A high-precision high-dimensional fractional order orbital angular momentum acoustic communication method under phase slip mediation

Abstract

The application provides a high-precision high-dimensional fractional order orbital angular momentum acoustic communication method under phase error mediation, combines annular active phased array technology, orbital angular momentum (OAM) multiplexing technology and convolutional neural network (CNN) machine learning technology, constructs a high-precision high-dimensional vortex acoustic beam communication system based on fractional order orbital angular momentum pair (P-FOAM), realizes high-capacity acoustic information transmission, constructs multiplexing vortex acoustic beams by using opposite polarity fractional order orbital angular momentum pairs in a limited range to realize high-dimensional information transmission, and uses phase error theory to guide annular sparse sampling of the acoustic field, constructs an optimized convolutional neural network training set, realizes high-precision rapid identification of high-dimensional fractional order orbital angular momentum, reduces the interval of fractional order orbital angular momentum, and increases the number of annular sampling rings and points, unlimitedly expands the dimension of data communication in a limited orbital angular momentum range, and provides a new method for high-speed, miniaturization and real-time application of a high-capacity vortex acoustic beam communication system based on orbital angular momentum.

Description

Technical Field

[0001] This invention relates to the field of acoustic vortex communication in acoustic communication applications, and particularly to a high-precision, high-dimensional fractional-order orbital angular momentum acoustic communication method mediated by phase misalignment. Technical Background

[0002] With the rapid development of science and technology, information is experiencing explosive growth. Traditional communication methods based on signal modulation using physical parameters such as frequency, phase, amplitude, and time can no longer meet the needs of today's society. Vortex beams, a special type of sound beam with a helical phase distribution, carry orbital angular momentum (OAM), which opens up new dimensions for wave-based communication such as light waves, sound waves, and electromagnetic waves. Furthermore, they offer advantages such as high security and high spectral efficiency, making them of great significance in the field of information transmission and communication.

[0003] To improve the channel capacity of vortex communication, high-order or fractional-order vortex beams are typically constructed. However, the generation of high-order vortex beams is limited by factors such as the number of active phased array sources and the complex and inflexible structure of passive phased array materials. Furthermore, high-order vortex beams exhibit severe divergence effects, placing higher demands on the design and implementation of receiver array systems. Additionally, while fractional-order vortex beams can increase the addressable coding length, they no longer satisfy orthogonality, making accurate information decoding theoretically difficult. Currently, in the field of fractional-order optical vortex communication, fractional-order orbital angular momentum decoding is typically achieved by utilizing the focal spot shift and the number of interference fringes in the intensity image formed by beam interference, or by employing machine learning methods. Fractional-order vortex beam multiplexing decoding remains undeveloped, primarily due to the following limitations: First, obtaining the radial sound field distribution often requires two-dimensional point-by-point scanning, which cannot guarantee the real-time performance of signal transmission and data decoding. Second, adjacent fractional-order vortex sound fields exhibit high similarity, making measurement difficult using conventional sound field characteristics. Furthermore, fractional-order vortex beams are susceptible to the influence of the transceiver system and channel environment, resulting in severe distortions in their sound pressure and phase distribution, significantly reducing the accuracy of fractional-order orbital angular momentum multiplexing decoding and easily generating inter-symbol interference during transmission. Therefore, there is an urgent need to establish a fractional-order orbital angular momentum multiplexing decoding method to theoretically enhance the characteristics of fractional-order vortex sound fields and practically improve the accuracy, stability, efficiency, and convenience of fractional-order vortex communication, thereby infinitely expanding the channel capacity of vortex communication within a limited orbital angular momentum range. Summary of the Invention

[0004] This invention addresses the problems of long two-dimensional sound field acquisition time, poor anti-interference ability, severe divergence effect, and difficulty in practical application in existing fractional-order orbital angular momentum communication technologies. It proposes a high-precision, high-dimensional fractional-order orbital angular momentum acoustic communication method under phase misalignment mediation. The method combines active phase control technology of ring array, fractional-order orbital angular momentum multiplexing technology, and deep learning to construct a high-dimensional and high-precision fractional-order vortex communication system, realizing efficient and high-capacity acoustic information transmission. This scheme is based on active phased array of a ring array to construct a coaxial coherent multiplexed vortex acoustic beam carrying fractional-order orbital angular momentum pairs with opposite polarities. This forms a stable petal-shaped sound pressure and phase fault distribution, enhancing the stability of the recognizable features of the fractional-order orbital angular momentum multiplexed vortex and improving the information transmission and anti-interference capabilities of the vortex acoustic beam. Furthermore, based on the one-to-one mapping relationship between the spatial angle of the sound field phase fault (sound pressure valley) and the orbital angular momentum, a single-ring or multi-ring sparse sampling model is constructed to improve the speed and efficiency of sound field sound pressure measurement and reduce the complexity of vortex acoustic beam communication data processing. Considering the impact of channel and environmental interference on the sound field in actual information transmission, a convolutional neural network based on a turbulence model is constructed. The amplitude and phase information of the ring sparse sampling are fused to construct an image training set, achieving high-precision high-dimensional fractional-order orbital angular momentum decoding.

