OFDM magnetic induction communication current control method and device based on multi-frequency resonance compensation

Abstract

The invention discloses an OFDM magnetic induction communication current control method and device based on multi-frequency resonance compensation, and belongs to the field of resonance circuit tuning, and the method comprises the steps: building a circuit model of a MuReC-OFDM-MI communication system comprising a transmitter and a receiver, presetting each subcarrier frequency and resonance frequency of OFDM, and then according to the parameters of the circuit model, calculating the frequency of each subcarrier according to the parameters of the circuit model; the method comprises the following steps of: calculating impedance of a transmitter and a receiver, then calculating transmitting power and reachable rate of a MuReC-OFDM-MI communication system according to a circuit model, establishing an optimization problem by taking limited average power of the transmitter as a constraint and reachable rate maximization as a target, solving the optimization problem by using a convex optimization theory, and finally, according to a solving result, calculating the maximum reachable rate of the MuReC-OFDM-MI communication system. Expanding to obtain the channel capacity of the MuReC-OFDM-MI communication system and a current control scheme for achieving the channel capacity when the OFDM subcarrier frequency point # imgabs0 # is obtained; the invention further provides equipment and a readable storage medium which are used for implementing the method. According to the invention, the reachable rate of the MuReC-OFDM-MI communication system is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of resonance circuit tuning, and specifically relates to a current control method and device for OFDM magnetic induction communication based on multi-frequency resonance compensation. Background Art

[0002] The electromagnetic wave communication technology has made remarkable progress, with significant improvements in aspects such as transmission rate, bit error rate, and bandwidth utilization. However, in the underwater environment, the dynamic underwater conditions and harsh propagation environment will seriously hinder the transmission of electromagnetic waves. In such scenarios, the magnetic induction (MI) communication technology based on the mutual inductance effect of coils exhibits advantages such as high penetration efficiency, stable channel state, and small antenna size.

[0003] Its basic principle is to induce an electromotive force in the receiving coil through the current change in the transmitting coil, thereby realizing signal transmission. Different from traditional electromagnetic wave communication, magnetic induction communication relies on near-field magnetic coupling and has advantages such as high penetration, strong channel stability, low power consumption, and small antenna size. These characteristics make it particularly suitable for complex environments and harsh scenarios. In underground wireless sensor networks (WUSN), magnetic induction communication is widely used in agricultural monitoring, underground resource exploration, and earthquake early warning; in the underwater environment, it is used for marine resource investigation, ecological monitoring, and seabed communication; in the industrial field, it is used for equipment monitoring and control in environments such as mines and pipelines.

[0004] Jianyu Wang, Wenchi Cheng, and Hailin Zhang proposed an optimal current control scheme for a magnetic induction through-the-earth communication system based on MISO-OFDM in their published paper "Optimal Current Control for MISO-OFDM Based Through-the-Earth Communications with Magnetic Induction" (J. Wang, W. Cheng and H. Zhang, "Optimal Current Control for MISO-OFDM Based Through-the-Earth Communications with Magnetic Induction," 2021 IEEE / CIC International Conference on Communications in China (ICCC), Xiamen, China, 2021, pp. 133-138, doi: 10.1109 / ICCC52777.2021.9580360.). The implementation process first establishes a system model and analyzes the characteristics of the magnetic induction channel, and constructs a frequency-domain channel matrix by combining OFDM technology; then, aiming at maximizing the system channel capacity, constructs an optimization problem with constraints, and uses the Lagrangian dual decomposition method to design an optimal current control algorithm, and realizes the optimal current amplitude control of each transmit antenna on each subcarrier through iterative solution; at the same time, combines the water-filling algorithm to dynamically adjust the subcarrier power, and preferentially allocates power to subcarriers with better channel conditions to improve the spectral efficiency. There are two deficiencies in this method: one is that the circuit is a single-resonant circuit, and only one OFDM carrier works at the resonant frequency, resulting in reduced transmission efficiency; the other is that the carrier frequencies of the system are discrete, resulting in wasted spectrum resources and low spectral utilization rate.

[0005] Gang Yang, Mohammad R. Vedady Moghadam, and Rui Zhang proposed a multi-user magnetic beamforming optimization framework for the magnetic resonance coupling multiple-input multiple-output (MIMO) wireless power transfer system in their published paper "Magnetic MIMO Signal Processing and Optimization for Wireless Power Transfer" (G. Yang, M. R. V. Moghadam and R. Zhang, "Magnetic MIMO Signal Processing and Optimization for Wireless Power Transfer," in IEEE Transactions on Signal Processing, vol. 65, no. 11, pp. 2860-2874, 1 June 1, 2017, doi: 10.1109 / TSP.2017.2673816.). In the implementation process, an optimization algorithm based on semidefinite relaxation (SDR) was designed by first defining the multi-user power region to characterize the power allocation boundary of each receiver (RX). Subsequently, for the single RX scenario, a closed-form solution was derived in which the optimal transmitter (TX) current is proportional to the TX-RX mutual inductance. Finally, for the multi-RX non-convex problem, time-sharing and randomization methods were proposed to approximate the optimal solution, and the global optimality of the time-sharing scheme without peak constraints was proven. In addition, a least-squares-based magnetic MIMO channel estimation method was developed to solve the problem of real-time acquisition of the mutual inductance matrix. The disadvantages of this method are that it only utilizes the spatial diversity gain brought by MIMO at a single frequency, resulting in strong frequency-selective fading and low spectral efficiency. Summary of the Invention

