Radio signal arrival time estimation method based on deep learning

Abstract

The invention relates to a radio signal arrival time estimation method based on deep learning, belongs to the field of radio signal processing, and solves the problem of low radio signal arrival time estimation precision in a complex electromagnetic environment. Comprising the following steps: preprocessing a complex baseband signal generated by simulation and pure noise data to obtain sample data in an IQ matrix form, and forming a signal sample set with a sample label; training the arrival time estimation model by using the signal sample set, and saving model parameters with the minimum loss function when the maximum number of iterations is reached, so as to obtain a trained arrival time estimation model; radio signals are collected in real time and processed to obtain corresponding complex baseband signals, a plurality of signal segments are intercepted based on a sliding window with a preset length and normalized, real parts and imaginary parts are extracted and stacked to form a plurality of corresponding IQ matrixes, and the IQ matrixes are input into a trained model to obtain a signal initial sampling point index estimation value; and estimating the value signal arrival time based on the signal starting sampling point index. And the estimation precision of the signal arrival time is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of radio signal processing, and particularly relates to a method for estimating the arrival time of radio signals based on deep learning. Background Art

[0002] The estimation of the arrival time of radio signals refers to determining the time when a radio signal arrives at the receiving end, which is a common key technology in wireless communication and one of the core technologies for realizing key functions such as positioning, navigation, and wireless ranging. With the rapid development of wireless communication technology, the application scenarios are becoming increasingly complex and diverse, posing higher requirements for the accuracy and reliability of arrival time estimation.

[0003] In traditional wireless communication scenarios, currently commonly used arrival time estimation methods mainly include peak detection method, correlation method, and time-frequency analysis method, etc. The peak detection method determines the signal arrival time by finding the amplitude peak of the received signal. Its principle is simple and the computational complexity is low. However, in practical applications, due to the existence of multipath effects, the signal will generate multiple reflection paths during propagation, resulting in multiple amplitude peaks in the received signal, which makes it difficult for the peak detection method to accurately judge which peak corresponds to the true signal arrival time, thus reducing the estimation accuracy. In addition, environmental noise and interference will also cause fluctuations in the amplitude of the received signal, further interfering with the detection of peaks.

[0004] The correlation method uses the known waveform of the signal to perform a correlation operation with the received waveform, and determines the signal arrival time by finding the maximum value of the correlation function. This method has extremely high requirements for signal synchronization and requires precise knowledge of the waveform structure of the signal to ensure the effectiveness of the correlation operation. In non-cooperative scenarios, such as in some wireless communication interference scenarios or monitoring scenarios of unknown signal sources, where prior waveform information of the signal cannot be obtained, the correlation method is difficult to play a role.

[0005] The time-frequency analysis method estimates the arrival time by performing a time-frequency transformation on the signal, mapping the signal from the time domain to the time-frequency domain, so as to more clearly observe the time-frequency characteristics of the signal. However, it is also susceptible to the influence of complex electromagnetic environments. Multipath effects will cause the signal to have a complex structure in the time-frequency domain, and the interference with the extraction of time-frequency characteristics will also have an impact, resulting in deviations in arrival time estimation.

[0006] The increasing complexity of the electromagnetic spectrum environment, such as the intensive use of spectrum resources and the intertwined coexistence of various wireless communication systems and interference sources, has brought unprecedented challenges to traditional estimation methods. For methods such as peak detection and time-frequency analysis, their estimation accuracy is easily affected by factors such as multipath effects, environmental noise, and interference. The correlation method has high requirements for signal synchronization and needs to use the known waveform of the signal to perform correlation with the received waveform, making it difficult to cope with non-cooperative scenarios. Summary of the Invention

[0007] In view of the above analysis, an embodiment of the present invention aims to provide a method for estimating the arrival time of radio signals based on deep learning, so as to solve the technical problems of low accuracy and poor generalization ability of the existing methods for estimating the arrival time of radio signals caused by multipath channels and noise injection.

[0008] The purpose of the present invention is mainly achieved through the following technical solutions: The present invention provides a method for estimating the arrival time of radio signals based on deep learning, including the following steps: Preprocess the simulated complex baseband signal and pure noise data to obtain sample data in the form of an IQ matrix, and form a signal sample set with the corresponding sample labels; wherein, the sample label corresponding to the complex baseband signal is the signal starting sampling point index value; Use the signal sample set to train the arrival time estimation model, save the model parameters with the smallest loss function when reaching the maximum number of iterations, and obtain the trained arrival time estimation model; Collect radio signals in real time, perform down-conversion processing to obtain the corresponding complex baseband signal, intercept it into multiple signal segments based on a predetermined length and normalize them, extract the real and imaginary parts respectively and stack them into corresponding multiple IQ matrices, and then input them into the trained arrival time estimation model in sequence until the signal starting sampling point index estimation value is found; calculate the signal arrival time based on the signal starting sampling point index estimation value and the serial number of the signal segment.

[0009] Further, the complex baseband signal includes a communication complex baseband signal and a radar complex baseband signal; the preprocessing of the simulated complex baseband signal and pure noise data to obtain sample data includes: Intercept the complex baseband signal into multiple signal segments based on a predetermined length, construct signal samples containing different arrival time information based on the signal segments to obtain the first sample signal; perform multipath channel simulation and / or noise injection on the first sample signal respectively to obtain the signal set corresponding to the first sample signal; The pure noise data takes sampling points; The signal set corresponding to the first sample signal is combined with the pure noise data with a length of sampling points to form a second sample signal; Normalize the second sample signal, and extract the real and imaginary parts and stack them into an IQ matrix as sample data.

[0010] Further, constructing signal samples containing different arrival time information based on the complex baseband signal to obtain the first sample signal includes: Intercept the complex baseband signal according to a predetermined length Signal truncation is performed to obtain multiple sub-complex baseband signals each with a length of ; for each sub-complex baseband signal, a sequence of all zeros with a length of sampling points is generated; where ; A subsequence of all zeros with a length of sampling points is intercepted and spliced in front of the starting point of the complex baseband signal; the remaining sampling points of the all-zero subsequence are spliced after the end point of the complex baseband signal to obtain a first sample signal corresponding to the complex baseband signal with a length of sampling points; where is the number of sampling points of the complex baseband signal, ; The sample label corresponding to the complex baseband signal is the signal starting sampling point index value ; the sample label corresponding to the pure noise data is .

