A waveform design method based on underwater acoustic data and energy simultaneous transmission

Abstract

The application discloses a waveform design method based on underwater acoustic energy and communication transmission, comprising the following steps: constructing an underwater acoustic energy and communication transmission system model; fitting the gain curve of an acoustic-electric transducer; analyzing the energy collection and communication performance of underwater acoustic energy and communication transmission; jointly optimizing the transmission waveform and power splitting factor with the maximum energy collection as the target; fitting the frequency response curve of the transducer based on measured data, and accurately depicting the frequency-dependent energy conversion efficiency; by introducing a nonlinear rectifier model, the high peak-to-average ratio characteristics of the multi-carrier waveform can be fully utilized to significantly improve the direct current output power of the rectifier circuit; in the whole transmission process, the power splitting factor and the beamforming vector are adjusted through the joint optimization algorithm, the minimum rate requirement of the underwater communication link is strictly guaranteed, and the energy transmission efficiency is maximized; the problem of inaccurate performance prediction and low efficiency of the simplified model in the actual underwater environment is effectively solved, and the energy self-sustaining ability of the underwater Internet of Things node is significantly improved.

Description

Technical Field

[0001] This invention relates to the field of underwater wireless communication and energy transmission technology, and in particular to a waveform design method based on underwater acoustic data and energy transmission. Background Technology

[0002] As human exploration of the ocean deepens, the Internet of Underwater Things (IoUT) plays a crucial role in marine environmental monitoring, resource development, and disaster early warning. However, underwater nodes are typically deployed in deep-sea or hazardous environments, making battery replacement and maintenance extremely difficult and expensive. Traditional battery-powered systems limit node endurance, making it difficult to meet the demands of continuous and stable data transmission, severely restricting the long-term operation and effectiveness of underwater networks.

[0003] Simultaneous Acoustic Information and Power Transfer (SAIPT) has emerged as a promising technology to address the dual challenges of underwater energy supply and information transmission. SAIPT utilizes sound waves as a unified carrier to transfer energy simultaneously during wireless data transmission. Through sound waves, mobile platforms, such as Autonomous Underwater Vehicles (AUVs), can simultaneously transmit information and deliver energy to sensor nodes, effectively overcoming the limitations of underwater battery power.

[0004] In existing research on underwater acoustic data transmission, the neglect of transducer frequency response characteristics and rectifier circuit nonlinearity leads to system model distortion and limited energy transmission efficiency.

[0005] Therefore, it is necessary to develop a waveform design method based on underwater acoustic digital energy transmission to solve the above problems. Summary of the Invention

[0006] The purpose of this invention is to design a waveform design method based on underwater acoustic digital energy transmission in order to solve the above problems.

[0007] The present invention achieves the above objectives through the following technical solutions:

[0008] A waveform design method based on underwater acoustic digital-energy simultaneous transmission includes the following steps:

[0009] S1. Construct a data and energy transmission system model based on underwater acoustics; the data and energy transmission system model specifically includes the SAIPT system model, underwater acoustic channel path loss model, underwater noise model, single-carrier transmission efficiency model, and signal model;

[0010] S2, Fitting of gain curve of acoustic-electric transducer;

[0011] S3. Analysis of the reception and communication performance of underwater acoustic data transmission; this step includes the following sub-steps:

[0012] S31. Analysis of underwater acoustic energy transmission performance;

[0013] S32. Analysis of underwater acoustic information transmission performance;

[0014] S4. Jointly optimize the transmit waveform and power division factor with the goal of maximizing received energy; this step includes the following sub-steps:

[0015] S41. Optimize the problem description;

[0016] S42, Optimized transmit beamforming;

[0017] S43, Power Division Factor Adjustment.

[0018] Specifically, a SAIPT system includes a SAIPT transmitter and a SAIPT receiver. A SAIPT system is a type of system that includes... An OFDM system with n orthogonal subcarriers, where the nth The frequency of each subcarrier is The subcarrier spacing is constant. ,and The carrier frequencies are arranged at uniform intervals and can be represented as:

[0019]

[0020] in, This indicates the resonant frequency of the transducer;

[0021] In the SAIPT transmitter, Indicates the first Deterministic energy transfer symbols on each subcarrier, with all subcarriers set to unit values, i.e. ;and The symbol vector represents the information transmission symbol on the nth subcarrier; after aggregating all subcarriers, the symbol vector is defined as follows: , ;

[0022] For energy transmission and information transmission, the amplitude-phase controller utilizes the corresponding coefficient vectors respectively. and To adjust and Each element; the adjusted vector is represented as , ,in This represents element-wise multiplication; subsequently, each corrected vector is modulated onto its corresponding subcarrier and superimposed to form electrical signals for energy transfer. and electrical signals used for information transmission Integrated transmission of electrical signals It is obtained by superimposing energy transmission signals and information transmission signals; after passing through a transducer, the combined electrical signals are transmitted. It is converted to send SAIPT signals. And transmit into the underwater acoustic channel;

[0023] through After propagation over a distance of m, the received SAIPT signal First, the receiving transducer converts the signal into a comprehensive received electrical signal. Using power division factor as Power divider, signal and They are then fed to a rectifier to generate DC output and to an information decoder.