[0006] In order to overcome the above-mentioned shortcomings of the prior art, the object of the present invention is to provide a method and device for current control of OFDM magnetic induction communication based on multi-frequency resonance compensation. By establishing a multi-resonance magnetic induction communication circuit, the mutual inductance of the coils is used to transmit information. Through circuit parameter modeling, a reachable rate model and a power model related to communication are obtained. According to multiple preset resonance frequencies, the parameters of the coils are obtained, so that a single coil resonates at multiple preset resonance frequencies, improving the transmission efficiency. Taking the reachable rate of the MuReC-OFDM-MI communication system as the optimization objective and the limited average power of the transmitter as the constraint, a mathematical optimization model is established, and the closed-form solution of the optimal current control method is obtained by using the KKT conditions. Using the current as the optimization variable is closer to the actual circuit than the power variable, and the current control strategy can be adjusted from the circuit level. Let the number of OFDM carrier frequencies , the channel capacity of the MuReC-OFDM-MI communication system and the current control method at this time are extended, further improving the utilization rate of spectrum resources to increase the achievable rate under limited spectrum resources and antenna resources.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows: An OFDM magnetic induction communication current control method based on multi-frequency resonance compensation, comprising the following steps: Step 1, establish a circuit model of the MuReC-OFDM-MI communication system, and preset the frequencies of each sub-carrier of OFDM and the resonance frequency. The circuit model includes a transmitter and a receiver; Step 2, calculate the parameters of each coil and capacitor in the circuit according to the circuit model established in Step 1 and the preset resonance frequency, and calculate the impedance of the transmitter and the receiver according to the parameters; Step 3, calculate the transmission power and achievable rate of the MuReC-OFDM-MI communication system according to the impedance of the transmitter and the receiver calculated in Step 2; Step 4, establish an average power limited constraint of the transmitter according to the transmission power obtained in Step 3; Step 5, based on the achievable rate obtained in Step 3 and the average power limited constraint obtained in Step 4, establish an optimization problem, and solve the optimization problem using convex optimization theory; Step 6, according to the result of the optimization problem obtained in Step 5, let the OFDM sub-carrier frequency , extend to obtain the channel capacity of the MuReC-OFDM-MI communication system and the current control scheme to achieve the channel capacity.

[0008] The transmitter in Step 1 includes a current source connected in series , a transmitting coil , a capacitor , an equivalent internal resistance resistor , parallel resonance circuits as a multi-frequency resonance compensation circuit. Among them, each parallel resonance circuit is composed of 1 coil and 1 supplementary capacitor connected in parallel. The coils in the parallel resonance circuit are wrapped with magnetic isolation materials and have no mutual inductance with each other; Among them, the output current of the current source is , the inductance value of the transmitting coil is , the capacitance value of the capacitor is , and the resistance value of the equivalent internal resistance resistor is , the inductance value of the coil is , and the capacitance value of the compensation capacitor is ; The receiver includes a receiving coil connected in series , a capacitor , an equivalent internal resistance , a load resistance , parallel resonance circuits as a multi - frequency resonance compensation circuit. Among them, each parallel resonance circuit is composed of 1 coil and 1 compensation capacitor connected in parallel. The coils in the parallel resonance circuit are wrapped with magnetic isolation materials and have no mutual inductance with each other; Among them, the inductance value of the receiving coil is , the capacitance value of the capacitor is , the resistance value of the equivalent internal resistance is , the resistance value of the load resistance is , the inductance value of the coil is , and the capacitance value of the compensation capacitor is .

[0009] The pre - set OFDM sub - carrier frequencies in step 1 include: defining the total bandwidth as , the center frequency of the bandwidth is , the corresponding running angular frequency is , applying OFDM modulation to divide the total bandwidth into sub - frequency bands, the bandwidth of each sub - frequency band is , the length of each OFDM symbol period is , the running frequency of the th sub - carrier is expressed as , the running angular frequency of the nth sub - carrier is expressed as , where , and the resonant frequency points are .

