Multi-array-element airspace zeroing anti-interference virtual method of MobileNet architecture

Abstract

The invention relates to a multi-array-element airspace zeroing anti-interference virtual method of a MobileNet architecture, and belongs to the field of Beidou and the field of radio communication and artificial intelligence crossing technologies. The method comprises the steps of radio-frequency signal acquisition and digital preprocessing, MobileNet model improved design, virtual array element extension implementation, airspace zeroing weight calculation and optimization, FPGA hardware acceleration execution, beam forming and anti-interference output. According to the virtual array element expansion technology, the number of effective array elements can be increased by 2-4 times, the spatial freedom degree is increased to 15-31 from 7, 4-8 independent nulls can be formed at the same time within the range of + / -60 degrees, and the multi-interference-source suppression ratio is increased to 35 dB or above from 20 dB of a traditional method; by means of the MobileNet lightweight model, the weight calculation complexity is reduced, and by combining the parallel calculation architecture of the FPGA, the real-time performance is obviously improved, the hardware resource consumption is greatly reduced, and the dynamic adaptive capacity is good.

Description

Technical Field

[0001] This invention belongs to the fields of BeiDou navigation and the interdisciplinary fields of radio communication and artificial intelligence, and specifically relates to a virtual method for anti-interference in the spatial domain zeroing of a multi-element array based on MobileNet architecture. Background Technology

[0002] With the rapid development of electronic warfare technology, the BeiDou Navigation Satellite System faces increasingly complex interference environments, including numerous, wide-bandwidth, and flexible interference sources (such as narrowband, broadband, and frequency-sweeping interference). These issues severely impact the positioning performance of the BeiDou system, and can even lead to satellite denial, rendering navigation and positioning services unavailable. Multi-element spatial nulling anti-interference technology utilizes the spatial degrees of freedom of the array antenna to create beam nulls in the interference direction, and is one of the core anti-interference methods currently used in BeiDou and radio communication. Its core principle is to adaptively adjust the weighting coefficients of each array element to minimize the gain of the array pattern in the interference direction while maximizing the gain in the target direction.

[0003] Traditional multi-element spatial zeroing anti-interference methods mainly rely on two types of techniques:

[0004] (1) Classical adaptive algorithm techniques (such as Least Mean Square Error (LMS), Recursive Least Squares (RLS), Sampling Matrix Inversion (SMI), etc.): The computational complexity of these algorithms is not high. Taking LMS as an example, its complexity is O(N²) (N represents the number of array elements). However, these algorithms have obvious shortcomings in practical applications—the convergence speed is relatively slow, and they are easily affected by noise interference, and their ability to track rapidly changing interference signals is insufficient. Moreover, once the number of array elements increases (for example, more than 32), or multiple interference sources need to be suppressed at the same time (such as multiple zero-containment scenarios), the computational load will increase significantly, making it difficult to meet the requirements of real-time processing.

[0005] (2) Deep learning methods (such as fully connected neural networks, convolutional neural networks, etc.): These methods rely on training data to learn the mapping relationship between interference features and optimal weights, which can better adapt to complex interference environments. However, there are two key problems: First, the number of model parameters is large. For example, the number of parameters in a fully connected network will increase exponentially with the input dimension. Second, the computational complexity is high. For example, convolutional layers require a large number of floating-point operations. If deployed directly on an FPGA, it will face the problems of excessive consumption of hardware resources (such as DSP and BRAM) and high processing latency, which cannot meet the real-time requirements in engineering applications.

[0006] In addition, most existing methods are designed for scenarios with a fixed number of physical array elements and do not make full use of "virtual array element" technology. This results in limited anti-interference capabilities when the number of physical array elements is limited. At the same time, current hardware acceleration solutions are mostly general designs and do not combine the characteristics of "radius pattern optimization" of spatial zeroing for customized optimization. For example, weight updates only require local information and require multi-channel parallel computing, which ultimately leads to low resource utilization.

[0007] Invention Patent: A method and system for DOA estimation technology based on spatial zeroing algorithm (CN202411693259.9). This patent uses an anti-interference processing algorithm to calculate adaptive weights and uses the DOA estimation algorithm to calculate the maxima of all spectral peaks, thereby calculating the interference null power. This patent discloses a spatial zeroing method based on power comparison, but it relies on accurate interference direction estimation and has poor adaptability to unknown interference.

[0008] In view of the shortcomings of existing technologies, this invention mainly aims to solve the following key problems:

[0009] 1. Real-time performance cannot meet the requirements: Traditional adaptive algorithms are slow to track rapidly changing disturbances, while deep learning models not only have a large number of parameters, but also suffer from high latency when deployed on FPGAs, making it difficult to meet real-time processing requirements.

[0010] 2. High hardware resource consumption: If deep learning models are deployed directly on FPGAs, the computational complexity and number of parameters of the models themselves will consume a large amount of chip computing and storage resources, causing the hardware to malfunction.

[0011] 3. Insufficient spatial degrees of freedom: Traditional methods rely on the actual number of physical array elements and fail to use virtual array element technology to expand the actual available spatial degrees of freedom, which limits the improvement of antenna anti-interference capability;

[0012] 4. Poor dynamic adaptability: Existing solutions have difficulty handling complex scenarios such as multiple interference sources and wideband interference at the same time, and their ability to adjust is weak when faced with changes in the interference environment. Summary of the Invention

[0013] (a) Technical problems to be solved

[0014] The technical problem to be solved by this invention is how to provide a virtual method for multi-element spatial zeroing anti-interference in the MobileNet architecture, so as to solve the problems of existing technologies such as inability to meet real-time requirements, high hardware resource consumption, insufficient spatial freedom, and poor dynamic adaptability.

[0015] (II) Technical Solution

[0016] To address the aforementioned technical problems, this invention proposes a virtual method for multi-element spatial domain zeroing to resist interference in a MobileNet architecture. This method includes the following steps:

[0017] S1. Radio Frequency Signal Acquisition and Digital Preprocessing

[0018] The radio receiver front end receives radio frequency signals through physical array antennas and converts the radio frequency signals into digital baseband signals for subsequent processing. The signal conversion includes A / D conversion, digital down-conversion, pulse compression, and clutter cancellation.

[0019] S2 and MobileNet Model Improvement Design

[0020] Design an improved MobileNet lightweight neural network to extract interference direction and signal-to-interference-plus-noise ratio features from the preprocessed baseband signal, estimate the interference direction, and obtain the weight correction amount;

[0021] S3, Virtual Array Element Expansion Implementation

[0022] Based on time delay compensation, physical array element signals are aligned, and then virtual array elements are generated through linear interpolation;

[0023] S4. Spatial Zeroing Weight Calculation and Optimization

[0024] By combining the interference direction estimation results with the virtual array element signal, an initial weight vector is generated using the least squares algorithm. Then, the weight is optimized using the weight correction amount output by the improved MobileNet, thereby suppressing the interference direction signal and enhancing the target direction signal.

[0025] S5, FPGA hardware accelerated execution

[0026] Virtual array element expansion and weight optimization are mapped to FPGA, and computational efficiency is improved through parallel computing units, pipeline design and low-precision quantization;

[0027] S6, Beamforming and Anti-interference Output

[0028] Based on the optimized weight vector, the signals of each virtual array element are weighted and summed to form a receiving beam pointing towards the target direction and suppressing interference, and outputting the anti-interference signal.

[0029] (III) Beneficial Effects

[0030] This invention proposes a virtual method for anti-interference in the spatial domain of multi-element nulling in a MobileNet architecture. Compared with existing technologies, the advantages of this invention are mainly reflected in the following aspects:

[0031] 1. Enhanced anti-interference capability: Virtual array element expansion technology can increase the number of effective array elements by 2 to 4 times (e.g., 8 physical array elements can be expanded to 16 to 32 virtual array elements), the spatial degrees of freedom have increased from 7 to 15 to 31, and 4 to 8 independent nulls can be formed simultaneously within a range of ±60°. The multi-source suppression ratio (SIR) has also increased from 20dB in the traditional method to more than 35dB.

[0032] 2. Significantly improved real-time performance: By leveraging the lightweight MobileNet model, the computational complexity of weights is reduced from O(N³) to O(NP²) (where P is the kernel size, typically 3-5); combined with the parallel computing architecture of FPGA, the processing latency is reduced from tens of milliseconds in traditional methods (such as the RLS algorithm which takes about 50 milliseconds) to sub-millisecond levels (no more than 2 milliseconds), which fully meets the real-time requirements of electronic warfare scenarios.

[0033] 3. Significantly reduced hardware resource consumption: By combining depthwise separable convolution and sparse design, the number of model parameters can be reduced by more than 85%. With the addition of 8-bit quantization technology, storage requirements are further reduced. The dedicated FPGA acceleration architecture relies on parallel computing units and memory optimization, which reduces DSP resource consumption by 60% and BRAM consumption by 40% compared to general solutions.

[0034] 4. Excellent dynamic adaptability: The multi-task output head can support multi-dimensional learning of interference type (narrowband / wideband) and interference direction, and with the addition of online parameter fine-tuning function, it can quickly adapt to changes in the interference environment (such as interference source movement, frequency agility, etc.), and the system robustness is significantly improved compared with traditional adaptive algorithms. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0036] Figure 2 A schematic diagram of the network structure for improving the MobileNet model;

[0037] Figure 3 A schematic diagram of the virtual array element expansion technology process;

[0038] Figure 4 This is a schematic diagram of the calculation and optimization process for airspace zeroing weights.

[0039] Figure 5 This is a schematic diagram of the FPGA hardware acceleration execution process. Detailed Implementation

[0040] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0041] This invention belongs to the fields of BeiDou navigation, radio communication and artificial intelligence. Specifically, it relates to a virtual method for spatial zeroing anti-interference of multi-element antenna systems based on the lightweight deep learning model MobileNet architecture and hardware acceleration through field-programmable gate arrays (FPGAs). It is applicable to intelligent anti-interference processing in radio communication, radar, satellite communication, 5G / 6G base stations and electronic countermeasures systems.

[0042] This invention implements a virtual multi-element spatial zeroing anti-interference antenna based on the MobileNet architecture and FPGA hardware acceleration. The virtual zeroing anti-interference antenna consists of a radio receiving front-end, an A / D conversion module, a digital down-conversion (DDC) module, an anti-interference processing unit (including the FPGA acceleration module described in this invention), and a waveform generator. Figure 1 As shown in the flowchart, the virtual zeroing implementation process involves six steps: RF signal acquisition and digital preprocessing, MobileNet model improvement design, virtual array element expansion implementation, spatial zeroing weight calculation and optimization, FPGA hardware acceleration execution, and beamforming and output. Taking an 8-element physical array element virtual 32-element antenna as an example, the multi-element spatial zeroing anti-interference virtual process is described in detail.

[0043] This invention proposes a virtual method for anti-interference in the spatial domain of a multi-element array based on the MobileNet architecture, specifically including:

[0044] S1. Radio Frequency Signal Acquisition and Digital Preprocessing

[0045] The radio receiver front end receives radio frequency signals through physical array antennas and converts the radio frequency signals into digital baseband signals for subsequent processing. The signal conversion includes A / D conversion, digital down-conversion, pulse compression, and clutter cancellation.

[0046] S2 and MobileNet Model Improvement Design

[0047] The design improves the MobileNet lightweight neural network to extract key features such as interference direction and signal-to-interference-plus-noise ratio (SNR) from the preprocessed baseband signal, estimate the interference direction, and obtain the weight correction amount.

[0048] S3, Virtual Array Element Expansion Implementation

[0049] Based on time delay compensation, physical array element signals are aligned, and then virtual array elements are generated through linear interpolation;

[0050] S4. Spatial Zeroing Weight Calculation and Optimization

[0051] By combining the interference direction estimation results with the virtual array element signal, an initial weight vector is generated using the least squares algorithm. Then, the weight is optimized using the weight correction amount output by the improved MobileNet, thereby suppressing the interference direction signal and enhancing the target direction signal.

[0052] S5, FPGA hardware accelerated execution

[0053] Virtual array element expansion and weight optimization are mapped to FPGA, and computational efficiency is improved through parallel computing units, pipeline design and low-precision quantization;

[0054] S6, Beamforming and Anti-interference Output

[0055] Based on the optimized weight vector, the signals of each virtual array element are weighted and summed to form a receiving beam pointing towards the target direction and suppressing interference, and outputting the anti-interference signal.

[0056] Example 1:

[0057] Step S1: Radio Frequency Signal Acquisition and Digital Preprocessing

[0058] The radio receiver front end receives radio frequency (RF) signals through an 8-element antenna and needs to convert the RF signals into digital baseband signals for subsequent processing. Signal conversion includes A / D conversion, digital down-conversion (DDC), pulse compression, and clutter cancellation to suppress noise and clutter and extract the effective target signal.

[0059] ①A / D Conversion: The radio frequency signal (assuming the center frequency is X-band and the bandwidth is 100MHz) is down-converted to intermediate frequency (IF) by a low noise amplifier (LNA) and a mixer, and then sampled by a 16-bit high-speed ADC (with a sampling rate of 2GHz) and finally converted into a digital intermediate frequency signal.

[0060] ② Digital downconversion (DDC): The intermediate frequency signal is further downconverted to the baseband (assuming 0 frequency output), and high frequency components are filtered out by digital filters (such as FIR low-pass filters) to output two 16-bit fixed-point baseband signals, I and Q (the sampling rate is set to 100MHz).

[0061] ③ Pulse compression: A matched filter (MF) is used to compress the pulse signal, suppress sidelobe signals, and improve the signal-to-noise ratio of target detection.

[0062] The impulse response of the matched filter is the time-reversed conjugate of the transmitted signal, and the calculation formula is expressed as formula (1).

[0063] (1)

[0064] in, Let s(t) be the impulse response of the matched filter, s(t) be the time-domain waveform of the transmitted signal, and t be time. It is the time-reversed conjugate of the transmitted signal, and its time length is the same as s(t) (both are T). It is finite in length and can be implemented in hardware such as FPGAs through delay lines and multipliers to achieve impulse response output.

[0065] ④ Clutter cancellation: For ground / sea clutter (Doppler shift close to 0), an adaptive filter (such as the LMS algorithm) is used to estimate the clutter components and eliminate the clutter components from the received signal to achieve the goal of static clutter interference suppression.

[0066] Step S2, Improved Design of MobileNet Model

[0067] We designed and improved the MobileNet lightweight neural network to extract key features such as interference direction and signal-to-interference-plus-noise ratio (SNR) from the preprocessed baseband signal, providing a basis for subsequent weight calculation. The model achieves low computational complexity and high feature extraction capability through optimized depthwise separable convolution, channel shuffling, and sparsity regularization. Implementation details are available in [link to implementation details]. Figure 2 .

[0068] ① Input layer: Channel C is positioned as 16, quantizing the 16-channel I / Q signal (16-bit fixed point) into an 8-bit fixed point (sign bit + 7 decimal bits), with an input dimension of 16×256 (channel × time point).

[0069] Step S1 explicitly defines an "8-element physical antenna," and each physical element outputs two baseband signals, I (in-phase) and Q (quadrature), after A / D conversion and DDC—this is the standard way to represent complex signals in digital communication (I is the real part, Q is the imaginary part). Following the correspondence of "1 physical element → 2 signals (I+Q) → 2 channels," the 8 physical elements naturally extend to: 8 elements × 2 (I / Q) = 16 signal channels.

[0070] ② Convolutional Layer 1 (DepthwiseConv):

[0071] A 3×3 depthwise separable convolutional kernel is used to process the input signal channel by channel (without cross-channel fusion) to extract local time-frequency features. The convolutional kernel parameters are randomly initialized with a stride of 1, and each end of the time dimension is padded with one zero point (referred to as "padding 1"). The output dimension is 16×256×16 (corresponding to channel × time × number of feature maps).

[0072] The calculation formula (channel-wise convolution) is formula (2):

[0073] (2)

[0074] in is the kernel weight for the i-th channel, and m is the time axis index of the kernel, m∈{0,1,2}, used to extract features of the input signal in the local spatiotemporal region (3×3 window). Let be the input signal value at time point j+m-1 of the i-th channel, where i is the input channel index (i∈{0,...,15}) and j is the time point index of the output feature (j∈{0,...,255}). Let i be the output feature value of the i-th channel at time j. For i input channel bias terms.

[0075] ③ Channel Shuffle Layer 1: The 16-channel feature map output from Convolutional Layer 1 is rearranged into 4 groups of 4 channels (16 → 4 groups of 4 channels) to solve the channel isolation problem of depthwise separable convolution and enhance the information interaction between channels. The shuffle rule is established as formula (3):

[0076] (3)

[0077] in, This is the intra-group offset, which is the relative position of the channel within the group, for example, 0~3. The number of groups in this invention is 4. The group index, i.e., the group number to which the channel belongs, is 0~3 in this invention. The channel shuffling layer forces the channel features of different groups to mix in subsequent convolutional layers through a "grouping → rearrangement" method, solving the channel isolation problem of depthwise separable convolution. The core is to achieve information complementarity between channels and improve the feature representation ability by rearranging the channel index (based on intra-group offset and group index). This invention divides 16 channels into 4 groups, i.e., G=4; ∈{0,1,2,3}; =∈{0,1,2,3}. For example, the original channel order is [0,1,2,...,15], and after shuffling it becomes [0,4,8,12,1,5,9,13,2,6,10,14,3,7,11,15] (4 channels per group, and the order between groups remains unchanged).

[0078] The calculation process is as follows:

[0079] Taking the 16-channel feature map output by convolutional layer 1 (C=16) as an example, it is grouped into G=4 groups, with each group containing 4 channels:

[0080] 1. Original Channel Index break down

[0081] The original channel sequence is [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15], each channel Decompose into ( , ):

[0082] c=0:G=0 (Group 0) =0 (0th in the group)

[0083] c=1:G=0、 =1 (the first one in the group)

[0084] c=2:G=0、 =2 (2nd in the group)

[0085] c=3:G=0、 =3 (3rd in the group)

[0086] c=4:G=1 (Group 1) =0 (0th in the group)

[0087] c=5:G=1、 =1 (the first one in the group) ...

[0089] c=15:G=3 (Group 3) =3 (3rd in the group)

[0090] 2. New channel index after mixed washing

[0091] According to the formula = ×G+ Calculate the new index for each original channel:

[0092] c=0:c′=0×4+0=0

[0093] c=1:c′=1×4+0=4

[0094] c=2:c′=2×4+0=8

[0095] c=3:c′=3×4+0=12

[0096] c=4:c′=0×4+1=1

[0097] c=5:c′=1×4+1=5 ...

[0099] c=15:c′=3×4+3=15

[0100] 3. Results of mixed washing

[0101] The final channel sequence after rinsing is as follows:

[0102] [0,4,8,12,1,5,9,13,2,6,10,14,3,7,11,15]

[0103] ④ Convolutional Layer 2 (DepthwiseConv+PointwiseConv): First, the output features of Convolutional Layer 1 (input dimension 16×256×16) are processed by a 3×3 depthwise separable convolution. The stride is set to 2 and the time dimension padding value is 1, which halves the time dimension from 256 to 128. The output intermediate feature dimension is 16×128×16 (the number of channels remains the same, the time point is compressed, and the number of feature maps remains the same). Then, the intermediate features are expanded by a 1×1 pointwise convolution (cross-channel fusion), increasing the number of channels from 16 to 32. Finally, the dimension of the output high-order global features is 32×128×16 (the number of channels is expanded, the time point remains 128, and the number of feature maps remains the same).

[0104] This design combines "depth convolution to compress the time dimension and point convolution to expand the channel dimension," which reduces temporal redundancy while enhancing the global correlation of features, providing a richer representation basis for the subsequent extraction of key features such as interference direction and SNR.

[0105] ⑤ Channel shuffling layer two: The 32-channel feature map output by convolutional layer two already contains richer spatiotemporal features (such as multipath reflection of the target, Doppler diffusion of interference, etc.). By shuffling again (32 → 8 groups × 4 channels), cross-group feature interaction is further promoted, enhancing the ability to model complex interference patterns. The 8-group × 4-channel structure facilitates subsequent global average pooling operations (the pooling layer will first locally average the 4-channel features within each group, and then globally average them), reducing information loss.

[0106] ⑥ Global Average Pooling Layer: For the 32×128×16 dimensional feature map output from convolutional layer 2 (32 for the number of channels, 128 for the time dimension, and 16 for the number of feature maps), a two-step pooling operation of "channel group averaging + global dimensionality compression" is used to extract global statistical information of the features, providing a global context for subsequent weight calculation. The specific processing logic is as follows:

[0107] Channel group averaging: Based on the “8 groups × 4 channels” structure formed by the channel mixing layer 2, the feature maps of the 4 channels in each group are locally averaged. At the same time point and the same feature map position, the feature values ​​of the 4 channels are averaged, and the 4 channels in each group are compressed into 1 channel to obtain 8×128×16 intermediate features (8 groups correspond to 8 channels, and the time point and the number of feature maps remain unchanged).

[0108] Global dimensionality compression: For the intermediate features of 8×128×16, global averaging is performed along the two dimensions of "time point (128)" and "number of feature maps (16)", that is, the feature average value of 128×16 positions is calculated, and the feature is finally compressed into a global feature vector of 8×1×1 (only 8 channel dimensions are retained, and the time and feature map dimensions are compressed to 1).

[0109] The global features extracted by this layer include key information such as the average energy of each channel (corresponding to the signal-to-interference-plus-noise ratio SNR) and phase consistency (corresponding to the direction of interference). It not only aggregates the core patterns of local spatiotemporal features, but also preserves the differences between channels. This provides global context support for the accurate correction of zero-adjustment weights in subsequent sparse fully connected layers, avoiding weight decision bias caused by local features.

[0110] ⑦ Sparse fully connected layer

[0111] Calculation of weight adjustment:

[0112] The 8-dimensional features obtained from global average pooling (output of the global pooling layer in step ⑥ is 8×1×1) are input into the fully connected layer, outputting two key results: a. 16-dimensional weight correction, used for dynamic optimization of virtual array element zeroing weights; b. Class probability distribution of interference directions (used to locate the angle of the interference source). Lightweight computation is achieved by constraining the sparsity of the fully connected layer weights through L1 regularization. The specific design is as follows: The weight adjustment amount is calculated using formula (4):

[0113] (4)

[0114] in, The output 16-dimensional weight correction amount (corresponding to the weight fine-tuning amount of 16 virtual array elements, which will be interpolated to the 32-dimensional weight correction amount in step S4). The weight parameters of the fully connected layer (matching the input feature dimension 8, not the weight adjustment amount itself); The input is an 8-dimensional global average pooling feature; Bias vector (initialized to 0).

[0115] Sparsity constraints:

[0116] During the training phase, L1 regularization is introduced (assuming L1 regularization strength λ=0.001) to constrain the sparsity of the weights W of the fully connected layer (sparse rate ≥50%, that is, the proportion of elements in W with absolute value less than the threshold ≥50%), reduce redundant computation, and adapt to FPGA hardware resources.

[0117] Loss function design (correlation of interference direction and weight correction):

[0118] The loss function needs to simultaneously optimize both the "accuracy of disturbance direction estimation" and the "accuracy of weight correction". The loss function is as follows:

[0119] (5)

[0120] in, : Classification loss for interference direction (cross-entropy). N is the sample size, and C is the number of discrete classes for the interference direction (e.g., dividing the range into 12 intervals within ±60°, C=12). The true orientation label (One-Hot encoding) for the i-th sample. Predict the probability that the i-th sample belongs to class c for the model (output by another branch of the fully connected layer). : Weighted regression loss (MSE). The optimal weight adjustment for the i-th sample (calculated offline by a traditional algorithm); This is the correction amount for the model prediction.

[0121] Sparsification reduces the computational complexity of the system and is a key step in realizing the "lightweight model + hardware acceleration" technical approach.

[0122] ⑧ The sparse fully connected layer ultimately outputs two types of results:

[0123] Interference direction estimation: a. By estimating the probability of direction categories Take the maximum value ( =30°), to obtain the angle of the interference source; b.16 dimensional value correction amount: ( ), used to fine-tune the initial zeroing weights of the virtual array elements (combined with the base weights output by MobileNet to obtain the final optimized weights).

[0124] Step S3: Implementation of Virtual Array Element Expansion

[0125] Based on time delay compensation and alignment of 8 physical array element signals, 32 virtual array elements are generated through linear interpolation, expanding the spatial degrees of freedom from 7 to 31, supporting the formation of multiple independent nulls within a ±60° range. Implementation process is detailed below. Figure 3 .

[0126] ①Time delay compensation

[0127] The physical array elements adopt a uniform linear array layout with varying element spacing. ( (Wavelength). Delay compensation uses the 0th physical element as a reference to compensate for the signal propagation delay of other physical elements relative to the 0th physical element—that is, to calculate the propagation time difference of the incident signal received by the i-th physical element (i=0,1,...,7) relative to the 0th physical element, and finally to make the phase of the desired signals received by all physical elements aligned. The method for calculating the relative propagation delay of the i-th physical element (i=0,1,...,7) is as shown in formula (6):

[0128] (6)

[0129] in, For the speed of light (3×10) 8 m / s).

[0130] Received signal for the i-th physical element (t) Perform time delay compensation to obtain the phase-aligned signal: (t)= (t- This eliminates the phase difference between array elements.

[0131] ② Specify the interpolation order

[0132] Virtual array elements are inserted between physical array elements. The interpolation order is determined. First, the number of virtual array elements is calculated as shown in formula (7).

[0133] (7)

[0134] in, The number of virtual array elements. L represents the number of physical array elements, and L represents the interpolation order (the number of virtual array elements inserted between each adjacent physical array element).

[0135] Combining the target virtual array element number 32, we substitute it into formula (7) to deduce the interpolation order:

[0136]

[0137] To simplify the engineering implementation, a hybrid interpolation strategy of "inserting 3 or 4 virtual array elements between adjacent physical array elements" is adopted: a hybrid interpolation strategy of "inserting 5 or 4 virtual array elements between adjacent physical array elements" is adopted: 5 virtual array elements are inserted between 4 fixed groups of adjacent physical array elements, and 4 virtual array elements are inserted between 3 fixed groups of adjacent physical array elements. The final total number of virtual array elements is 32, which accurately matches the target requirements. Since the distribution deviation at the middle position has the least impact on the overall array uniformity, the spatial phase consistency of the virtual array elements can be preserved to the greatest extent, which meets the core requirement of spatial zeroing for a "uniform linear array". Therefore, 5 virtual array elements are inserted at the middle interval and 4 virtual array elements are inserted at both ends. That is, 4 virtual array elements are inserted between i=0~1, i=1~2, and i=6~7, and 5 array elements are inserted between i=2~6. The final total number of virtual array elements = 4×5+3×4=20+12=32, and the total number of array elements = 32+8=40 (this invention only uses the signals of 32 virtual array elements for processing). This design avoids the engineering implementation difficulties of non-integer interpolation order and strictly meets the expansion target of 32 virtual array elements, ensuring that the spatial degrees of freedom are increased to 31.

[0138] ③ Linear interpolation virtual array elements

[0139] The signal of each virtual array element is obtained by weighted averaging of the signals of two adjacent physical array elements, with the weights determined by the relative distance between the virtual array element position and the physical array element position.

[0140] a. Interval division of virtual array element positions

[0141] Let k represent the index of the physical array element (k=0,1,...,7), corresponding to the positions of the 8 physical array elements as follows:

[0142] (8)

[0143] in If the distance between array elements is denoted as , then As the first physical array element, This is the last physical array element.

[0144] For the m-th virtual array element (m=0,1,...,31), its position It must fall between two adjacent physical array elements, that is:

[0145] (9)

[0146] (Note: Here, "physical array element" is explicitly defined as "left physical array element i and right physical array element i+1", where i is the index of the left physical array element, with values ​​(0,1,...,6) and i+1 is the index of the right physical array element, ensuring that the position of the virtual array element is constrained by the adjacent physical array element interval.)

[0147] The position of the m-th virtual array element The corresponding left physical element index i is determined by the relative position of the virtual element within the total interval. Since the total length covered by the 8 physical elements is 7d (from... When 32 virtual array elements are evenly distributed, the position of the m-th virtual array element is: (The total length is divided into 31 equal segments, with each segment spaced 7d / 31).

[0148] Therefore, the formula for calculating the left-left physical matrix element index i is:

[0149] (10)

[0150] Rounding down gives i, meaning i satisfies... The largest integer. For example, when m=4, (7×4) / 31≈0.903, rounding down gives i=0, that is, the virtual array element falls between the 0th and 1st physical array elements.

[0151] b. Calculation of interpolation weights

[0152] The signal of virtual array element m is obtained by weighted averaging of the signals of left physical array element i and right physical array element i+1. The weights must satisfy the normalization constraint "left + right = 1". As shown in formulas (11) to (13):

[0153] + =1 (11)

[0154] The weight value is determined by the relative distance between the virtual array element and its adjacent physical array element, where the weight of the left physical array element is... It is proportional to the distance from the virtual array element to the right physical array element:

[0155] (12)

[0156] in, The distance from virtual array element m to the right physical array element i+1 is given by the denominator. The fixed spacing between adjacent physical array elements; this weight design follows the "inverse distance principle" of linear interpolation: the closer a virtual array element is to its left physical array element i, the higher the weight ratio. The larger, The closer the value is to 1, the more it ensures that the virtual array element signal inherits the spatial continuity of the physical array element signal, thus avoiding interpolation distortion; the definitions of other variables are the same as before.

[0157] Right physical array element weight For the remaining proportion:

[0158] (13)

[0159] From the above formula, we can derive the virtual array element signal. The expression is formula (14):

[0160] (14)

[0161] in, , is the index of the left physical array element; and From the virtual array element position Position of the left physical array element Right physical array element position Calculation of relative distance; and It is the signal after time delay compensation for the left physical array element i and the right physical array element i+1. This ensures that the virtual array element signal inherits the phase alignment characteristics of the physical array element.

[0162] c. The final output is a 32-channel aligned virtual array element signal. Here, "output" refers to the output of the virtual array element expansion module. The 32 virtual signals generated through interpolation will serve as inputs for subsequent "spatial zeroing weight calculation" and "FPGA hardware acceleration," rather than being directly output to the receiver. These signals, having undergone delay compensation and interpolation processing, possess spatial phase characteristics consistent with the physical array element signals and can be equivalent to the received signals of 32 physical array elements, laying the foundation for the subsequent formation of multiple null traps.

[0163] Step S4: Calculation and optimization of spatial zeroing weights

[0164] By combining the interference direction estimation results with the virtual array element signals, an initial weight vector is generated using the least squares algorithm. Then, the weights are optimized using the weight correction parameters output by the improved MobileNet algorithm to suppress interference direction signals and enhance target direction signals. The implementation process is detailed below. Figure 4 .

[0165] ① Calculation of initial weight vector

[0166] Assuming the target direction The number of interference sources is K, and the direction of interference is... , j=1,2,...,K, the covariance matrix R of the received signal is estimated by formula (15):

[0167] (15)

[0168] in, Let M be the 32-dimensional virtual array element signal vector (32×1) of the nth snapshot, and M be the number of snapshots, i.e. the number of discrete samples during the observation time, which is 32. yes The conjugate transpose of . Virtual array element signal It is the result of the physical array element signal after time delay compensation and linear interpolation, which includes the superposition of target signal, interference signal and noise. The specific expression is shown in formula (16):

[0169] (16)

[0170] in, It is the target signal. It is the j-th interference source signal. It's noise.

[0171] Target direction navigation vector The definition is given in formula (17):

[0172] (17)

[0173] in, For signal frequency, The time delay from the i-th virtual array element to the target signal is denoted as . The target direction navigation vector is essentially the phase distribution of the target signal across the 32 virtual array elements, used to "guide the weights to form high gain in the target direction". As a complex vector (each element is a complex number containing phase information), its core physical meaning is "the phase distribution template of the target signal on 32 virtual array elements". The essence of weight calculation is to match the weights with this "phase template" while avoiding the phase distribution of interference signals, ultimately achieving "target enhancement and interference suppression".

[0174] Initial weight vector Calculated by the SMI algorithm, see formula (18):

[0175] (18)

[0176] in, The initial weight vector is 32×1, which matches the number of virtual matrix elements; It is the inverse of the covariance matrix, and the interference direction is suppressed by "the inverse operation on the covariance of the interference signal"; This is the step size factor (default value is 0.01) to ensure weight convergence and avoid signal saturation.

[0177] ② Weight vector correction based on MobileNet

[0178] Improve the 16-dimensional weight correction of MobileNet output It needs to be expanded to 32 dimensions (to match the initial weight dimensions). The expansion method is "adjacent correction interpolation" (using the spatial continuity of virtual array elements to map the 16-dimensional weight correction to 32 virtual array elements).

[0179] The extended 32-dimensional weight correction is used to adjust the initial weight vector, focusing on compensating for array element errors caused by channel amplitude and phase inconsistencies, as well as multipath errors caused by environmental factors. The optimized weight vector is shown in formula (19):

[0180] (19)

[0181] in, This is the learning factor (default value is 0.1), which can be adjusted online based on the real-time anti-interference effect. and Both are 32-dimensional vectors. This is the adjustment amount for the expanded 32-dimensional weight values.

[0182] ③ Output a 32-dimensional optimized weight vector Used in subsequent beamforming modules—by weighted summation with the signals of 32 virtual array elements, beamforming in the target direction. Maintain high gain in the direction of interference. A zero trap is formed to achieve anti-interference output.

[0183] Step S5: FPGA hardware acceleration execution

[0184] The weight calculation process, including virtual array element expansion and weight optimization, is mapped to the FPGA. Through parallel computing units, pipelined design, and low-precision quantization, computational efficiency is improved, achieving real-time processing (target latency ≤2ms). See the implementation flow below. Figure 5 .

[0185] ① Input preprocessing unit

[0186] The 32-channel 16-bit fixed-point virtual array element semaphores are converted into 8-bit fixed-point (sign bit + 7 decimal bits). Based on dual-port RAM cache, it supports parallel reading of burst 256 data points (bandwidth requirement: 32 channels × 8 bits × 256 points / clock cycle = 6.5536Gbps, clock frequency is set to 150MHz, consistent with the clock of subsequent MAC units).

[0187] ② Convolution calculation unit

[0188] To improve the depthwise separable convolutional layer of MobileNet, a line buffer was designed to store the three most recent input data sets (each set has 32 channels × 8 bits, corresponding to three consecutive points in the time dimension). A sliding window (3×3) extracts local regions every clock cycle. Channel-wise convolutions are computed in parallel by 16 MAC units (9 multiply-accumulate operations per channel per clock cycle), achieving a throughput of 16×9×150MHz=2.16GOPS.

[0189] ③ Channel Mixed Washing Unit

[0190] A 4×4 crossbar switch is used to achieve non-blocking rearrangement of 16 channels into 4 groups of 4 channels. Each shuffling path is delayed by 1 clock cycle to ensure real-time cross-group feature interaction.

[0191] ④ Weight Optimization Unit

[0192] It integrates a sparse matrix accelerator, stores the weight mask of the improved MobileNet output, and performs multiply-add operations only on the virtual matrix element channels corresponding to non-zero weights (e.g., 16 non-zero weights in 32-dimensional weights, reducing the amount of computation by 50%), thereby reducing FPGA resource consumption.

[0193] ⑤ Control and Status Unit

[0194] The inference process (convolution → shuffling → pooling → fully connected) is managed by a state machine, and the output signal-to-interference-plus-noise ratio (SINR) is calculated in real time, as shown in formula (20):

[0195] (20)

[0196] in, This is the noise covariance matrix. If the SINR is lower than the threshold, an online parameter fine-tuning mechanism is triggered. To optimize the conjugate transpose of the weight vector (32×1 complex vector); The target direction navigation vector (32×1 complex vector); The covariance matrix of the interference signal is a 32×32 complex matrix, estimated from the interference signal. Let be the noise covariance matrix (a 32×32 complex matrix, estimated from noise sampling during periods without signal). In this formula, the numerator is... The output power of the target signal is given by the denominator, which is the total output power of interference and noise.

[0197] ⑥ The FPGA outputs a 32-dimensional optimization weight vector through a parallel interface. (8-bit fixed-point complex vector) is directly transmitted to the subsequent beamforming module to ensure real-time weighted processing.

[0198] Step S6, Beamforming and Anti-interference Output

[0199] Based on the optimized weight vector The signals of each virtual array element are weighted and summed to form a receiving beam pointing towards the target direction and suppressing interference, and the anti-interference signal is output.

[0200] ① Weighted summation

[0201] 32-channel virtual array element signal x(n) and weight vector The beam output signal is obtained by conjugate dot product, as shown in formula (21):

[0202] (twenty one)

[0203] Where x(n) is the 32-dimensional virtual array element signal vector of the nth snapshot (a 32×1 complex vector, which is completely consistent with x(n) in formulas 15 and 16, maintaining the same sign for discrete snapshots). It is the conjugate transpose of a 32-dimensional optimized weight vector (a 1×32 complex vector).

[0204] ② Simulation performance verification

[0205] a. Radiation pattern verification: Create a deep null (gain ≤ -30dB) in the interference direction (e.g., 30°, -45°) and a beam gain ≥ 0dB in the target direction (e.g., 0°) to ensure significant attenuation of the interference signal;

[0206] b. SINR Improvement: In scenarios with multiple interference sources (such as 2 interference sources, input signal-to-interference ratio -5dB), the output SINR is improved from 10dB to over 25dB, with a significant anti-interference enhancement effect;

[0207] c. Real-time performance verification: Processing latency ≤ 2ms (total time from the input of the first snapshot signal to the generation of the first beam output signal), meeting real-time communication requirements.

[0208] The core points of this invention, and the technical points that are intended to be protected, are as follows:

[0209] 1. Improved design of the lightweight deep learning model MobileNet: To address the problems of large parameter count and difficulty in deploying traditional deep learning models on FPGA, this invention makes customized improvements to the MobileNet architecture, which can retain its original feature extraction capabilities while significantly reducing computational complexity and hardware resource consumption.

[0210] 2. Virtual Array Element Expansion Technology: This invention breaks through the limitation of traditional spatial zeroing relying on the number of physical array elements. It generates virtual array elements through the method of "delay compensation + interpolation expansion", thereby improving spatial processing capabilities.

[0211] 3. Customized FPGA hardware acceleration design: Combining the computational characteristics of the MobileNet model (such as depthwise separable convolution and sparse weights) and the requirement for parallel processing in spatial domain zeroing, a dedicated hardware acceleration architecture was designed to achieve real-time processing with low latency and low resource consumption.

[0212] 4. Dynamic Quantization and Low-Precision Calculation Strategy: To further reduce FPGA resource consumption, this invention adopts dynamic quantization technology. During model training, 32-bit floating-point numbers are used. During the inference stage, the dynamic range of the input signal is first calculated, and then the activation value is quantized into an 8-bit fixed-point number (1 sign bit + 7 decimal bits), while the weights are quantized into an 8-bit symmetric fixed-point number.

[0213] Compared with existing technologies, the advantages of this invention are mainly reflected in the following aspects:

[0214] 1. Enhanced anti-interference capability: Virtual array element expansion technology can increase the number of effective array elements by 2 to 4 times (e.g., 8 physical array elements can be expanded to 16 to 32 virtual array elements), the spatial degrees of freedom have increased from 7 to 15 to 31, and 4 to 8 independent nulls can be formed simultaneously within a range of ±60°. The multi-source suppression ratio (SIR) has also increased from 20dB in the traditional method to more than 35dB.

[0215] 2. Significantly improved real-time performance: By leveraging the lightweight MobileNet model, the computational complexity of weights is reduced from O(N³) to O(NP²) (where P is the kernel size, typically 3-5); combined with the parallel computing architecture of FPGA, the processing latency is reduced from tens of milliseconds in traditional methods (such as the RLS algorithm which takes about 50 milliseconds) to sub-millisecond levels (no more than 2 milliseconds), which fully meets the real-time requirements of electronic warfare scenarios.

[0216] 3. Significantly reduced hardware resource consumption: By combining depthwise separable convolution and sparse design, the number of model parameters can be reduced by more than 85%. With the addition of 8-bit quantization technology, storage requirements are further reduced. The dedicated FPGA acceleration architecture relies on parallel computing units and memory optimization, which reduces DSP resource consumption by 60% and BRAM consumption by 40% compared to general solutions.

[0217] 4. Excellent dynamic adaptability: The multi-task output head can support multi-dimensional learning of interference type (narrowband / wideband) and interference direction, and with the addition of online parameter fine-tuning function, it can quickly adapt to changes in the interference environment (such as interference source movement, frequency agility, etc.), and the system robustness is significantly improved compared with traditional adaptive algorithms.

[0218] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A multi-element spatial nulling anti-jamming virtual method of MobileNet architecture, characterized in that, The method includes the following steps: S1. Radio Frequency Signal Acquisition and Digital Preprocessing The radio receiver front end receives radio frequency signals through physical array antennas and converts the radio frequency signals into digital baseband signals for subsequent processing. The signal conversion includes A / D conversion, digital down-conversion, pulse compression, and clutter cancellation. S2 and MobileNet Model Improvement Design Design an improved MobileNet lightweight neural network to extract interference direction and signal-to-interference-plus-noise ratio features from the preprocessed baseband signal, estimate the interference direction, and obtain the weight correction amount; S3, Virtual Array Element Expansion Implementation Based on time delay compensation, physical array element signals are aligned, and then virtual array elements are generated through linear interpolation; S4. Spatial Zeroing Weight Calculation and Optimization By combining the interference direction estimation results with the virtual array element signal, an initial weight vector is generated using the least squares algorithm. Then, the weight is optimized using the weight correction amount output by the improved MobileNet, thereby suppressing the interference direction signal and enhancing the target direction signal. S5, FPGA hardware accelerated execution Virtual array element expansion and weight optimization are mapped to FPGA, and computational efficiency is improved through parallel computing units, pipeline design and low-precision quantization; S6, Beamforming and Anti-interference Output Based on the optimized weight vector, the signals of each virtual array element are weighted and summed to form a receiving beam pointing towards the target direction and suppressing interference, and outputting the anti-interference signal.

2. The multi-element spatial zeroing anti-interference virtual method for the MobileNet architecture as described in claim 1, characterized in that, S1 includes: a radio receiving front end receives radio frequency signals through an 8-element antenna, and needs to convert the radio frequency signals into digital baseband signals for subsequent processing; the signal conversion includes A / D conversion, digital down-conversion, pulse compression and clutter cancellation processes to achieve noise and clutter suppression and extract effective target signals; ①A / D Conversion: The radio frequency signal is down-converted to intermediate frequency by a low-noise amplifier and mixer, and then sampled by a 16-bit high-speed ADC to finally convert it into a digital intermediate frequency signal; ② Digital downconversion: The intermediate frequency signal is further downconverted to the baseband, and high-frequency components are filtered out by a digital filter to output two 16-bit fixed-point baseband signals, I and Q; ③ Pulse compression: A matched filter is used to compress the pulse signal, suppress sidelobe signals, and improve the signal-to-noise ratio of target detection; ④ Clutter cancellation: For ground / sea clutter, an adaptive filter is used to estimate the clutter components and eliminate the clutter components from the received signal to achieve the goal of static clutter interference suppression.

3. The multi-element spatial zeroing anti-interference virtual method for the MobileNet architecture as described in claim 2, characterized in that, The impulse response of the matched filter is the time-reversed conjugate of the transmitted signal, and the calculation formula is expressed as formula (1). （1） in, Let s(t) be the impulse response of the matched filter, s(t) be the time-domain waveform of the transmitted signal, and t be time. It is the time-reversed conjugate of the transmitted signal, and its time length is the same as s(t). It is finite in length and can be implemented as an impulse response output in FPGA hardware through delay lines and multipliers.

4. The multi-element spatial zeroing anti-interference virtual method for the MobileNet architecture as described in claim 1, characterized in that, S2 includes: designing and improving the MobileNet lightweight neural network to extract interference direction and signal-to-interference-plus-noise ratio features from the preprocessed baseband signal, providing a basis for subsequent weight calculation, specifically including: ① Input layer: Channel C is positioned as 16, and the 16-channel I / Q signal is quantized into 8-bit fixed point. The input dimension of channel × time point is 16 × 256. ② Convolutional Layer 1: Uses depthwise separable convolutional kernels to process the input signal channel by channel and extract local time-frequency features; the convolutional kernel parameters are randomly initialized, the stride is 1, and one zero point is filled at each end of the time dimension. The output dimension is 16×256×16 (channels × time × feature mapping number). The channel-wise convolution formula (2) is: （2） in is the kernel weight for the i-th channel, and m is the time axis index of the kernel, m∈{0,1,2}, used to extract features of the input signal in the local spatiotemporal region; Let be the input signal value at time point j+m-1 of the i-th channel, where i is the input channel index (i∈{0,...,15}) and j is the time point index of the output feature (j∈{0,...,255}). Let i be the output feature value of the i-th channel at time j. For i input channel bias terms; ③ Channel shuffling layer one: The 16-channel feature map output from convolutional layer one is rearranged into 4 groups × 4 channels to establish the shuffling rule as formula (3): （3） in, This is the intra-group offset, which is the relative position of the channel within the group. For the number of groups, The group index is the group number to which the channel belongs. The channel shuffling layer forces the channel features of different groups to be mixed in subsequent convolutional layers through "grouping → rearrangement". ④ Convolutional Layer 2: First, the output features of Convolutional Layer 1 are processed through depthwise separable convolution. The stride is set to 2 and the time dimension padding value is 1, which halves the time dimension from 256 to 128, and the output intermediate feature dimension is 16×128×16. Then, the intermediate features are expanded through 1×1 pointwise convolution, increasing the number of channels from 16 to 32. Finally, the dimension of the high-order global feature is 32×128×16. ⑤ Channel shuffling layer 2: The 32-channel feature map output by the second convolutional layer already contains richer spatiotemporal features. By shuffling again and rearranging it into 8 groups × 4 channels, cross-group feature interaction is further promoted, and the ability to model complex interference patterns is strengthened. ⑥ Global average pooling layer: For the 32×128×16 dimension feature map output by the second convolutional layer, the global statistical information of the features is extracted through a two-step pooling operation of "channel group averaging + global dimension compression", which provides a global context for subsequent weight calculation. Channel group averaging: Based on the "8 groups × 4 channels" structure formed by the channel mixing layer 2, the feature maps of the 4 channels in each group are locally averaged. That is, at the same time point and the same feature map position, the feature values ​​of the 4 channels are averaged, and the 4 channels in each group are compressed into 1 channel to obtain 8×128×16 intermediate features. Global Dimension Compression: For the intermediate features of 8×128×16, perform global averaging along the two dimensions of "time point" and "number of feature maps", that is, calculate the feature average value of 128×16 positions, and finally compress the features into a global feature vector of 8×1×1. ⑦ Sparse fully connected layer Calculation of weight adjustment: The 8×1×1 global feature vector obtained after global average pooling is input into the fully connected layer, and two key outputs are generated: The 16-dimensional weight correction is used for the dynamic optimization of the zeroing weights of virtual array elements; The probability distribution of the interference direction category is used to locate the angle of the interference source; Lightweight computation is achieved by constraining the sparsity of the weights in the fully connected layer using L1 regularization; the specific design is as follows: The weight adjustment amount is calculated using formula (4): （4） in, The output 16-dimensional weight correction amount; The weight parameters of the fully connected layer; The input is an 8-dimensional global average pooling feature; Bias vector; Sparsity constraints: L1 regularization is introduced during the training phase to constrain the sparsity of the weights W of the fully connected layer. Loss function design: The loss function needs to simultaneously optimize both the "accuracy of disturbance direction estimation" and the "accuracy of weight correction". The loss function is as follows: （5） in, : Disturbance direction classification loss; N is the sample size, C is the number of discrete categories in the interference direction. The true orientation label for the i-th sample; Predict the probability that the i-th sample belongs to class c for the model; Weighted regression loss MSE; Let be the optimal weight adjustment amount for the i-th sample; This is the correction amount for the model prediction; ⑧ The sparse fully connected layer ultimately outputs two types of results: Interference direction estimation: by estimating the probability of direction categories Take the maximum value to obtain the angle of the interference source; 16-dimensional weight value correction amount , used to fine-tune the initial zeroing weights of virtual array elements.

5. The multi-element spatial zeroing anti-interference virtual method for the MobileNet architecture as described in claim 4, characterized in that, S3 includes: ①Time delay compensation The physical array elements adopt a uniform linear array layout with element spacing of [missing information]. , The wavelength is used as the reference for time delay compensation. The time delay compensation is based on the 0th physical element and compensates for the signal propagation delay of other physical elements relative to the 0th physical element. That is, the propagation time difference of the incident signal received by the i-th physical element (i=0,1,...,7) relative to the 0th physical element is calculated, so that the phase of the desired signal received by all physical elements is finally aligned. The relative propagation delay of the i-th physical element is calculated as shown in formula (6): （6） in, At the speed of light, The incident direction angle of the target signal; Received signal for the i-th physical element (t) Perform time delay compensation to obtain the phase-aligned signal: (t)= (t- This eliminates the phase difference between array elements; ② Specify the interpolation order Virtual array elements are inserted between physical array elements. The interpolation order is determined. First, the number of virtual array elements is calculated as shown in formula (7). （7） in, The number of virtual array elements. L represents the number of physical array elements and L is the interpolation order. Combining the target virtual array element number 32, we substitute it into formula (7) to deduce the interpolation order: ③ Linear interpolation virtual array elements The signal of each virtual array element is obtained by weighted averaging of the signals of two adjacent physical array elements, and the weight is determined by the relative distance between the virtual array element position and the physical array element position. a. Interval division of virtual array element positions Let k denote the index of the physical array element, k=0,1,...,7, corresponding to the positions of the 8 physical array elements as follows: （8） in If the distance between array elements is denoted as , then As the first physical array element, This is the last physical array element; For the m-th virtual array element, m=0,1,...,31, its position... It must fall between two adjacent physical array elements, that is: （9） The position of the m-th virtual array element The corresponding left physical element index i is determined by the relative position of the virtual element within the total interval; since the total length covered by the 8 physical elements is 7d, when the 32 virtual elements are evenly distributed, the position of the m-th virtual element is... ; Therefore, the formula for calculating the left-left physical matrix element index i is: （10） Rounding down gives i, meaning i satisfies... The largest integer; b. Calculation of interpolation weights The signal of virtual array element m is obtained by weighted averaging of the signals of left physical array element i and right physical array element i+1. The weights must satisfy the normalization constraint "left + right = 1". As shown in formulas (11) to (13): + =1 （11） The weight value is determined by the relative distance between the virtual array element and its adjacent physical array element, where the weight of the left physical array element is... It is proportional to the distance from the virtual array element to the right physical array element: （12） in, The distance from virtual array element m to the right physical array element i+1 is given by the denominator. The fixed spacing between adjacent physical array elements; this weight design follows the "inverse distance principle" of linear interpolation: the closer a virtual array element is to its left physical array element i, the higher the weight ratio. The larger, The closer it is to 1, the more it ensures that the virtual array element signal inherits the spatial continuity of the physical array element signal and avoids interpolation distortion; Right physical array element weight For the remaining proportion: （13） From the above formula, we can derive the virtual array element signal. The expression is formula (14): （14） in, , is the index of the left physical array element; and From the virtual array element position Position of the left physical array element Right physical array element position Calculation of relative distance; and It is the signal after time delay compensation of the left physical array element i and the right physical array element i+1; c. The final output is a 32-channel aligned virtual array element signal. The 32 virtual signals generated by interpolation will be used as inputs for subsequent "spatial zeroing weight calculation" and "FPGA hardware acceleration".

6. The multi-element spatial zeroing anti-interference virtual method for the MobileNet architecture as described in claim 5, characterized in that, To simplify the engineering implementation, a hybrid interpolation strategy of "inserting 5 or 4 virtual array elements between adjacent physical array elements" is adopted: 5 virtual array elements are inserted between 4 fixed groups of adjacent physical array elements, and 4 virtual array elements are inserted between 3 fixed groups of adjacent physical array elements, resulting in a total of 32 virtual array elements, which accurately matches the target requirements; specifically, 5 virtual array elements are inserted in the middle interval and 4 virtual array elements are inserted at both ends, i.e., 4 virtual array elements are inserted between i=0~1, i=1~2, and i=6~7, and 5 array elements are inserted between i=2~6, resulting in a total number of virtual array elements = 4×5+3×4=20+12=32.

7. The multi-element spatial zeroing anti-interference virtual method for the MobileNet architecture as described in claim 5, characterized in that, S4 includes: ① Calculation of initial weight vector Assuming the incident direction angle of the target signal The number of interference sources is K, and the direction of interference is... , j=1,2,...,K, the covariance matrix R of the received signal is estimated by formula (15): （15） in, Let M be the 32-dimensional virtual array element signal vector of the nth snapshot, and M be the number of snapshots, i.e. the number of discrete samples within the observation time, which is 32. yes The conjugate transpose; virtual array element signal It is the result of the physical array element signal after time delay compensation and linear interpolation, which includes the superposition of target signal, interference signal and noise. The specific expression is shown in formula (16): （16） in, It is the target signal. It is the j-th interference source signal. It's noise; Target direction navigation vector The definition is given in formula (17): （17） in, For signal frequency, The time delay from the i-th virtual array element to the target signal; the target direction navigation vector is essentially the phase distribution of the target signal on the 32 virtual array elements, used to "guide the weights to form high gain in the target direction"; As a complex vector, its core physical meaning is "the phase distribution template of the target signal on 32 virtual array elements". The essence of weight calculation is to match the weight with this "phase template" while avoiding the phase distribution of interference signals, and finally achieve "target enhancement and interference suppression". Initial weight vector Calculated by the SMI algorithm, see formula (18): （18） in, The initial weight vector is dimensional and matches the number of elements in the virtual matrix; It is the inverse of the covariance matrix, and the interference direction is suppressed by "the inverse operation on the covariance of the interference signal"; Step size factor; ② Weight vector correction based on MobileNet Improve the 16-dimensional weight correction of MobileNet output It needs to be expanded to 32 dimensions, and the expansion method is "adjacent correction interpolation"; The extended 32-dimensional weight correction is used to adjust the initial weight vector. The optimized weight vector is shown in formula (19): （19） in, The learning factor is adjusted online based on the real-time anti-interference effect. and Both are 32-dimensional vectors. This is the adjustment amount for the expanded 32-dimensional weight values; ③ Output a 32-dimensional optimized weight vector Used in subsequent beamforming modules; by weighted summation with 32 virtual array element signals, beamforming is achieved in the target direction. Maintain high gain in the direction of interference. A zero trap is formed to achieve anti-interference output.

8. The multi-element spatial domain zeroing anti-interference virtual method for the MobileNet architecture as described in claim 7, characterized in that, S5 includes: ① Input preprocessing unit The 32-channel 16-bit fixed-point virtual array element signal is converted into 8-bit fixed-point signal, and based on dual-port RAM cache, it supports parallel reading of burst 256-point data. ② Convolution calculation unit To improve the depthwise separable convolutional layer of MobileNet, a row buffer is designed to store the three most recent sets of input data, a sliding window extracts local regions every clock cycle, and channel-wise convolution is computed in parallel by 16 MAC units. ③ Channel Mixed Washing Unit A 4×4 cross switch is used to achieve non-blocking rearrangement of 16 channels into 4 groups of 4 channels, with each shuffling path delayed by 1 clock cycle to ensure real-time cross-group feature interaction. ④ Weight Optimization Unit An integrated sparse matrix accelerator stores the weight mask of the improved MobileNet output, and performs multiply-accumulate operations only on the virtual matrix channel corresponding to non-zero weights; ⑤ Control and Status Unit The inference process is managed by a state machine: convolution → shuffling → pooling → fully connected, and the output signal-to-interference-plus-noise ratio is calculated in real time. ⑥ The FPGA outputs a 32-dimensional optimization weight vector through a parallel interface. The data is directly transmitted to the subsequent beamforming module to ensure real-time weighted processing.

9. The multi-element spatial zeroing anti-interference virtual method for the MobileNet architecture as described in claim 8, characterized in that, The signal-to-interference-to-noise ratio is shown in formula (20): （20） in, This is the noise covariance matrix; if the SINR is lower than the threshold, an online parameter fine-tuning mechanism is triggered. To optimize the conjugate transpose of the weight vector; Navigation vector for the target direction; The covariance matrix of the interference signal is obtained by estimating the interference signal. The noise covariance matrix is ​​estimated from noise sampling during periods without signal; in this formula, the numerator is... The output power of the target signal is given by the denominator, which is the total output power of interference and noise.

10. The multi-element spatial zeroing anti-interference virtual method for the MobileNet architecture as described in claim 9, characterized in that, S6 includes: 32-channel virtual array element signal x(n) and weight vector The beam output signal is obtained by conjugate dot product, as shown in formula (21): （21） Where x(n) is the 32-dimensional virtual array element signal vector of the nth snapshot; It is the conjugate transpose of a 32-dimensional optimized weight vector.

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