[0024] In the underwater acoustic channel path loss model, the path loss of the underwater acoustic channel can be modeled using the following formula, with the path loss unit being dB:

[0025] ,

[0026] in, (m) represents the distance between the transmitter and the receiver. The signal frequency is expressed in Hz. For diffusion factor, Absorption coefficient as a function of frequency, in dB / m; diffusion factor It characterizes the geometric features of propagation, where Corresponding to spherical diffusion, Corresponding to cylindrical diffusion, while Represents the actual diffusion situation; absorption coefficient Thorp's formula is usually used for empirical approximation.

[0027] Specifically, in the underwater noise model, underwater noise mainly consists of four components: turbulence noise, shipping noise, wind and wave noise, and thermal noise. The power spectral density of these four noise components can be empirically expressed as a function of frequency, and the unit of power spectral density is dBre. Pa / Hz, that is:

[0028]

[0029] in , , and The power spectral densities correspond to turbulence, shipping, wind and waves, and thermal noise, respectively. Frequency is expressed in kHz. This is a shipping activity factor, with a value of 0-1, where 0 indicates the least impact and 1 indicates the greatest impact. This indicates wind speed, measured in m / s, and is typically 1-12.

[0030] The total power spectral density of underwater noise is expressed as:

[0031]

[0032] Furthermore, underwater noise power is expressed as dB re Pa units Or expressed in watts. The calculation formula is as follows:

[0033]

[0034] in, Indicates the minimum operating frequency. Represents system bandwidth. This represents the overall efficiency of the circuit, which includes a power amplifier and a transducer.

[0035] Specifically, in the single-carrier transmission efficiency model, the frequency is... Distance is The energy transfer efficiency at a point is defined as:

[0036] in, and They represent the frequencies respectively. and distance The collected electrical power and transmitted electrical power of the integrated electrical signal;

[0037] and The relationship between them is given by the following formula:

[0038]

[0039] in, Transmitting electrical power, measured in watts. The collected power is expressed in dBW. and They represent the frequencies respectively. Transducer gain of transmitter and receiver, in dB;

[0040] Converting formula (7) to its linear form, we get:

[0041]

[0042] in, and These represent the linear transducer gains of the transmitter and receiver, respectively.

[0043] If the transmitter and receiver use the same transducer, then Without loss of generality, the above expression can be further simplified to:

[0044] ,

[0045] Therefore, energy transfer efficiency Can be written as:

[0046] ,

[0047] also, Defined as the first Each subcarrier at distance The energy transfer efficiency at that point can be expressed as:

[0048] .

[0049] Furthermore, in the signal model, the transmitted signal is synthesized. It can be represented as:

[0050] (12)

[0051] in , ;

[0052] According to S14, the received electrical signals are integrated. It can be represented as:

[0053]

[0054] in and The received electrical signals, representing information transmission and energy transmission respectively, are defined as follows:

[0055] .

[0056] Specifically, in step S2, the gain of the acoustic-electric transducer can be calculated based on its transmitted voltage response and impedance frequency response, i.e.:

[0057]

[0058] in, Indicates frequency as The relationship between the voltage excitation of the transducer and the sound pressure response, expressed in dB re 1 Pa / V @1m, The complex impedance of a transducer at the same frequency; the gain of a linear transducer. and The relationship is represented as ;

[0059] The measured voltage response and impedance data of the transducer can be used in conjunction with formula (15) and discrete linear gain values ​​can be obtained through linear transformation. Since these measurements are only available at a limited number of sampling points, curve fitting is required to derive a continuous gain function covering the entire operating frequency band, which can then be used for system modeling and waveform optimization.

[0060] Using the MATLAB curve fitting toolbox, various curve fitting methods were applied to the transducer data to obtain fitting results. Based on the fitting results, the sinusoidal sum model exhibits the best performance on the transducer. The sinusoidal sum model is expressed as:

[0061] ,

[0062] in, , and They represent the first The amplitude coefficients, frequency scaling factors, and phase offsets of each sinusoidal basis function are all obtained by fitting the gain data using the least squares method.