[0010] The calculation method of the transmitter impedance in step 2 includes: Based on the transmitter circuit in the established circuit model, obtain the reactance value of the transmitter : (1 - 1) Where is the operating frequency, is the capacitance of the transmitter value of the capacitance; is the transmitting coil of the transmitter value of the inductance, and are respectively the inductance value of the coil and the capacitance value of the capacitance of the parallel resonance circuit of the transmitter; For take the partial derivative with respect to the angular frequency : (2-1) Take the limit of Equation (2-1): Among them, define as the resonance frequency of each parallel resonance circuit of the transmitter, and its expression is: (6-1) At the same time, define ; Let , combine Equation (2-1) with Equations (3-1) to (5-1), where contains a zero point, contains a zero point, then the reactance has a total of zero points. Substitute Equation (6-1) into Equation (2-1) to get: (7-1) Rewrite Equation (7-1) based on the distribution of the zero points and the resonance frequency as: (8-1) Among them, is a constant, is the preset th resonance frequency. Let , get . Subsequently, the capacitance value of the capacitance , the compensation capacitance value of the capacitance of the parallel resonance circuit of the transmitter is Obtained by the partial fraction expansion method: (9-1) (10-1) When the resonance frequencies of each parallel resonance circuit of the transmitter satisfy , the value of is randomly selected, the coil of the parallel resonance circuit of the transmitter coil inductance value of , ; Finally, according to the capacitance of the transmitter capacitance value of , the compensation capacitance of the transmitter parallel resonance circuit capacitance value of , the coil of the transmitter coil parallel resonance circuit inductance value of , constant calculate the transmitter impedance ; The calculation method of the receiver impedance in step 2 includes: Based on the receiver circuit in the established circuit model, obtain the receiver reactance : (1 - 2) Among them, is the operating frequency, is the capacitance of the receiver capacitance value of is the receiving coil of the receiver inductance value of and are the inductance value of the coil and the capacitance value of the capacitance of the parallel resonance circuit of the receiver respectively; Take the partial derivative of with respect to the angular frequency : (2 - 2) Take the limit of equation (2 - 2): Among them, define as the resonance frequency of each parallel resonance circuit of the receiver, and its expression is: (6 - 2) At the same time, define ; Let , combine equation (2 - 2) with equations (3 - 2) to (5 - 2), where contains a zero point, contains a zero point, then the reactance has a total of zero points. Substitute equation (6 - 2) into equation (2 - 2) to get: (7 - 2) Based on the zero point and resonance frequency of equation (7 - 2) The distribution is rewritten as: (8 - 2) where, is a constant, is the pre - set th resonance frequency. Let , we get . Subsequently, the capacitance of the receiver and the capacitance value , the capacitance of the parallel resonance circuit of the receiver and the capacitance value are obtained by the partial - fraction expansion method: (9 - 2) (10 - 2) When the resonance frequencies of each parallel resonance circuit of the receiver satisfy , the value of is randomly selected from . Then the inductance value of the coil ; Finally, according to the capacitance of the receiver, the capacitance value , the compensation capacitance of the parallel resonance circuit of the receiver, the capacitance value , the inductance value of the coil of the parallel resonance circuit of the receiver, and the constant , the receiver impedance is calculated.

[0011] Step 3 specifically includes: Use to represent the symbol transmitted by the transmitter on the th sub - carrier, and it follows the distribution , where represents the current control factor of the transmitter on the th sub - carrier. Then the analog transmission signal of the th sub - carrier of the transmitter is expressed as: (11) where is the angular frequency of the th sub - carrier; According to Faraday's law of electromagnetic induction and Kirchhoff's law, the received signal received by the receiver is expressed as: (12) Among them, is the mutual inductance value between the transmitting coil and the receiving coil, is the impedance of the receiver corresponding to the th subcarrier. The mutual inductance value is expressed as: (13) Among them, is the distance between the two coils, and are the direction coefficient and eddy current coefficient of the two coils, and are the number of turns of the transmitting and receiving coils respectively, and are the radii of the transmitting and receiving coils respectively, is the magnetic permeability. Defining the voltage of the load resistance of each receiving coil of the receiver as the received signal, then the band-pass received signal of the receiver corresponding to the th subcarrier is: (14) Among them, is the resistance value of the load resistance, is the band-pass noise; According to Faraday's law of electromagnetic induction and Kirchhoff's law, the voltage of the transmitter current source is obtained as: (15) Among them, is the impedance of the transmitter. Based on Equation (15), the transmission power of the th subcarrier of the MuReC-OFDM-MI communication system is: (16) Among them, is the equivalent resistance of the MuReC-OFDM-MI communication system at the transmitter, is the equivalent internal resistance of the transmitter resistance value, is the equivalent internal resistance of the receiver resistance value; Based on Equation (14), the received power and achievable rate of the MuReC-OFDM-MI communication system are respectively: (17) (18) Among them, is the channel gain coefficient, is the bandwidth of each sub-band of OFDM.

[0012] The average power constraint in step 4 is as follows: (19) Wherein, is the total transmitter power constraint, is the bandwidth of each sub - band of OFDM, represents the current control factor of the transmitter at the th sub - carrier, is the equivalent resistance of the transmitter.

[0013] The optimization problem in step 5 is expressed as: (20) Wherein, is the bandwidth of each sub - band of OFDM, is the channel gain coefficient, represents the current control factor of the transmitter at the th sub - carrier, is the equivalent resistance of the MuReC - OFDM - MI communication system at the transmitter, is the total transmitter power constraint; The Lagrangian function of the optimization problem is: (21) Wherein, is a non - positive Lagrange multiplier. Taking the derivative with respect to , the KKT conditions of the optimization problem are as follows: (22) Subsequently, the result of the optimization problem is obtained: (23) Wherein, is the optimal Lagrange multiplier, obtained by numerical methods, which satisfies: (24).

[0014] Step 6 specifically includes: Let the OFDM sub - carrier frequency point , and the channel capacity and the corresponding average power constraint of the MuReC - OFDM - MI communication system are: (25) (26) Wherein, is the current control factor of the transmitter corresponding to the frequency , is the channel gain coefficient, is the equivalent resistance of the MuReC-OFDM-MI communication system at the transmitter, is the total power constraint of the transmitter, is the operating frequency, is the load resistance, is the transmitting coil and the receiving coil is the mutual inductance between them, is the noise power, is the equivalent internal resistance of the transmitter of the resistance value, is the equivalent internal resistance of the receiver of the resistance value, is the frequency corresponding receiver impedance, and expanding the result of solving the optimization problem to obtain a current control scheme: (27) where the Lagrange multiplier satisfies: (28).

