Error code evaluation method for FSK (Frequency Shift Keying) data transmission system of unmanned aerial vehicle under high-power microwave action

Abstract

A method for evaluating error codes of an FSK (Frequency Shift Keying) data transmission system of an unmanned aerial vehicle under the action of high-power microwaves takes binary frequency shift keying (2FSK) as a core, combines with a typical NHPM interference scene, and performs mathematical modeling analysis on narrowband high-power microwave interference existing in a working environment of the unmanned aerial vehicle and an internal incoherent demodulator model to evaluate the error codes of the FSK data transmission system of the unmanned aerial vehicle. The method comprises the following steps: applying NHPM to an internal link of an incoherent demodulator of a target system to carry out mathematical description, so as to obtain an error rate analytical expression under a normal working condition and an NHPM interference condition, and substituting a data transmission system parameter and an interference parameter into the analytical expression to describe an error rate mathematical expected value generated under a specific environment. Therefore, an effective means is provided for evaluating the bit error rate of a data transmission system of the unmanned aerial vehicle with known high-power microwave interference parameters, and the reliability of frequency shift keying communication of the unmanned aerial vehicle in the NHPM interference environment is improved.

Description

Technical Field

[0001] This invention belongs to the field of data transmission technology, and specifically relates to a method for evaluating the bit error rate of an unmanned aerial vehicle (UAV) FSK data transmission system under high-power microwave conditions. Background Technology

[0002] In practical applications, UAV data transmission equipment typically selects an appropriate modulation scheme based on the specific communication environment and data transmission requirements. Frequency Shift Keying (FSK) digital modulation technology has the advantages of strong anti-interference capability and simple implementation, and is widely used in UAV data transmission systems.

[0003] Unmanned aerial vehicle (UAV) data transmission systems require reliable data transmission in complex electromagnetic environments. FSK (Frequency-Side Array) technology transmits information through carrier frequency variations, without strict requirements on phase information, making it suitable for scenarios with low transmission rates and high reliability requirements. FSK demodulation uses incoherent demodulators, which are less sensitive to phase information and channel multipath fading, making it a preferred solution for specific scenarios.

[0004] Current research on the bit error rate (BER) of FSK UAV interference processes is relatively simplistic, and the modeling theory for BER when applying NHPM interference to UAVs is incomplete. For example, the article "Research on Evaluation Method of Electromagnetic Irradiation Test for UAVs" published by Zhang Dongxiao, Zhang Daming, Tian Qingmin, et al. [J]. Journal of Ordnance Engineering College, 2015, 27(03):28-32., qualitatively points out the electromagnetic interference path and the threshold law of BER loss in data transmission systems, but the interference mechanism of BER generation in data transmission systems has not been fully analyzed. Therefore, it is necessary to further quantify the influence law of BER. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention aims to disclose a method for evaluating the bit error rate (BER) of a UAV FSK data transmission system under high-power microwave interference. Using binary frequency shift keying (2FSK) as the core and combining it with typical NHPM interference scenarios, the method mathematically models and analyzes the narrowband high-power microwave interference and the internal incoherent demodulator model present in the UAV's operating environment. It mathematically describes the internal components of the incoherent demodulator under NHPM interference, obtaining analytical expressions for the BER under normal operating conditions and NHPM interference conditions. These analytical expressions, by substituting data transmission system parameters and interference parameters, can describe the expected value of the BER generated under specific conditions. This provides an effective means for evaluating the BER of a UAV data transmission system with known high-power microwave interference parameters, improving the reliability of UAV frequency shift keying communication under NHPM interference conditions.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A method for evaluating the bit error rate of an unmanned aerial vehicle (UAV) FSK data transmission system under high-power microwave irradiation includes the following steps:

[0008] Step 1: Based on mathematical modeling of the demodulator's internal frequency-selective bandpass filter (BPF), mixer multiplier pass filter, and sampling decision stages, analyze the bit error rate P of the signal transmission channel in the envelope decision process after signal processing of the dual-channel time-domain signal under normal communication mode. Ne传 'and the error rate P of the empty number channel Ne空 The mathematical analytical expression of '.

[0009] Step one is as follows:

[0010] Based on the 2FSK dual-channel model for transmitting signals and signals, and considering the incoherent demodulator model used in the UAV frequency shift keying data transmission system, the frequency-selective bandpass filter (BPF), mixer multiplier, low-pass filter, and sampling decision stage within the demodulator are abstracted into mathematical processing stages for analysis. The demodulator's time-domain input signal x(t) consists of two parts: the symbol signal and the channel spatial white noise n(t).