[0005] To solve the aforementioned technical problems, this invention employs the following technical solution: It utilizes active phased array technology with a ring array to construct a coaxial coherent multiplexed vortex sound beam carrying fractional-order orbital angular momentum pairs with opposite polarities, forming a stable petal-shaped sound pressure and phase fault distribution; based on the one-to-one mapping relationship between the spatial angle of the sound field phase fault and orbital angular momentum, it guides the construction of a single-ring / multi-ring sparse sampling model; further considering the influence of the actual transmission channel environment on the sound field, it constructs a convolutional neural network based on a turbulence model, fusing the sound pressure amplitude and phase information from the ring sparse sampling to construct an optimized image training and testing set; and utilizes CNN training to achieve high-precision fractional-order vortex communication within a limited orbital angular momentum range. The specific steps are as follows:

[0006] (1) Based on the active phase control technology and orbital angular momentum multiplexing technology of ring array, the phase encoding of a single ring transducer array with N sound sources is used to construct a coaxial coherent multiplexed vortex sound beam carrying fractional orbital angular momentum pairs with opposite polarities, forming a stable petal-shaped sound pressure and phase misalignment distribution, enhancing the stability of the recognizable features of fractional orbital angular momentum multiplexed vortex, and improving the information transmission capability and anti-interference capability of the vortex sound beam.

[0007] (2) The fractional vortex sound beam is described as the superposition of countless integer vortex sound beams. Its phase error is the rotational superposition of the phase error after interference of adjacent integer vortices. Its rotation angle is positively correlated with the fractional orbital angular momentum.

[0008] (3) The relationship between the sound pressure / phase distribution of the vortex sound field and the accuracy of orbital angular momentum recognition is used to guide the design of the ring sparse sampling array, and the sampled sound pressure and phase information are fused to construct a holographic image distributed along the circumference. The greatly reduced amount of data can improve the recognition speed and efficiency of orbital angular momentum.

[0009] (4) Considering the influence of channel and environmental interference on the sound field in actual information transmission, a convolutional neural network based on the turbulence model is constructed. The amplitude and phase information of the ring sparse sampling are fused to construct the image training set, and high-precision high-dimensional fractional orbital angular momentum decoding is realized.

[0010] (5) Further reducing the fractional orbital angular momentum interval and increasing the number of ring sampling rings and points can infinitely expand the dimension of data communication within the limited orbital angular momentum range, realizing the high-speed, miniaturized and real-time operation of large-capacity vortex beam communication application systems.

[0011] Furthermore, in step (1), N transducers are uniformly distributed on an annular disk of radius a to construct a single-ring emission array. The sound wave frequency is f, and the angle between adjacent sound sources is Δα = 2π / N. Using the same amplitude A and initial phases φ... n1 =2π(n-1)l / N and φ n2 Two cosine signals, =2π(n-1)l / N, are synthesized to obtain a composite signal 2Acosωt·cos[2πl(n-1) / N], which excites the nth transducer. Further, a coaxial coherent multiplexed vortex beam carrying fractional orbital angular momentum pairs with opposite polarities is constructed by superimposing the radiated sound fields from N phased-point sound sources, where l is the order of the fractional orbital angular momentum, i.e., the fractional topological charge. If the topological charge of the multiplexed vortex beam containing S pairs of fractional orbital angular momentum pairs with opposite polarities is l... s Then the excitation signal of the nth sound source is Similarly, multiple fractional-order orbital angular momentum multiplexing beams are formed based on phase control theory.

[0012] Furthermore, in step (2), the sound pressure of the coaxial coherent multiplexed vortex beam carrying fractional orbital angular momentum of opposite polarity is described as follows:

[0013]

[0014] Where l and m are the fractional and integer orders of orbital angular momentum, respectively, and A(m,r) and γ(m,r) represent the sound pressure amplitude distribution and signal phase, respectively, both of which depend only on the radius and the magnitude of the topological charge. A fractional-order coherent vortex beam can be described as the superposition of countless integer-order coherent vortex beams with different weights. Its phase shift is the rotational superposition of the phase shifts after interference between adjacent integer-order vortices, with a rotation angle of approximately lπ / m. Furthermore, the spatial angle of the phase shift in a fractional-order coherent vortex beam is approximately inversely proportional to the topological charge. This inverse relationship needs to be determined based on parameters such as the initial phase of the actual transmission array.

[0015] Furthermore, in step (3), the relationship between the fractional-order orbital angular momentum recognition accuracy, phase shift spatial angular resolution, and the number of sampling points is determined when the topological charge l = 0.5 to 3.0, preferably at l = 2.0, and l can be selected between 0.5 and 3.0 according to the actual situation. A ring-shaped sparse sampling array is constructed based on the relationship between the number of sampling points and the orbital angular momentum recognition accuracy to collect sound pressure and phase information, which are respectively set as the RG channel of the color image, and the B channel and other pixels are set to zero, thereby constructing holographic sound field information distributed along the circumference. The sparse ring sampling array structure may include single-ring / double-ring / multi-ring array models, and the number of sampling points in a single ring is between 16 and 128.

[0016] Furthermore, in step (4), a fractional-order coherent multiplexed vortex beam is constructed within the topological charge range of 0.5 to 3.0, preferably within the range of l = 0.6 to 2.4, which can be further subdivided and expanded within the range of 0.5 to 3.0 according to actual conditions. Considering the influence of the channel environment on the sound field, a layer of random power spectrum phase screen with negligible thickness is introduced at the receiver. The ring-sampled power spectrum is randomly filtered using a random complex matrix C with a mean of 0 and a variance of 1, and the sound pressure formula within the cross-section of the fractional-order multiplexed vortex beam is obtained as follows: Where s represents the number of the vortex acoustic beam, and ψ(x,y) = F -1 {C×σ(k x ,k y )}, F -1 {·} denotes the inverse Fourier transform symbol, σ(k x ,k y ) represents the spectral variance, k x and k y These are the frequency domain coordinates of the phase screen.