[0011] Further, the time of arrival estimation model sequentially includes an input layer, an adaptive correction module, a feature extraction module, a feature focusing module, and a time of arrival prediction module; The input layer is used to receive the IQ matrix; The adaptive correction module is used to eliminate the offset generated by multipath and noise on the IQ matrix and output a corrected time-domain IQ matrix; The feature extraction module is used to capture the fusion features of different scales of the corrected time-domain IQ matrix; The feature focusing module is used to perform signal feature selection in the time channel based on the self-attention mechanism and output the focused signal features; The time of arrival prediction module contains neurons and is used to output probabilities of the signal starting sampling point index estimation values and the probability of one pure noise data.

[0012] Further, the adaptive correction module sequentially includes a Fourier transform layer, a fully connected frequency-domain weight learning layer, and a Fourier inverse transform reconstruction layer; The Fourier transform layer is used to perform a time-domain to frequency-domain transformation on the IQ matrix to obtain a frequency-domain signal; The fully connected frequency-domain weight learning layer is used to learn the weights of the frequency-domain signal, suppress the phase offset components caused by multipath, and attenuate the high-frequency or low-frequency regions dominated by noise to obtain a corrected frequency-domain signal; The Fourier inverse transform reconstruction layer is used to perform an inverse fast Fourier transform on the corrected frequency-domain signal to restore it to a time-domain signal and output an adaptively corrected time-domain IQ matrix.

[0013] Further, the feature extraction module includes first, second, and third convolutional layers with different receptive fields in parallel, and a Concat splicing layer; The first convolutional layer has a convolutional kernel size of , a number of channels of , padding of , and a stride of , and is used to extract local features of the adaptively corrected time-domain IQ matrix; The second convolutional layer has a convolutional kernel size of , a number of channels of , padding of , and a stride of , and is used to extract medium-scale features of the adaptively corrected time-domain IQ matrix; The third convolutional layer has a convolutional kernel size of , a number of channels of , padding of , and a stride of , and is used to extract global features of the adaptively corrected time-domain IQ matrix; where ; The Concat splicing layer splices the local features, medium-scale features, and global features output by the first, second, and third convolutional layers along the channel dimension to obtain a fused feature.

[0014] Further, the feature focusing module includes a self-attention feature focusing layer; where the output of the Concat splicing layer is connected in a residual connection with the output of the self-attention feature focusing layer; The self-attention feature focusing layer sequentially includes a self-attention layer, a focusing residual connection, and layer normalization; The self-attention layer is used to map the fused feature into Q, K, and V matrices through a linear transformation; calculate attention weights based on the Q, K, and V matrices, and output a weighted fused feature; The focusing residual connection and layer normalization connect and normalize the fused feature and the weighted fused feature; output the focused feature and transfer it to the time-of-arrival prediction module.

[0015] Further, the loss function is as follows: ; Where is the second sample signal; is the normalized second sample signal; , are the real and imaginary parts of the normalized second sample signal, respectively; is a parameterized function of the time-of-arrival estimation model, used to obtain the probability distribution predicted by the model; is a learnable parameter, is the true label corresponding to the input sample, is the number of categories output by the model.

[0016] Furthermore, the signal arrival time is calculated based on the estimated value of the signal start sampling point index and the sequence number of the signal segment , as follows: ; where, is the time when the receiver collects the signal, is the sampling rate of the receiver; is the estimated value of the signal start sampling point index; is the first time to obtain the sequence number of the signal segment of the estimated value of the signal start sampling point within.

[0017] Furthermore, the multipath channel simulation includes Rice channel and Rayleigh channel simulation; The noise injection includes additive white Gaussian noise, generalized Gaussian noise and colored noise injection.

[0018] Compared with the prior art, the present invention can at least achieve one of the following beneficial effects: 1. The present invention trains the time-of-arrival estimation model based on the original radio signal, directly learns the signal start point features, and does not require manual feature extraction; it reduces the usage threshold, is applicable to unknown signal types and non-cooperative scenarios; it solves the problems in traditional methods that rely on manually designed features, require complex signal processing experience, and have poor generalization ability; 2. The present invention introduces Rice and Rayleigh channel conversion and various noise injections into the signal sample set used for training, generates signal samples closer to the real environment, and the sample data is more in line with the actual electromagnetic environment, effectively improving the adaptability and accuracy of signal arrival time estimation under complex electromagnetic spectra; it solves the problem that the signal arrival time estimation accuracy of traditional methods drops significantly due to multipath effects and noise injection in existing methods; 3. The adaptive correction module in the present invention suppresses multipath and noise injection, dynamically corrects the signal through frequency-domain weight learning, and suppresses multipath phase offset and noise frequency bands; it solves the problem that multipath causes signal distortion and it is difficult to distinguish the main path from the delayed path in existing methods; 4. In the present invention, the feature extraction module and the feature focusing module are based on multi-scale feature fusion and self-attention mechanism; multi-scale convolutions are used to extract local, medium, and global features in parallel, covering signal mutations; self-attention focuses to dynamically enhance the time-channel features near the starting point and suppress irrelevant fields, solving the problem of missing key information in single-scale features in existing methods. 5. In the present invention, the sample data covers communication signals and radar signals. Based on various modulation types, the time-of-arrival estimation model adaptively learns the features of heterogeneous signals through the feature extraction module, solving the problem of poor adaptability to specific modulation types in traditional methods.

[0019] In the present invention, the above technical solutions can also be combined with each other to achieve more preferred combination schemes. Other features and advantages of the present invention will be described in the subsequent specification. Moreover, some advantages can be made obvious from the specification or understood by implementing the present invention. The objectives and other advantages of the present invention can be realized and obtained from the content specifically pointed out in the specification and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The drawings are only used for the purpose of showing specific embodiments and are not considered as a limitation of the present invention. Throughout the drawings, the same reference signs represent the same components. Figure 1 It is a flowchart of a method for estimating the time of arrival of radio signals based on deep learning according to an embodiment of the present invention. Figure 2 It is a schematic diagram of the network structure of the time-of-arrival estimation model in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0021] The following will specifically describe the preferred embodiments of the present invention with reference to the drawings. The drawings form a part of this application and are used together with the embodiments of the present invention to explain the principles of the present invention, rather than to limit the scope of the present invention.

