A deep learning bandwidth estimation method incorporating spectral prior knowledge

Abstract

This invention discloses a deep learning-based bandwidth estimation method incorporating prior spectrum knowledge, belonging to the field of wireless communication signal parameter estimation. Specifically, it involves: first, collecting simulated signals from both the transmitting and receiving ends as a group; estimating the bandwidth of each group of simulated signals; then, obtaining two-dimensional real-valued arrays of each signal through I and Q channels, and writing them into an h5 file along with the estimated bandwidth to form a simulated RF signal dataset; next, extracting spectral features from each simulated signal from the receiving end in the dataset to obtain its respective frequency domain amplitude and corresponding frequency, which are then used as a training set to input into a Roinformer neural network for regression learning; finally, transmitting signals in real-time from the transmitting end, directly inputting them into the trained Roinformer neural network, and directly outputting the corresponding bandwidth estimate. This invention significantly reduces the error rate in bandwidth estimation tasks, is applicable to the fields of communication signal processing and spectrum analysis, and has broad application value.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication signal parameter estimation, specifically a deep learning bandwidth estimation method that incorporates prior spectrum knowledge. Background Art

[0002] In non-cooperative communication, the accurate estimation of signal bandwidth is crucial for obtaining communication content by monitoring the electromagnetic spectrum. Bandwidth estimation is a key step in signal processing and a prerequisite for signal analysis and processing. According to Shannon's theorem, the maximum data transmission rate of a channel is related to its bandwidth: the larger the bandwidth, the higher the channel capacity, and the higher the data transmission rate.

[0003] By accurately estimating bandwidth, communication systems can be optimized within limited frequency resources, ensuring data transmission at the best possible rate. This is especially crucial in wireless communication, where systems share limited spectrum resources; therefore, accurate bandwidth estimation helps reduce inter-signal interference, rationally allocate frequency resources, and improve system stability and efficiency. Furthermore, bandwidth estimation can effectively improve power and spectral efficiency, allowing for the appropriate adjustment of modulation and coding schemes, thereby optimizing transmission efficiency.

[0004] Traditional bandwidth estimation methods, including autocorrelation analysis, spectral entropy method, and instantaneous frequency method, rely on prior models and statistical characteristics of the signal. However, in real-world communication environments, signal types are diverse and affected by noise, interference, and nonlinear distortion, making it difficult for traditional methods to achieve accurate estimates under complex conditions.

[0005] In addition, while pure deep learning methods can automatically extract signal features and are suitable for complex signal environments, they are highly dependent on a large amount of data and lack generalization ability for different scenarios. Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a deep learning bandwidth estimation method incorporating prior spectral knowledge. First, a simulated radio frequency signal dataset is generated. Then, prior spectral features are extracted, and a Roinformer network is constructed to perform regression learning on the extracted spectral features. By introducing spectrum-related prior knowledge, this invention can not only automatically learn the features of complex signals but also maintain high generalization in diverse environments, thereby achieving more stable and accurate results in bandwidth estimation.

[0007] The specific steps of the deep learning bandwidth estimation method incorporating prior spectrum knowledge are as follows:

[0008] Step 1: Given the signal parameters of the transmitting end, the simulated signal of the transmitting end is obtained through digital modulation; the receiving end samples the transmitting end by setting the sampling rate to obtain the simulated signal of the receiving end, and the simulated signals of the transmitting end and the receiving end are combined into one group.

[0009] The parameters of the transmitted signal include bandwidth, roll-off factor, and modulation method.

[0010] Seven common digital modulation schemes were selected, including BASK, QASK, BFSK, QFSK, BPSK, QPSK, and 16QAM.

[0011] Step 2: For each set of simulated signals from the transmitter and receiver, use MATLAB to estimate the bandwidth and save the simulated signals of each set with acceptable bandwidth.