[0011] x(t)=s(t)+n(t) (1)

[0012] Where x(t) is the synthesized signal coupled into the incoherent demodulator by the receiving antenna, and s(t) and n(t) are the white noise signals of the communication signal, respectively;

[0013] Assuming the incoherent demodulator operates under normal conditions, based on the synthesized signal of the communication signal and white noise passing through the frequency-selective bandpass filter, and considering the typical mathematical characteristics of the Rice distribution and Rayleigh distribution in the signal transmission channel and the empty signal channel respectively, analyze the bit error rate P of the signal transmission channel in the envelope decision process after signal processing of the dual-channel time-domain signal. Ne传 'and the error rate P of the empty number channel Ne空 The mathematical analytical expression of ':

[0014]

[0015] Among them, SNR 11 and SNR 10 These are the signal-to-noise ratio (SNR) of high-level "1" and low-level "0" signals transmitted through the signal transmission channel. 21 and SNR 20 These are the signal-to-noise ratios of high-level "1" and low-level "0" transmissions via the empty number channel, respectively.

[0016] Due to the symmetrical characteristics of the dual channels of the incoherent demodulator, the bit error rate expressions of both channels have the same functional form f1(*), and the variables are related to the signal-to-noise ratio of the corresponding channels.

[0017] Step 2: Considering the presence of co-frequency continuous wave interference signals at the signal input of the incoherent demodulator, based on the communication signal analysis process in Step 1 and the bit error rate expression of the dual channels under normal communication mode, the internal bit error rate P of the co-frequency continuous wave interference time-domain signal for one symbol after processing is obtained. e Mathematical analytical expression.

[0018] Step two is as follows:

[0019] Suppose there is a continuous wave interference signal at the signal input of the incoherent demodulator, and the center frequency of this interference is f. j The communication carrier frequency f of one of the signal transmission channels or the empty signal channel 传 or f 空 Similarly, considering that the NHPM interference signal and the communication signal are superimposed on the receiving antenna and coupled into the incoherent demodulator, it can be analyzed that the bit error rate P of the system after processing of the time-domain signal of the same-frequency continuous wave interference for one symbol is... e Mathematical analytical expression:

[0020]

[0021] Among them, SIR 11 and SIR 10 These are the signal-to-interference ratios (SIRs) of transmitting high-level "1" and low-level "0" signals via the signal transmission channel. 21 and SIR 20 These are the signal-to-interference ratios (SIRs) of the high-level "1" and low-level "0" transmissions of the empty channel, respectively. At this time, the dual-channel expression still has the same function expression form f2(*).

[0022] Step 3: Considering the presence of co-frequency NHPM interference at the signal input of the incoherent demodulator, based on the bit error rate expression of the dual channels in the normal communication mode in Step 1 and the co-frequency continuous wave interference in Step 2, the internal bit error rate P of the communication system under co-frequency NHPM interference is derived according to the time-domain duty cycle relationship of the two modes. e传同频 ′, P e空同频 The mathematical analytical expression of ′.

[0023] Step three is as follows:

[0024] Considering the process of each symbol decision point being affected by interference within the symbol as a uniformly distributed mathematical model, we introduce the Bayesian probability of pulse width and communication symbol time, and introduce mathematical parameters of the overall pulse interference train. We classify symbols according to two cases: interference and normal within a finite signal duration, and let their occurrence ratios be p1 and p2, respectively. Then, we can obtain the analytical expression for the 2FSK bit error rate under co-frequency NHPM interference:

[0025]

[0026] Among them, t w For NHPM pulse width, T m The duration of a single codeword.

[0027] Step 4: Considering the presence of out-of-band continuous wave interference at the signal input of the incoherent demodulator, based on the bit error rate expression of the dual-channel system under normal communication mode in Step 1 and the same-frequency continuous wave interference analysis method in Step 2, and introducing interference analysis with different center frequencies, the internal bit error rate P of the communication system under out-of-band continuous wave interference is obtained. e传 ", P e空 The mathematical analytical expression of ″.

[0028] Step four is as follows:

[0029] Suppose there is an out-of-band NHPM interference signal at the input of the incoherent demodulator. Considering a large frequency difference, the NHPM only interferes with one channel. The center frequency of this interference is related to f. j Given different communication carrier frequencies f0, considering the process of the NHPM interference signal being superimposed on the receiving antenna and coupled into the incoherent demodulator, a residual power model needs to be introduced for discussion. This yields an analytical expression for the bit error rate (BER), which is an expression for the sampling function sinc(t). This allows us to obtain the time-domain signal of the NHPM interference at different center frequencies, and to determine the BER P within the 2FSK system, specifically for the signal transmission channel. e传 "and the error rate P of the empty number channel" e空 Mathematical analytical expression:

[0030]

[0031] Step 5: Considering the presence of out-of-band NHPM interference at the signal input of the incoherent demodulator, based on the bit error rate expression of the dual channels in the normal communication mode in Step 1 and the out-of-band continuous wave interference analysis method in Step 4, the internal bit error rate P of the communication system under out-of-band NHPM interference is derived according to the time-domain duty cycle relationship of the two modes. e传带外 ′, P e空带外 The mathematical analytical expression of ′.