[0022] With the rapid development of artificial intelligence technology, deep learning has been successfully applied to deal with problems such as signal detection, recognition, and direction finding. Without loss of generality, deep learning technology will also provide an effective solution for the field of radio signal time-of-arrival estimation to achieve efficient estimation in complex scenarios. The present invention discloses a method for estimating the time of arrival of signals based on deep learning, providing important support for the development of modern wireless communication and positioning systems.

[0023] A specific embodiment of the present invention discloses a deep learning signal detection method adaptable to the change of the number of receiving antennas, as Figure 1 shown, including the following steps: Step S1: Preprocess the complex baseband signal and pure noise data generated by simulation to obtain sample data in the form of an IQ matrix, and form a signal sample set with the corresponding sample labels. Among them, the sample label corresponding to the complex baseband signal is the signal starting sampling point index value; Step S2: Use the signal sample set to train the time-of-arrival estimation model, save the model parameters with the minimum loss function when reaching the maximum number of iterations, and obtain the trained time-of-arrival estimation model; Step S3: Collect radio signals in real time, perform down-conversion processing to obtain the corresponding complex baseband signal, intercept it into multiple signal segments based on a predetermined length sliding window and normalize them. Respectively extract the real part and the imaginary part and stack them into the corresponding multiple IQ (In-Phase, Quadrature) matrices, and then input them into the trained time-of-arrival estimation model in turn until the signal starting sampling point index estimation value is found. Calculate the signal arrival time based on the signal starting sampling point index estimation value and the serial number of the signal segment.

[0024] The IQ matrix is used to represent the real part (in-phase component) and the imaginary part (quadrature component) of the complex baseband signal, and is often used in radio signal processing.

[0025] Step S1 includes steps S11 - S14.

[0026] Based on radio signal knowledge, simulate and generate different types of complex baseband signals. The complex baseband signals include communication complex baseband signals and radar complex baseband signals, which are used to simulate actual communication scenarios and radar scenarios; and generate pure noise data, which is used to simulate noise interference in the actual environment.

[0027] The complex baseband signals include communication complex baseband signals and radar complex baseband signals. Preprocessing the complex baseband signals and pure noise data generated by simulation to obtain sample data includes: Intercept the complex baseband signal into multiple signal segments based on a predetermined length, and construct signal samples containing different time-of-arrival information based on the signal segments to obtain the first sample signal; Perform multipath channel simulation and / or noise injection on the first sample signal respectively to obtain the signal set corresponding to the first sample signal; The pure noise data has a length of sampling points; The signal set corresponding to the first sample signal is combined with the pure noise data with a length of sampling points to form the second sample signal; Specifically, it includes performing multipath channel simulation and noise injection; performing multipath channel simulation and noise injection in sequence (first performing multipath channel simulation and then performing noise injection).

[0028] Normalize the second sample signal, and extract the real and imaginary parts and stack them into an IQ matrix as sample data.

[0029] The multipath channel simulation includes Rice channel and Rayleigh channel simulations; The noise injection includes additive white Gaussian noise, generalized Gaussian noise, and colored noise injection.

[0030] Step S11: Simulate and generate complex baseband signals of communication signals and radar signals, as well as pure noise data.

[0031] Communication signals are used for information transmission (such as voice, data), representing typical narrowband, high data rate scenarios with various modulation methods; communication signals emphasize spectral efficiency and noise resistance; the signal has high stationarity and is suitable for verifying the performance of the model in conventional scenarios; Radar signals are used for target detection and parameter estimation (such as ranging, velocity measurement), representing broadband, high time-bandwidth product scenarios with complex waveforms. Radar signals emphasize resolution ability and anti-Doppler effect; the signal has a large dynamic range and is suitable for verifying the robustness of the model under high dynamics and multipath interference.

[0032] Simulate and generate different types of complex baseband signals. Exemplarily, it includes at least communication signals and radar signals. In practical applications, it can be increased according to specific requirements.

[0033] Joint training of the arrival time estimation model for communication signals and radar signals can adapt to a wider range of signal characteristics, avoid overfitting, and enhance adaptability.

[0034] (1) Generate the complex baseband signal corresponding to the communication signal.

[0035] Based on a randomly generated binary bit stream, simulate and generate a time-continuous complex baseband signal of a predetermined length corresponding to the communication signal as follows: Randomly generate a binary bit stream , as follows: Formula (1) where is the length of the binary bit stream.

[0036] According to different modulation types, complete the mapping from the bit stream to symbols. Group every bits in the bit stream. If each symbol contains bits, then: Formula (2) where is the number of constellation points of the modulation method.

[0037] Different modulation types include QPSK (Quadrature Phase Shift Keying), PSK (Phase Shift Keying), FSK (Frequency Shift Keying), PAM (Pulse Amplitude Modulation), ASK (Amplitude Shift Keying), QAM (Quadrature Amplitude Modulation), and CPM (Continuous Phase Modulation) modulation types; First, perform bit grouping, and divide the bit stream into groups of every consecutive bits based on different modulation types; Secondly, then perform symbol mapping, and map each group of bits to a complex symbol through the Map(.) function ; Finally, generate the complex baseband signal, and generate the baseband signal after passing the symbol sequence through pulse shaping filtering.

[0038] Exemplarily, for QPSK modulation, , then , each symbol consists of two bits; for 16-QAM ( = 16), , each symbol consists of 4 bits.

[0039] Perform the mapping of the bit stream to symbols based on multiple modulation types to obtain the corresponding symbol sequence.

[0040] The mapping from the bit stream to symbols is as follows: Formula (3) where is to map bits to the symbol on the complex plane, is the index symbol.

[0041] Exemplarily, for the QPSK modulation method, , then the bit combinations {0,0}, {0,1}, {1,0}, {1,1} are respectively mapped to

[0042] For QPSK modulation, , the bit stream

[0043] Symbol mapping is as follows: The first symbol {0, 1} → ; The second symbol {1, 0} → ; The third symbol {1, 1} → .

[0044] For each symbol, it usually undergoes pulse shaping filtering (such as a raised cosine filter) to generate a time - continuous complex baseband signal.

[0045] Perform pulse shaping filtering on each symbol in the symbol sequence to obtain a time - continuous complex baseband signal of a predetermined length.

[0046] After pulse shaping, a time - continuous complex baseband signal is generated , as follows: Equation (4) where, is the symbol period, that is, the duration of each symbol, in seconds; is a rectangular pulse, and is the impulse response of the pulse shaping filter (such as a raised cosine filter), which is used to limit the signal bandwidth and reduce inter - symbol interference; is the nth symbol mapped from the binary bit stream .