[0012] The bandwidth of a set of simulated signals from both the transmitting and receiving ends is estimated, specifically as follows:

[0013] First, for the simulated signal x[n] at the transmitting or receiving end, its length is N and its sampling frequency is f. s The power spectral density estimate is expressed as:

[0014]

[0015] In the formula, X(f) is the discrete Fourier transform of the simulated signal x[n]:

[0016]

[0017] Where, f n It is the frequency value of the nth discrete frequency component in the frequency domain.

[0018] Then, using the power spectral density estimates within the start and end frequency ranges of the simulated signal spectrum, the total power P of the signal is calculated. total :

[0019]

[0020] In the formula, f1 and f2 are the start and end frequencies of the signal spectrum, respectively.

[0021] Finally, when the total signal power accumulates to 90%, the low-frequency and high-frequency boundary ranges of the simulated signal spectrum are calculated [f]. L f H The bandwidth B within ];

[0022] The following conditions must be met:

[0023]

[0024] B = f H -f L

[0025] Where, f L and f HIt is the low-frequency and high-frequency boundary when the signal power accumulates to 90%.

[0026] The bandwidth estimation results are evaluated as follows: If the relative difference between the estimated bandwidth at the transmitter and the estimated bandwidth at the receiver (based on the estimated bandwidth at the transmitter) exceeds 20%, the simulated signals for that set of transmitter and receiver signals are not saved. Otherwise, the data quality is considered good, the check is passed, and the simulated signals for that set of transmitter and receiver signals are saved.

[0027] Step 3: Pass the qualified simulated signals from each group of transmitters and receivers through the IQ channels to obtain their respective two-dimensional real number arrays. Combine these arrays with their estimated bandwidths and write them into an h5 file to form a simulated radio frequency signal dataset.

[0028] The real and imaginary parts of the one-dimensional complex array of the transmitter signal data in the current group of simulation signals are split into I-path and Q-path respectively and stored to generate a two-dimensional real array.

[0029] The same operation is performed on the received signal data. The real and imaginary parts of the one-dimensional complex array are split into I-path and Q-path respectively for storage, generating a two-dimensional real array.

[0030] Step 4: Extract the spectral features of each simulated signal from the receiver in the simulated RF signal dataset to obtain its respective frequency domain amplitude and corresponding frequency;

[0031] The specific extraction process is as follows:

[0032] 1) Combine the two-dimensional real number array of the current received simulated signal s into a complex signal x′(n);

[0033] The complex signal x′(n) is represented as follows:

[0034] x′(n)=I(n)+jQ(n)

[0035] In the formula, I(n) is the first dimension of the two-dimensional real number array, corresponding to the real part of the signal, and Q(n) is the second dimension of the two-dimensional real number array, corresponding to the imaginary part of the signal.

[0036] 2) Perform a fast Fourier transform on the complex signal x′(n) to convert it from the time domain to the frequency domain, and obtain the complex representation of the frequency X(k);

[0037] Its formula is expressed as:

[0038]

[0039] In the formula, x′(n) is a complex sequence of the time-domain signal, X(k) is a complex sequence in the frequency domain, and M is the number of points of the FFT.

[0040] 3) Calculate the amplitude |X(k)| in the complex representation of the frequency X(k);

[0041] The calculation formula is:

[0042]

[0043] In the formula, Re(X(k)) and Im(X(k)) are the real and imaginary parts of the complex representation of frequency X(k), respectively.

[0044] 4) Convert the amplitude |X(k)| to a logarithmic scale to obtain the frequency domain amplitude A of the simulated signal s. dB ;

[0045] Its formula is expressed as:

[0046] A dB =20·log 10 |X(k)|

[0047] Step 5: Use the frequency domain amplitude and frequency of each signal as the training set, input them into the Roinformer neural network for regression task learning, output the estimated signal bandwidth of each signal, and compare it with the estimated bandwidth written into the h5 file. When the difference is within the threshold range, it means that the Roinformer neural network has completed learning.

[0048] Specifically:

[0049] First, the Roinformer neural network consists of multiple Informer modules connected through convolution, pooling, and downsampling operations. Each Informer module contains a ProbSparse self-attention mechanism and a distillation operation.