[0063] Specifically, in step S31, in the energy harvesting branch, the signal after power division... The rectifier generates a DC output, which can then be used to power the underwater node.

[0064] Based on the nonlinear diode model of the rectifier, the DC output and input signal... The relationship between them is represented as follows:

[0065] ,

[0066] in, and Represents the rectifier constant. This represents the impedance of the transducer, while It is proportional to the DC output power; therefore, maximizing the DC output power is equivalent to maximizing ;

[0067] Considering ,and For deterministic signals, formula (17) can be reformulated as:

[0068]

[0069] Furthermore, the channel vectors of all subcarriers are denoted as:

[0070]

[0071] Define the matrix as Specifically, it can be expanded as follows:

[0072]

[0073] For subsequent analysis, a set of auxiliary matrices is introduced. ; It is Matrix, which is obtained by retaining only The selected subset of elements is obtained by setting all other elements to zero; for ,matrix reserve No. Elements on the diagonal of the bar; for Its reservation of the first Elements on the lower diagonal; and for Its retention The main diagonal elements;

[0074] Next, each term in formula (18) can be rewritten in matrix form, that is:

[0075]

[0076] By substituting formula (21) into (18). The expression can be rewritten in the following matrix form:

[0077]

[0078] also, and It can be decomposed into real and imaginary parts, thereby converting the expression from the complex field to the real field, which reduces the complexity of subsequent optimizations; The expression is restated as:

[0079]

[0080] in:

[0081] ,

[0082]

[0083] and ;

[0084] In step S32, after passing through the power divider, the signal components... It is allocated for information transmission; according to Shannon's capacity formula, the achievable data rate of the system is expressed as:

[0085]

[0086] in, and These represent additive white Gaussian noise from the underwater acoustic channel and noise introduced by the down-conversion process, respectively.

[0087] Specifically, in step S41, in the SAIPT system, the objective is to maximize the harvested energy power while ensuring the minimum communication rate requirement. Based on this, the optimization problem of the SAIPT system is constructed as follows:

[0088]

[0089] in This represents the minimum communication rate requirement;

[0090] Since problem P1 is non-convex and difficult to solve directly, an alternating optimization strategy is adopted; specifically, the power division factor is first fixed. Optimize the coefficient vector of information transmission and energy transmission and Then, while maintaining and Update if nothing changes These two steps are performed alternately until convergence is achieved.

[0091] In step S42, firstly, the present invention maintains the power division factor. With a fixed value, optimize the coefficient vectors used for information transmission respectively. and the coefficient vector used for energy transfer To transform this non-convex problem into a convex problem, we need to... about and Perform a first-order Taylor expansion; based on this, the objective function... Approximately:

[0092]

[0093] in express exist gradient at;

[0094] Therefore, problem P1 can be transformed into:

[0095]

[0096] To handle the nonconvexity of the rate constraint, auxiliary variables are introduced. and as follows:

[0097]

[0098] Therefore, problem P2 can be further reconstructed as:

[0099]

[0100] By further performing a first-order Taylor expansion on the constraints of problem P3, the optimization problem is reconstructed as follows:

[0101]

[0102] in express The One component;

[0103] Therefore, by transforming the rate constraint and performing a first-order Taylor expansion on both the objective function and the constraint conditions, the beamforming vector can be optimized by iteratively solving problem P4 using a successive convex approximation method; in each iteration, the first-order Taylor expansion point... and The beamforming vector obtained from the previous iteration is updated, while the initial unfolding point is a randomly generated feasible vector that satisfies the constraints.

[0104] Specifically, in step S43, while maintaining the beamforming vector and With a fixed power division factor The optimization problem can be described as follows:

[0105] (31)

[0106] because Follow Monotonically increasing, while Follow Since it is monotonically decreasing, a binary search method can be used to determine the value that exactly satisfies the rate constraint. Value, thereby achieving Maximize;

[0107] Ultimately, by using a fixed power allocation factor Alternate optimization of beamforming vectors and And optimization under a fixed beamforming vector This process achieves joint optimization of all variables; the alternating optimization process is executed iteratively until convergence, thereby obtaining an effective solution to the original problem; the alternating optimization process will start from multiple randomly generated initial points, and among the obtained solutions, the solution that maximizes the DC output will be selected as the optimal result.