[0047] For different modulation types, the mapping method from the binary bit stream to the symbol is different; for example, for the K - order PSK modulation type, the mapping from the bit stream to the symbol is as follows: Equation (5) where, is the symbol number. Each symbol corresponds to a point on the unit circle in the complex plane, and the rotation angle is ; is the imaginary unit, satisfying , represents the imaginary part of the complex number, enabling the signal to be represented in the complex plane, thus facilitating modulation and demodulation operations.

[0048] For - order FSK modulation type, the mapping from the bit stream to the symbol is as follows: Equation (6) where, is the carrier frequency, is the frequency interval; is the time variable, representing the duration of the signal at this frequency.

[0049] For For K - level PAM modulation, each symbol is directly mapped to a real number with a different amplitude, and the mapping from the bit stream to the symbol is as follows: Formula (7) For K - level ASK modulation, the mapping from the bit stream to the symbol is as follows: Formula (8) where, is the carrier amplitude; each symbol transmits a carrier with a different amplitude.

[0050] For the K - level QAM modulation type, the mapping from the bit stream to the symbol is as follows: Formula (9) where, is the row - column number; each symbol point is distributed on a two - dimensional rectangular grid, and both the amplitude and phase are modulated.

[0051] For the CPM modulation type, the mapping from the bit stream to the symbol is as follows: Formula (10) where, is the modulation index; is the bit sequence; is the phase pulse response; n represents the discrete time index, which is used to represent the nth symbol position in the symbol sequence. Each phase changes continuously, and the modulated information is hidden in the phase change rate.

[0052] (2) Generate the complex baseband signal corresponding to the radar signal.

[0053] Generate a time - continuous complex baseband signal based on the linear frequency - modulated signal (LFM, Linear Frequency Modulation) as follows: Formula (11) where, is the initial center frequency (e.g., 10 MHz), is the signal frequency modulation slope (e.g., 100 MHz / s), is the initial phase (e.g., 0).

[0054] Generate a time - continuous complex baseband signal based on the binary - coded signal (Barker, Barker Code) as follows: Formula (12) where, is the Barker code phase, taking 0 or .

[0055] Generate a time-continuous complex baseband signal based on the Pulse Repetition Interval (PRI) jitter signal as follows: The interval between the arrival times of two adjacent pulses from the same radar radiation source is called the Pulse Repetition Interval, or PRI. For a PRI jitter signal, the PRI value randomly jumps or follows a certain distribution around the central value as follows: Formula (13) where, is the number of arrivals, represents the central value of the PRI jump, is the reference pulse interval (e.g., 1 ms), is the th value of the PRI jump.

[0056] PRI stagger signal: There are 2 to 7 fixed PRI values repeating in a certain order. The mathematical model can be expressed as Formula (14) where, is one of the

[0057] fixed PRI values, and mod represents the modulo operation. Generate a time-continuous complex baseband signal as follows: Frequency agility signal, generate a time-continuous complex baseband signal as follows: Formula (16) where, is the initial carrier frequency (e.g., 1 GHz), is the frequency agility offset (e.g., ).

[0058] (3) Generate pure noise data Generate pure noise data based on the additive Gaussian white noise, generalized Gaussian white noise, and colored noise models. The length of the pure noise data is time sampling points.

[0059] The function of step S11 is to generate the corresponding complex baseband signals for the communication signal and the radar signal, and generate pure noise data for generating joint sample data to train the arrival time estimation model.

[0060] Step S12: Based on the complex baseband signal, construct signal sample data containing different arrival time information to obtain the first sample signal data.

[0061] Constructing a signal sample containing different arrival time information based on the complex baseband signal to obtain the first sample signal includes: Truncate the complex baseband signal according to a predetermined length to obtain a plurality of sub-complex baseband signals with a length of ; for each sub-complex baseband signal, generate a sequence of all zeros with a length of sampling points; where ; Intercept a sub-sequence of all zeros with a length of sampling points and splice it in front of the starting point of the complex baseband signal; the remaining sub-sequence of all zeros with sampling points is spliced behind the end point of the complex baseband signal to obtain a signal sample corresponding to the complex baseband signal with a length of sampling points; where ; The sample label corresponding to the complex baseband signal is the signal starting sampling point index value ; the sample label corresponding to the pure noise data is .

[0062] Establish the first sample signal in the form of , consisting of a complex baseband signal with a predetermined length of continuous time and a sequence of all zeros, and is the corresponding sample label. For each complex baseband signal corresponding to a radio signal and having continuous time, generate a sequence of all zeros with a length of ; exemplarily, the length takes a value of 100 sampling time points.

[0063] For complex baseband signals (including communication signals and radar signals, pure noise data does not require this processing step), intercept a sub-sequence of all zeros with a length of and splice it in front of the starting point of the radio signal, and splice the remaining sub-sequence of all zeros with sampling time points behind the end point of the radio signal to obtain a signal sample , with a length of ; takes a value selected from 1 to that satisfies a uniform distribution. The sample label is the signal starting sampling point index ; for a length of of , the sampling point sequence is .

[0064] The all-zero subsequences concatenated before the starting point of the radio signal, with an index of 0 value ; therefore, the starting sampling point of the radio signal is .

[0065] For pure noise data, directly take the noise data with the length of sampling points; there is no signal data in the pure noise data; there is no corresponding starting sampling point; for distinction, the starting sampling point, that is, the sample label is set to

[0066] In the actual wireless communication environment, radio signals may arrive at the receiving end at different times. By adding all-zero sequences with different lengths before and after the signal, the situation where the signal arrives at the receiving end of the receiver at different times can be simulated. This helps the time-of-arrival estimation model learn the signal characteristics at different arrival times, thereby improving the accuracy of the time-of-arrival estimation model for time-of-arrival estimation.

[0067] The function of step S12 is to construct signal sample data containing different time-of-arrival information based on the complex baseband signal, and to simulate the situation where only pure noise data may be collected in actual applications, and generate sample data corresponding to the pure noise data; it is used to train the time-of-arrival estimation model to improve its learning ability and estimation accuracy for signal characteristics at different times of arrival.

[0068] Step S13: Perform multipath channel simulation and / or noise injection on the first sample signal in sequence to obtain a signal set corresponding to the first sample signal.