[0050] The process of the ProbSparse self-attention mechanism can be represented as follows:

[0051]

[0052] In the formula, This indicates that the dimension of the query matrix Q in the real number field is L. Q ×d; The dimension of the key matrix K in the real number field is L. K ×d; The dimension of the value matrix V in the real number field is L. V ×d; d represents the characteristic dimension (number of columns) of the matrix; d k It is the characteristic dimension (number of columns) of the key matrix K.

[0053] Step 6: The transmitter transmits signals in real time, which are then input into the learned Roinformer neural network, directly outputting the corresponding bandwidth estimate.

[0054] The advantages of this invention are:

[0055] (1) This invention simulates and generates communication signals with different signal bandwidths through parameterization methods, ensuring that the dataset covers a wide range of practical application scenarios and ensuring the richness of signal samples. It generates baseband simulation signals at the transmitting end and uniformly resamples and zeros is added to the signals at the receiving end. Combined with the efficient storage method of h5 file format, it ensures data consistency and thus improves the generalization ability of deep models.

[0056] (2) This invention uses the power spectrum amplitude information of the signal frequency domain to extract features, directly captures the energy distribution of the signal, effectively compresses the data, reduces redundant information in the time domain data, and uses the power spectrum amplitude and frequency of the frequency domain as the input of the model to perform deep learning bandwidth estimation by fusing spectrum prior knowledge, so that the model can learn bandwidth characteristics more efficiently and improve learning efficiency and accuracy.

[0057] (3) This invention employs a Roinformer neural network, which effectively extracts global features from long sequences through a multi-head probabilistic sparse self-attention mechanism and distillation operation, and significantly reduces computational complexity. High parallelism accelerates model training, enhances the ability to process long sequence data, and has significant advantages in regression tasks that estimate continuous numerical attributes such as signal bandwidth. Attached Figure Description

[0058] Figure 1 This is a diagram illustrating the overall framework for generating simulated radio frequency signal datasets and constructing neural networks for bandwidth estimation in this invention.

[0059] Figure 2 This is the frequency domain diagram of the transmitter simulation signal generated in this invention;

[0060] Figure 3 This is the frequency domain diagram of the simulated receiver signal generated in this invention;

[0061] Figure 4 This is the frequency domain diagram of the receiver simulation signal generated in this invention, taking the length of the first 4096 points;

[0062] Figure 5 This is a flowchart of the method for constructing a neural network incorporating prior spectrum knowledge for bandwidth estimation according to the present invention;

[0063] Figure 6 This is a graph showing the loss function and error rate during the training process of the bandwidth estimation model constructed in this invention;

[0064] Figure 7 This is a scatter plot of the estimated and true values ​​of the bandwidth estimation model constructed in this invention; Detailed Implementation

[0065] The invention will now be described in detail with reference to the implementation steps and accompanying drawings.

[0066] Given the susceptibility of bandwidth estimation to inaccuracies under complex environments, this invention employs a deep learning-based bandwidth estimation method incorporating prior spectrum knowledge, such as... Figure 1 As shown, the specific steps are as follows:

[0067] Step 1: Given the signal parameters of the transmitting end, the simulated signal of the transmitting end is obtained through digital modulation; the receiving end samples the transmitting end by setting the sampling rate to obtain the simulated signal of the receiving end, and the simulated signals of the transmitting end and the receiving end are combined into one group.

[0068] The parameters of the transmitted signal include bandwidth, roll-off factor, and modulation method.

[0069] Seven common digital modulation schemes were selected, including BASK, QASK, BFSK, QFSK, BPSK, QPSK, and 16QAM.

[0070] Step 2: For each set of simulated signals from the transmitter and receiver, use MATLAB to estimate the bandwidth and save the simulated signals of each set with acceptable bandwidth.

[0071] The bandwidth of a set of simulated signals from both the transmitting and receiving ends is estimated, specifically as follows:

[0072] First, for the simulated signal x[n] at the transmitting or receiving end, its length is N and its sampling frequency is f. s The power spectral density estimate is expressed as:

[0073]

[0074] In the formula, X(f) is the discrete Fourier transform of the simulated signal x[n]:

[0075]

[0076] Where, f n It is the frequency value of the nth discrete frequency component in the frequency domain.