[0017] Furthermore, step (4) considers the effects of factors such as the offset (-1.5~1.5mm), rotation (-1.5~1.5°), deflection (-1.5~1.5°), single-loop / double-loop sampling method, and atmospheric turbulence of the transceiver array, but is not limited to this offset, rotation, and deflection range, nor is it limited to the double-loop sampling method. An optimized convolutional neural network training and testing set is constructed to achieve high-precision and rapid identification of high-dimensional fractional-order orbital angular momentum. In addition, it is not limited to CNN-type convolutional neural networks, but can include various machine learning methods such as deep neural networks.

[0018] Furthermore, in step (4), the standard deviation between the decoding result and the theoretical result is used to... To evaluate the accuracy and stability of data transmission and decoding, where P' m With P m Let represent the experimental and theoretical decoding probability distributions, respectively, and K represent the number of information classifications.

[0019] Furthermore, in step (5), further reducing the fractional orbital angular momentum interval and increasing the number of ring sampling rings and points can infinitely expand the dimension of data communication within a limited orbital angular momentum range, thereby realizing the high-speed, miniaturized and real-time operation of a large-capacity vortex beam communication application system.

[0020] This invention provides a high-precision, high-dimensional fractional-order orbital angular momentum acoustic communication system mediated by phase misalignment. The system comprises: A) a computer; B) an active phased-array drive system; C) a motion control module; D) a single-ring transmitting array; E) a single-ring / dual-ring acquisition system; and F) a digital oscilloscope. The computer synthesizes multiple pairs of coherently multiplexed vortex excitation signals carrying fractional-order orbital angular momentum with opposite polarities. These signals are amplified by a power amplifier to drive the single-ring transmitting transducer array. The transducers are used to sample the single-ring / dual-ring acoustic signals, and the sound pressure information is acquired by the digital oscilloscope and fed into a convolutional neural network for fractional-order orbital angular momentum pattern recognition.

[0021] Beneficial effects: This invention addresses the problems of long acquisition time, poor anti-interference ability, severe divergence effect and difficulty in practical application of existing fractional-order vortex communication technology. It utilizes a coaxial coherent multiplexed vortex sound beam carrying fractional-order orbital angular momentum pairs with opposite polarities to form a stable petal-shaped sound pressure and phase fault distribution. It also uses the one-to-one mapping relationship between the spatial angle of phase fault and orbital angular momentum to guide the establishment of a ring sparse sampling model. A convolutional neural network based on a turbulence model is constructed to fuse the sparsely sampled sound pressure and phase information to establish an image training set and a test set. High-precision fractional-order orbital angular momentum multiplexing decoding is achieved through CNN training. This invention introduces multiple pairs of fractional-order orbital angular momentum coherent multiplexing decoding technology with opposite polarities into the field of acoustic vortex communication. It can effectively improve the identifiable characteristics of the sound beam, the anti-interference ability of information transmission, and the speed and efficiency of sound field measurement. It can reduce the complexity of data processing in vortex sound beam communication and can wirelessly expand the data communication capacity within a limited orbital angular momentum range. It helps to realize the high-speed, miniaturized, and real-time operation of large-capacity vortex sound beam communication systems and has good promotional value in acoustic vortex communication and its practical applications. Attached image description:

[0022] Figure 1 Schematic diagram of phase-disorder mediated fractional-order orbital angular momentum acoustic communication based on ring sparse sampling and machine learning;

[0023] Figure 2 Characteristic analysis of coherent vortex acoustic beams carrying fractional-order orbital angular momentum of opposite polarity;

[0024] Figure 3(a). Block diagram of the construction and experimental measurement system of fractional-order orbital angular momentum multiple-pair multiplexed vortex acoustic beam based on a ring transceiver array;

[0025] Figure 3(b). Photographs of some of the actual equipment, including the self-made multi-channel phase control system and high-precision scanning measurement system;

[0026] Figure 4 A schematic diagram of a convolutional neural network architecture; where (a) a 5.17-bit multiplexed vortex channel with 0.2 precision within the topological load range of 0.8–2.2, (b) an 8-bit multiplexed vortex channel with 0.2 precision within the topological load range of 0.8–2.2, and (c)

[0027] A 10-bit multiplexed vortex channel with a precision of 0.2 within the topology load range of 0.6 to 2.4 and a single topology load vortex channel with a precision of 0.025 within the topology load range of (d) 1 to 2.

[0028] Figure 5 (a) Radial sound pressure and phase distribution at z0 = 250 mm (~30λ) without turbulence influence;

[0029] Figure 5(b) Radial sound pressure and phase distribution at z0 = 250 mm (~30λ) under turbulent influence;

[0030] Figure 5 (c) Experimental measurement of radial sound pressure and phase distribution at z0 = 250 mm (~30λ);

[0031] Figure 5 (d). Pattern recognition probability distribution (histogram), recognition accuracy distribution (top left), and recognition standard deviation distribution (bottom left) during 16-point single-loop sampling;

[0032] Figure 5 (e). Pattern recognition probability distribution (histogram), recognition accuracy distribution (top left), and recognition standard deviation distribution (bottom left) during 32-point single-loop sampling;

[0033] Figure 5 (f). Pattern recognition probability distribution (histogram), recognition accuracy distribution (top left), and recognition standard deviation distribution (bottom left) when using 32-point double-ring sampling;

[0034] Figure 6 (a) Accuracy and loss function of 8-bit data transmission decoding based on CNN with 32-point double-ring sparse sampling;

[0035] Figure 6 (b). Accuracy and loss function of 10-bit data transmission decoding based on CNN with 32-point double-ring sparse sampling;

[0036] Figure 7 Extended P-FOAM pattern recognition based on annular sparse sampling.