[0069] There are three ways to perform multipath channel simulation and / or injection on the first sample signal as follows: (1) Perform multipath channel simulation on the first sample signal to obtain a corresponding signal sample set ; (2) Perform noise injection on the first sample signal to obtain a corresponding signal sample set ; (3) Perform multipath channel simulation and noise injection on the first sample signal in sequence to obtain a corresponding signal sample set .

[0070] Combine with the original complex baseband signal , and combine with the pure noise data to obtain sample data .

[0071] Multipath channel simulation includes Rice channel and Rayleigh channel simulation; Noise injection includes additive Gaussian white noise, generalized Gaussian white noise, and colored noise injection; The purpose of performing multipath channel simulation and noise injection is to simulate the multipath effect and noise injection in a real electromagnetic environment, enhance the diversity and complexity of sample data, and thus improve the robustness and estimation accuracy of the time-of-arrival estimation model in complex scenarios.

[0072] Use the multipath channel and noise model to transform the signal samples to obtain signal samples with different signal-to-noise ratios that are closer to the real electromagnetic spectrum environment 。

[0073] The multipath channel model at least includes the Rice channel and the Rayleigh channel; the noise model at least includes additive Gaussian white noise, generalized Gaussian white noise, and colored noise. In practical applications, additions and deletions can be made according to specific requirements.

[0074] a) Rice channel transformation The Rice channel is a channel model in mobile communication and wireless communication systems. For the Rice channel, it is usually used to describe that in the transmission process, there is a LOS (Line of Sight) signal and multiple NLOS (Non-Line of Sight) signals. The signal amplitude distribution in this channel model is the Rice distribution.

[0075] The Rice distribution is a probability distribution used to describe the amplitude distribution of the received signal in the case of a dominant LOS and multiple NLOSs, and is applicable to the signal propagation characteristics in a scattering environment.

[0076] The Rice channel transformation is as follows: Equation (17) where is the signal after Rice channel transformation, is Gaussian white noise (usually complex Gaussian noise), is the Rician Factor; is the complex baseband signal.

[0077] The Rician Factor represents the ratio of the signal power of the direct path to the scattered path. The Rician Factor is expressed as: Equation (18) where is the amplitude of the direct path, is the power of the multipath scattering path (i.e., the non-direct path).

[0078] The larger the Rice factor value, the stronger the direct-path signal and the more concentrated the signal amplitude distribution; conversely, the smaller the Rice factor value, the more dispersed the signal amplitude distribution. When approaches zero, the Rice distribution approaches the Rayleigh distribution.

[0079] b) Rayleigh channel transformation For the Rayleigh channel model, it is used to describe the situation where there is no direct path in the wireless signal propagation process, that is, it is completely composed of multipath reflection or scattering paths. The amplitude distribution of the Rayleigh fading channel is the Rayleigh distribution. The channel model formula is as follows: Formula (19) where, is the signal after Rayleigh channel transformation; is the Rayleigh fading coefficient, usually a complex Gaussian random variable, whose amplitude conforms to the Rayleigh distribution, describing the time-varying characteristics of the channel, including the changes in amplitude and phase; in formula (19) the amplitude of is a random variable with a Rayleigh distribution, and its probability density function is given by formula (20).

[0080] The probability density function of the Rayleigh distribution is as follows: Formula (20) where, is the amplitude of the received signal, which is a non-negative scalar random variable; is the standard deviation of Rayleigh fading, reflecting the power of multipath signals.

[0081] For the transformation of the noise model, mainly different types of noise are superimposed on the complex baseband signal.

[0082] c) Additive white Gaussian noise injection Additive white Gaussian noise is superimposed on the complex baseband signal as follows: Formula (21) where, is the signal after additive white Gaussian noise injection is superimposed on the complex baseband signal; w is related to the noise type. If it is additive white Gaussian noise, it is usually Gaussian noise with zero mean and variance of ; is the coefficient to control the noise power size, which can control the noise power size to complete the transformation of different signal-to-noise ratios.

[0083] d) Generalized white Gaussian noise transformation For generalized Gaussian white noise, its probability density function (PDF) can be described by an exponential family. It is widely used to simulate the noise in actual signals, especially when the noise exhibits a heavier tail.

[0084] The probability density function of generalized Gaussian white noise is as follows: Equation (22) where is the shape parameter that determines the tail characteristics of the noise distribution; is the scale parameter that controls the width of the noise distribution and affects the amplitude of the noise. is the gamma function, which is used to normalize the probability density function to ensure that its integral result is 1.

[0085] When is small, the distribution has a heavier tail, indicating that there are more extreme values in the noise; when the generalized Gaussian noise degenerates into additive Gaussian white noise.

[0086] Inject generalized Gaussian white noise into the complex baseband signal to obtain the corresponding signal samples; the injection of this generalized Gaussian white noise follows the generalized Gaussian white noise probability density in Equation (22).

[0087] e) Colored noise transformation Colored noise is a type of noise different from white noise, and its power spectral density varies with frequency. Colored noise can usually be generated by filtering additive Gaussian white noise.

[0088] The power spectral density of the colored noise transformation is as follows: Equation (23) where is the cut-off frequency (or characteristic frequency) of the colored noise; is the reference power spectral density of the noise. The power spectral density of colored noise decays as the frequency increases and usually has the characteristic of high gain for low-frequency noise.

[0089] Inject colored noise into the complex baseband signal to obtain the corresponding signal samples; the injection of this colored noise follows the colored noise injection probability density in Equation (23).

[0090] Different channel models (such as Rayleigh channel, Rice channel) and noise models (such as additive Gaussian white noise, generalized Gaussian noise, colored noise) generate corresponding signal sample sets to be closer to the actual environment when simulating and analyzing the performance of communication systems.

[0091] The function of step S13 is to simulate multipath channels and inject noise into the first sample signal, simulating multipath effects and noise injection in a real electromagnetic environment, enhancing the diversity and complexity of the sample data, thereby improving the robustness and estimation accuracy of the time-of-arrival estimation model in complex scenarios.

[0092] Step S14: Construct a signal sample set based on the second sample signal.

[0093] (1) For each second sample signal Perform normalization.

[0094] Exemplarily, the normalization method can select the z-score method to calculate the mean u and standard deviation σ of the signal x , ,

[0100] , , ,

[0096] ,

[0098] , ,

[0099] , , ,

[0094] ,

[0101] ,

[0097] , , , Figure 2 , , , , ,

[0095] , , new , , and perform normalization calculation using the following formula: Formula (24) Extract the real and imaginary parts of the normalized signal and stack them into an IQ matrix.