[0077] Then, using the power spectral density estimates within the start and end frequency ranges of the simulated signal spectrum, the total power P of the signal is calculated. total :

[0078]

[0079] In the formula, f1 and f2 are the start and end frequencies of the signal spectrum, respectively.

[0080] Finally, when the total signal power accumulates to 90%, the low-frequency and high-frequency boundary ranges of the simulated signal spectrum are calculated [f]. L f H The bandwidth B within ];

[0081] Bandwidth B refers to the frequency range [f L f H Between ], the following conditions must be met:

[0082]

[0083] B = f H -f L

[0084] Where, f L and f H It is the low-frequency and high-frequency boundary when the signal power accumulates to 90%.

[0085] The following judgment is made based on the obtained estimation results: If the relative difference between the estimated bandwidth of the transmitter and the estimated bandwidth of the receiver (based on the estimated bandwidth of the transmitter) exceeds 20%, the simulated signals of that group of transmitters and receivers will not be saved. If the check passes, the data quality is considered good, and the simulated signals of that group of transmitters and receivers will be saved.

[0086] Step 3: Pass the qualified simulated signals from each group of transmitters and receivers through the IQ channels to obtain their respective two-dimensional real number arrays. Combine these arrays with their estimated bandwidths and write them into an h5 file to form a simulated radio frequency signal dataset.

[0087] The signal data from the transmitting and receiving ends are stored in two separate channels, I and Q. The real and imaginary parts of a one-dimensional complex array are taken respectively to generate a two-dimensional real array. Each digital modulation method generates an h5 file.

[0088] Specifically:

[0089] The real and imaginary parts of the one-dimensional complex array of the transmitter signal data in the current group of simulation signals are split into I-path and Q-path respectively and stored to generate a two-dimensional real array.

[0090] The same operation is performed on the received signal data. The real and imaginary parts of the one-dimensional complex array are split into I-path and Q-path respectively for storage, generating a two-dimensional real array.

[0091] Step 4: Extract the spectral features of each simulated signal from the receiver in the simulated RF signal dataset to obtain its respective frequency domain amplitude and corresponding frequency;

[0092] Specifically:

[0093] The specific extraction process is as follows:

[0094] 1) Combine the two-dimensional real number array of the current received simulated signal s into a complex signal x′(n);

[0095] The complex signal x′(n) is represented as follows:

[0096] x′(n)=I(n)+jQ(n)

[0097] In the formula, I(n) is the first dimension of the two-dimensional real number array, corresponding to the real part of the signal, and Q(n) is the second dimension of the two-dimensional real number array, corresponding to the imaginary part of the signal.

[0098] 2) Perform a Fast Fourier Transform (FFT) on the complex signal x′(n) to transform it from the time domain to the frequency domain, and obtain the complex representation of the frequency X(k);

[0099] X(k) contains amplitude and phase information, and its formula is expressed as:

[0100]

[0101] In the formula, x′(n) is a complex sequence of the time-domain signal, X(k) is a complex sequence in the frequency domain, and M is the number of points of the FFT.

[0102] 3) Calculate the amplitude |X(k)| in the complex representation of the frequency X(k);

[0103] The calculation formula is:

[0104]

[0105] In the formula, Re(X(k)) and Im(X(k)) are the real and imaginary parts of the complex representation of frequency X(k), respectively.

[0106] 4) Convert the amplitude |X(k)| to a logarithmic scale, i.e., use 20log for the bandwidth amplitude. 10 Using |X(k)| as an example, we obtain the frequency domain amplitude A of the simulated signal s. dB ;

[0107] Its formula is expressed as:

[0108] A dB =20·log 10 |X(k)|

[0109] Step 5: Use the frequency domain amplitude and frequency of each signal as the training set, input them into the Roinformer neural network for regression task learning, output the estimated signal bandwidth of each signal, and compare it with the estimated bandwidth written into the h5 file. When the difference is within the threshold range, it means that the Roinformer neural network has completed learning.