[0108] The beneficial effects of this invention are:

[0109] This invention fits the frequency response curve of the transducer based on measured data, breaking the traditional assumption of an ideal transducer and accurately characterizing the frequency-dependent energy conversion efficiency. By introducing a nonlinear rectification model, it can fully utilize the peak-to-average power ratio (PAPR) of multi-carrier waveforms to significantly improve the DC output power of the rectifier circuit. Throughout the transmission process, by adjusting the power splitting factor and beamforming vector through a joint optimization algorithm, it maximizes energy transmission efficiency while strictly ensuring the minimum rate requirement of the underwater communication link. The method of this invention effectively solves the problems of inaccurate performance prediction and low efficiency of simplified models in actual underwater environments, and significantly improves the energy self-sustaining capability of underwater IoT nodes. Attached Figure Description

[0110] Figure 1 This is a flowchart of the present invention;

[0111] Figure 2 This is a model diagram of an underwater acoustic data transmission system. Detailed Implementation

[0112] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0113] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0114] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0115] In the description of this invention, it should be understood that the terms "upper," "lower," "inner," "outer," "left," "right," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of this invention is in use, or the orientation or positional relationship commonly understood by those skilled in the art. They are only used to facilitate the description of this invention and to simplify the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0116] Furthermore, the terms "first," "second," etc., are used only to distinguish descriptions and should not be interpreted as indicating or implying relative importance.

[0117] In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, terms such as "set" and "connection" should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be a connection within two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0118] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0119] The meanings of the parameters involved in this embodiment are shown in Table 1:

[0120] Table 1 Parameter Meaning

[0121]

[0122] like Figure 1 As shown, the specific implementation process of the waveform design method based on underwater acoustic data and energy simultaneous transmission of the present invention is as follows:

[0123] S1. Construct a data and energy transmission system model based on underwater acoustics. Specifically, this step includes the following sub-steps:

[0124] S11, SAIPT system model. The system model is as follows: Figure 2 As shown. This system is based on Orthogonal Frequency Division Multiplexing (OFDM) technology and includes a SAIPT transmitter and a SAIPT receiver. This invention contemplates a system comprising... An OFDM system with n orthogonal subcarriers, where the nth The frequency of each subcarrier is The subcarrier spacing is constant. ,and The carrier frequencies are arranged at uniform intervals and can be represented as:

[0125]

[0126] in, This indicates the resonant frequency of the transducer.

[0127] Figure 1 The upper part shows the SAIPT transmitter. Specifically, Indicates the first Deterministic energy transfer symbols on each subcarrier (all subcarriers are set to unit values, i.e.) ),and This represents the information transmission symbol on the nth subcarrier. After aggregating all subcarriers, the symbol vector is defined as follows: , .

[0128] For energy transmission and information transmission, the amplitude-phase controller utilizes the corresponding coefficient vectors respectively. and To adjust and Each element of the vector. The adjusted vector is represented as... , ,in This represents element-wise multiplication. Subsequently, each corrected vector is modulated onto its corresponding subcarrier and superimposed to form electrical signals for energy transfer. and electrical signals used for information transmission Integrated transmission of electrical signals It is obtained by superimposing energy transmission signals and information transmission signals. After passing through a transducer, the combined electrical signal is transmitted. It is converted to send SAIPT signals. It then transmits into the underwater acoustic channel.

[0129] through After propagation over a distance of m, the received SAIPT signal First, the receiving transducer converts the signal into a comprehensive received electrical signal. Using the power division factor as Power divider, signal and They are then fed to a rectifier to generate DC output and to an information decoder.

[0130] S12. Path Loss Model for Underwater Acoustic Channel. The path loss (unit: dB) of an underwater acoustic channel can be modeled using the following formula:

[0131] ,

[0132] in, (m) represents the distance between the transmitter and the receiver. (Hz) represents the signal frequency. It is the diffusion factor (similar to the path loss exponent in a radio channel). Absorption coefficient as a function of frequency (unit: dB / m). Diffusion factor. It characterizes the geometric features of propagation, where Corresponding to spherical diffusion, Corresponding to cylindrical diffusion, while This represents the actual diffusion scenario. Absorption coefficient. Thorp's formula is usually used for empirical approximation.

[0133] S13. Underwater Noise Model. Underwater noise mainly consists of four components: turbulence noise, shipping noise, wind and wave noise, and thermal noise. The power spectral density (psd) of these four noise components (unit: dB re) Pa / Hz can be empirically expressed as a function of frequency, i.e.:

[0134]

[0135] in , , and The power spectral densities correspond to turbulence, shipping, wind and waves, and thermal noise, respectively. Indicates frequency (kHz), This is a shipping activity factor (values ​​range from 0 to 1, where 0 indicates the least impact and 1 indicates the greatest impact). This indicates wind speed (m / s, usually 1-12).