[0032] Step five is as follows:

[0033] After introducing the Bayesian probabilities of pulse width and communication symbol time, and considering the mathematical parameters of the overall pulse interference train, the symbols are classified according to the two cases of interference and normal operation within a finite signal duration. Let their occurrence ratios be q1 and q2, respectively. Then, the analytical expression for the bit error rate under 2FSK out-of-band NHPM interference at different center frequencies can be obtained:

[0034]

[0035] The present invention also includes:

[0036] A system, including a processor, is capable of running the aforementioned error assessment method for an unmanned aerial vehicle (UAV) FSK data transmission system under high-power microwave conditions.

[0037] An apparatus comprising:

[0038] Memory: Used to store the computer program for the error evaluation method of an unmanned aerial vehicle FSK data transmission system under high-power microwave action;

[0039] Processor: Used to implement the error evaluation method for an FSK data transmission system of a UAV under high-power microwave action when executing the computer program.

[0040] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the error assessment method for an FSK data transmission system of a UAV under high-power microwave action.

[0041] Compared with the prior art, the present invention has the following beneficial technical effects:

[0042] 1. Based on the principles of mathematical statistics and mathematical modeling techniques, this invention establishes a mathematical model for the signal transmission and decision mechanism of the incoherent demodulator used in frequency shift keying communication. It systematically classifies and elucidates the process of the signal-coupled incoherent demodulator in dual-channel communication, and can reveal the impact of multi-dimensional system parameters on communication performance. It is applicable to incoherent demodulators with different parameter models and number of channels, and has both high accuracy and wide applicability. It provides a reliable basis for evaluating the bit error rate of common target incoherent demodulators.

[0043] 2. This invention integrates actual interference environment data and uses an interference error analysis mathematical model based on NHPM waveform parameters. This model can more effectively fit the actual combat scenarios of UAVs, thereby obtaining more realistic evaluation conclusions under different specific interference conditions, broadening the application scope, and making up for the shortcomings in the quantitative analysis of error effects of frequency shift keying UAVs under NHPM interference.

[0044] 3. In response to out-of-band NHPM interference, this invention derives an analytical expression for the bit error rate through a residual power model, focuses on exploring the mathematical relationship between the interference center frequency and the carrier center frequency, and quantitatively analyzes the impact mechanism of frequency deviation on the bit error rate, thereby improving the accuracy of the description of the bit error rate of UAV data transmission systems under out-of-band interference environments.

[0045] In summary, this invention uses basic Binary Frequency Shift Keying (2FSK) as a model and applies a noncoherent demodulator to demodulate two carrier frequencies ω.1， The digital information represented by ω2 is processed in the signal transmission channel and the space channel respectively, which has stronger noise resistance and is more suitable for environments with intentional electromagnetic interference or industrial noise. At the same time, the non-coherent demodulator used simplifies the carrier synchronization circuit, greatly reduces hardware complexity and power consumption, and is suitable for small UAV platforms. Attached Figure Description

[0046] Figure 1 This is a logic block diagram of the error rate assessment derivation method of the present invention.

[0047] Figure 2 This is a model diagram of the incoherent demodulator for the UAV dual-channel 2FSK transmission system used in this invention.

[0048] Figure 3 The time-domain analysis diagram of the NHPM interference process designed for this invention. Detailed Implementation

[0049] The present invention will now be described in detail with reference to the accompanying drawings.

[0050] A method for evaluating the bit error rate of an unmanned aerial vehicle (UAV) FSK data transmission system under high-power microwave irradiation includes the following steps:

[0051] Step 1: Mathematical analytical expression of the bit error rate in normal working mode, which is based on the mathematical modeling of the frequency selection bandpass filter (BPF), the mixer multiplier pass filter, and the sampling decision stage within the demodulator. This analyzes the bit error rate P of the signal transmission channel in the envelope decision process after signal processing of the dual-channel time-domain signal under normal communication mode. Ne传 'and the error rate P of the empty number channel Ne空 The mathematical analytical expression of '.

[0052] Specifically, this involves establishing a model of a single-channel incoherent demodulator used in a UAV 2FSK data transmission system, such as... Figure 2 As shown, the input signal inside the model is the time-domain voltage signal after antenna coupling. The frequency shift keying signal is represented by the level signals of two carriers with different center frequencies, representing the "1" and "0" of the digital signal. There are two channels inside the demodulator. After the dual-frequency signal is separated by the frequency-selective bandpass filter, it is input into the two channels for processing. The separated signals are mixed and demodulated with the mixer multiplier of the corresponding center frequency. After the low-pass filter filters out the high-frequency components, only the signal envelope enters the decision stage. The sampling decision compares the numerical values ​​of the signal envelopes of the two channels at the decision time point to restore the analog envelope signal to the corresponding symbol digital level.