[0015] An OFDM magnetic induction communication current control device based on multi-frequency resonance compensation, comprising: A memory: used to store a computer program for implementing an OFDM magnetic induction communication current control method based on multi-frequency resonance compensation; A processor: used to implement an OFDM magnetic induction communication current control method based on multi-frequency resonance compensation when executing the computer program.

[0016] A computer-readable storage medium, the computer-readable storage medium stores a computer program, and the computer program realizes the steps of an OFDM magnetic induction communication current control method based on multi-frequency resonance compensation when executed by a processor.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: First, the present invention establishes a circuit-level MuReC-OFDM-MI communication system, realizes the establishment of an optimization problem with current as the decision variable, directly models the transmitted power, received power, transmitted signal and received signal from circuit parameters, and connects information theory and circuit theory, making the present invention closer to the actual situation of physical layer transmission.

[0018] Second, the present invention uses the OFDM modulation method to obtain frequency reuse gain, improves the spectral efficiency, and improves the achievable rate of the MuReC-OFDM-MI communication system.

[0019] Thirdly, a multi - frequency resonance compensation circuit is added to both the transceiver of the present invention, which expands the available frequency band of the coil. According to the preset frequency, a design scheme for circuit parameters is derived, improving the spectrum utilization rate and effectively increasing the channel capacity of the MuReC - OFDM - MI communication system.

[0020] In summary, compared with the prior art, the present invention establishes a circuit model for the magnetic induction communication system, connects information theory and circuit theory, introduces OFDM modulation, improves the spectrum efficiency, and develops a parameter design scheme for the MuReC coil, greatly increasing the achievable rate of the MuReC - OFDM - MI communication system. Brief Description of the Drawings

[0021] Figure 1 It is a flowchart of the current control method of the present invention.

[0022] Figure 2(a) is a circuit diagram of the transmitter of the MuReC - OFDM - MI communication system of the present invention; Figure 2(b) is a circuit diagram of the receiver of the MuReC - OFDM - MI communication system of the present invention.

[0023] Figure 3 It is a graph showing the relationship between the transmitting impedance and frequency of the multi - frequency resonance compensation (MuReC) in the simulation experiment of the present invention.

[0024] Figure 4 It is a graph comparing the achievable rates of each carrier of different current control strategies and different circuit models in the simulation experiment of the present invention.

[0025] Figure 5 It is a graph comparing the total achievable rates of different current control strategies and different circuit models in the simulation experiment of the present invention. Detailed Embodiment

[0026] The following describes the present invention in detail with reference to the drawings.

[0027] Refer to Figure 1 , and further describe in detail the implementation steps of the OFDM magnetic induction communication current control method based on multi - frequency resonance compensation of the present invention.

[0028] Step 1, establish a circuit model of the MuReC - OFDM - MI communication system, and preset the frequencies of each sub - carrier of OFDM and the resonance frequency. The circuit model includes a transmitter and a receiver; Referring to Figure 2(a), the transmitter includes a current source connected in series , a transmitting coil , a capacitor , an equivalent internal resistance resistor , A parallel resonance circuit is used as a multi - frequency resonance compensation circuit. Among them, each parallel resonance circuit is composed of 1 coil and 1 supplementary capacitor connected in parallel. The coils in the parallel resonance circuit are wrapped with magnetic isolation materials and have no mutual inductance with each other; Referring to Fig. 2(b), the receiver includes a receiving coil connected in series a capacitor an equivalent internal resistance resistor a load resistor A parallel resonance circuit is used as a multi - frequency resonance compensation circuit. Among them, each parallel resonance circuit is composed of 1 coil and 1 compensation capacitor connected in parallel. The coils in the parallel resonance circuit are wrapped with magnetic isolation materials and have no mutual inductance with each other; The output current of the current source is The inductance value of the transmitting coil is The capacitance value of the capacitor is The resistance value of the equivalent internal resistance resistor is The inductance value of the coil is The capacitance value of the compensation capacitor is The inductance value of the receiving coil is The capacitance value of the capacitor is The resistance value of the equivalent internal resistance resistor is The resistance value of the load resistor is The inductance value of the coil is The capacitance value of the compensation capacitor is .

[0029] In order to make the coils of the transmitter and the receiver resonate at multiple specified frequencies simultaneously, a multi - frequency resonance compensation (MuReC) coil circuit is equipped for the transmitter and the receiver. Among them, the transmitting coil and the equivalent internal resistance resistor are the inductance and self - resistance of the coils of the transmitter and the receiver respectively. The compensation circuit composed of the capacitor the coil and the compensation capacitor is used to generate the required resonance frequency points. Define the total bandwidth as The center frequency of the bandwidth is​ , the corresponding operating angular frequency is , applying OFDM modulation to divide the total bandwidth into sub - frequency bands, so the bandwidth of each sub - frequency band is , the length of each OFDM symbol period is , the th sub - carrier's operating frequency is expressed as , the operating angular frequency of the nth sub - carrier can be expressed as , where , and the resonant frequency points are .