[0037] Table 1. Relationship between OAM resolution, number of sampling points, and angular resolution of coherent vortex beams

[0038] Table 2. Encoding rules and classifications of numbers and characters

[0039] Table 3. Accuracy of letter “NJNU” recognition in 8-bit and 10-bit channels Detailed Implementation

[0040] The technical solution of the present invention will be described in detail below, but the scope of protection of the present invention is not limited to the embodiments described.

[0041] Example 1: A high-precision, high-dimensional fractional-order orbital angular momentum acoustic communication method mediated by phase misalignment, the specific operation of which is as follows:

[0042] (1) Principle of constructing fractional-order orbital angular momentum coherent multiplexing vortex sound beam

[0043] The system principle of using a ring transceiver array to construct a pair of fractional-order OAM multiplexed vortex acoustic beams for information transmission and decoding is as follows: Figure 1 As shown, a ring-shaped emission array is constructed by uniformly distributing N = 16 transducers on a ring disk with a radius of a = 5 cm. The angle between adjacent sound sources is Δα = 2π / N, and the excitation frequency is f = 40 kHz. Using transducers with the same amplitude A and initial phases φ... n1 =2π(n-1)l / 16 and φ n2 The two cosine signals Acos[ωt+2πl(n-1) / 16] and Acos[ωt-2πl(n-1) / 16] are synthesized, i.e., 2Acosωt·cos[2πl(n-1) / 16] excites the nth transducer. According to the point source propagation theory, N phased point sound sources at the free space observation point... The sound pressure generated at that location is:

[0044]

[0045] Where A is the vibration velocity of the sound source. From observation point P to sound source M n The distance, α = 2π(n-1) / 16, k = ω / c0 is the wave number, ρ0 = 1.225 kg / m 3 c0 = 340 m / s represents the density of the medium and the speed of sound, and ω = 2πf represents the angular frequency of the sound wave.

[0046] A fractional-order vortex sound beam can be described as the superposition of an infinite number of integer-order vortex sound beams, i.e. Substituting it into Formula 1, we get:

[0047]

[0048] Since the sound pressure within the cross-section of the integer-order vortex beam is distributed in a ring shape and the phase is distributed in a spiral shape, the sound field at the z = z0 plane is expressed as: Where A(r,m) and γ(r,m) represent the sound pressure amplitude distribution and signal phase, respectively. Both are only related to the radius and the magnitude of the topological charge, and satisfy the relationships A(r,m) = A(r,-m) and γ(r,m) = γ(r,-m). Therefore, the sound pressure of the coupled sound field formed by the interference of two fractional-order vortex beams carrying opposite polarities can be further expressed as:

[0049]

[0050] Equation 3 shows that fractional-order coherent vortex sound beams can be described as the superposition of countless integer-order coherent vortex sound beams with different weights. The phase distribution still retains the phase change characteristics, and there is a spatial rotation of lπ / m on the basis of adjacent integer-order phase changes. This one-to-one mapping spatial rotation relationship and special sound pressure distribution provide a physical basis for fractional-order orbital angular momentum pattern recognition.

[0051] To achieve synchronous transmission of multidimensional data, it is necessary to construct an S-pair of fractional-order orbital angular momentum coherently multiplexed vortex acoustic beams carrying opposite polarities. Considering the impact of non-ideal transmission on the sound field during actual measurements, a negligible-thickness random power spectrum phase screen is introduced into the receiving array. A random complex matrix with a mean of 0 and a variance of 1 is used to randomly filter the ring-sampled power spectrum, thus obtaining the sound pressure within the cross-section of the multiplexed vortex acoustic beam as follows:

[0052]

[0053] Where s represents the number of the vortex acoustic beam, and ψ(x,y) = F -1 {C×σ(k x ,k y )}, F -1 {·} represents the inverse Fourier transform symbol. For the spectral variance, The power spectrum phase screen is Δx, the sampling interval is k. x and k y These are the frequency domain coordinates of the phase screen. k is the wave number. is the atmospheric refractive index structure constant.