[0136] Therefore, the total power spectral density of underwater noise can be expressed as:

[0137]

[0138] Furthermore, underwater noise power is expressed in dB re μPa units. Or expressed in watts. The calculation formula is as follows:

[0139]

[0140] in, Indicates the minimum operating frequency. Represents system bandwidth. The overall efficiency of a circuit (including power amplifiers and transducers).

[0141] S14, Single-carrier transmission efficiency model. This invention uses a frequency of... Distance is The energy transfer efficiency at a point is defined as:

[0142] in, and They represent the frequencies respectively. and distance The collected electrical power and transmitted electrical power of the integrated electrical signal are measured.

[0143] and The relationship between them is given by the following formula:

[0144]

[0145] in, Transmitting electrical power (unit: watts). The collected power (unit: dBW), and and They represent the frequencies respectively. Transducer gain of transmitter and receiver (unit: dB).

[0146] Converting formula (7) to its linear form, we get:

[0147]

[0148] in, and These represent the linear transducer gains of the transmitter and receiver, respectively. The specific expressions for the transducer gains will be given in S2.

[0149] In practical system design, if the transmitter and receiver use the same transducer, then Without loss of generality, the above expression can be further simplified to:

[0150]

[0151] Therefore, energy transfer efficiency Can be written as:

[0152]

[0153] also, Defined as the first Each subcarrier at distance The energy transfer efficiency at that point can be expressed as:

[0154]

[0155] S15, Signal Model. As described in S11, synthesize the transmitted signal. It can be represented as:

[0156]

[0157] in , ;

[0158] According to S14, the received electrical signals are integrated. It can be represented as:

[0159]

[0160] in and The received electrical signals, representing information transmission and energy transmission respectively, are defined as follows:

[0161]

[0162] S2. Fitting the gain curve of the acoustic-electric transducer. The gain of the acoustic-electric transducer can be calculated based on its transmitted voltage response (TVR) and impedance frequency response, i.e.:

[0163]

[0164] in, This represents the relationship between the voltage excitation and sound pressure response of the transducer at frequency f (unit: dB re 1 μ Pa / V @1m). This represents the complex impedance of the transducer at the same frequency. Linear transducer gain. and The relationship can be represented as .

[0165] The measured TVR and impedance data of the BII-7511 transducer can be used in conjunction with formula (15) and discrete linear gain values ​​can be obtained through linear transformation. Since these measurements are only available at a limited number of sampling points, curve fitting is required to derive a continuous gain function covering the entire operating frequency band, which can then be used for system modeling and waveform optimization.

[0166] Using the MATLAB curve fitting toolbox, this invention applied various curve fitting methods to the BII-7511 transducer data. The fitting results are summarized in Table 2.

[0167] Table 2. BII-7511 Gain Curve Fitting Results

[0168]

[0169] The sinusoidal sum model exhibits optimal performance on the BII-7511 transducer, accurately capturing its resonant gain characteristics. Despite containing 24 parameters, its superior smoothness and fitting accuracy make it the optimal choice for subsequent system modeling. The sinusoidal sum model can be expressed as:

[0170] ,

[0171] in, , and Let X represent the amplitude coefficient, frequency scaling factor, and phase offset of the i-th sinusoidal basis function, respectively. All these parameters are obtained by fitting the gain data using the least squares method.

[0172] S3. Analysis of the reception and communication performance of underwater acoustic data transmission. Specifically, this step includes the following sub-steps:

[0173] S31. Analysis of underwater acoustic energy transfer performance. In the energy harvesting branch, the signal after power splitting... The rectifier generates a DC output, which can then be used to power the underwater node.

[0174] Based on the nonlinear diode model of the rectifier, the DC output and input signal... The relationship between them can be represented as:

[0175] ,

[0176] in, and Represents the rectifier constant. This represents the impedance of the transducer, while It is proportional to the DC output power. Therefore, maximizing the DC output power is equivalent to maximizing... .

[0177] Considering ,and For deterministic signals, formula (17) can be reformulated as:

[0178]

[0179] Furthermore, the channel vectors of all subcarriers are denoted as:

[0180]

[0181] Define the matrix as Specifically, it can be expanded as follows:

[0182]

[0183] To facilitate subsequent analysis, this invention further introduces a set of auxiliary matrices. Specifically, It is Matrix, which is obtained by retaining only It is obtained by selecting a subset of elements and setting all other elements to zero. For ,matrix reserve No. Elements on the diagonal of the bar; for Its reservation of the first Elements on the lower diagonal; and for Its retention The main diagonal element.