[0030] Step 2: According to the circuit model established in Step 1 and the preset resonant frequency, calculate the parameters of each coil and capacitor in the circuit. The parameters include: , , , , and calculate the impedance of the transmitter and receiver according to the parameters; Based on the transmitter circuit in the established circuit model, obtain the reactance value of the transmitter: (1 - 1) where, is the operating frequency, is the capacitance of the transmitter ; is the inductance of the transmitter's transmitting coil , and are the inductance of the coil and the capacitance of the capacitor in the parallel resonant circuit of the transmitter respectively; Take the partial derivative of with respect to the angular frequency : (2 - 1) Take the limit of Equation (2 - 1): where, define as the resonant frequency of each parallel resonant circuit of the transmitter, and its expression is: (6 - 1) At the same time, define ; Let , combine Equation (2 - 1) with Equations (3 - 1) - (5 - 1), where, contains a zero point, contains a zero point, then the reactance There are a total of zeros. Substituting Equation (6-1) into Equation (2-1), we get: (7-1) Rewriting Equation (7-1) based on the distribution of the zeros and the resonant frequencies yields: (8-1) where is a constant, is the preset th resonant frequency. Let , we obtain . Subsequently, the capacitance value of the capacitor of the transmitter, and the capacitance value of the compensation capacitor of the parallel resonant circuit of the transmitter are obtained by the partial fraction expansion method: (9-1) (10-1) When the resonant frequencies of the parallel resonant circuits of the transmitter satisfy , is randomly selected from , then the inductance value of the coil of the parallel resonant circuit of the transmitter coil is ; Finally, based on the capacitance value of the capacitor of the transmitter, the capacitance value of the compensation capacitor of the parallel resonant circuit of the transmitter, the inductance value of the coil of the parallel resonant circuit of the transmitter coil, and the constant , the transmitter impedance is calculated; The method for calculating the receiver impedance in Step 2 includes: Based on the receiver circuit in the established circuit model, the reactance of the receiver is obtained: (1-2) where is the operating frequency, is the capacitance value of the capacitor of the receiver; is the inductance value of the receiving coil and are the inductance value of the coil and the capacitance value of the capacitor of the parallel resonant circuit of the receiver respectively; For find the partial derivative with respect to the angular frequency : (2-2) Find the limit of Equation (2-2): Among them, define as the resonant frequency of each parallel resonant circuit of the receiver, and its expression is: (6-2) At the same time, define ; Let , combine Equation (2-2) with Equations (3-2) to (5-2), where contains a zero point, contains a zero point, then the reactance has a total of zero points. Substitute Equation (6-2) into Equation (2-2) to get: (7-2) Rewrite Equation (7-2) based on the distribution of the zero point and the resonant frequency as: (8-2) Among them, is a constant, is the preset th resonant frequency. Let , and get . Subsequently, the capacitance value of the capacitor of the receiver, and the capacitance value of the capacitor of the parallel resonant circuit of the receiver are obtained by the partial fraction expansion method: (9-2) (10-2) When the resonant frequencies of each parallel resonant circuit of the receiver satisfy , the value of is randomly selected from , then the inductance value of the coil of the receiver coil, ; Finally, according to the capacitance value of the capacitor The compensation capacitor of the receiver parallel resonance circuit The capacitance value The coil of the receiver parallel resonance circuit The inductance value Constant The receiver impedance is calculated .

[0031] Step 3: According to the impedances of the transmitter and receiver calculated in Step 2, calculate the transmission power and achievable rate of the MuReC-OFDM-MI communication system; Use To represent the symbol transmitted by the transmitter on the th subcarrier, and it follows the distribution , where Represents the current control factor of the transmitter on the th subcarrier. Then the analog transmission signal of the transmitter on the th subcarrier is expressed as: (11) Where Is the angular frequency of the th subcarrier; According to Faraday's law of electromagnetic induction and Kirchhoff's law, the received signal received by the receiver is expressed as: (12) Where Is the mutual inductance value between the transmitting coil And the receiving coil , Is the impedance of the receiver corresponding to the th subcarrier. The mutual inductance value Is expressed as: (13) Where Is the distance between the two coils, And Are the direction coefficient and eddy current coefficient of the two coils, And Are the number of turns of the transmitting and receiving coils respectively, And Are the radii of the transmitting and receiving coils respectively, Is the magnetic permeability. Defining the voltage of the load resistance of each receiving coil of the receiver as the received signal, then the band-pass received signal of the receiver corresponding to the th subcarrier is: (14) Where is the resistance value of the load resistor, is the band - pass noise; the band - pass received signal of each sub - carrier is obtained by down - converting, sampling, and discrete Fourier transform (DFT) of the total band - pass received signal. The specific steps are as follows: Define as the total band - pass received signal of the underground RX. Based on the superposition principle, is written as: (14 - 1) After down - conversion, the equivalent base - band output of the underground RX is as follows: (14 - 2) where, is the base - band noise. Next, the underground RX performs equidistant sampling, DFT, and pre - decoding of the received signal within the period to obtain the output corresponding to the th sub - carrier.

[0032] According to Faraday's law of electromagnetic induction and Kirchhoff's law, the transmitter current - source voltage is: (15) where, is the transmitter impedance. Based on Equation (15), the transmission power of the th sub - carrier of the MuReC - OFDM - MI communication system is: (16) where, is the equivalent resistance of the MuReC - OFDM - MI communication system at the transmitter, is the resistance value of the equivalent internal resistance of the transmitter ; is the resistance value of the equivalent internal resistance of the receiver ; Based on Equation (14), the received power and achievable rate of the MuReC - OFDM - MI communication system are respectively: (17) (18) where, is the channel gain coefficient, is the bandwidth of each sub - band of OFDM.