[0054] (2) Phase shift theory guides ring sparse sampling

[0055] This invention selects a propagation distance z0 = 250 mm (30λ) and numerically simulates and measures the distribution of coherent vortex sound fields carrying different topological charges within the range of [-50, 50] mm in 0.5 mm increments. Figure 2 As shown in (a). To take into account the characteristic distribution of the coherently multiplexed vortex sound field of multiple pairs of fractional-order orbital angular momentum, the average value (17 mm) of the peak sound pressure radius at topological loads ±1 and ±2 is selected as the standard, along the... Figure 2 (a) The white ring plots the annular sound pressure and phase distribution of fractional-order orbital angular momentum coherent beams under different topological loads, as shown in the figure. Figure 2 As shown in (b), when the topological charge l = ±1.0, the two vortex acoustic beams carrying fractional orbital angular momentum of opposite polarities interfere with each other to form a left-right symmetrical sound field distribution, creating a radial low sound pressure band in the vertical direction, i.e., located in... The phase misalignment occurs at l = ±1.2. When l = ±1.2, the fractional-order orbital angular momentum order is relatively small, and the phase singularities of the ±l-order vortex beams shift to both sides, forming tilted low sound pressure bands. This still divides the coherent vortex sound field into two symmetrical parts. Influenced by the phase distribution of the fractional-order vortex beams, the phase misalignment boundary rotates clockwise by 0.2π, which is highly consistent with theoretical analysis. When the topological charge further increases to ±1.4, the spatial angle of the phase misalignment is approximately 10°. When l = ±1.5, due to the generation of new phase singularities by the single fractional-order vortex beams, which gradually move closer to the center, the sound field is divided into four non-uniformly distributed symmetrical petals. As the topological charge l continues to increase, the non-uniform petal-shaped sound field distribution continues to rotate clockwise. When l = ±1.6, the phase misalignment azimuth angle is approximately -11°, until four uniformly distributed petals are formed at l = ±2.0, with the phase misalignment azimuth angle reaching -45°. As the topological charge increases from ±1.0 to ±2.0, the radius corresponding to the peak sound pressure level gradually increases from 13.5 to 20.5 mm.

[0056] Furthermore, the spatial angle and topological charge relationship of the sound pressure valley point / phase dislocation point between l = ±1 and ±4.0 were simulated and calculated at intervals of 0.01, such as... Figure 2 As shown in (c), the results indicate that the spatial angle of the phase fault point decreases with increasing l, and the trend gradually slows down, showing an overall inverse relationship between the two. Considering that small topological load pairs (l<0.5) cannot form stable acoustic pressure valley / phase misalignment abrupt change points, and that with large topological loads (l>3), the spatial angle change of the acoustic pressure valley / phase misalignment abrupt change points is too small, which will affect the decoding accuracy based on edge phase misalignment, the relationship between P-FOAM resolution, phase misalignment spatial angle phase resolution, and number of sampling points was investigated near l=2.0. The results are shown in Table 1.

[0057] Table 1. Relationship between OAM resolution, number of sampling points, and angular resolution of coherent vortex beams.

[0058] Minimum rotation angle 15.9 7.4 3.5 1.2 Maximum number of sampling points 12 25 52 150

[0059] Taking an OAM resolution of 0.2 as an example, the minimum spatial rotation angle of the sound pressure valley / phase misalignment point is approximately Δψ = 15.9°, therefore, at most... A single ring of discrete sampling points is sufficient to achieve P-FOAM pattern recognition with an accuracy of 0.2. Furthermore, as the number of ring sampling points increases, the spatial rotation angle resolution becomes stronger, and the OAM pattern recognition accuracy becomes higher, providing a physical basis for constructing a receiver array design based on ring sparse sampling.

[0060] (3) Experimental measurement system based on sparse sampling P-FOAM multiplexed vortex beam

[0061] The experimental measurement system based on sparse sampling P-FOAM multiplexed vortex beams is shown in Figure 3(a), and Figure 3(b) shows a partial physical diagram of the experimental system. Sixteen ultrasonic transducers (NU40C10T-2, Porcelain Technology, China) with a radius of 2 mm and a center frequency of 40 kHz are uniformly fixed on an acrylic disk with a radius of a = 50 mm to form a transmitting array. Sixteen phase-tunable 40 kHz square wave signals are generated using an FPGA (Altera Cyclone IV, Altera Corporation, USA). After filtering by a low-pass filter, a phase-controllable cosine signal is obtained. This cosine signal is then amplified by a power amplifier (OPA552, Texas Instruments, USA) to output an initial phase and amplitude-tunable signal to excite the transducer array, constructing multiple pairs of ±1st order OAM multiplexed vortex beams in free space. The receiving transducer was controlled using LabVIEW software to perform two-dimensional scanning (Newport M-ILS250, Newport Corporation, USA), with scanning measurements and single / dual-ring sparse sampling in 2mm steps within the range of -50 to 50mm. Sound pressure and phase information of the sound field were acquired using a digital oscilloscope (Agilent DSO9064A, Agilent Corporation, USA) and sent to a computer for further training and decoding.

[0062] (4) Convolutional Neural Network Construction

[0063] In sound field measurement, a transducer performs 32-point uniform sparse sampling along the circumference using a single-ring / double-ring method to obtain the sound pressure amplitude and phase distribution. These are then fed into the R and G channels of an RGB image, respectively, while the B channel is set to zero. The resulting image is fused to obtain a one-dimensional effective hologram containing both sound pressure amplitude and phase, which is used for subsequent CNN convolutional neural network training. The hierarchical diagram and specific network parameter settings of the CNN are shown below. Figure 4 As shown, it mainly consists of convolutional layers, downsampling layers, fully connected layers, and an output layer. Considering the potential angular deflection of -1.5 to 1.5°, array translation of -1.5 to 1.5 mm, radial rotation of the source spatial position of -1.5 to 1.5° in the measurement transmission array system, and 10... -12 Atmospheric refractive index structure constant To mitigate the influence of environmental parameters, MATLAB software was used to numerically simulate different vortex sound beams, generating 400 training images and 100 test images. Experimental measurement data were not included in the training and test sets. The training process was completed on a computer with an i9-10900K CPU and an RTX3080 GPU (Intel i9-10900K CPU@3.07GHz, GPU: NVIDIA GeForce RTX3080 GPU, RAM: 32GB and ROM: 2.5TB).