[0110] Specifically:

[0111] First, the Roinformer network structure adopts an encoder architecture. The encoder is responsible for mapping the input sequence, i.e., the signal spectral features output by the spectral feature extraction module, to a continuous representation space. It consists of multiple Informer modules, each containing a ProbSparse self-attention mechanism and a distillation operation, responsible for extracting features from the historical time series. Different attention modules perform feature downsampling after convolution and pooling operations, and extract important features through distillation. The process of the ProbSparse self-attention mechanism is represented as follows:

[0112]

[0113] In the formula, This indicates that the dimension of the query matrix Q in the real number field is L. Q ×d; The dimension of the key matrix K in the real number field is L. K ×d; The dimension of the value matrix V in the real number field is L. V ×d; d represents the characteristic dimension (number of columns) of the matrix; d k It is the characteristic dimension (number of columns) of the key matrix K. T represents the transpose of the matrix.

[0114] The model performance is comprehensively evaluated using two evaluation metrics: Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE). The evaluation metrics are defined as follows:

[0115]

[0116] In the formula, Represents the predicted value, y i represents the true value, and n represents the number of predicted samples.

[0117] Step 6: The transmitter transmits signals in real time, which are then input into the learned Roinformer neural network, directly outputting the corresponding bandwidth estimate.

[0118] Finally, through experimental simulation, the bandwidth estimation effect of the Roinformer network model was obtained, and a comprehensive evaluation of the Roinformer network was conducted.

[0119] Example:

[0120] The overall system framework of this invention for generating simulation signal datasets and estimating RF signal bandwidth parameters is as follows: Figure 1As shown, the method comprises two parts: generating a simulated radio frequency signal dataset and constructing a neural network for radio frequency signal bandwidth estimation. The specific components and steps are as follows:

[0121] Part I: Generation of Simulated RF Signal Datasets

[0122] Step 1: Given the transmitter signal parameters, generate the transmitter simulation signal;

[0123] Specifically:

[0124] First, given the bandwidth, roll-off factor, and modulation scheme of the transmitted signal, the sampling rate can be calculated using the formula:

[0125]

[0126] Where, f s Here, B is the sampling rate, SPS is the signal bandwidth, and α is the roll-off factor. The bandwidth range is (1×10⁻⁶). 5 3×10 7 )Hz, with a roll-off factor of 0.03;

[0127] The modulation scheme uses seven common digital modulation schemes, including BASK, QASK, BFSK, QFSK, BPSK, QPSK, and 16QAM, to generate the baseband signal.

[0128] Use MATLAB functions to generate the transmitter signal. The data format is a one-dimensional complex array with a length of 1024. Use MATLAB to estimate the bandwidth containing 90% of the signal power and use it as the label value.

[0129] The bandwidth of a signal is defined as the frequency range that contains a certain percentage of the total power of the signal.

[0130] The calculation steps are as follows:

[0131] 1) Calculate the power spectral density (PSD) of the signal, i.e., the distribution of power in the frequency domain, P. xx (f). Calculate the power spectral density based on the Discrete Fourier Transform (DFT).

[0132] Suppose the signal is x[n], its length is N, and the sampling frequency is f. s Then, the estimate of its power spectral density can be expressed as:

[0133]

[0134] In the formula, X(f) is the discrete Fourier transform of the signal x[n]:

[0135]

[0136] 2) Calculate the cumulative power within the frequency range and find the frequency range where the signal power reaches the specified percentage.

[0137] Accumulated power can be expressed in integral or discrete summation form; the total power P of the signal total for:

[0138]

[0139] In the formula, f1 and f2 are the start and end frequencies of the signal spectrum, respectively.

[0140] 3) Determine the frequency range that contains 90% of the total power; the difference between these frequency ranges is the bandwidth of the signal.