[0033] Step 4: Since the energy of the transmitter is limited, based on the transmission power obtained in Step 3, establish the average power - limited constraint of the transmitter, expressed as: (19) Among them, is the total transmitter power constraint. To facilitate the subsequent derivation of the channel capacity of the MuReC-OFDM-MI communication system, a constant quantity is added to this power constraint , is the bandwidth of each sub-band of OFDM, represents the current control factor of the transmitter at the th sub-carrier, is the equivalent resistance of the transmitter.

[0034] Step 5: Based on the achievable rate obtained in Step 3 and the average power limited constraint obtained in Step 4, establish an optimization problem and solve the optimization problem using convex optimization theory. The optimization problem is expressed as: (20) Among them, is the bandwidth of each sub-band of OFDM, is the channel gain coefficient, represents the current control factor of the transmitter at the th sub-carrier, is the equivalent resistance of the MuReC-OFDM-MI communication system at the transmitter, is the total transmitter power constraint; The Lagrangian function of the optimization problem is: (21) Among them, is a non-positive Lagrange multiplier. Taking the derivative of , the KKT conditions of the optimization problem are obtained as follows: (22) Subsequently, the result of the optimization problem is obtained, that is, the current control scheme of the MuReC-OFDM-MI communication system is: (23) Among them, is the optimal Lagrange multiplier, which is obtained by numerical methods and satisfies: (24).

[0035] Step 6: According to the result of the optimization problem obtained in Step 5, let the OFDM sub-carrier frequency point , and expand to obtain the channel capacity of the MuReC-OFDM-MI communication system and the current control scheme to achieve the channel capacity.

[0036] Let the OFDM sub-carrier frequency point , the channel capacity and the corresponding average power constraint of the MuReC-OFDM-MI communication system are obtained as follows: (25) (26) Among them, is the current control factor of the transmitter at frequency , is the channel gain coefficient, is the equivalent resistance of the MuReC-OFDM-MI communication system at the transmitter, is the total power constraint of the transmitter, is the operating frequency, is the load resistance, is the transmitting coil and the receiving coil the mutual inductance between them, is the noise power, is the equivalent internal resistance of the transmitter resistance value of, is the equivalent internal resistance of the receiver resistance value of, is the frequency corresponding receiver impedance. By expanding the result of solving the optimization problem, the current control scheme is obtained: (27) Among them, the Lagrange multiplier satisfies: (28).

[0037] An OFDM magnetic induction communication current control device based on multi-frequency resonance compensation includes: Memory: used to store the computer program for implementing the OFDM magnetic induction communication current control method based on multi-frequency resonance compensation; Processor: used to implement the OFDM magnetic induction communication current control method based on multi-frequency resonance compensation when executing the computer program.

[0038] The present invention also provides a computer-readable storage medium, and the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the OFDM magnetic induction communication current control method based on multi-frequency resonance compensation are implemented.

[0039] Simulation experiment Referring to Figure 3 , this figure shows the impedance characteristics of the MuReC coil The value of is set to , , , , ; , , , 。As shown in the figure, the resonant frequencies of the MuReC coil are effectively tuned to 0.996 MHz, 0.998 MHz, 1 MHz, 1.002 MHz, and 1.004 MHz, which verifies the effectiveness of the given parameter design scheme. In addition, it can be observed that contains a zero point , contains a zero point, which is consistent with the analysis in Step 2.

[0040] Figure 4 shows the achievable rates of each carrier of the single-carrier SISO-MI communication system, the OFDM-MI communication system based on uniform current control, the MuReC-OFDM-MI communication system based on uniform current control, and the MuReC-OFDM-MI communication system based on optimal current control (the present invention), where the total power is set to 10 mW, the number of subcarriers of OFDM is set to , the direction coefficient is 2, and the distance is set to 15 m. The single-carrier SISO-MI communication system has current only at the center frequency, and the achievable rate on the remaining carriers is 0; the OFDM-MI communication system based on uniform current control has the same current on each carrier; the circuit of the MuReC-OFDM-MI communication system has multiple resonant frequencies, and each resonant point is basically equivalent. Whether it is uniform current control or optimal current control (the present invention), there will be a large resonant rate near the resonance, and the optimal current control (the present invention) will control the current more at near the zero point, and the current is almost 0 near the pole, so a larger total achievable rate than the average current control can be obtained. Compared with single-carrier modulation, OFDM multi-carrier modulation reduces the achievable rate at the resonant frequency and obtains a larger total achievable rate.

[0041] Figure 5 shows the total achievable rates of different circuit schemes and current control schemes at different transmission powers, where the total power is set to , the number of subcarriers of OFDM is set to N = 32, and the direction coefficient is 2. As shown in the figure, in order to increase the total achievable rate, there is also current passing through OFDM at non-resonant frequencies. Compared with the carrier SIMO-MI, the total achievable rate is increased by 294%. In order to make more carrier frequencies distributed around the zero point, the MuReC circuit scheme is used to enable a single transceiver coil to obtain multiple resonant frequencies. It can be seen that under the uniform current control strategy, the performance of the MuReC circuit is even inferior to that of the traditional circuit scheme because MuReC will introduce a pole between two zero points, and the power on the carriers near the pole is wasted. Using the optimal current control scheme, the MuReC circuit can obtain better performance than the traditional circuit. Under the same transmit power, the achievable rate based on MuReC-OFDM-MI is always greater than that of other transmission methods, which verifies the effectiveness of the proposed current control scheme.

