts ,in , The transmit power is set to... Additive white Gaussian noise power set to Image patch resampling to the aperture grid employs interpolation: area interpolation for downsampling and bilinear interpolation for upsampling. Training uses the Adam optimizer with an initial learning rate of... Superatomic array size Take different values ​​according to the horizontal axis in the diagram. The configuration is scanned, with all other parameters remaining unchanged. During the semantic encoding phase, the harmonic number of each layer is compared with the propagation layer number: the harmonic number of the semantic encoding layer is taken as... The number of propagation layers in the semantic encoding stage is taken as follows Under the different configurations described above, the comparison recognition accuracy varies with the size of the superatomic array. The changing trends are used to evaluate the impact of harmonic degrees of freedom and layer depth on wave domain inference performance.

Claims

1. A wave domain inference method based on SIM multi-harmonic modulation and frequency domain mixing, characterized in that, The system includes a transmitter and a receiver. The transmitter includes a transmitting antenna and a SIM disposed in front of the transmitting antenna. The SIM includes... The first metasurface layer, the SIM's first The first layer is the source coding layer, and the rest are semantic coding layers. Each layer consists of... An array of passive superatoms This represents the number of superatoms arranged along the horizontal direction of the array. The number of superatoms arranged along the vertical direction of the array; the receiving end includes An array of receiving antennas is formed; the transmitting antenna is used to radiate narrowband electromagnetic waves as the incident field, and the SIM is positioned in front of the transmitting antenna and within the forward radiation region of the transmitting antenna. The incident field is sequentially incident on the 0th source coding layer and the 1st to 2nd layers of the SIM. The semantic coding layer consists of layers arranged sequentially along the main propagation direction and coupled between layers through free space propagation; each layer's superatoms apply time-varying modulation and phase modulation to the incident carrier, thereby generating a spectral response in the output field that includes the carrier frequency and its harmonic mixing components; the receiver's... A receiving array composed of several receiving antennas is arranged in front of and facing the last layer of the SIM, and is used to receive the emitted electromagnetic field after processing by the SIM; the wave domain inference method based on the set system includes the following steps: S1. Image multi-scale sliding window fusion and source coding coefficient construction: Setting the input image A sliding window scale is used, and fusion weights are set. At each scale, sliding window segmentation and resampling are performed to obtain image patches; for the source coding layer... Each superatomic structure uses pixel values ​​as complex modulation coefficients with real parts and imaginary parts of 0. ,in Indicates harmonic index, Indicates a superatomic index. Represents the scale index and applies passive normalization constraints to the coefficients for each scale: ， Scale fusion is then performed to obtain the final coefficients of the source coding layer. : ， S2, Source coding layer multi-frequency superposition modulation and generation of multi-harmonic output: For the Layer Each superatom is subjected to a time-varying modulation function consisting of the superposition of multiple single-frequency signals: ， The set of modulation frequencies satisfies the equal-interval frequency grid constraint. , For the preset frequency interval, Indicates the number of harmonics in the 0th layer; let Then the output of layer 0 is: ， in For the incident carrier, For transmission power, The vector represents the fixed propagation coefficients from the transmitting antenna to the 0th layer; S3, Semantic coding layer layer-by-layer propagation and frequency domain mixing coding: For the Layer A time-varying modulation function is applied to each superatom. , in For trainable complex modulation coefficients, For the first Number of layer harmonics; let Then the first The layer output satisfies: ， in The inter-layer propagation matrix is ​​used; passive amplitude constraints are applied to the modulation coefficients of each semantic coding layer to ensure that they satisfy... ; after completing the first After layer-by-layer propagation and frequency domain mixing coding, the SIM in the first layer... The emitted wave domain vector signal of the layer is represented as: ， in It is a continuous-time complex electromagnetic field vector signal with each superatomic position as a sampling point; S4. Receive and process signals: The receiving channel is defined using the Riesling fading model, and the received signal at the receiver is... ,in For the received channel moment, for The execution frequency selection yields the selected [item]. One harmonic component , , And construct energy feature vectors Introducing trainable temperature parameters ,make Construct the classification probability: ， one-hot label Construct cross-entropy loss and update it jointly based on mini-batch gradient descent. , and Furthermore, the passive constraint normalization is performed on the modulation coefficients after each parameter update; S5, Category Mapping and Inference Output: The receiver employs a uniform linear array (ULA) and establishes a correspondence between semantic categories and the "receive antenna index – harmonic index" to ensure the number of categories meets the requirements. During the inference phase, the category is output based on the maximum energy criterion.

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