[0141] Bandwidth B refers to the frequency range [f L f H Between ], the following conditions must be met:

[0142]

[0143] B = f H -f L

[0144] Where, f L and f H It is the low-frequency and high-frequency boundary when the signal power accumulates to 90%.

[0145] Digital modulation shifts the spectrum of a digital baseband signal to a higher frequency, creating a frequency band signal suitable for transmission in a communication channel. The general expression for the modulated signal received by a communication system is:

[0146]

[0147] In the formula, A(t) is the instantaneous amplitude, and f c f(t) is the carrier frequency, and f(t) is the modulation frequency. θ is the modulation phase, θ is the initial phase, and e(t) is the noise.

[0148] Amplitude Shift Keying (APS) is a modulation method in which the amplitude of a sinusoidal carrier wave varies with the digital baseband signal. The time-domain expression for M-ary Amplitude Shift Keying (MASK) is:

[0149]

[0150] Where a i Let be an M-ary amplitude sequence, taking values ​​{(2m-M-1), m=1,2,...,M}. In the 2ASK signal, a i ={1, -1}; in the QASK signal, a i={-3,-1,1,3}.

[0151] Frequency shift keying (MFSK) is a modulation method that changes the frequency of a sinusoidal carrier wave according to the digital baseband signal. In an M-ary MFSK system, the carrier wave has M possible frequency values. The time-domain expression for MFSK is:

[0152]

[0153] In the formula, T s f is the symbol width. c f is the carrier frequency. i ∈{f1,f2,f3,...f M}, BFSK modulated signal M=2, f i There are two possible values; for the QFSK signal, M=4, f i There are four possible values.

[0154] Phase-shift keying (PSK) is a modulation method that modulates the phase of a sinusoidal carrier wave according to changes in the digital baseband signal. In an M-ary PSK system, the carrier phase has M possible values. In an MPSK signal, each symbol consists of log₂M digital bits. The time-domain expression of an MPSK modulated signal is:

[0155]

[0156] In the formula, For the carrier at t=iT s The phase at time, and Where θ is the initial phase. The BPSK modulated signal i = {0,1}, and the carrier phase... QPSK modulated signal, i = {0, 1, 2, 3}, carrier phase

[0157] The simulated signal spectrum of the transmitter is shown below. Figure 2 As shown.

[0158] Step 2: Given the sampling rate of the receiver signal, generate the receiver simulation signal;

[0159] Specifically:

[0160] First, the receiver's sampling rate is 100MHz, satisfying the Nyquist theorem. The transmitter signal is then resampled using MATLAB. The original signal x[n] is changed from the original sampling rate f. s Switch to the new sampling rate f s ′.

[0161]

[0162] In the formula, p and q are the scaling factors for upsampling and downsampling, respectively, and the sampling rate is changed to a fraction of the original sampling rate. The calculation steps are as follows:

[0163] 1) Upsample the original signal x[n] to interpolate it to a higher sampling rate. The interpolation coefficient is p, meaning p-1 samples are inserted between every two adjacent samples. The original signal x[n] is then interpolated to x... up [n]. The interpolation process is achieved by inserting zeros between the original signal samples, and combined with an interpolation filter for smoothing, i.e.:

[0164]

[0165] 2) Because the signal may contain high-frequency components (frequencies higher than half the new sampling rate) before downsampling, aliasing can occur. A low-pass filter is needed to suppress these high-frequency components. For the upsampled signal x... up [n] performs low-pass filtering to eliminate high-frequency components. Filter h[n] is a filter with a cutoff frequency of... An ideal low-pass filter. The filtered signal x filt [n] is represented as:

[0166]

[0167] 3) The filtered signal is downsampled, and one sample is retained every q samples, thereby reducing the sampling rate.

[0168] y[n]=x filt [nq]

[0169] The simulated signal spectrum at the receiver is shown below. Figure 3 As shown in the figure. Because different transmitters have the same signal length but different sampling rates, the received signal lengths differ after resampling at the same receiver sampling rate. The first 4096 points are uniformly selected, with zeros padded if the length is less than 4096. The received signal data format is a one-dimensional complex array with a length of 4096. The frequency domain diagram of the received simulated signal with the first 4096 points is shown in the figure. Figure 4 As shown.