Claims

1. A current control method for OFDM magnetic induction communication based on multi-frequency resonance compensation, characterized in that Including the following steps: Step 1: Establish a circuit model of the MuReC-OFDM-MI communication system, and preset the frequencies of each sub-carrier of OFDM and the resonant frequency. The circuit model includes a transmitter and a receiver; Step 2: Calculate the parameters of each coil and capacitor in the circuit according to the circuit model established in Step 1 and the preset resonant frequency, and calculate the impedances of the transmitter and the receiver according to the parameters; Step 3: Calculate the transmit power and achievable rate of the MuReC-OFDM-MI communication system according to the impedances of the transmitter and the receiver calculated in Step 2; Step 4: Establish a limited average power constraint for the transmitter according to the transmit power obtained in Step 3; Step 5: Based on the achievable rate obtained in Step 3 and the limited average power constraint obtained in Step 4, establish an optimization problem, and solve the optimization problem using convex optimization theory; Step 6. According to the result of the optimization problem obtained in Step 5, let the OFDM subcarrier frequency points , and expand to obtain the channel capacity of the MuReC-OFDM-MI communication system and the current control scheme to achieve the channel capacity.

2. The method according to claim 1, wherein The transmitter described in step 1 includes a current source connected in series , a transmitting coil , a capacitor , an equivalent internal resistance , parallel resonance circuits as multi-frequency resonance compensation circuits, where each parallel resonance circuit consists of 1 coil and 1 supplementary capacitor connected in parallel. The coils in the parallel resonance circuit are wrapped with magnetic isolation materials and have no mutual inductance with each other; Among them, the current source has an output current of , the inductance value of the transmitting coil is , the capacitance value of the capacitor is , the resistance value of the equivalent internal resistance resistor is , the inductance value of the coil is , the capacitance value of the compensation capacitor is ; The receiver includes a receiving coil connected in series , a capacitor , an equivalent internal resistance resistor , a load resistor , parallel resonance circuits as multi-frequency resonance compensation circuits, where each parallel resonance circuit consists of 1 coil and 1 compensation capacitor connected in parallel. The coils in the parallel resonance circuit are wrapped with magnetic isolation materials and have no mutual inductance with each other; Among them, the receiving coil has an inductance value of , and the capacitor has a capacitance value of , the equivalent internal resistance resistor has a resistance value of , the load resistor has a resistance value of , the coil has an inductance value of , and the compensation capacitor has a capacitance value of .

3. The method according to claim 1, wherein The pre-set sub-carrier frequencies of OFDM described in step 1 include: defining the total bandwidth as , the center frequency of the bandwidth as , the corresponding running angular frequency as , applying OFDM modulation to divide the total bandwidth into sub-bands, the bandwidth of each sub-band is , the length of each OFDM symbol period is , the running frequency of the -th sub-carrier is expressed as , the running angular frequency of the n-th sub-carrier is expressed as , where , and each resonance frequency point is .

4. The method according to claim 1, wherein The calculation method of the transmitter impedance in Step 2 includes: Based on the transmitter circuit in the established circuit model, obtain the reactance value of the transmitter : (1-1) Among them, is the operating frequency, is the capacitance of the transmitter of the capacitance value; is the transmitting coil of the transmitter of the inductance value, and are respectively the inductance value of the coil and the capacitance value of the capacitance of the parallel resonance circuit of the transmitter; For find the partial derivative with respect to the angular frequency : (2-1) Taking the limit of Equation (2-1): Among them, it is defined that is the resonance frequency of each parallel resonance circuit of the transmitter, and its expression is: (6-1) Define simultaneously ; Let , combine Equation (2-1) with Equations (3-1) to (5-1), where contains one zero point contains one zero point, then the reactance in total has zero points. Substitute Equation (6-1) into Equation (2-1) to obtain: (7-1) Rewrite Equation (7-1) based on the distribution of the zero point and the resonant frequency as follows: (8-1) Among them, is a constant, is the preset th resonance frequency. Let , we get . Subsequently, the capacitance of the transmitter, , and the capacitance of the compensation capacitor of the parallel resonance circuit of the transmitter are obtained by the partial fraction expansion method: (9-1) (10-1) When the resonant frequencies of the parallel resonant circuits of the transmitter satisfy , and the value is randomly selected from , the inductance value of the coil of the parallel resonant circuit of the transmitter coil is , ; Finally, according to the capacitance of the transmitter the capacitance value , the compensation capacitance of the parallel resonance circuit of the transmitter the capacitance value , the coil of the parallel resonance circuit of the transmitter coil the inductance value , the constant calculate the impedance of the transmitter ; The calculation method of the receiver impedance in Step 2 includes: Based on the receiver circuit in the established circuit model, the reactance of the receiver is obtained : (1-2) Among them, is the operating frequency, is the capacitance of the receiver and its capacitance value; is the receiving coil of the receiver and its inductance value, and are respectively the inductance value of the coil and the capacitance value of the capacitance in the parallel resonance circuit of the receiver; For Find the partial derivative with respect to the angular frequency : (2-2) Taking the limit of Equation (2-2): Among them, it is defined that is the resonance frequency of each parallel resonance circuit of the receiver, and its expression is: (6-2) Define simultaneously ; Let , combine Equation (2-2) with Equations (3-2) to (5-2), where contains one zero point, contains one zero point, then the reactance in total has zero points. Substitute Equation (6-2) into Equation (2-2) to obtain: (7-2) Rewrite Equation (7-2) based on the distribution of the zero point and the resonant frequency as follows: (8-2) Among them, is a constant, is the pre-set th resonant frequency. Let , and we get . Subsequently, the capacitance value of the capacitor of the receiver , and the capacitance value of the capacitor of the parallel resonant circuit of the receiver is obtained by the partial fraction expansion method: (9-2) (10-2) When the resonance frequencies of the parallel resonance circuits of the receiver meet , The value of is randomly selected from , then the inductance value of the coil of the receiver coil is , ; Finally, according to the capacitance of the receiver the capacitance value , the compensating capacitance of the parallel resonant circuit of the receiver the capacitance value , the coil of the parallel resonant circuit of the receiver the inductance value , the constant calculate the impedance of the receiver .