[0095] Formula (25) The dimension of the IQ matrix is , where P is the total number of signal samples.

[0096] Randomly divide it into a training set and a validation set at a ratio of 8:2.

[0097] The function of step S1 is to generate a signal sample set for training the time-of-arrival model.

[0098] Step S2: Include steps S21 - S22.

[0099] Step S21: Construct a time-of-arrival estimation model.

[0100] As Figure 2 shown, the time-of-arrival estimation model sequentially includes an input layer, an adaptive correction module, a feature extraction module, a feature focusing module, and a time-of-arrival prediction module. Among them, the time-of-arrival prediction module is the output layer of the model, containing neurons, corresponding to N probability results of the estimated value of the signal starting sampling point index, and 1 probability result of pure noise data.

[0101] The time-of-arrival estimation model sequentially includes an input layer, an adaptive correction module, a feature extraction module, a feature focusing module, and a time-of-arrival prediction module; The input layer is used to receive the IQ matrix; The adaptive correction module is used to eliminate the offset generated by multipath and noise on the IQ matrix and output the corrected time-domain IQ matrix; The feature extraction module is used to capture the fusion features of different scales of the corrected signal; The feature focusing module is used to perform signal feature selection in the time channel based on the self-attention mechanism and output the focused signal features; The time-of-arrival prediction module includes neurons, which are used to output the probabilities of the estimated values of the starting sampling points of the signal and the probability of a pure noise data.

[0102] (1) Input layer, which receives the IQ matrix of the signal samples and inputs it to the adaptive correction module.

[0103] (2) Adaptive correction module, specifically as follows: The adaptive correction module successively includes a Fourier transform layer, a fully connected frequency-domain weight learning layer, and an inverse Fourier transform reconstruction layer; The Fourier transform layer is used to perform a time-domain to frequency-domain transformation on the IQ matrix to obtain a frequency-domain signal; The fully connected frequency-domain weight learning layer is used to learn the weights of the frequency-domain signal, suppress the phase offset components caused by multipath, and attenuate the high-frequency or low-frequency regions dominated by noise, to obtain a corrected frequency-domain signal; The inverse Fourier transform reconstruction layer is used to perform an inverse fast Fourier transform on the corrected frequency-domain signal to restore it to a time-domain signal and output the adaptively corrected time-domain IQ matrix.

[0104] The Fourier transform layer performs a fast Fourier transform (FFT, Fast Fourier Transform) on the IQ matrix of each signal sample data to convert the time-domain signal into a frequency-domain signal representation.

[0105] Input time-domain IQ matrix , where represents the complex domain.

[0106] Formula (26) where is the frequency-domain signal representation of the sample data.

[0107] The fully connected frequency-domain weight learning layer is a fully connected layer, with the input being , learning the frequency-domain weight matrix , and dynamically adjusting the gain of each frequency component as follows: Formula (27) where is the corrected frequency-domain signal. The fully connected frequency-domain weight learning is used to suppress the phase offset components caused by multipath.

[0108] The inverse Fourier transform reconstruction layer performs an inverse fast Fourier transform (IFFT) to restore it to a time-domain signal; the corrected time-domain IQ matrix has significantly reduced multipath simulation and noise injection interference.

[0109] The adaptive correction module corrects the signal by learning a set of weights in the frequency domain. After mainly performing a Fourier transform on the signal, it passes through a fully connected frequency-domain weight learning layer and then reconstructs the signal through an inverse Fourier transform. Its main function is to eliminate the offsets caused by multipath, noise, etc. to the signal.

[0110] (3) The feature extraction module is as follows: Exemplarily, it includes three convolutional layers with different convolutional kernels in parallel.

[0111] The feature extraction module includes the first, second, and third convolutional layers with different receptive fields in parallel, and a Concat splicing layer; The first convolutional layer has a convolutional kernel size of , a number of channels of , a padding of , a stride of , and is used to extract local features of the adaptively corrected time-domain IQ matrix; The second convolutional layer has a convolutional kernel size of , a number of channels of , a padding of , a stride of , and is used to extract medium-scale features of the adaptively corrected time-domain IQ matrix; The third convolutional layer has a convolutional kernel size of , a number of channels of , a padding of , a stride of , and is used to extract global features of the adaptively corrected time-domain IQ matrix; where ; The Concat splicing layer concatenates the local features, medium-scale features, and global features output by the first, second, and third convolutional layers along the channel dimension to obtain a fused feature.

[0112] Exemplarily, the first convolutional layer has a convolutional kernel size of , a number of channels of 64, a padding of 0, and a stride of 1; the second convolutional layer has a convolutional kernel size of , a number of channels of 64, a padding of 1, and a stride of 1; the third convolutional layer has a convolutional kernel size of , the number of channels is 64, the padding is 2, and the stride is 1.

[0113] The role of the feature extraction module is to effectively capture signal features at different scales to obtain corresponding fused features.

[0114] (4) Feature aggregation module, specifically.

[0115] The feature focusing module includes a self-attention feature focusing layer, and a concatenated residual connection between the output of the Concat splicing layer and the output of the self-attention feature focusing layer; The self-attention feature focusing layer sequentially includes a self-attention layer, a focusing residual connection, and layer normalization; The self-attention layer is used to map the fused feature into Q, K, and V matrices through a linear transformation; calculate the attention weights based on the Q, K, and V matrices, and output the weighted fused feature; The focusing residual connection and layer normalization connect and normalize the fused feature and the weighted fused feature; output the focused feature and transfer it to the time-of-arrival prediction module.

[0116] The feature aggregation module receives the fused feature to the self-attention layer.

[0117] The self-attention layer maps the input fused feature into a query matrix Q, a key matrix K, and a value matrix V through a linear transformation, as follows: Formula (28) Where, is the fused feature matrix; , and are transformation matrices respectively. Calculate the attention weights to obtain the weighted fused feature .

[0118] Perform the focusing residual connection and layer normalization as follows: Formula (29) Where, is the focused feature output by the feature focusing module.

[0119] The feature focusing module selects features in the time channel based on the self-attention mechanism, enabling the neural network to focus on important features.

[0120] (5) Time-of-arrival prediction module, specifically.

[0121] The feature focusing module outputs the feature and inputs it to the time-of-arrival prediction module, which is the output layer of the network and includes neurons and is a standard fully connected layer.