[0184] Next, each term in formula (18) can be rewritten in matrix form, that is:

[0185]

[0186] By substituting formula (21) into (18). The expression can be rewritten in the following matrix form:

[0187]

[0188] also, and It can be decomposed into real and imaginary parts, thus transforming the expression from the complex field to the real field and reducing the complexity of subsequent optimizations. Based on this, The expression can be restated as:

[0189]

[0190] in:

[0191] ,

[0192]

[0193] and ;

[0194] S32. Underwater acoustic information transmission performance analysis. After the power divider, the signal components... It is allocated for information transmission. According to Shannon's capacity formula, the achievable data rate of the system can be expressed as:

[0195]

[0196] in, and These represent additive white Gaussian noise from the underwater acoustic channel and noise introduced by the down-conversion process, respectively.

[0197] S4. Jointly optimize the transmit waveform and power division factor with the goal of maximizing received energy. Specifically, this step includes the following sub-steps:

[0198] S41. Optimization Problem Description. In the SAIPT system, the objective is to maximize the harvested energy power while ensuring the minimum communication rate requirement. Therefore, the optimization problem of the SAIPT system is constructed as follows:

[0199]

[0200] in This represents the minimum communication rate requirement.

[0201] Since the problem (P1) is non-convex and difficult to solve directly, this invention employs an alternating optimization (AO) strategy. Specifically, the power division factor is first fixed. Optimize the coefficient vector of information transmission and energy transmission and Then, while maintaining and Update if nothing changes These two steps are performed alternately until convergence is achieved.

[0202] S42, Transmit Beamforming Optimization. Firstly, this invention maintains the power division factor... With a fixed value, optimize the coefficient vectors used for information transmission respectively. and the coefficient vector used for energy transfer To transform this non-convex problem into a convex problem, this invention... about and Perform a first-order Taylor expansion. Based on this, the objective function... It can be approximated as:

[0203]

[0204] in express exist The gradient at that point.

[0205] Therefore, problem (P1) can be transformed into:

[0206]

[0207] To handle the nonconvexity of the rate constraint, auxiliary variables are introduced. and as follows:

[0208]

[0209] Therefore, problem (P2) can be further restructured as follows:

[0210]

[0211] By further performing a first-order Taylor expansion on the (P3) constraint, the optimization problem can be reconstructed as:

[0212]

[0213] in express The Each component.

[0214] Therefore, by transforming the rate constraint and performing a first-order Taylor expansion on both the objective function and the constraint conditions, the beamforming vector can be optimized by iteratively solving the problem (P4) using a successive convex approximation method. In each iteration, the first-order Taylor expansion point... and The beamforming vector obtained from the previous iteration is updated, while the initial unfolding point is a randomly generated feasible vector that satisfies the constraints.

[0215] S43, Power Division Factor Adjustment. This section focuses on adjusting the power division factor while maintaining the beamforming vector. and With a fixed power division factor The optimization problem can be described as follows:

[0216] (31)

[0217] because Follow Monotonically increasing, while Follow Monotonically decreasing (considering formula (24) denominator (relatively small), therefore a binary search method can be used to determine the value that exactly satisfies the rate constraint. Value, thereby achieving Maximize.

[0218] Ultimately, by using a fixed power allocation factor Alternate optimization of beamforming vectors and And optimization under a fixed beamforming vector This method enables joint optimization of all variables. The alternating optimization process is executed iteratively until convergence, thus obtaining an efficient solution to the original problem. To avoid convergence to local optima, the alternating optimization process starts from multiple randomly generated initial points. Among the obtained solutions, the one that maximizes the DC output is selected as the optimal result.

[0219] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A waveform design method based on underwater acoustic digital energy transmission, characterized in that, Includes the following steps: S1. Construct a data and energy transmission system model based on underwater acoustics; the data and energy transmission system model specifically includes the SAIPT system model, underwater acoustic channel path loss model, underwater noise model, single-carrier transmission efficiency model, and signal model; S2, Fitting of gain curve of acoustic-electric transducer; S3. Analysis of the reception and communication performance of underwater acoustic data transmission; this step includes the following sub-steps: S31. Analysis of underwater acoustic energy transmission performance; S32. Analysis of underwater acoustic information transmission performance; S4. Jointly optimize the transmit waveform and power division factor with the goal of maximizing received energy; this step includes the following sub-steps: S41. Optimize the problem description; S42, Optimized transmit beamforming; S43, Power Division Factor Adjustment.

2. The waveform design method based on underwater acoustic digital energy transmission according to claim 1, characterized in that, The SAIPT system consists of one SAIPT transmitter and one SAIPT receiver. The SAIPT system is an OFDM system containing N orthogonal subcarriers, where the frequency of the nth subcarrier is... The subcarrier spacing is constant. ,and The carrier frequencies are arranged at uniform intervals and can be represented as: ， in, This indicates the resonant frequency of the transducer; In the SAIPT transmitter, Indicates the first Deterministic energy transfer symbols on each subcarrier, with all subcarriers set to unit values, i.e. ;and The symbol vector represents the information transmission symbol on the nth subcarrier; after aggregating all subcarriers, the symbol vector is defined as follows: , ; For energy transmission and information transmission, the amplitude-phase controller utilizes the corresponding coefficient vectors respectively. and To adjust and Each element; the adjusted vector is represented as , ,in This represents element-wise multiplication; subsequently, each corrected vector is modulated onto its corresponding subcarrier and superimposed to form electrical signals for energy transfer. and electrical signals used for information transmission Integrated transmission of electrical signals It is obtained by superimposing energy transmission signals and information transmission signals; after passing through a transducer, the combined electrical signals are transmitted. It is converted to send SAIPT signals. And transmit into the underwater acoustic channel; The received SAIPT signal after propagation over a distance of dm First, the receiving transducer converts the signal into a comprehensive received electrical signal. Using power division factor as Power divider, signal and They are then fed to a rectifier to generate DC output and to an information decoder.

3. The waveform design method based on underwater acoustic digital energy transmission according to claim 2, characterized in that, In the underwater acoustic channel path loss model, the path loss of the underwater acoustic channel can be modeled using the following formula, with the path loss unit being dB: ， ， Where d(m) represents the distance between the transmitter and receiver, f is the signal frequency in Hz, and k is the diffusion factor. The absorption coefficient varies with frequency, expressed in dB / m; the diffusion factor k characterizes the geometric properties of propagation, where k=2 corresponds to spherical diffusion, k=1 corresponds to cylindrical diffusion, and... Represents the actual diffusion situation; absorption coefficient Thorp's formula is usually used for empirical approximation.

4. The waveform design method based on underwater acoustic digital-energy simultaneous transmission according to claim 3, characterized in that, In the underwater noise model, underwater noise mainly consists of four components: turbulence noise, shipping noise, wind and wave noise, and thermal noise. The power spectral density of these four noise components can be empirically expressed as a function of frequency, and the unit of power spectral density is dBre. Pa / Hz, that is: ， in , , and These correspond to the power spectral densities of turbulence, shipping, wind and waves, and thermal noise, respectively; f represents the frequency in kHz; s is the shipping activity factor, ranging from 0 to 1, where 0 indicates minimal impact and 1 indicates maximum impact; w represents the wind speed in m / s, typically 1-12. The total power spectral density of underwater noise is expressed as: ， Furthermore, underwater noise power is expressed as dB re Pa units Or expressed in watts. The calculation formula is as follows: ， in, B represents the minimum operating frequency, and B represents the system bandwidth. This represents the overall efficiency of the circuit, which includes a power amplifier and a transducer.

5. The waveform design method based on underwater acoustic digital energy transmission according to claim 4, characterized in that, In the single-carrier transmission efficiency model, the energy transmission efficiency at frequency f and distance d is defined as: , in, and These represent the collected electrical power and transmitted electrical power of the combined electrical signal at frequency f and distance d, respectively. and The relationship between them is given by the following formula: ， in, Transmitting electrical power, measured in watts. The collected power is expressed in dBW. and These represent the transducer gains of the transmitter and receiver at frequency f, respectively, in dB. Converting formula (7) to its linear form, we get: ， in, and These represent the linear transducer gains of the transmitter and receiver, respectively. If the transmitter and receiver use the same transducer, then Without loss of generality, the above expression can be further simplified to: ， ， Therefore, energy transfer efficiency Can be written as: ， ， also, Defined as the energy transmission efficiency of the nth subcarrier at a distance d, it can be expressed as: 。 6. The waveform design method based on underwater acoustic digital energy transmission according to claim 5, characterized in that, In the signal model, the transmitted signal is synthesized. It can be represented as: （12）， in , ; According to S14, the received electrical signals are integrated. It can be represented as: ， in and The received electrical signals, representing information transmission and energy transmission respectively, are defined as follows: 。 7. The waveform design method based on underwater acoustic digital energy transmission according to claim 6, characterized in that, In step S2, the gain of the acoustic-electric transducer can be calculated based on its transmitted voltage response and impedance frequency response, that is: ， in, This represents the relationship between the voltage excitation and sound pressure response of the transducer at frequency f, expressed in dB. Pa / V @1m, The complex impedance of a transducer at the same frequency; the gain of a linear transducer. and The relationship is represented as ; The measured voltage response and impedance data of the transducer can be used in conjunction with formula (15) and discrete linear gain values ​​can be obtained through linear transformation. Since these measurements are only available at a limited number of sampling points, curve fitting is required to derive a continuous gain function covering the entire operating frequency band, which can then be used for system modeling and waveform optimization. Using the MATLAB curve fitting toolbox, various curve fitting methods were applied to the transducer data to obtain fitting results. Based on the fitting results, the sinusoidal sum model exhibits the best performance on the transducer. The sinusoidal sum model is expressed as: ， ， in, , and Let X represent the amplitude coefficient, frequency scaling factor, and phase offset of the i-th sinusoidal basis function, respectively. All these parameters are obtained by fitting the gain data using the least squares method.