5. The method according to claim 1, characterized in that Step 3 specifically includes: Use to represent the symbol transmitted by the transmitter on the th subcarrier, and it follows the distribution , where represents the current control factor of the transmitter on the th subcarrier. Then, the analog transmission signal of the transmitter on the th subcarrier is expressed as: (11) Among them, is the angular frequency of the subcarrier; According to Faraday's law of electromagnetic induction and Kirchhoff's law, the received signal received by the receiver is expressed as: (12) Wherein, is the mutual inductance value between the transmitting coil and the receiving coil, is the impedance of the receiver corresponding to the n-th subcarrier, and the mutual inductance value is expressed as: (13) Wherein, is the distance between the two coils, and are the direction coefficient and eddy current coefficient of the two coils, and are the number of turns of the transmitting and receiving coils respectively, and are the radii of the transmitting and receiving coils respectively, is the magnetic permeability. Defining the voltage of the load resistance of each receiving coil of the receiver as the received signal, then the band - pass received signal of the receiver corresponding to the th sub - carrier is: (14) Among them, is the resistance value of the load resistor, is the band-pass noise; According to Faraday's law of electromagnetic induction and Kirchhoff's law, the voltage of the transmitter current source is obtained as: (15) Among them, is the transmitter impedance. Based on Equation (15), the transmission power of the th subcarrier of the MuReC-OFDM-MI communication system is: (16) Among them, is the equivalent resistance of the MuReC-OFDM-MI communication system at the transmitter, is the equivalent internal resistance of the transmitter resistance value, is the equivalent internal resistance of the receiver resistance value; Based on Equation (14), the received power and achievable rate of the MuReC-OFDM-MI communication system are respectively: (17) (18) Among them, is the channel gain coefficient, is the bandwidth of each sub - band of OFDM.

6. The method according to claim 1, characterized in that, The limited average power constraint in Step 4 is: (19) Among them, is the total transmitter power constraint, is the bandwidth of each sub - band of OFDM, represents the current control factor of the transmitter at the th sub - carrier, is the equivalent resistance of the transmitter.

7. The method according to claim 1, wherein The optimization problem in Step 5 is expressed as: (20) Among them, is the bandwidth of each sub - band of OFDM, is the channel gain coefficient, represents the current control factor of the transmitter on the th sub - carrier, is the equivalent resistance of the MuReC - OFDM - MI communication system at the transmitter, is the total power constraint of the transmitter; The Lagrangian function of the optimization problem is: (21) wherein, is a non-positive Lagrange multiplier. Taking the derivative of yields the KKT conditions of the optimization problem as follows: (22) Subsequently, the result of the optimization problem is obtained: (23) wherein, is the optimal Lagrange multiplier, obtained by numerical methods, which satisfies: (24)。 8. The method according to claim 1, wherein Step 6 specifically includes: Let the OFDM subcarrier frequency points , and the channel capacity and the corresponding average power constraint of the MuReC-OFDM-MI communication system are obtained as follows: (25) (26) Among them, is the current control factor of the transmitter at frequency corresponding to, is the channel gain coefficient, is the equivalent resistance of the MuReC-OFDM-MI communication system at the transmitter, is the total power constraint of the transmitter, is the operating frequency, is the load resistance, is the transmitting coil and the receiving coil the mutual inductance between them, is the noise power, is the equivalent internal resistance of the transmitter resistance value of, is the equivalent internal resistance of the receiver resistance value of, is the frequency corresponding receiver impedance. Expanding the result of solving the optimization problem, a current control scheme is obtained: (27) Among them, the Lagrange multiplier satisfies: (28)。 9. An OFDM magnetic induction communication current control device based on multi-frequency resonance compensation, characterized in that Including: A memory: for storing a computer program for implementing an OFDM magnetic induction communication current control method based on multi-frequency resonance compensation as described in any one of claims 1 to 8; A processor: for implementing an OFDM magnetic induction communication current control method based on multi-frequency resonance compensation as described in any one of claims 1 to 8 when executing the computer program.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, and when the computer program is executed by the processor, the steps of an OFDM magnetic induction communication current control method based on multi-frequency resonance compensation as described in any one of claims 1 to 8 are implemented.

Images