[0064] (5) High-dimensional data transmission

[0065] To achieve multidimensional data transmission based on P-FOAM, eight pairs of topological loads were selected in increments of 0.2 between ±0.8 and ±2.2. One or two pairs were selected to construct a multiplexed vortex acoustic field, which can be divided into... The class is capable of encoding and transmitting the ten Arabic numerals 0-9 and the 26 English letters A-Z. See Table 2 for the specific encoding catalog.

[0066] Table 2 Encoding Rules and Classifications of Numbers and Characters

[0067]

[0068]

[0069] The 1 and 0 represent whether the topological load pair is included or not, respectively. For example, the letter "N" can represent the multiplexing of two pairs of OAMs, ±1.2 and ±1.8. Figure 5 (a) Sound pressure and phase distribution of the ideal multiplexed vortex sound field when transmitting the four characters "NJNU". Further considering environmental interference in the actual measurement system, a random power spectrum phase screen is introduced into the ideal simulation results using an atmospheric turbulence model. The simulation results are as follows: Figure 5 As shown in (b) Figure 5 (c) shows the experimental measurement results. As can be seen from the figure, the sound pressure and phase distribution of the multiple OAM multiplexed vortex sound field are more complex, exhibiting an asymmetric and non-uniform sound pressure distribution. Although the specific values ​​of the multiplexed OAM cannot be directly obtained, the characteristics of its sound pressure valley points / phase misalignment points are still very significant, intuitively demonstrating the anti-interference capability of P-FOAM pattern recognition under phase misalignment mediation. In addition, the experimental measurement results are highly consistent with the simulation results under the turbulence model, indicating the rationality and reliability of using the turbulence model to generate training and test sets, ensuring high-accuracy recognition while avoiding the cumbersome experimental measurement.

[0070] Sound pressure and phase information were obtained by sparse sampling at 16 points on a ring with r = 17 mm. This information was then input into a convolutional neural network for 36-class classification training, resulting in a channel capacity of approximately log2(K) = 5.17 bits for data decoding. The decoding result is as follows: Figure 5 (d) As shown in the bar chart, the horizontal axis represents the category, and the vertical axis is the probability distribution of the corresponding category. Figure 5 (d) The top left corner shows the relationship between recognition accuracy and loss function with the number of iterations during CNN training, while the bottom left corner shows the standard deviation of the decoding results. As can be seen from the figure, the recognition accuracy after 50 iterations is approximately 97.55%, but the probability of misidentifying the letters N and J as H and F, respectively, is nearly 15%. This is mainly due to the significant difference between the two pairs of topological charges; using a single-ring 16-point sampling method cannot fully capture the sound pressure and phase information of the two vortex beams, thus affecting the feature extraction of the convolutional neural network. The standard deviation (SD) of the decoding results using the experimental data "NJNU" is also shown. To evaluate the accuracy and stability of decoding, where P' m With P m ... Figure 5 As shown in (e) and (f), decoding using 32-point single-loop and 32-point dual-loop sampling methods both took approximately 11 minutes, with accuracy improved to 99.15% and 99.88% respectively. This preliminarily demonstrates the feasibility of increasing the number of sampling points to improve decoding accuracy. Furthermore, although the SD value decreased slightly using 32-point single-loop sampling, this was not significant, indicating that when the sampling points meet the requirements... Figure 2 (c) After meeting the resolution requirements of the phase-misalignment-mediated theory, increasing the number of sampling points does not significantly improve the stability and security of fractional-order multiplexed vortex communication. However, the SD (discrepancy rate) for recognizing the letters "NJNU" using a 32-point dual-ring sampling method can quickly drop to zero, indicating a further improvement in system stability. Moreover, the structural design of the receiving array is easier to implement. Therefore, the dual-ring sampling method based on vortex radius differentiation can improve decoding stability and application versatility. We can also infer that using multi-ring sparse sampling can further improve the accuracy of P-FOAM pattern recognition and achieve more complex high-dimensional data transmission.

[0071] To further expand the applicability of high-dimensional data transmission, eight pairs of P-FOAM multiplexing were selected at intervals of 0.2 within the range of l = ±0.8 to ±2.2. One encoding method is used, selecting 10 pairs of P-FOAMs within the range of l = 0.6 to 2.4 and multiplexing them to obtain... The accuracy and loss function of decoding 8-bit and 10-bit data transmission using a CNN based on 32-point double-ring sparse sampling are as follows: Figure 6 The solid and hollow square curves in (a) and 6(b) are shown. To demonstrate the advantages of using the sound pressure valley / phase dislocation abrupt change point coherently constructed by vortex beams carrying opposite topological charges for OAM decoding of multidimensional data transmission, a comparison is made here with the training process that uses only positive fractional-order vortex multiplexed beams for data decoding. The results are as follows: Figure 6 As shown in (a) and 6(b) with solid and hollow pentagrams, the training and decoding time for both sampling methods is approximately 5 hours. The recognition accuracy based on P-FOAM multiplexing reaches 96.78% and 96.58%, respectively, which is significantly higher than the decoding accuracy of traditional FOAM multiplexing (89.56% and 90.16%). For 8-bit data transmission, the training loss function of CNN based on pairwise OAM multiplexing can be reduced to 0 after 10 iterations, which is 5 times that of traditional OAM multiplexing. In the 10-bit data transmission case, the training loss function of CNN based on pairwise OAM multiplexing can be reduced to 0 after 100 iterations, and its reduction rate is also greater than that of training loss based on traditional multiplexed sound beams. Using 95% as the evaluation standard, it can be seen that the dual-ring 32-point sparse sampling can achieve data transmission with 8-bit and 10-bit channel capacity. Similarly, the experimental measurement results of the letters "NJNU" are fed into 8-bit and 10-bit CNN networks for recognition, and correct decoding results are obtained. The relevant decoding accuracy is shown in Table 3.