[0122] Output the probability of the estimated value of the starting sampling point of each possible signal. This module includes neurons, and each neuron corresponds to a possible starting position of the signal; The estimated value of the sampling point index is represented as pure noise data. The module predicts the probability distribution of the signal starting point, providing a basis for the arrival time estimation.

[0123] Specifically, the focused features output by the receiving feature focusing module are linearly transformed through the weight and bias parameters of the fully connected layer, and then the output is converted into a probability distribution form by using the softmax function.

[0124] Step S22: Use the signal sample set to train the arrival time estimation model. When the maximum number of iterations is reached, save the model parameters with the minimum loss function to obtain the trained arrival time estimation model.

[0125] During the training process, the parameters of the model are updated by minimizing the cross-entropy loss function, and the Adam optimizer is used for parameter optimization and update; set the learning rate dynamic adjustment strategy to dynamically adjust the learning rate during the training process. The learning rate restricts the scale of each parameter update, and the dynamic adjustment strategy can prevent large deviations in the model parameter update and speed up the training speed; at the same time, monitor the training loss on the validation set. If the loss continuously increases during the training process, stop the training, otherwise stop the training when the preset maximum number of iterations is reached.

[0126] The loss function is as follows: Equation (30) Among them, is the second sample signal; is the normalization of the second sample signal; and respectively extract the real part and the imaginary part of the normalized second sample signal; is the parameterized function of the arrival time estimation model, used to obtain the probability distribution predicted by the model; is the learnable parameter, is the true label corresponding to the input sample, is the number of classes output by the model.

[0127] Exemplarily, the maximum number of iterations is set to 500 times.

[0128] During the training process, save the parameters of the arrival time estimation model for each training cycle. When the maximum number of iterations is reached, select the arrival time estimation model with the minimum loss on the validation set as the final trained arrival time estimation model.

[0129] The function of step S2 is to construct and train a time-of-arrival estimation model. By using a neural network model that includes an input layer, an adaptive correction module, a feature extraction module, a feature focusing module, and a time-of-arrival prediction module, the signal sample set is learned. When the maximum number of iterations is reached, the model parameters with the minimum loss function are saved to obtain the trained time-of-arrival estimation model.

[0130] Step S3, specifically.

[0131] The receiver collects actual radio signals in real time; records the time when the receiver collects the signals ; Based on a sliding window with a predetermined length, the actually collected radio signals are intercepted to obtain multiple signal segments; the signal segment serial number starts from 1; The sliding window step size can be set according to application requirements. Exemplarily, the sliding window step size is , to achieve sliding point by point.

[0132] The length of each signal segment is sampling points.

[0133] If the length of the radio signal is less than sampling points, there is only one signal segment, and the insufficient part is filled with zero sequences; If the radio signal is greater than sampling points in length, the signal segments are intercepted with a sliding window with a step size of .

[0134] After the receiver performs down-conversion processing, the complex baseband signal corresponding to each signal segment is obtained; the IQ matrix is extracted by normalizing the complex baseband signal corresponding to each signal segment to obtain a corresponding number of IQ matrices; The multiple IQ matrices are sequentially input into the trained time-of-arrival estimation model. If the estimated values of the signal starting sampling point indexes obtained from all signal segments are all , then the actually collected radio signal in real time is pure noise data; Otherwise, based on the estimated value of the signal starting sampling point index and the serial number of the signal segment, the signal arrival time is calculated as follows: Formula (31) Where, is the time when the receiver collects the signal, is the sampling rate of the receiver; is the estimated value of the signal starting sampling point index; is the serial number of the signal segment when the estimated value of the signal starting sampling point index within is first obtained.

[0135] The function of step S3 is to collect radio signals in real time. If the radio signals collected in real time include communication signals or radar signals, after down-conversion processing and normalization, the IQ matrix is extracted, and the estimated value of the signal starting sampling point index is obtained by inputting it into the trained time-of-arrival estimation model, and then the signal arrival time is calculated; otherwise, the radio signals collected in real time are pure noise data.

[0136] In summary, a deep learning signal detection method adaptable to the change of the number of receiving antennas in the embodiment of the present invention has the following beneficial effects: 1. The present invention trains a time-of-arrival estimation model based on the original radio signals, directly learns the characteristics of the signal starting point, and does not require manual feature extraction; it reduces the use threshold, is applicable to unknown signal types and non-cooperative scenarios; it solves the problems in traditional methods that rely on manually designed features, require complex signal processing experience, and have poor generalization ability. 2. The present invention introduces Rice and Rayleigh channel conversions and various noise injections into the signal sample set used for training, generates signal samples closer to the real environment, and the sample data is more in line with the actual electromagnetic environment, effectively improving the adaptability and accuracy of signal arrival time estimation in complex electromagnetic spectra; it solves the problem that the signal arrival time estimation accuracy of traditional methods drops significantly due to multipath effects and noise injection in existing methods. 3. The adaptive correction module in the present invention suppresses multipath and noise injection, dynamically corrects the signal through frequency-domain weight learning, and suppresses multipath phase offset and noise frequency bands; it solves the problem in existing methods that multipath causes signal distortion and it is difficult to distinguish the main path from the delayed path. 4. The feature extraction module and feature focusing module in the present invention are based on multi-scale feature fusion and self-attention mechanism; multi-scale convolutions extract local, medium, and global features in parallel to cover signal mutations; self-attention focuses to dynamically strengthen the time channel features near the starting point and suppress irrelevant fields; it solves the problem that key information is missed by single-scale features in existing methods. 5. The sample data in the present invention covers communication signals and radar signals, based on various modulation types, and the time-of-arrival estimation model adaptively learns the heterogeneous signal features through the feature extraction module; it solves the problem of poor adaptability to specific modulation types in traditional methods.

[0137] Those skilled in the art can understand that all or part of the processes of implementing the method in the above embodiments can be completed by instructing relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. Among them, the computer-readable storage medium is a disk, an optical disk, a read-only memory, or a random access memory, etc.