[0170] Step 3: Estimate the bandwidth of the generated signal to determine whether the simulation signal is qualified;

[0171] Specifically:

[0172] First, MATLAB is used to estimate the bandwidth of both the simulated transmitter and receiver signals. The estimation results are then used to make a judgment. If the estimated values ​​differ significantly, there is a function estimation error in the generation and calculation process of that signal set, and the data set is not saved. If the check passes, the data quality is considered good, and the data set is saved.

[0173] The code is as follows:

[0174]

[0175] Step 4: Write the qualified signal data into an h5 file to generate a simulation signal dataset;

[0176] Specifically:

[0177] First, write the data into an h5 file. In modern communication systems, IQ modulation is a common technique for transmitting modulated signals in both I and Q channels. IQ modulation transmits two signals simultaneously on one frequency band, thereby improving spectral efficiency. The modulated signal s(t) is shown below:

[0178]

[0179] In the formula, I(t) and Q(t) are the in-phase and quadrature components of the signal, respectively, and f c Let θ be the carrier frequency, θ0 be the initial phase, and t be the signal duration.

[0180] The received signal data is stored in two paths, I and Q. The real and imaginary parts of a one-dimensional complex array are taken respectively to generate a two-dimensional real array of length 4096, in the format (4096, 2). Each digital modulation method generates an h5 file, with each file containing 50,000 data entries.

[0181] Part II: Constructing a Spectral Feature Extraction Neural Network for Bandwidth Estimation

[0182] Step 1: Construct a spectral feature extraction module to extract spectral features from the original time-domain signal;

[0183] Specifically:

[0184] First, while it's possible to learn by directly inputting time-domain IQ signals, the time-domain information may not directly reflect the signal's spectral characteristics. Bandwidth is closely related to the distribution of spectral energy, and time-domain IQ signals are difficult to directly capture the signal's frequency characteristics. Furthermore, time-domain signals contain a lot of redundant information; directly inputting them may increase model complexity and reduce learning efficiency.

[0185] Frequency domain amplitude information is an effective feature for bandwidth estimation, directly reflecting the energy distribution of a signal at various frequencies, which is crucial for bandwidth identification. The Fast Fourier Transform (FFT) converts a signal to the frequency domain, revealing its energy distribution across different frequencies. For bandwidth estimation tasks, frequency features are more valuable than time-domain features. Calculating frequency domain amplitude can be viewed as a further compression and abstraction of signal features. Compared to directly inputting complex or IQ signals in the time domain, amplitude information reduces data redundancy to some extent and focuses on the signal's energy characteristics, which helps neural networks learn signal features more efficiently.

[0186] The flowchart of the method for constructing a neural network for bandwidth estimation is as follows: Figure 5 As shown, the specific steps are as follows:

[0187] 1) Combine the I and Q channels of the training set input signal into a complex signal. The complex signal x(n) is represented as follows:

[0188] x(n) = I(n) + jQ(n)

[0189] 2) Performing a Fast Fourier Transform (FFT) on a complex signal in the time domain can convert the signal from the time domain to the frequency domain.

[0190] The FFT is a highly efficient Discrete Fourier Transform (DFT) that utilizes the symmetry and periodicity of the twitch factor in the DFT algorithm. By continuously decomposing a long sequence into shorter sequences, it effectively reduces the number of multiplications and additions, as well as the number of twitch factors, thus reducing the computational complexity of the algorithm. Its formula is expressed as:

[0191]

[0192] In the formula, x(n) is a complex sequence of the time-domain signal, X(k) is a complex sequence in the frequency domain, and M is the number of points in the FFT.

[0193] The X(k) obtained after FFT is a complex representation of frequency, containing amplitude and phase information. The amplitude is the distribution of signal energy, while the phase is related to the coherence characteristics of the signal.

[0194] 3) