BPSK signal processing method based on circular antenna array and adaptive beam forming

Abstract

The invention discloses a BPSK (Binary Phase Shift Keying) signal processing method based on a circular antenna array and adaptive beam forming, and relates to the technical field of array signal processing and digital communication simulation. The method comprises the following steps: constructing a full-link integrated simulation environment, generating a BPSK radio frequency signal formed by root raised cosine, superposing noise and constructing a steering vector to form an array signal; and evaluating signal-to-noise ratio gains and pointing precision of different array configurations by traversing a total space angle, and determining an optimal array. For segmented dynamic input signals, weight vectors of various adaptive criteria are calculated in real time to perform dynamic beam forming and demodulation. And the system optimizes the optimal adaptive criterion according to the output signal-to-noise ratio and the pointing precision index. Closed-loop verification from modulation emission and dynamic beam forming to demodulation evaluation is realized, array configuration and algorithm can be cooperatively optimized under a high-fidelity dynamic channel, signal-to-noise ratio gain and pointing precision of a system are remarkably improved, and reliable simulation reference and engineering guidance are provided for real-time array processing.

Description

Technical Field

[0001] This invention relates to the field of array signal processing and digital communication simulation technology, and in particular to a BPSK signal processing method based on a circular antenna array and adaptive beamforming. Background Technology

[0002] Array signal processing, as an important research branch in the field of electronic information, has significant applications in a wide range of fields such as information communication, radar detection, and navigation and positioning. It involves arranging a group of antennas and other sensors into an array according to a specific geometric relationship, and using this array to receive signals from signal sources such as space fields. After processing, it aims to enhance useful signals, reduce noise interference, lower bit error rate, and improve bandwidth utilization. Digital beamforming (DBF) is the core component of array signal processing. The input to the antenna array typically comes from analog or digital signals in space; therefore, beamforming is also known as spatial filtering. It weights and sums the array signals, concentrating the gain in the same direction, thereby achieving high gain and high accuracy in a specific or optimal direction, and enabling complex applications such as information extraction, radar detection, and navigation and positioning.

[0003] In existing technologies, the workflow typically focuses on the theoretical derivation and modular simulation verification of the beamforming algorithm itself. This involves proposing or improving an adaptive criterion (such as LCMV, MVDR) or optimization method (such as diagonal loading, robust design), and then verifying the algorithm's performance in areas such as pattern synthesis, interference suppression, or convergence speed in a simulation environment using ideal or typical signal models as input. However, existing technologies have certain limitations, exhibiting deficiencies and gaps in terms of technical integration, engineering guidance, and system innovation. The integration of technologies needs to be improved, and there is a lack of system-level solutions: existing technologies mostly focus on the simulation of single algorithm modules, and there are few technical solutions that incorporate the complete signal transmission links in actual use environments such as communication signal modulation into the simulation verification and evaluation system, or complete solutions that organically combine and co-simulate multiple technical aspects such as array beamforming processing and end-to-end performance evaluation. The engineering guidance is relatively indirect, lacking a clear design path and quantitative indicators: For application scenarios with increasingly higher frequencies and more important real-time performance, existing simulation technologies lack a process of directly transferring clear and quantifiable system-level performance indicators to design goals and evaluation standards. They mostly stay at algorithm design, comparison and verification, and fail to form a clear engineering design path from algorithm performance to system indicators in the actual engineering environment. In terms of overall and system innovation, there is a lack of deep integration and optimization between algorithms and modules from a macro perspective: most focus on single aspects such as algorithm design or a certain dimension of performance, and rarely integrate the entire process of signal modulation and demodulation, array configuration, adaptive criteria and beamforming algorithm to evaluate practical performance. There is a lack of deep integration with multi-dimensional system performance evaluation at a macro level, and the implementation of cross-module system-level optimization at the overall level. Replacing simple array gain with an overall signal-to-noise ratio gain index that considers all aspects is relatively unfavorable for considering the mutual influence between various aspects and obtaining a more globally optimal system design scheme. Summary of the Invention

[0004] The purpose of this invention is to provide a BPSK signal processing method based on a circular antenna array and adaptive beamforming, which aims to solve or improve at least one of the above-mentioned technical problems.

[0005] To achieve the above objectives, the present invention provides the following solution: A BPSK signal processing method based on a circular antenna array and adaptive beamforming includes: A periodic BPSK baseband signal is generated, which is then processed using root-raised cosine pulse shaping and up-converted twice to RF to generate an RF signal. Gaussian white noise is used to generate the noise matrix of the radio frequency signal, and the steering vector of each antenna array is constructed. The combination of these vectors generates the array signal matrix. The beam signals are obtained by performing conventional beamforming on each array signal matrix. After down-conversion, low-pass filtering, coherent demodulation, and matched filtering on the beam signals, sampling and decision are performed to obtain the output bit stream. By traversing the entire space angle, the output signal-to-noise ratio of each antenna array is calculated. Based on the beam response characteristics, the signal-to-noise ratio gain, pointing accuracy, and discrimination are calculated. The performance of each antenna array is analyzed to determine the optimal array. Generate segmented dynamic input signals, calculate the variable steering vector of the optimal array, and generate segmented dynamic array signal matrices; The weight vectors of each adaptive criterion are generated in real time based on the dynamic input signal and the dynamic array signal matrix. Based on the weight vectors of each adaptive criterion, beamforming is performed on the dynamic array signal matrix to generate dynamic beam signals, which are then restored to binary bit streams to generate dynamic output signals. Based on the weight vector of each adaptive criterion, the entire space angle is traversed, the output signal-to-noise ratio of each adaptive criterion is calculated, and the signal-to-noise ratio gain and pointing accuracy are calculated. The adaptive criterion with the largest signal-to-noise ratio gain and the smallest pointing accuracy is selected as the optimal criterion. The BPSK signal is processed using the optimal array and optimal criteria.

[0006] Furthermore, a periodic BPSK baseband signal is generated, which is then processed using root-raised cosine pulse shaping and up-converted twice to RF to generate an RF signal, including: A periodic alternating code pattern is used as the original input bit stream to generate the input bit stream; Constellation mapping operation using binary phase shift keying converts the input bitstream into a bipolar baseband symbol sequence; The bipolar baseband symbol sequence is subjected to root-raised cosine pulse shaping to generate a continuous-time baseband pulse signal; Complex exponential modulation is used to shift the baseband pulse signal to the intermediate frequency band to generate an intermediate frequency signal; A secondary upconversion mechanism is used to shift the spectrum of the intermediate frequency signal to generate a radio frequency signal.

[0007] Furthermore, Gaussian white noise is used to generate the noise matrix of the radio frequency signal, and the steering vectors of each antenna array are constructed. These are then combined to generate the array signal matrix, including: Based on the radio frequency signal, uniform spatial additive white Gaussian noise is introduced and its power is normalized to generate a noise matrix. The steering vector for each antenna array is constructed, and its expression is: In the formula, These are the azimuth angle and elevation angle of the signal direction, respectively; The wavelength of the radio frequency signal; For the first The distance between each array element and the origin of the coordinate system; The unit vector upwards from the signal at the 1st The projection of each array element in the direction of its location; The steering vector is multiplied by the radio frequency signal and then the noise matrix is ​​added to obtain the array signal matrix at the input.

[0008] Furthermore, conventional beamforming is performed on each array signal matrix to obtain beam signals. After down-conversion, low-pass filtering, coherent demodulation, and matched filtering, the beam signals are sampled and decided to obtain the output bit stream, including: Digital beamforming technology is used to perform spatial filtering on the array signal matrix to generate beam signals; The beam signal is mixed with the intermediate frequency to generate a complex intermediate frequency signal; A low-pass filter is used to remove high-frequency spurious components and out-of-band noise from the complex intermediate frequency signal, generating a useful intermediate frequency signal. A local real carrier wave is used to coherently demodulate the intermediate frequency useful signal to generate a baseband signal; Matched filtering is applied to the baseband signal to maximize the output signal-to-noise ratio and eliminate inter-symbol interference, resulting in a bipolar baseband signal. By employing optimal timing sampling and threshold decision, the bipolar baseband signal is recovered into a binary bit stream, generating the output bit stream.

[0009] Furthermore, by traversing the entire spatial angle, the output signal-to-noise ratio of each antenna array is calculated. Based on the beam response characteristics, the signal-to-noise ratio gain, pointing accuracy, and discrimination are calculated. The performance of each antenna array is analyzed to determine the optimal array, including: The output signal-to-noise ratio of each antenna array is calculated by traversing all angles in space. Based on the beam response characteristics, the signal-to-noise ratio gain and pointing accuracy are calculated, and the antenna array with the largest signal-to-noise ratio gain and the smallest pointing accuracy is selected as the optimal array.

[0010] Furthermore, by traversing the entire spatial angle, the output signal-to-noise ratio of each antenna array is calculated, including: The beam is directed across the entire space, a weighted vector is constructed for each direction, and beamforming is performed on the array signal matrix X and noise matrix N respectively to generate the beam signal. and noise ; The output signal-to-noise ratio for each direction is calculated using the power separation method, and the expression is: In the formula, This is the total output power; Output noise power; This is for the output signal-to-noise ratio.

[0011] Furthermore, a segmented dynamic input signal is generated, the variable steering vector of the optimal array is calculated, and a segmented dynamic array signal matrix is ​​generated, including: Divide the time axis into equal parts and generate dynamic input signals according to different incident angles; The dynamic input signal is grouped, and the azimuth and elevation angles corresponding to each group are generated to generate dynamic incident angle data. Based on the dynamic incident angle data, a time-varying steering vector for the optimal array is generated; Based on the group length, a time window is defined, local data of the radio frequency signal and noise matrix are extracted, and combined with the time-varying steering vector to generate a local array signal matrix. After merging all local array signal matrices, a dynamic array signal matrix is ​​obtained.

[0012] Furthermore, based on the dynamic input signal and the dynamic array signal matrix, the weight vectors of each adaptive criterion in real time include: In conventional beamforming, the weight vector is the guide vector corresponding to the beam direction, expressed as: The maximum signal-to-noise ratio criterion aims to maximize the output signal-to-noise ratio, and its expression is: In the formula, To output signal-to-noise ratio; The weight vector; This is the noise matrix; For statistical expectation calculation; The complex amplitude of the signal; It is a radio frequency signal; Output signal-to-noise ratio To find the maximum value, the expression for the weight vector is: In the formula, The weight vector for the maximum signal-to-noise ratio criterion; Noise matrix covariance; To minimize the value and prevent covariance Zero; It is the identity matrix; It is a dynamic guiding vector; The minimum mean square error criterion aims to minimize the mean square error of both the beam output and the desired reference signal. Its expression is: In the formula, Let the mean squared error cost function be used. For statistical expectation calculation; This is the desired reference signal; It is a local dynamic array signal matrix; make Taking the minimum value, the weight vector expression for the minimum mean square error criterion is: In the formula, The weight vector for the minimum mean square error criterion; The covariance matrix of the dynamic input signal; Covariance matrix With expected reference signal The cross-correlation matrix between them; The minimum variance criterion for linear constraints has the following expression for the weight vector: In the formula, This is the weight vector for the minimum variance criterion under linear constraints.

[0013] Furthermore, based on the weight vectors of each adaptive criterion, beamforming is performed on the dynamic array signal matrix to generate a dynamic beam signal, which is then restored to a binary bit stream to generate a dynamic output signal, including: The expression for generating dynamic beam signals is: In the formula, The dynamic beam signal of the i-th adaptive criterion; Total number of time groups; Let be the conjugate transpose weight vector of the i-th criterion in the k-th group; Let k be the local array signal matrix of the kth group; The length of the time window; The dynamic beam signals corresponding to each adaptive criterion are restored into binary bit streams to generate dynamic output signals.

[0014] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: This invention discloses a BPSK signal processing method based on a circular antenna array and adaptive beamforming. The method achieves closed-loop verification from signal modulation and transmission, array reception, adaptive beamforming to demodulation evaluation by constructing a full-link integrated simulation environment. This scheme can perform collaborative optimization and quantitative evaluation of array configuration, weight vector algorithm, and system signal-to-noise ratio under high-fidelity dynamic channel conditions.

[0015] It effectively solves the beam pointing deviation problem in complex environments, significantly improves the system's signal-to-noise ratio gain and beam pointing accuracy, and enhances anti-interference capabilities.

[0016] It provides multi-dimensional performance evaluation metrics, offering solid data support for algorithm optimization based on different adaptive criteria (such as MSNR, MMSE, LCMV, etc.).

[0017] The system is designed to be comprehensive and closely resembles real-world engineering scenarios. It can serve as a simulation benchmark and verification platform for high-frequency real-time array processing systems, significantly reducing R&D trial-and-error costs and accelerating the engineering implementation process. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic flowchart of the method of the present invention; Figure 2 This is a schematic diagram showing the positions of each antenna array element in this embodiment; Figure 3 This is a schematic diagram illustrating the principle of digital beamforming in this embodiment; Figures 4-9 This is a comparison diagram of the dual waveforms of the input bit stream and the output bit stream for each antenna array in this embodiment; Figures 10-15 This is a heatmap showing the relationship between the signal-to-noise ratio gain of each antenna array and the azimuth and elevation angles in this embodiment. Figure 16 This is a schematic diagram comparing the dynamic input signals and dynamic output signals corresponding to each adaptive criterion in this embodiment; Figure 17 This is a timing diagram of the signal-to-noise ratio gain corresponding to each adaptive criterion in this embodiment; Figure 18 This is a heatmap showing the relationship between the signal-to-noise ratio gain of each adaptive criterion and the azimuth and elevation angles when stationary in this embodiment. Figure 19 This is a heatmap showing the relationship between the signal-to-noise ratio gain of each adaptive criterion and the azimuth and elevation angles when the azimuth angle shifts in this embodiment. Figure 20 This is a heatmap showing the relationship between the signal-to-noise ratio gain of each adaptive criterion and the azimuth and pitch angles when the pitch angle shifts in this embodiment. Figure 21 This is a heatmap showing the relationship between the signal-to-noise ratio gain of each adaptive criterion and the azimuth and elevation angles when both the azimuth and elevation angles are offset in this embodiment. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] The purpose of this invention is to provide a BPSK signal processing method based on a circular antenna array and adaptive beamforming, which aims to solve or improve at least one of the above-mentioned technical problems.

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] like Figure 1As shown, this invention provides a BPSK signal processing method based on a circular antenna array and adaptive beamforming, comprising: This embodiment was performed in the MATLAB simulation environment. The input signal modulation method was selected as Binary Phase Shift Keying (BPSK) digital modulation, with 8 sampling points per symbol and an intermediate frequency (IF) of 70MHz. According to the Nyquist criterion, to effectively suppress spectral aliasing and ensure distortion-free signal recovery, the sampling rate was set to four times the IF, i.e., 280MHz; the corresponding minimum discrete interval of the time axis was set to the reciprocal of the sampling rate.

[0024] In the antenna array assembly parameters, the element spacing should be set to half the wavelength of the incident signal. For an array design using a 70MHz intermediate frequency signal, the corresponding wavelength is 4.29 meters, and the half-wavelength spacing is 2.14 meters. This results in an excessively large array physical size, making it difficult to meet the space constraints of a laboratory setting and the channel synchronization requirements of the FPGA hardware. Therefore, an RF up-conversion mechanism is introduced, setting the RF frequency to 2GHz, with a corresponding spacing of approximately 7.5cm.

[0025] like Figure 2 As shown, the array configurations are six commonly used array types: an eight-element uniform linear array, a 4×4 uniform L-shaped array, an eight-element uniform circular array, a 2×2 four-element uniform square array, a 2×4 eight-element uniform rectangular array, and a seven-element uniform hexagonal array consisting of six surrounding array elements and one central array element.

[0026] The adaptive criteria adopted are the maximum signal-to-noise ratio (MSNR) criterion, the minimum mean square error (MMSE) criterion, and the linearly constrained minimum variance (LCMV) criterion.

[0027] This embodiment employs a modular, independent modeling software architecture strategy. Given the six array configurations and the number of array elements... To avoid logical redundancy and potential calculation errors caused by multiple conditional branches (If-Else) or complex nested loops in a single program, this embodiment establishes an independent simulation script file for each array configuration, in order to avoid significant differences in spatial coordinate matrices.

[0028] Parameter instantiation operations include: The scripts define an octagonal uniform linear array, an octagonal uniform circular array, and a 2×4 uniform rectangular array. The scripts for 4×4 uniform L-shaped arrays and seven-element uniform hexagonal arrays are set. The fourth one defines the number of array elements. .

[0029] Based on the aforementioned sampling rate of 280MHz, a discrete-time axis for simulation is constructed. According to the Nyquist sampling theorem, the time resolution is set to the reciprocal of the sampling period. The left endpoint of the time axis is set to 0, and the right endpoint is the total length of the signal. To reduce computation and facilitate waveform observation, the right endpoint is set to... Therefore, the total number of time points is T = 28000.

[0030] Step 1: Generate a periodic BPSK baseband signal, perform root-raised cosine pulse shaping, and up-convert twice to RF to generate an RF signal, including: Step 11: Calculate the total number of theoretical symbols based on the total number of time points and the number of sampling points per symbol. Then, round down the total number of theoretical symbols to determine the initial number of valid symbols. Use a periodic alternating code pattern (i.e., a "0-1-0-1..." sequence) as the original input bitstream to generate the input bitstream, including: The expression for the initial number of significant signs is: In the formula, The initial number of valid symbols; The total number of theoretical symbols; This is a round-down operation; This represents the total number of time points; And the number of sampling points per symbol.

[0031] The expression for the input bitstream is: In the formula, This is the input bit stream.

[0032] Step 12, using binary phase shift keying (BPSK) constellation mapping operation, converts the input bitstream into a bipolar baseband symbol sequence, including: Based on the BPSK modulation principle, logic "0" and logic "1" are mapped to two opposite polarity levels with a phase difference, generating a bipolar baseband symbol sequence, expressed as: In the formula, It is a bipolar baseband symbol sequence; This is the input bit stream.

[0033] In the above steps, the original logic bit 0 is mapped to -1; the original logic bit 1 remains +1. The resulting bipolar baseband symbol sequence is a bipolar baseband symbol sequence with zero mean and normalized power. This eliminates the DC component and meets the power efficiency requirements of the RF transmitter.

[0034] Step 13: Perform root-raised cosine (RRC) pulse shaping on the bipolar baseband symbol sequence to generate a continuous-time baseband pulse signal, including: The expression for the baseband pulse signal is: In the formula, It is a baseband pulse signal; It is a bipolar baseband symbol sequence; The impulse response of the rooted cosine pulse shaping filter is shown in this embodiment with a roll-off factor of 0.5. The symbol period is 8 times the bit period in this embodiment, corresponding to 8 sampling points per symbol.

[0035] The above steps are processed in a digital simulation environment as follows: Based on the set roll-off factor and cutoff length (corresponding to a delay of 4 symbol periods), a discretized root-raised cosine filter impulse response sequence is constructed. The bipolar baseband symbol sequence is further oversampled by 8 times, i.e., inserted between adjacent symbols. A zero value is generated to produce an oversampling rate sequence, which is then matched to the system sampling rate. The oversampled sequence is linearly convolved with the impulse response sequence of the root-raised cosine filter (using a sliding summation) to output the final baseband pulse signal. .

[0036] Step 14: The baseband pulse signal is shifted to the intermediate frequency band using complex exponential modulation to generate an intermediate frequency signal, including: According to Euler's formula, sinusoidal carrier modulation can be transformed into a dot product operation in the complex domain. The expression for the intermediate frequency signal is: In the formula, It is an intermediate frequency signal; It is a baseband pulse signal; The imaginary unit; This is the intermediate frequency.

[0037] The above steps are processed in a digital simulation environment as follows: Construction and Timeline Equal-length complex number sequences It also contains information on both in-phase (I) and quadrature (Q) components.

[0038] The baseband pulse signal is multiplied element-by-element by a complex sequence to generate an intermediate frequency signal. .

[0039] Compared to traditional trigonometric function multiplication, complex number multiplication can be efficiently implemented in digital signal processors (DSPs) or high-performance computing units through parallel matrix operations, which significantly reduces the computational latency when processing large-scale array signals.

[0040] Step 15: Using a secondary up-conversion mechanism, the intermediate frequency signal is spectrum-shifted to generate a radio frequency signal, including: In the formula, It is a radio frequency signal; It is an intermediate frequency signal; This is the intermediate frequency; Radio frequency; This is the local oscillator frequency interpolation for the second mixing.

[0041] The above steps are processed in a digital simulation environment as follows: By constructing a frequency of The complex exponential local oscillator sequence is used to generate a radio frequency signal by performing point-by-point complex multiplication with the intermediate frequency signal. This is the complex radio frequency baseband equivalent signal carrying complete phase and amplitude information. It retains the original BPSK modulation characteristics and also possesses the spatial attributes suitable for 2 GHz band array propagation, and can be directly used as the input excitation for subsequent multi-channel spatial channel models.

[0042] Step 2: Generate the noise matrix of the radio frequency signal using Gaussian white noise, construct the steering vector of each antenna array, and combine them to generate the array signal matrix, including: Step 21: Based on the radio frequency signal, introduce uniform spatial additive white Gaussian noise and perform power normalization to generate a noise matrix, including: The average power of a radio frequency signal is calculated using the following expression: In the formula, Average power; This represents the total number of time points; It is a radio frequency signal; Based on the target signal-to-noise ratio, the average noise power of a single array element is calculated using the following expression: In the formula, The average noise power of a single array element; The target signal-to-noise ratio; Based on the average noise power of a single array element, a noise matrix is ​​constructed, expressed as follows: In the formula, This is the noise matrix; and For Gaussian white noise components, it represents... A standard normal random matrix of dimension , where are the in-phase and quadrature components of the noise, respectively; This represents the number of array elements.

[0043] Step 22, construct the steering vector for each antenna array, including: The element spacing is set to half the wavelength of the radio frequency signal, expressed as: In the formula, The spacing between array elements; The wavelength of the radio frequency signal; Radio frequency; The speed of light; Establish a right-handed Cartesian coordinate system, define a unit vector representing the direction of the signal, and use the azimuth angle... and pitch angle Determined, including: Azimuth : Defined as the angle between the projection of the signal direction onto the horizontal plane and the x-axis normal, i.e., the positive y-axis direction, and therefore the value range is -180° to 180°; Pitch angle : Defined as the angle between the direction of the signal and the horizontal plane, so the value range is 0° to 90°.

[0044] Under the far-field assumption, for a fixed signal direction, both angles are constants, and the expression for the steering vector is: In the formula, These are the azimuth angle and elevation angle of the signal direction, respectively; The wavelength of the radio frequency signal; For the first The distance between each array element and the origin of the coordinate system; The unit vector upwards from the signal at the 1st The projection of each array element in the direction of the two is the path difference of the incident signal relative to the origin of the coordinate system. For a uniform linear array, the array elements are uniformly distributed along the x-axis. Let the first element be located at the origin. Then the i-th element differs from the origin by a certain distance. Individual element spacing The projection of the incoming signal onto the x-axis is achieved by first projecting the incoming signal onto the horizontal plane and then onto the x-axis. The expression is: For uniform L-shaped, square, and rectangular matrices, first define the number of array elements on the x-axis and y-axis, respectively. and The method for calculating the path difference along the x-axis is the same as for the linear array described above; along the y-axis, the array elements still differ from the origin. Individual element spacing The projection of the incoming signal onto the y-axis is achieved by first projecting the incoming signal onto the horizontal plane and then onto the y-axis. The expression is: For an 8-element uniform circular array, assume the center of the circle is located at the origin. Since the distance between adjacent array elements is... Using the Pythagorean theorem, the distance from each array element to the center can be calculated as follows: Let the first array element be located at In the direction of, then the first The difference between the azimuth angle of each element and the first element is . indivual The signal is projected onto the horizontal plane and then projected onto the first... At the azimuth angle of each array element, Multiplying by the cosine of the difference between the two angles, the expression is: For a hexagonal array, assume the center is located at the origin. The array element at the center has no path difference, which is 0. The outer array elements form a uniform six-element circular array, and adjacent elements form an equilateral triangle with the central element. The distance from each element to the center is... All for The expression is: Based on the specific direction of the signal, calculate the value of each array. and Substituting the expression for the guide vector, we obtain the guide vector for each array.

[0045] Step 23: Multiply the steering vector by the RF signal and add the noise matrix to obtain the array signal matrix at the input, including: The expression for the array signal matrix is: In the formula, It is an array signal matrix; For guiding vector; It is a radio frequency signal; This is the noise matrix of the array elements.

[0046] Step 3: Perform conventional beamforming on each array signal matrix to obtain beam signals. After down-conversion, low-pass filtering, coherent demodulation, and matched filtering of the beam signals, perform sampling and decision-making to obtain the output bit stream, including: like Figure 3 As shown, step 31 involves using digital beamforming (DBF) technology to perform spatial filtering on the array signal matrix to generate beam signals, including: The expression for the beam signal is: In the formula, Beam signal; For the azimuth and elevation angles of the beam; Let be the array signal matrix at time t; This is the conjugate transpose operation, which means first taking the complex conjugate and then transposing it; This is the weight vector corresponding to the pointing angle.

[0047] For conventional beamforming, note that in the beam pointing direction, if the received signal of each element is compensated with an opposite phase to cancel the phase difference caused by the incident light, and the signals of each element are superimposed in phase at the output, the maximum gain can be obtained. Therefore, the weight vector... Take as beam direction On the guide vector: Determining the beam direction in the above steps Then, based on the completed digital beamforming, the beam signal is obtained. Specifically, when the beam points to... and the true origin of the signal When signals overlap, the useful signals are superimposed to the greatest extent, resulting in the highest signal-to-noise ratio at the output. (Set beam direction) The true origin of the signal Perform conventional beamforming to obtain beam signals. .

[0048] Step 32, mixing the beam signal with the intermediate frequency to generate a complex intermediate frequency signal, including: The expression for the complex intermediate frequency signal is: In the formula, It is a complex intermediate frequency signal; Beam signal; Radio frequency; This is the intermediate frequency.

[0049] Step 33: Using a Butterworth low-pass filter, high-frequency spurious components and out-of-band noise are removed from the complex intermediate frequency signal to generate the useful intermediate frequency signal, including: The expression for the intermediate frequency useful signal is: In the formula, This is a useful intermediate frequency signal; It is a complex intermediate frequency signal; For discrete-time indexing; , These are the orders of the polynomials in the numerator and denominator, respectively.

[0050] Step 34: Using a local real carrier, coherently demodulate the intermediate frequency useful signal to generate a baseband signal, expressed as: In the formula, It is a baseband signal; This is a useful intermediate frequency signal.

[0051] Step 35: Perform matched filtering on the baseband signal to maximize the output signal-to-noise ratio (SNR) and eliminate inter-symbol interference (ISI), obtaining the bipolar baseband signal, expressed as: In the formula, It is a bipolar baseband signal; It is a baseband signal; The impulse response of the rooted cosine pulse shaping filter; For integration variables; Step 36: Using optimal timing sampling and threshold decision, the bipolar baseband signal is recovered into a binary bit stream to generate the output bit stream, including: After matched filtering, the signal waveform presents a pulse with a clear main lobe within each symbol period. According to the Nyquist criterion, the moment when the inter-symbol interference (ISI) is zero and the signal-to-noise ratio (SNR) is maximum is located at the peak of the pulse.

[0052] The number of sampling points per symbol is 8. The matched filter introduces a fixed group delay, and the optimal sampling point is the fixed phase point after the delay needs to be compensated.

[0053] Assuming the delay caused by the filter is D sampling points, then the... The best sampling index of symbols The expression is: In the formula, For optimal sampling index; For symbol indexing; The number of samples per symbol is 8 in this embodiment; Delay for the group; This is the initial synchronization offset; The bipolar baseband signal is sampled according to the optimal sampling index to generate optimal sampled data, expressed as: In the formula, For optimal sampling data; It is a bipolar baseband signal; Thresholding is applied to the optimal sampled data to generate the output bitstream, expressed as: In the formula, This is the output bit stream.

[0054] Step 4: By traversing the entire spatial angle, calculate the output signal-to-noise ratio (SNR) of each antenna array. Based on the beam response characteristics, calculate the SNR gain, pointing accuracy, and discrimination. Analyze the performance of each antenna array to determine the optimal array, including: Step 41: Calculate the output signal-to-noise ratio of each antenna array by traversing the entire spatial angle, including: The beam is directed across the entire space, a weighted vector is constructed for each direction, and beamforming is performed on the array signal matrix X and noise matrix N respectively to generate the beam signal. and noise ; The output signal-to-noise ratio for each direction is calculated using the power separation method, and the expression is: In the formula, This is the total output power; Output noise power; This is for the output signal-to-noise ratio.

[0055] Step 42: Based on the beam response characteristics, calculate the signal-to-noise ratio gain and pointing accuracy, analyze the performance of each antenna array, and determine the optimal array, including: Signal-to-noise ratio (SNR) gain reflects the array's ability to amplify signals and its noise suppression level; its expression is: In the formula, For signal-to-noise ratio gain; The input signal-to-noise ratio is a preset baseline value for the simulation experiment in this embodiment; Pointing accuracy, reflecting the accuracy of beamforming, is expressed as: In the formula, To estimate the direction of arrival, i.e., the beam pointing coordinates corresponding to when the output signal-to-noise ratio reaches its maximum value; This refers to pointing accuracy, used to quantify angular deviation; the smaller the value, the higher the accuracy. This represents the actual direction of the signal, indicating the coordinates of the actual incident angle of the signal source set in the simulation. The antenna array with the highest signal-to-noise ratio gain and the lowest pointing accuracy is selected as the optimal array.

[0056] Step 5: Generate a segmented dynamic input signal, calculate the variable steering vector of the optimal array, and generate a segmented dynamic array signal matrix, including: Step 51: Divide the time axis into equal parts and generate dynamic input signals according to different incident angles, including: When the time axis t ranges from 0 to T / 4, the azimuth and elevation angles remain unchanged, and the signal direction is stationary. This is set to the same stationary point as in the array simulation, i.e., (0°, 60°). When the time axis t is taken from T / 4 to T / 2, the pitch angle remains unchanged, while the azimuth angle changes with time, gradually moving from 0° to -60°. When the time axis t takes values ​​from T / 2 to 3T / 4, the azimuth angle remains unchanged at -60°, while the pitch angle gradually moves from 60° to 30°. When the time axis t is set to 3T / 4 to T, the pitch angle remains unchanged at 30°, while the azimuth angle gradually moves from -60° back to 0°.

[0057] In the above steps, the direction of the incident signal is dynamic in order to simulate adaptive beamforming. This is because the adaptive algorithm is applicable to systems that change over time; only by changing over time can the tracking capability of the adaptive algorithm be demonstrated. Considering that the direction of the signal is represented by two variables, azimuth and elevation, the total signal duration is divided into four equal parts relative to the initial direction (0°, 60°), simultaneously including azimuth offset, elevation offset, and offset of both angles. This facilitates the comparison of the tracking accuracy of the adaptive algorithm and ensures that the generated incident signal meets the requirements of a dynamic signal.

[0058] Step 52: Group the dynamic input signals and generate the corresponding azimuth and elevation angles for each group, generating dynamic incident angle data, including: For moments on the timeline The signals are grouped into sets of 10 time points, each group corresponding to a signal direction and an average power. The number of groups is 10. ; In this embodiment, to ensure the total number is an integer and to prevent excessive computation during subsequent time-cycle calculations, the total length of the time axis t should be adjusted appropriately. Here, the left endpoint remains 0, and the right endpoint is 3.2 × 10⁻⁵ s. Therefore, the total number of time points is 8960, divided into 140 groups, with each group containing 35 groups. The linspace function is used in the program to generate the azimuth and elevation angles for each group.

[0059] Step 53: Generate the time-varying steering vector of the optimal array based on the dynamic incident angle data.

[0060] In this embodiment, the optimal array is an eight-element uniform circular array. The time-varying steering vector is obtained by substituting the steering vector expression of the eight-element uniform circular array into the dynamic incident angle data.

[0061] Step 54: Define a time window based on the group length, extract local data of the RF signal and noise matrix, combine with the time-varying steering vector to generate a local array signal matrix, and merge all local array signal matrices to obtain the dynamic array signal matrix, including: Based on group length Determine the step size of the time window and the starting time: Termination time: ; Local data of the radio frequency signal and noise matrix are extracted based on the time window; The time-varying steering vector is multiplied by the radio frequency signal and then added to the noise matrix to obtain the local array signal matrix. After merging all the local array signal matrices, the dynamic array signal matrix is ​​obtained.

[0062] Step 6: Based on the dynamic input signal and the dynamic array signal matrix, generate the weight vectors of each adaptive criterion in real time, including: The weight vector for conventional beamforming is the beam pointing direction. The corresponding steering vector, since the beam direction is fixed and it lacks adaptive tracking capability, is still taken as the maximum direction (0°, 60°) during the stationary phase, and its expression is: For the maximum signal-to-noise ratio (MSNR) criterion, the ultimate goal of optimization is to maximize the output signal-to-noise ratio, expressed as: In the formula, To output signal-to-noise ratio; The weight vector; This is the noise matrix; For statistical expectation calculation; The complex amplitude of the signal; It is a radio frequency signal; Output signal-to-noise ratio To find the maximum value, the expression for the weight vector is: In the formula, The weight vector for the maximum signal-to-noise ratio criterion; Noise matrix The covariance is determined by first using the var function. The variance of each element is calculated, and then multiplied by the eye matrix with the number of elements, and then diagonalized to obtain the result. To minimize the value and prevent covariance Zero; It is the identity matrix; It is a dynamic guiding vector; For the Minimum Mean Square Error (MMSE) criterion, the ultimate goal of optimization is to minimize the mean square error of the beam output and the desired reference signal, expressed as: In the formula, Let the mean squared error cost function be used. For statistical expectation calculation; The desired reference signal is, in this embodiment, a baseband pulse signal. The corresponding segmented data; It is a local dynamic array signal matrix; make Taking the minimum value, the weight vector expression for the minimum mean square error criterion is: In the formula, The weight vector for the minimum mean square error criterion; The covariance matrix of the dynamic input signal; Covariance matrix With expected reference signal The cross-correlation matrix between them; For the Linearly Constrained Minimum Variance (LCMV) criterion, the constraint is that the signal output in the reference direction has no attenuation, and the expression for the weight vector is: In the formula, This is the weight vector for the minimum variance criterion under linear constraints.

[0063] Step 7: Based on the weight vectors of each adaptive criterion, beamforming is performed on the dynamic array signal matrix to generate a dynamic beam signal, which is then restored to a binary bit stream to generate a dynamic output signal, including: Step 71, the expression for generating the dynamic beam signal is: In the formula, The dynamic beam signal of the i-th adaptive criterion; Total number of time groups; Let be the conjugate transpose weight vector of the i-th criterion in the k-th group; Let k be the local array signal matrix of the kth group; This represents the length of the time window.

[0064] Step 72: Restore the dynamic beam signals corresponding to each adaptive criterion into binary bit streams to generate dynamic output signals.

[0065] Step 8: Based on the weight vectors of each adaptive criterion, traverse the entire space angle, calculate the output signal-to-noise ratio of each adaptive criterion, and calculate the signal-to-noise ratio gain and pointing accuracy. Select the adaptive criterion with the largest signal-to-noise ratio gain and the smallest pointing accuracy as the optimal criterion.

[0066] Step 9: Process the BPSK signal using the optimal array and optimal criteria.

[0067] To verify the effectiveness of the method of this invention, the input and output bit streams of each antenna array are offset-mapped, with the input bit stream incremented by 1 and the output bit stream decremented by 2. A dual-waveform comparison diagram is plotted, and by observing whether the two signals completely overlap in the time domain, it is determined whether there are bit errors in the current antenna array, thus verifying the basic availability of the receiving link. Figures 4-9 As shown, no bit errors were found in the recovered output bit stream under any of the six antenna array configurations.

[0068] To further verify this, a heatmap was generated showing the relationship between the signal-to-noise ratio gain of each antenna array and the azimuth and elevation angles, such as... Figures 10-15 As shown, the plot is drawn with azimuth angle θ and elevation angle θ. A heatmap of the output signal-to-noise ratio relative to the input signal-to-noise ratio (10dB) is generated on the coordinate axis, and the point with the highest output signal-to-noise ratio, the true direction of arrival, and the corresponding gain value are marked on the graph. Gain and accuracy comparison data for different array configurations under conventional DBF are then generated, as shown in Table 1.

[0069] Table 1

[0070] according to Figures 10-15 As shown in Table 1, the performance of each antenna array in this embodiment is as follows: (1) Due to the limited number of hardware channels, other array types have insufficient array elements in a single direction compared to linear arrays, so their azimuth resolution is not as good as that of linear arrays. (2) Linear arrays, lacking array elements in other directions, do not have the ability to distinguish the direction of the signal's elevation angle, and cannot distinguish the current azimuth from the azimuth directly opposite it (therefore...). Figure 4The azimuth accuracy of the centerline array is displayed as 180°; while other array types also have this capability, their ability to distinguish elevation angles is generally not as good as their azimuth accuracy. (3) Due to the computational burden, the step size was set to 1°. It was observed that, except for linear arrays and L-shaped arrays, the pointing accuracy of azimuth and elevation angles was within 1° and the difference was not significant. (4) In terms of signal-to-noise ratio gain, the uniform linear array is the highest, followed by the circular array and the rectangular array; in terms of azimuth resolution and accuracy, the linear array is the highest, followed by the circular array; in terms of pitch resolution and accuracy, the rectangular array and the circular array are the highest.

[0071] Based on the above analysis, the octagonal uniform circular array is the array configuration with the best overall performance.

[0072] When selecting the optimal criterion, the dynamic input and output signals corresponding to each adaptive criterion are compared. For example... Figure 16 As shown, conventional beamforming exhibits significant bit errors within a timeframe after the signal direction deviates, while none of the three adaptive algorithms show any bit errors, thus verifying their advantages in time-varying scenarios.

[0073] Calculate the signal-to-noise ratio (SNR) gain for each adaptation criterion and generate a time series diagram of the SNR gain, as follows: Figure 17 As shown, it can be observed that the signal-to-noise ratio of conventional beamforming decreases significantly after directional shift, and the average gain is even lower than before beamforming; while the three adaptive criteria can maintain a high signal-to-noise ratio gain at all times, with MSNR higher than MMSE and higher than LCMV, which is consistent with the theoretical maximum gain of the MSNR criterion that directly uses signal-to-noise ratio as a constraint.

[0074] Plot the relationship between signal-to-noise ratio gain and azimuth and elevation angles to compare pointing accuracy. To reduce computational load, four time points are selected: As a representative time period of the static phase, to prevent Distortion occurs due to initialization. At this point, the azimuth angle deviates the farthest from the initial angle, while the pitch angle remains at the initial angle. At this point, the pitch angle deviates from the initial angle the farthest, while the azimuth angle remains at the initial angle; At this point, both the azimuth and elevation angles deviate from the initial angles to the greatest extent.

[0075] Take each criterion separately , , , Using the weight vector as the weight vector, the steering vector traverses all directions in space with an azimuth angle range of -180° to 180° and an elevation angle range of 0° to 90° as the experimental signal direction. Beamforming is then performed on each direction, and the signal-to-noise ratio gain is calculated. The azimuth angle is then used as the weight vector. Pitch angle Use the coordinate axes to plot a heatmap of the output signal-to-noise ratio (SNR) relative to the input SNR (10dB). To avoid memory shortages or excessively long runtimes, the angle change step size is set to 1°. Label the point with the highest output SNR, the true origin point, and the corresponding gain value on the graph. Since the default heatmap legend in MATLAB shows a linear change, and there are actually locations with extremely low SNR, causing most of the graph to be red, a custom legend is needed. This legend should be set to green when the SNR is the same as the input SNR (10dB), red for the maximum value, and blue for the minimum value. For example... Figures 18-21 As shown.

[0076] according to Figures 18-21 The analysis generated comparison data of signal-to-noise ratio gain and accuracy for different adaptive criteria, as shown in Table 2.

[0077] Table 2

[0078] according to Figures 16-21 The effects of each adaptive criterion are obtained from Table 2: (1) Conventional beamforming has a fixed beam direction and no tracking capability. When the signal direction shifts, the output signal-to-noise ratio is greatly reduced, resulting in obvious bit errors caused by noise. This verifies the necessity of using an adaptive algorithm for tracking. (2) In terms of signal-to-noise ratio gain, MSNR is the highest, followed by MMSE; for the LCMV criterion, since this simulation only uses one constraint in order to control the variables, the gain is not as good as the former two. (3) Due to the limited number and position of array elements, the tracking ability of various algorithms for pitch angle is generally not as good as that for azimuth angle. When the step size is set to 1°, it is observed that the azimuth angle tracking accuracy of the three criteria is within 1° and the difference is not significant. In terms of pitch angle accuracy, MSNR is stable within 1°, MMSE is stable within 3°, and LCMV can also reach within 1°, but it fluctuates greatly during the time change process, so the average level is not as good as the former two. (4) In terms of algorithm principle, MMSE only relies on autocorrelation matrix and cross-correlation matrix, and has the ability to track and locate even when the signal direction is completely unknown, rather than the other methods that require a known signal direction or reference direction for time-by-time tracking, thus having a scenario advantage.

[0079] Based on the above analysis, the MSNR adaptive DBF algorithm has the best overall performance in terms of signal-to-noise ratio gain and accuracy; when the scene is completely unknown, the MMSE adaptive DBF algorithm has the best overall performance.

[0080] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0081] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A BPSK signal processing method based on a circular antenna array and adaptive beamforming, characterized in that, include: A periodic BPSK baseband signal is generated, which is then processed using root-raised cosine pulse shaping and up-converted twice to RF to generate an RF signal. Gaussian white noise is used to generate the noise matrix of the radio frequency signal, and the steering vector of each antenna array is constructed. The combination of these vectors generates the array signal matrix. The beam signals are obtained by performing conventional beamforming on each array signal matrix. After down-conversion, low-pass filtering, coherent demodulation, and matched filtering on the beam signals, sampling and decision are performed to obtain the output bit stream. By traversing the entire space angle, the output signal-to-noise ratio of each antenna array is calculated. Based on the beam response characteristics, the signal-to-noise ratio gain, pointing accuracy, and discrimination are calculated. The performance of each antenna array is analyzed to determine the optimal array. Generate segmented dynamic input signals, calculate the variable steering vector of the optimal array, and generate segmented dynamic array signal matrices; The weight vectors of each adaptive criterion are generated in real time based on the dynamic input signal and the dynamic array signal matrix. Based on the weight vectors of each adaptive criterion, beamforming is performed on the dynamic array signal matrix to generate dynamic beam signals, which are then restored to binary bit streams to generate dynamic output signals. Based on the weight vector of each adaptive criterion, the entire space angle is traversed, the output signal-to-noise ratio of each adaptive criterion is calculated, and the signal-to-noise ratio gain and pointing accuracy are calculated. The adaptive criterion with the largest signal-to-noise ratio gain and the smallest pointing accuracy is selected as the optimal criterion. The BPSK signal is processed using the optimal array and optimal criteria.

2. The BPSK signal processing method based on a circular antenna array and adaptive beamforming according to claim 1, characterized in that, The generation of the periodic BPSK baseband signal employs root-raised cosine pulse shaping and undergoes two up-conversions to RF to generate an RF signal, including: A periodic alternating code pattern is used as the original input bit stream to generate the input bit stream; Constellation mapping operation using binary phase shift keying converts the input bitstream into a bipolar baseband symbol sequence; The bipolar baseband symbol sequence is subjected to root-raised cosine pulse shaping to generate a continuous-time baseband pulse signal; Complex exponential modulation is used to shift the baseband pulse signal to the intermediate frequency band to generate an intermediate frequency signal; A secondary up-conversion mechanism is used to shift the spectrum of the intermediate frequency signal to generate a radio frequency signal.

3. The BPSK signal processing method based on a circular antenna array and adaptive beamforming according to claim 1, characterized in that, The method of generating a noise matrix for radio frequency signals using Gaussian white noise, constructing steering vectors for each antenna array, and combining them to generate an array signal matrix includes: Based on the radio frequency signal, uniform spatial additive white Gaussian noise is introduced and its power is normalized to generate a noise matrix. The steering vector for each antenna array is constructed, expressed as follows: In the formula, These are the azimuth angle and elevation angle of the signal direction, respectively; The wavelength of the radio frequency signal; For the first The distance between each array element and the origin of the coordinate system; The unit vector upwards from the signal at the 1st The projection of each array element in the direction of its location; The steering vector is multiplied by the radio frequency signal and then the noise matrix is ​​added to obtain the array signal matrix at the input end.

4. The BPSK signal processing method based on a circular antenna array and adaptive beamforming according to claim 1, characterized in that, The process involves performing conventional beamforming on each array signal matrix to obtain beam signals, then performing down-conversion, low-pass filtering, coherent demodulation, and matched filtering on the beam signals, followed by sampling and decision-making to obtain the output bitstream, including: Digital beamforming technology is used to perform spatial filtering on the array signal matrix to generate beam signals; The beam signal is mixed with the intermediate frequency to generate a complex intermediate frequency signal; A low-pass filter is used to remove high-frequency spurious components and out-of-band noise from the complex intermediate frequency signal, generating a useful intermediate frequency signal. A local real carrier wave is used to coherently demodulate the intermediate frequency useful signal to generate a baseband signal; Matched filtering is applied to the baseband signal to maximize the output signal-to-noise ratio and eliminate inter-symbol interference, resulting in a bipolar baseband signal. By employing optimal timing sampling and threshold decision, the bipolar baseband signal is recovered into a binary bit stream, generating the output bit stream.

5. The BPSK signal processing method based on a circular antenna array and adaptive beamforming according to claim 1, characterized in that, The process involves traversing the entire spatial angle, calculating the output signal-to-noise ratio (SNR) of each antenna array, calculating the SNR gain, pointing accuracy, and discrimination based on beam response characteristics, analyzing the performance of each antenna array, and determining the optimal array. This includes: The output signal-to-noise ratio of each antenna array is calculated by traversing all angles in space. Based on the beam response characteristics, the signal-to-noise ratio gain and pointing accuracy are calculated, and the antenna array with the largest signal-to-noise ratio gain and the smallest pointing accuracy is selected as the optimal array.

6. The BPSK signal processing method based on a circular antenna array and adaptive beamforming according to claim 5, characterized in that, The step of calculating the output signal-to-noise ratio of each antenna array by traversing the entire spatial angle includes: The beam is directed across the entire space, a weighted vector is constructed for each direction, and beamforming is performed on the array signal matrix X and noise matrix N respectively to generate the beam signal. and noise ; The output signal-to-noise ratio for each direction is calculated using the power separation method, and the expression is: In the formula, This is the total output power; Output noise power; This is for the output signal-to-noise ratio.

7. The BPSK signal processing method based on a circular antenna array and adaptive beamforming according to claim 1, characterized in that, The process of generating a segmented dynamic input signal, calculating the variable steering vector of the optimal array, and generating a segmented dynamic array signal matrix includes: Divide the time axis into equal parts and generate dynamic input signals according to different incident angles; The dynamic input signal is grouped, and the azimuth and elevation angles corresponding to each group are generated to generate dynamic incident angle data. Based on the dynamic incident angle data, a time-varying steering vector for the optimal array is generated; Based on the group length, a time window is defined, local data of the radio frequency signal and noise matrix are extracted, and combined with the time-varying steering vector to generate a local array signal matrix. After merging all local array signal matrices, a dynamic array signal matrix is ​​obtained.

8. The BPSK signal processing method based on a circular antenna array and adaptive beamforming according to claim 1, characterized in that, The weight vectors for each adaptive criterion in real time, based on the dynamic input signal and the dynamic array signal matrix, include: In conventional beamforming, the weight vector is the guide vector corresponding to the beam direction, expressed as: The maximum signal-to-noise ratio criterion aims to maximize the output signal-to-noise ratio, and its expression is: In the formula, To output signal-to-noise ratio; The weight vector; This is the noise matrix; For statistical expectation calculation; The complex amplitude of the signal; It is a radio frequency signal; Output signal-to-noise ratio To find the maximum value, the expression for the weight vector is: In the formula, The weight vector for the maximum signal-to-noise ratio criterion; Noise matrix covariance; To minimize the value and prevent covariance Zero; It is the identity matrix; It is a dynamic guiding vector; The minimum mean square error criterion aims to minimize the mean square error of both the beam output and the desired reference signal. Its expression is: In the formula, Let the mean squared error cost function be used. For statistical expectation calculation; This is the desired reference signal; It is a local dynamic array signal matrix; make Taking the minimum value, the weight vector expression for the minimum mean square error criterion is: In the formula, The weight vector for the minimum mean square error criterion; The covariance matrix of the dynamic input signal; Covariance matrix With expected reference signal The cross-correlation matrix between them; The minimum variance criterion for linear constraints has the following expression for the weight vector: In the formula, This is the weight vector for the minimum variance criterion under linear constraints.

9. The BPSK signal processing method based on a circular antenna array and adaptive beamforming according to claim 1, characterized in that, The step of beamforming the dynamic array signal matrix according to the weight vectors of each adaptive criterion to generate a dynamic beam signal, and then restoring it to a binary bit stream to generate a dynamic output signal includes: The expression for generating dynamic beam signals is: In the formula, The dynamic beam signal of the i-th adaptive criterion; Total number of time groups; Let be the conjugate transpose weight vector of the i-th criterion in the k-th group; Let k be the local array signal matrix of the kth group; The length of the time window; The dynamic beam signals corresponding to each adaptive criterion are restored into binary bit streams to generate dynamic output signals.

Images