[0138] As described above, it is only the preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for estimating the time of arrival of radio signals based on deep learning, characterized in that, Including: Preprocessing the complex baseband signal and pure noise data generated by simulation to obtain sample data in the form of an IQ matrix, and forming a signal sample set with the corresponding sample labels; wherein, the sample label corresponding to the complex baseband signal is the signal starting sampling point index value. Training the time of arrival estimation model using the signal sample set, saving the model parameters with the minimum loss function when reaching the maximum number of iterations, and obtaining the trained time of arrival estimation model. Realtime collecting radio signals, obtaining the corresponding complex baseband signals after down-conversion processing, intercepting them into multiple signal segments based on a predetermined length sliding window and normalizing them, respectively extracting the real and imaginary parts and stacking them into corresponding multiple IQ matrices, and then sequentially inputting them into the trained time of arrival estimation model until the signal starting sampling point index estimated value is found; calculating the signal arrival time based on the signal starting sampling point index estimated value and the serial number of the signal segment.

2. The method for estimating the time of arrival of a radio signal based on deep learning according to claim 1, wherein The complex baseband signal includes a communication complex baseband signal and a radar complex baseband signal. The preprocessing of the complex baseband signal and pure noise data generated by simulation to obtain sample data includes: Intercepting the complex baseband signal into multiple signal segments based on a predetermined length, constructing signal samples containing different time of arrival information based on the signal segments to obtain the first sample signal. Performing multipath channel simulation and / or noise injection on the first sample signal respectively to obtain the signal set corresponding to the first sample signal. The length of the pure noise data is sampling points; The signal set corresponding to the first sample signal is combined with pure noise data of sampling points to form a second sample signal; Normalizing the second sample signal, and extracting the real and imaginary parts and stacking them into an IQ matrix as sample data.

3. The method for estimating the time of arrival of radio signals based on deep learning according to claim 2, wherein Constructing signal samples containing different time of arrival information based on the complex baseband signal to obtain the first sample signal, including: Truncate the complex baseband signal according to a predetermined length to obtain a plurality of sub-complex baseband signals each having a length of ; for each sub-complex baseband signal, generate a sequence of all zeros having a length of sampling points; wherein ; The all-zero subsequence with a length of sampling points is spliced before the starting point of the complex baseband signal; the remaining all-zero subsequence with a length of sampling points is spliced after the ending point of the complex baseband signal, and a first sample signal with a length of sampling points corresponding to the complex baseband signal is obtained; where is the number of sampling points of the complex baseband signal, ; The sample label corresponding to the complex baseband signal is the index value of the signal start sampling point ; The sample label corresponding to the pure noise data is .

4. The method for estimating the time of arrival of a radio signal based on deep learning according to claim 3, wherein The time of arrival estimation model sequentially includes an input layer, an adaptive correction module, a feature extraction module, a feature focusing module, and a time of arrival prediction module. The input layer is used to receive the IQ matrix. The adaptive correction module is used to eliminate the offset generated by multipath and noise on the IQ matrix, and output the corrected time-domain IQ matrix. The feature extraction module is used to capture the fusion features of different scales of the corrected time-domain IQ matrix. The feature focusing module is used to perform signal feature selection in the time channel based on the self-attention mechanism, and output the focused signal features. The arrival time prediction module includes neurons for outputting the probability of the estimated value of the signal start sampling point index and the probability of a pure noise data.

5. The method for estimating the time of arrival of radio signals based on deep learning according to claim 4, wherein The adaptive correction module sequentially includes a Fourier transform layer, a fully connected frequency-domain weight learning layer, and an inverse Fourier transform reconstruction layer. The Fourier transform layer is used to perform the transformation from the time domain to the frequency domain on the IQ matrix to obtain the frequency-domain signal. The fully connected frequency-domain weight learning layer is used to learn the weights of the frequency-domain signal, suppress the phase offset component caused by multipath, and attenuate the high-frequency or low-frequency region dominated by noise, and obtain the corrected frequency-domain signal. The inverse Fourier transform reconstruction layer is used to perform the inverse fast Fourier transform on the corrected frequency-domain signal to restore it to the time domain signal, and output the adaptively corrected time-domain IQ matrix.

6. The method for estimating the time of arrival of a radio signal based on deep learning according to claim 5, wherein The feature extraction module includes the first, second, and third convolutional layers with different receptive fields in parallel, and a Concat splicing layer. The first convolutional layer has a convolution kernel size of , a number of channels of , a padding of , and a stride of , and is used to extract local features of the adaptively corrected time-domain IQ matrix; The second convolutional layer has a convolution kernel size of , a number of channels of , a padding of , and a stride of , and is used to extract medium-scale features of the adaptively corrected time-domain IQ matrix; The third convolutional layer has a convolution kernel size of , a number of channels of , a padding of , and a stride of , and is used to extract the global features of the adaptively corrected time-domain IQ matrix; where ; The Concat concatenation layer concatenates the local features, medium-scale features, and global features of the outputs of the first, second, and third convolutional layers along the channel dimension to obtain fused features.

7. The method for estimating the time of arrival of radio signals based on deep learning according to claim 6, characterized in that The feature focusing module includes a self-attention feature focusing layer; wherein, a concatenation residual connection is made between the output of the Concat concatenation layer and the output of the self-attention feature focusing layer; The self-attention feature focusing layer sequentially includes a self-attention layer, a focusing residual connection, and layer normalization; The self-attention layer is used to map the fused features into Q, K, and V matrices through a linear transformation; calculate attention weights based on the Q, K, and V matrices, and output the weighted fused features; The focusing residual connection and layer normalization connect and normalize the fused features and the weighted fused features; output the focused features and transfer them to the time-of-arrival prediction module.

8. The method for estimating the time of arrival of a radio signal based on deep learning according to claim 2, characterized in that The loss function is as follows: ； Among them, is the second sample signal; is the normalized second sample signal; , are the real part and the imaginary part of the normalized second sample signal respectively; is a parameterized function of the time-of-arrival estimation model, used to obtain the probability distribution predicted by the model; is a learnable parameter, is the true label corresponding to the input sample, is the number of categories output by the model.

9. The method for estimating the time of arrival of a radio signal based on deep learning according to claim 1, wherein The time of arrival of the signal is calculated based on the estimated value of the starting sampling point index of the signal and the serial number of the signal segment , as follows: ； wherein, is the time when the receiver acquires the signal, is the sampling rate of the receiver; is the estimated value of the starting sampling point index of the signal; is for the first time to obtain is the serial number of the signal segment of the estimated value of the starting sampling point index of the signal within.

10. The method for estimating the time of arrival of a radio signal based on deep learning according to any one of claims 2-9, characterized in that, The multipath channel simulation includes Rice channel and Rayleigh channel simulations; The noise injection includes additive white Gaussian noise, generalized Gaussian noise, and colored noise injection.

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