[0053] First, for the frequency-selective bandpass filter, dual-channel upper and lower cutoff frequencies are designed to allow only one frequency signal to pass through. The signal enters two mixer-multiplier stages, where the input signal is multiplied by a sinusoidal signal with the same carrier center frequency. At this point, both channel signals are converted to positive polarity envelopes before being input into the low-pass filter stage. The mathematical model is a definite integral operation with the cutoff frequency slightly higher than the carrier frequency, where the upper and lower limits of integration are the time intervals T between two adjacent symbol moments. n With T n+1 The output signal enters the decision stage, which compares the envelope values ​​of the two signals. When the envelope value of the signal transmission channel is higher than that of the empty signal channel, a high level "1" is output; similarly, when the envelope value of the empty signal channel is higher than that of the signal transmission channel, a low level "0" is output. This completes the level recovery and decision process for one symbol. After performing the above operations on all time-domain symbols within the total signal duration T0, the recovered digital signal group is obtained. This recovered digital signal group can be compared with the original input digital signal to calculate the tested bit error rate P. e .

[0054] Assuming the signal is a set of definite 01 arrays that follow a two-point distribution, the randomness of the model output signal comes from the level symbols at the symbol judgment time, the value of the channel white noise envelope that follows a normal distribution, and parameters such as the phase and pulse width of the interference signal, all of which follow statistical laws. Therefore, the output of the analytical expression for the bit error rate is the expected value of the bit error rate under this condition.

[0055] Under normal operating conditions, the dual channels contain a single-level 2FSK signal and a spatial white noise signal, respectively. Let n1(t) and n0(t) characterize the narrowband Gaussian noise, with a mean of 0 and variances (average power) of N1 and N0, respectively. This includes both channel noise and man-made interference noise, which are statistically independent and satisfy N1 = N... t +N j1 =2σ1 2 N0 = N t +N j0 =2σ0 2 Generally, the two noise intensities can be considered equal, i.e., σ1 = σ2 = σ. The derivation method's logic diagram is as follows: Figure 1 As shown.

[0056] When sending a "1", the signal transmission channel transmits both the main symbol signal and narrowband Gaussian noise signal, while the empty number channel transmits only narrowband Gaussian noise signal, not the main symbol signal. Similarly, when sending a "0", the symbol signal is transmitted in the empty number channel. The combined signals from the signal transmission channel and the empty number channel output in these two cases are as follows:

[0057]

[0058] Where n1(t) and n2(t) are the narrowband Gaussian noise outputs of the signal transmission channel and the empty signal channel, respectively. When the mixed signal passes through the bandpass filter, if the signal bandwidth is much smaller than the center frequency of the bandpass filter, then the narrowband Gaussian noise signal in the channel is considered to constitute a narrowband random process.

[0059] For a channel with only narrowband noise, the two orthogonal components of the noise are independent and both obey N(0,σ). 2 The normal distribution of ). Due to According to the properties of the normal distribution, two independent random variables n with the same variance that follow a normal distribution... c (t) and n s When α(t) is a set of orthogonal bases, its envelope a(t) remains a random variable and follows a Rayleigh distribution with parameter σ. The probability density function of the Rayleigh distribution can be expressed as:

[0060]

[0061] For a single-channel synthesized signal, it can be considered that an offset sinusoidal component is superimposed on the noise signal. In this case, the signal follows a generalized Rayleigh distribution, also known as a Rice distribution. When the offset component is set to zero, the Rice distribution degenerates into a Rayleigh distribution. The probability density function of the Rice distribution can be expressed as:

[0062]

[0063] Where x is the envelope of the synthesized signal, parameter A is the peak value of the main signal amplitude, and I0(x) is the modified 0th-order Bessel function of the first kind with respect to x.

[0064] Therefore, the incoherent demodulation error problem under normal communication can be transformed into a joint distribution problem of random process variables that respectively follow Rayleigh and Rice distributions, and a joint distribution function can be introduced.