8. The waveform design method based on underwater acoustic digital energy transmission according to claim 7, characterized in that, In step S31, in the energy harvesting branch, the signal after power division... The rectifier generates a DC output, which can then be used to power the underwater node. Based on the nonlinear diode model of the rectifier, the DC output and input signal... The relationship between them is represented as follows: ， ， in, and Represents the rectifier constant. This represents the impedance of the transducer, while It is proportional to the DC output power; therefore, maximizing the DC output power is equivalent to maximizing ; Considering ,and For deterministic signals, formula (17) can be reformulated as: ， Furthermore, the channel vectors of all subcarriers are denoted as: ， Define the matrix as Specifically, it can be expanded as follows: ， For subsequent analysis, a set of auxiliary matrices is introduced. ; It is A matrix, which is obtained by keeping only a selected subset of elements in M ​​and setting all other elements to zero; for ,matrix Retain the elements on the diagonal of the k-th line in M; for It retains the elements on the k-th lower diagonal; while for k=0, it retains the elements on the main diagonal of M. Next, each term in formula (18) can be rewritten in matrix form, that is: ， By substituting formula (21) into (18). The expression can be rewritten in the following matrix form: ， also, and It can be decomposed into real and imaginary parts, thereby converting the expression from the complex field to the real field, which reduces the complexity of subsequent optimizations; The expression is restated as: ， in: ， ， and ; In step S32, after passing through the power divider, the signal components... It is allocated for information transmission; according to Shannon's capacity formula, the achievable data rate of the system is expressed as: ， in, and These represent additive white Gaussian noise from the underwater acoustic channel and noise introduced by the down-conversion process, respectively.

9. A waveform design method based on underwater acoustic digital-energy simultaneous transmission according to claim 8, characterized in that, In step S41, in the SAIPT system, the objective is to maximize the harvested energy power while ensuring the minimum communication rate requirement. Based on this, the optimization problem of the SAIPT system is constructed as follows: ， in This represents the minimum communication rate requirement; Since problem P1 is non-convex and difficult to solve directly, an alternating optimization strategy is adopted; specifically, the power division factor is first fixed. Optimize the coefficient vector of information transmission and energy transmission and Then, while maintaining and Update if nothing changes These two steps are performed alternately until convergence is achieved. In step S42, firstly, the present invention maintains the power division factor. With a fixed value, optimize the coefficient vectors used for information transmission respectively. and the coefficient vector used for energy transfer To transform this non-convex problem into a convex problem, we need to... about and Perform a first-order Taylor expansion; based on this, the objective function... Approximately: ， in express exist gradient at; Therefore, problem P1 can be transformed into: ， To handle the nonconvexity of the rate constraint, auxiliary variables are introduced. And t are as follows: ， Therefore, problem P2 can be further reconstructed as: ， By further performing a first-order Taylor expansion on the constraints of problem P3, the optimization problem is reconstructed as follows: ， in express The nth component; Therefore, by transforming the rate constraint and performing a first-order Taylor expansion on both the objective function and the constraint conditions, the beamforming vector can be optimized by iteratively solving problem P4 using a successive convex approximation method; in each iteration, the first-order Taylor expansion point... and The beamforming vector obtained from the previous iteration is updated, while the initial unfolding point is a randomly generated feasible vector that satisfies the constraints.

10. A waveform design method based on underwater acoustic digital-energy simultaneous transmission according to claim 9, characterized in that, In step S43, while maintaining the beamforming vector and With a fixed power division factor The optimization problem can be described as follows: (31) ， because Follow Monotonically increasing, while Follow Since it is monotonically decreasing, a binary search method can be used to determine the value that exactly satisfies the rate constraint. Value, thereby achieving Maximize; Ultimately, by using a fixed power allocation factor Alternate optimization of beamforming vectors and And optimization under a fixed beamforming vector This process achieves joint optimization of all variables; the alternating optimization process is executed iteratively until convergence, thereby obtaining an effective solution to the original problem; the alternating optimization process will start from multiple randomly generated initial points, and among the obtained solutions, the solution that maximizes the DC output will be selected as the optimal result.

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