[0072] Table 3 shows the accuracy of letter “NJNU” recognition in 8-bit and 10-bit channels.

[0073]

[0074] As the effective addressable symbol length increases, the number of codes increases exponentially. Furthermore, due to experimental measurement errors, the recognition accuracy of the second letter N is approximately 64.3%. The decoding accuracy of all other characters can reach over 90%. Therefore, it can be further inferred that high-precision and ultra-high-dimensional data transmission can be achieved within a certain topological load range based on phase misdirection theory, and the P-FOAM multiplexing vortex decoding accuracy can be further improved by optimizing the multi-ring sparse sampling method.

[0075] To demonstrate the infinite scalability and generalization capability of P-FOAM pattern recognition based on ring sparse sampling under the phase misinterpretation theory, a multiplexed vortex beam with l = ±1.5 is used as an example (e.g. Figure 7 As shown in (a), relevant theoretical and experimental explorations were conducted. Discrete sampling was performed at 32, 64, and 128 points along a circle with r = 17 mm to obtain the ring sound pressure and phase distribution. The theoretical and experimental results are as follows: Figure 7 (b) shows the solid and dashed lines. The graph demonstrates that the agreement between the theoretical and experimental results increases with the number of sampling points. Here, one-dimensional circular effective data with different numbers of sampling points is selected as the input to the CNN for training. Classification and recognition of P-FOAMs with resolutions of 0.2, 0.1, 0.05, and 0.025 are performed, and the recognition accuracy and loss function distribution are shown below. Figure 7 As shown in (c), the inset plot represents the probability distribution of the relevant P-FOAM. With an accuracy of 95%, the recognizable precision of P-FOAM increases with the number of sampling points. Single-ring sampling with 32, 64, and 128 points achieves P-FOAM recognition resolutions of 0.1, 0.05, and 0.025, respectively. Figure 2 (c) The results in the embedded table are consistent. As the required decoding accuracy increases, although the corresponding decoding accuracy decreases from 98% to 77%, the probability of l = ±1.5 is the highest, reflecting the CNN's ability to recognize P-FOAM. Compared with cutting-edge research on optical FOAM multiplexing decoding, previous optical methods used deep learning to perform high-intensity training on thousands of ultra-high resolution intensity images (original resolution up to 1920*1080, further sampled and compressed to 224*224) captured by cameras to achieve high-precision FOAM pattern recognition. However, we only need 128-point single-ring sampling to achieve ultra-high resolution P-FOAM pattern recognition (0.025) in acoustics, with a recognition accuracy of 95%. This highlights the absolute advantage of phase-misaligned mediation theory in the infinite capacity expansion of fractional-order vortex communication. Furthermore, multi-ring sampling measurements can be introduced into the CNN to further improve recognition accuracy and data transmission resolution, which is of great significance for optimizing P-FOAM communication performance.

[0076] It should be noted that the above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Equivalent substitutions or replacements made based on the above technical solutions are all within the scope of protection of the present invention, and the scope of protection of the present invention is determined by the claims.

Claims

1. A high-precision, high-dimensional fractional-order orbital angular momentum acoustic communication method mediated by phase misalignment, characterized in that, The method includes the following steps: (1) Based on the active phase control technology and orbital angular momentum multiplexing technology of ring array, the phase encoding of a single ring transducer array with N sound sources is used to construct a coaxial coherent multiplexed vortex sound beam carrying fractional orbital angular momentum pairs with opposite polarities, forming a stable petal-shaped sound pressure and phase misalignment distribution, enhancing the stability of fractional orbital angular momentum multiplexed vortex identification features, and improving the information transmission capability and anti-interference capability of the vortex sound beam; (2) The fractional-order vortex sound beam is described as the superposition of countless integer-order vortex sound beams. Its phase error is the rotational superposition of the phase error after interference of adjacent integer-order vortices. Its rotation angle is positively correlated with the fractional-order orbital angular momentum. (3) The relationship between the sound pressure / phase distribution of the vortex sound field and the accuracy of orbital angular momentum recognition is used to guide the design of the ring sparse sampling array, and the sampled sound pressure and phase information are fused to construct a holographic sound field distributed along the circumference, which greatly reduces the amount of data and improves the recognition speed and efficiency of orbital angular momentum. (4) Considering the influence of channel and environmental interference on the sound field in actual information transmission, a convolutional neural network based on the turbulence model is constructed, and the amplitude and phase information of the ring sparse sampling are fused to construct the image training set, thus realizing high-precision high-dimensional fractional orbital angular momentum decoding. (5) Reduce the fractional orbital angular momentum interval and increase the number of ring sampling rings and points to infinitely expand the dimension of data communication within the limited orbital angular momentum range, thereby realizing the high-speed, miniaturized and real-time operation of the high-capacity vortex beam communication application system.