[0065]

[0066] To obtain the above integral, we introduce the Marcum Q function, taking into account the properties of the Rice distribution. The expression for the Marcum Q function is as follows:

[0067]

[0068] Considering the Rice distribution probability density function, P(X≥bσ) can be expressed as:

[0069]

[0070] That is, the probability distribution function of any random variable following a Rice distribution can be characterized by the Marcum Q function. Combining the integral properties of the 0th-order Bessel function and integration by parts, we can calculate:

[0071]

[0072] P(v2 > v1) is the bit error rate when the UAV 2FSK demodulation model sends "1" under normal operation. In communication theory, the noise part is defined as the signal-to-noise ratio SNR, and an analytical expression in the form of P Ne传 ′ = f1(SNR 11 , SNR 10 ), P Ne空 ′ = f1(SNR 21 , SNR 20 ) can be obtained. Then the bit error rate of specifically sending "1" can be expressed by the signal-to-noise ratio as:

[0073]

[0074] Similarly, when sending "0", when there is a bit error situation where the discriminator misjudges sending "0" as "1", the envelope v1 of the mark channel at the symbol decision point is higher than the envelope v2 of the space channel. Then the bit error rate can be converted to find P eN1 = P(v2 < v1). The calculation process will not be elaborated. After integration by parts and Bessel function integration operations, the bit error rate of sending "0" can be expressed as:

[0075]

[0076] From the above derivation, it can be seen that the mark channel and the space channel are symmetric in structure. Similar methods can be used in subsequent derivations to simplify the analysis of the dual channels.

[0077] Step 2: Consider the mathematical analytical expression of the bit error rate considering continuous interference of the same frequency, that is, consider that there is a continuous wave interference signal of the same frequency at the signal input end of the non-coherent demodulator. Based on the communication signal analysis process in Step 1 and the bit error rate expression of the dual channels in the normal communication mode, it is obtained that after processing the time-domain signal of the continuous wave interference of the same frequency for a symbol, the mathematical analytical expression of the internal bit error rate P e ′ of the system.

[0078] Specifically: When the single-tone interference can enter the mark channel, it is considered that the center frequency of the single-tone interference signal completely coincides with the center frequency of the band-pass filter of the mark channel; when the single-tone interference can enter the space channel, it is considered that the center frequency of the single-tone interference signal completely coincides with the center frequency of the band-pass filter of the space channel. The single-tone interference signal can be expressed as:

[0079]

[0080] Among them, A j,k (k = 1, 2) respectively represent the amplitudes of the single-tone interference applied to the mark channel or the space channel; ω kThese represent the interference center frequencies, which are equal to the center frequencies of the empty signal or the signal transmission channel carrier, respectively; φ k These represent the phases of the interference signals in the two channels. Each symbol can only represent one level signal, and the corresponding single-tone interference acts on either the empty signal channel or the signal transmission channel. Therefore, there are four interference modes in total, consisting of the two transmitted symbol levels and the two channel interference scenarios, all unified by a single expression:

[0081]

[0082] When the signal transmission channel is interfered, A j1 ≠0, A j2 =0; A when there is interference from an empty channel j1 =0, A j2 ≠ 0; When the symbol "1" is sent, A1 ≠ 0, A2 = 0; When the symbol "0" is sent, A1 = 0, A2 ≠ 0; The synthesized signal output from the signal transmission channel and the empty signal channel is a random process, and the output envelopes both follow a Rice distribution. The detector makes a decision on the signal transmission channel and the empty signal channel. When the output of the signal transmission channel is greater than the output of the empty signal channel, it is judged as "1"; otherwise, it is judged as "0". When "1" is sent, the bit error rate of misjudging as "0" can be represented by P(b2>b1):

[0083]

[0084] The probability of a comparison between two random variables that follow the same σ-parameter Rice distribution can be calculated using the symmetry property of the Marcum Q function:

[0085]

[0086] After simplifying by substituting the signal and interference amplitudes for the four cases, we can obtain the expressions for the four cases. By averaging the probabilities of sending "1" and "0" for each channel and integrating the average over the phase difference in [0, 2π], we can obtain an expression of the form P. e传 =f2(SNR) 11 SIR 11 SNR 10 SIR 10 ) and P e空 =f2(SNR) 21 SIR 21 SNR 20 SIR 20 An analytical expression of the form ) is specifically expressed as:

[0087]

[0088] Among them, the signal transmission channel SNR1 = 0.5 (SNR 11 +SNR10 SIR1 = 0.5 (SIR) 11 +SIR 10 Similarly, for channels with empty numbers, SNR2 = 0.5 (SNR... 21 +SNR 20 SIR2 = 0.5 (SIR) 21 +SIR 20 ).

[0089] Step 3: Analyze the mathematical expression of the bit error rate (BER) considering co-frequency NHPM interference. This involves considering the presence of co-frequency NHPM interference at the input of the incoherent demodulator. Based on the BER expression for the dual-channel communication mode in Step 1 and the co-frequency continuous wave interference in Step 2, the BER is derived according to the time-domain duty cycle relationship between the two modes, yielding the BER P within the communication system under co-frequency NHPM interference. e传同频 ′, P e空同频 The mathematical analytical expression of ′.

[0090] For a time period T0, the symbol rate is N m If the 1-bit control signal is analyzed as the object of interference, then the total number of symbols N and the duration T of each symbol are related. m For 2FSK communication under NHPM interference, bit errors only occur during the period of NHPM pulse action. Therefore, the presence or absence of NHPM pulse interference within each symbol time can be used as a criterion to decompose the interference process into normal and interference periods for superposition analysis. Figure 3 As shown.

[0091] During the symbol time, the average bit error rate is determined by the continuous duty cycle q1 and (1-q1) of two working periods and the bit error rate P′. e 、P′ Ne The decision is made that interference may occur if and only if the pulse duration covers the symbol determination time. Therefore, the average bit error rate within the symbol time can be expressed as the corrected bit error rate P1' during the interference period. e :

[0092]

[0093] Substituting the above two equations into an expression that includes the duty cycle, we can analyze the effect of the interference pulse width, obtaining an expression of the form... and The analytical expression for bit error rate under the same frequency NHPM pulse is as follows:

[0094]

[0095] Wherein, Q(a,b) function: Marcum Q function with a and b as key parameters; SNR1, SNR0: signal-to-noise ratio of the signal transmission channel and the empty number channel, SIR1, SIR0: signal-to-interference ratio of the signal transmission channel and the empty number channel; N p : Number of interferences; t wn The pulse width of the nth interference pulse; T m T0: Symbol time; Total control signal time; N m Symbol rate; f PRF Interference repetition frequency; T 干扰 Interference duration; φ j1 : Send "1" interference phase; φ j0 Send "0" interference phase.

[0096] Step 4: Consider the mathematical analytical expression of the bit error rate (BER) for out-of-band continuous interference. This involves considering the presence of out-of-band continuous wave interference at the input of the non-coherent demodulator. Based on the BER expression for the dual-channel communication mode in Step 1 and the co-frequency continuous wave interference analysis method in Step 2, and introducing interference analysis for different center frequencies, the BER P of the communication system under out-of-band continuous wave interference is obtained. e传 ", P e空 The mathematical analytical expression of ″.

[0097] In 2FSK communication mode, the two communication channels have different carrier center frequencies. To prevent frequency band overlap during channel mixing and demodulation, the 2FSK signal enters the data receiver for processing after passing through the antenna RF front-end. In the splitter, there are two center frequencies, one for the signal transmission and the other for the space channel. A bandpass filter with a very narrow bandwidth and low overlap band sends the two frequencies of the synthesized signal to their respective channels for mixing. The narrow bandwidth of the frequency-selective bandpass filter causes the envelope of the 2FSK signal carrying noise to form a narrowband random process. When the coupling center frequency within the channel is ω... j When dealing with out-of-band interference signals, it is assumed that the interference signal can only act on one of the channels and needs to be within the cutoff frequency of the corresponding channel's bandpass filter to participate in the back-end demodulation process.

[0098] Assume there exists an amplitude of A j The center frequency is ω j Out-of-band single-tone continuous wave interference applies directional interference to the signal transmission channel. The center frequency of this interference differs from the center frequency of the 2FSK signal by a small value Δω, allowing it to pass through the bandpass filter of the signal transmission channel into the back end. The synthesized signal at this point can be expressed as:

[0099] x 传 (t)=Acos(ω1t)+A j cos(ω j t+φ j1)+n1(t) (17)

[0100] The combined envelope of the noise component and the communication signal still follows a Rice distribution. However, since the frequency of the interference signal is inconsistent with the center frequency of the communication carrier, the interference signal and the communication signal cannot be directly mathematically combined and applied to the A parameter of the Rice distribution. Instead, the interference signal manifests as an additional high-frequency component, which may enter the back end through a bandpass filter. Therefore, it is necessary to calculate the equivalent power of the interference signal and correlate it with the envelope of the narrowband noise signal.

[0101] Let the frequency difference between the signal center frequency and the interference center frequency be Δf = f1 - f j Given an angular frequency Δω = 2πΔf, after the interference signal enters the back-end mixer of the filter, the signal can be expressed as:

[0102]

[0103] In the formula, the angular frequency is ω1+ω j The high-frequency components are eliminated after being filtered by a low-pass filter, while the low-frequency component with an angular frequency of Δω can pass through the low-pass filter. Mathematically, this is represented by integrating the signal within one symbol time. The residual power of this envelope can be expressed by the second moment of the envelope component within one symbol time:

[0104]

[0105] Similarly, the power can be expressed as a sampling function expression related to the difference frequency and symbol time. Substituting the obtained integral calculation result, we get the expression for the residual instantaneous power introduced by the interference. This residual power will directly affect the noise interference power. When using the noise variance σ1 to characterize the noise power, the variance of the equivalent noise interference power when transmitting "1" can be expressed as σ1'. 2 :

[0106]

[0107] By introducing the signal-to-noise ratio (SNR) and signal-to-interference ratio (SINR) parameters of the two channels, we can obtain a result of the form P. e传 "=f3(SNR 11 SIR 11 SNR 10 SIR 10 ) and P e空 "=f3(SNR 21 SIR 21 SNR 20 SIR 20 An analytical expression of the form ) is specifically expressed as:

[0108]

[0109] Step 5: Analyze the mathematical expression of the bit error rate considering out-of-band NHPM interference. This involves considering the presence of out-of-band NHPM interference at the input of the incoherent demodulator. Based on the bit error rate expression for the dual-channel mode in Step 1 and the out-of-band continuous wave interference analysis method in Step 4, the internal bit error rate P of the communication system under out-of-band NHPM interference is derived according to the time-domain duty cycle relationship between the two modes. e传带外 ′, P e空带外 The mathematical analytical expression of ′.

[0110] Specifically, by decomposing the interference process into normal periods and interference periods and performing superposition analysis, a result in the form of... and The bit error rate expressions for the out-of-band NHPM interference signal transmission channel and the empty signal channel can be written as follows:

[0111]

[0112] Where Δf: frequency difference; SNR1, SNR0: signal-to-noise ratio of the signal transmission channel or the empty signal channel; SIR1, SIR0: signal-to-interference ratio of the signal transmission channel or the empty signal channel; N p : Number of interferences; t wn The pulse width of the nth interference pulse; T m T0: Symbol time; Total control signal time; N m Symbol rate; f PRF Interference repetition frequency; T 干扰 Interference duration.

[0113] In summary, by combining equations (8), (9), (16), and (21), this invention can calculate the expected value of the bit error rate of the frequency shift keying dual-channel communication system under determined parameter environment under normal communication, co-frequency NHPM interference, and out-of-band NHPM interference, thereby realizing the evaluation of the bit error effect of the UAV frequency shift keying data transmission system.

[0114] The present invention also includes:

[0115] A system, including a processor, is capable of running the aforementioned error assessment method for an unmanned aerial vehicle (UAV) FSK data transmission system under high-power microwave conditions.

[0116] An apparatus comprising:

[0117] Memory: Used to store the computer program for the error evaluation method of an unmanned aerial vehicle FSK data transmission system under high-power microwave action;

[0118] Processor: Used to implement the error evaluation method for an FSK data transmission system of a UAV under high-power microwave action when executing the computer program.

[0119] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the error assessment method for an FSK data transmission system of a UAV under high-power microwave action.

Claims

1. A method for evaluating bit error rate of an unmanned aerial vehicle (UAV) FSK data transmission system under high power microwave (HPM) effect, characterized in that, The method comprises the following steps: Step one, based on the demodulator inside the frequency band selection filter BPF, mixing multiplier filter and sampling decision of each link mathematical modeling, normal communication mode under the analysis of double channel time domain signal after signal processing envelope decision process channel error rate P Ne传 ' and the empty channel error rate P Ne空 ' mathematical analysis expression; Step two, considering the existence of the same frequency continuous wave jamming signal in the non-coherent demodulator signal input terminal, based on the communication signal analysis process and the double channel bit error rate expression under normal communication mode in step one, it is concluded that the system internal bit error rate P e ′mathematical analysis expression; Step three, considering the existence of the same frequency NHPM interference signal in the non-coherent demodulator signal input terminal, based on the step one double channel bit error rate expression under normal communication mode and step two same frequency continuous wave interference, according to the time domain duty cycle relationship of two modes, the internal bit error rate P of the communication system under the same frequency NHPM interference is obtained e传同频 ′, P e空同频 ′ mathematical analytic expression; Step four, considering the existence of out-of-band continuous wave interference signal at the input end of the non-coherent demodulator, based on the error rate expression of the double channel in step one under normal communication mode and the analysis mode of step two continuous wave interference at the same frequency, and introducing interference analysis of different center frequencies, the internal error rate P of the communication system under the out-of-band continuous wave interference is obtained e传 The mathematical analysis expression of "P e空 " is obtained. Step five, considering the existence of out-of-band NHPM interference signal at the input end of the non-coherent demodulator, based on the bit error rate expression of the double channel in step one under normal communication mode and the out-of-band continuous wave interference analysis mode in step four, the bit error rate P e传带外 ′ e空带外 ′ of the communication system under the out-of-band NHPM interference is obtained by deduction according to the time domain duty cycle relationship of the two modes.