2. The high-precision, high-dimensional fractional-order orbital angular momentum acoustic communication method under phase misalignment mediation according to claim 1, characterized in that, In step (1), N transducers are uniformly distributed on an annular disk of radius a to construct a single-ring emission array. The sound wave frequency is f, and the angle between adjacent sound sources is . Using the same amplitude A, the initial phases are respectively and Two cosine signals and To synthesize, we obtain To excite the nth transducer, a coaxial coherent multiplexed vortex acoustic beam carrying fractional-order orbital angular momentum pairs with opposite polarities is constructed by superimposing the radiated sound fields from N phased-point sound sources. Here, l represents the order of the fractional orbital angular momentum, i.e., the fractional-order topological charge. If the topological charges of the multiplexed vortex acoustic beam containing S pairs of fractional-order orbital angular momentum pairs with opposite polarities are respectively... Then the excitation signal of the nth sound source is Similarly, based on phase control theory, multiple pairs of fractional-order orbital angular momentum multiplexed sound beams are formed, wherein the number of transducers... .

3. The high-precision, high-dimensional fractional-order orbital angular momentum acoustic communication method under phase misalignment mediation according to claim 1, characterized in that, In step (2), the connection between the coherent fractional-order vortex sound beam and the coherent integer-order vortex sound beam is established, and the relationship between the phase shift space angle and the fractional-order orbital angular momentum is analyzed. The sound pressure of the sound beam formed by the interference of the two vortex sound beams carrying fractional-order orbital angular momentum with opposite polarities is described as follows: ,in Spatial coordinates The sound pressure at that location, where l and m are the fractional and integer vortex orders, respectively. , Let represent the sound pressure amplitude distribution and signal phase, respectively. Both depend only on the radius and the magnitude of the topological charge. A fractional-order coherent vortex beam is described as the superposition of countless integer-order coherent vortex beams with different weights. Its phase error is the rotational superposition of the phase errors after interference of adjacent integer-order vortices, with a rotation angle of . .

4. The high-precision, high-dimensional fractional-order orbital angular momentum acoustic communication method under phase misalignment mediation according to claim 1, characterized in that, In step (3), the phase shift space angle of the fractional-order coherent vortex beam is approximately inversely proportional to the topological charge. This inverse relationship needs to be determined based on the parameters of the launch array, and the fractional-order orbital angular momentum is identified by the difference in spatial rotation of the phase shift.

5. The high-precision, high-dimensional fractional-order orbital angular momentum acoustic communication method under phase misalignment mediation according to claim 1, characterized in that, In step (3), when the topological charge l = 0.5~3.0, a suitable topological charge is selected to determine the relationship between the fractional order orbital angular momentum recognition accuracy, the phase shift spatial angular resolution and the number of sampling points. Based on the relationship between the number of sampling points and the orbital angular momentum recognition accuracy, a ring-shaped sparse sampling array is constructed to collect sound pressure and phase information, which are respectively set as the RG channel of the color image, and the B channel and other pixels are set to zero. Thus, holographic sound field information distributed along the circumference is constructed. The sparse ring sampling array structure includes single ring / double ring / multi-ring array models, and the number of sampling points in a single ring is between 16 and 128.

6. The high-precision, high-dimensional fractional-order orbital angular momentum acoustic communication method under phase misalignment mediation according to claim 1, characterized in that, In step (4), a fractional-order coherent multiplexed vortex beam is constructed within the topological charge range of 0.5 to 3.

0. A random complex matrix C with a mean of 0 and a variance of 1 is used to perform random filtering on the ring-sampled power spectrum, yielding the sound pressure formula within the cross-section of the fractional-order multiplexed vortex beam: Where 's' represents the vortex acoustic beam number. , This represents the inverse Fourier transform symbol. For the spectral variance, and These are the frequency domain coordinates of the phase screen.

7. The high-precision, high-dimensional fractional-order orbital angular momentum acoustic communication method under phase misalignment mediation according to claim 1, characterized in that, In step (4), the standard deviation between the CNN pattern recognition decoding result and the theoretical result is used. The accuracy and stability of data transmission and decoding are evaluated, among which... and These represent the experimental and theoretical decoding probability distributions, respectively. Indicates the number of information categories.

8. The high-precision, high-dimensional fractional-order orbital angular momentum acoustic communication method under phase misalignment mediation according to claim 1, characterized in that, In step (5), the dimension of data communication is infinitely expanded within the limited orbital angular momentum range, thereby realizing the high-speed, miniaturized and real-time operation of the large-capacity vortex beam communication application system.

9. The high-precision, high-dimensional fractional-order orbital angular momentum acoustic communication method under phase misalignment mediation according to claim 1, characterized in that, This is achieved through a high-precision, high-dimensional fractional-order orbital angular momentum acoustic communication system mediated by phase misalignment. The system includes A. a computer, B. an active phased-array drive system, C. a motion control module, D. a single-ring transmitting array, E. a single-ring / dual-ring acquisition system, and F. a digital oscilloscope. The computer synthesizes multiple pairs of fractional-order orbital angular momentum multiplexed vortex excitation signals, which are amplified by a power amplifier to drive the single-ring transmitting transducer array. The transducers are used to sample the single-ring / dual-ring acoustic signals, and the sound pressure information is acquired by the digital oscilloscope and fed into a convolutional neural network for P-FOAM pattern recognition and decoding.

Images