2. The method of claim 1, wherein, Step one is specifically: Based on the 2FSK mark-space double-channel model, the non-coherent demodulator model used by the frequency shift keying data transmission system of the unmanned aerial vehicle is considered, and each link of the frequency band pass filter BPF, the mixing multiplier, the low pass filter and the sampling decision in the demodulator is abstracted as a mathematical processing link for analysis, wherein the time domain input signal x(t) of the demodulator is composed of a symbol signal and a channel space white noise n(t): x(t)=s(t)+n(t) (1) Wherein, x(t) is the combined signal of the receiving antenna coupled into the non-coherent demodulator, s(t) and n(t) are the communication signal white noise signal respectively; Assuming that the non-coherent demodulator works in normal condition, based on the typical mathematical characteristics of the Rice Distribution and Rayleigh Distribution of the communication signal and the white noise through the selected band-pass filter, the mathematical analytic expression of the error rate P Ne传 ' of the mark channel and the error rate P Ne空 ' of the space channel after the envelope decision process of the two-channel time-domain signal after signal processing is analyzed. wherein SNR 11 and SNR 10 are the signal-to-noise ratios for the transmission of the high level "1" and the low level "0" by the mark channel, respectively, and SNR 21 and SNR 20 are the signal-to-noise ratios for the transmission of the high level "1" and the low level "0" by the space channel, respectively. Due to the symmetry of the non-coherent demodulator double-channel, the error code expressions of the two channels have the same function form f1(*), and the variables are related to the signal-to-noise ratio of the corresponding channel.

3. The method of claim 2, wherein the method further comprises: determining the error rate of the FSK data transmission system under the high-power microwave effect based on the error rate of the FSK data transmission system under the high-power microwave effect and the error rate of the FSK data transmission system under the high-power microwave effect. Step two is specifically: Suppose there is a continuous wave jamming signal at the input of the non-coherent demodulator, the center frequency of the jamming signal is f j The communication carrier frequency f 传 or f 空 is the same, considering that the NHPM jamming signal and the communication signal are superimposed on the receiving antenna and coupled into the non-coherent demodulator, it can be analyzed that for a symbol, the in-time domain signal of the same frequency continuous wave jamming signal after processing, the system internal bit error rate P e The mathematical analytical expression is: where SIR 11 and SIR 10 are the signal-to-interference ratios of the high level "1" and low level "0" sent by the on-channel, respectively, and SIR 21 and SIR 20 are the signal-to-interference ratios of the high level "1" and low level "0" sent by the off-channel, respectively; the double-channel expression still has the same functional expression form f2(*).

4. The method of claim 3, wherein, Step three is specifically: Considering that the influence of each symbol decision point in the symbol on the interference process is a uniformly distributed mathematical model, the Bayesian probability of pulse width and communication symbol time is introduced, and the mathematical parameters of the whole pulse interference string are introduced, the symbols are classified according to the interference and normal two cases in the limited signal duration, and the occurrence proportions are p1 and p2 respectively, then the 2FSK error rate analytical expression under the same frequency NHPM interference can be obtained: where t w is the NHPM pulse width, T m is the single symbol duration.

5. The method of claim 3, wherein the method further comprises: Step four is specifically: The NHPM out-of-band interference signal exists at the input end of the non-coherent demodulator. Considering a large frequency difference, the NHPM only interferes with one of the two channels, and the center frequency f j Different from the communication carrier frequency f0, considering the process of superimposing the NHPM interference signal and the communication signal on the receiving antenna and coupling into the non-coherent demodulator, a residual power model needs to be introduced for discussion, and the bit error rate analytical expression is about the sampling function sinc(t). The time domain signal of the NHPM interference with different center frequencies can be obtained, and the bit error rates P e传 ” and P e空 ” of the mark channel and the space channel in the decision 2FSK system are obtained.

6. The method of claim 5, wherein the method further comprises: Step five is specifically: After introducing the Bayesian probability of pulse width and communication symbol time, considering the mathematical parameters of the whole pulse interference string, the symbols are classified according to the interference and normal two cases in the limited signal duration, and the occurrence proportions are q1 and q2 respectively, then the 2FSK out-of-band NHPM interference error rate analytical expression under different center frequencies can be obtained:

7. A system comprising a processor, characterized in that A method for evaluating the error code of a FSK data transmission system of an unmanned aerial vehicle under the action of high power microwaves according to any one of claims 1-7.

8. An apparatus, comprising: It comprises: A memory for storing the computer program of the method for evaluating the error code of a FSK data transmission system of an unmanned aerial vehicle under the action of high power microwaves according to any one of claims 1-7; A processor for executing the computer program to realize the method for evaluating the error code of a FSK data transmission system of an unmanned aerial vehicle under the action of high power microwaves according to any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a computer program, and the computer program is executed by the processor to realize the method for evaluating the error code of a FSK data transmission system of an unmanned aerial vehicle under the action of high power microwaves according to any one of claims 1-7.

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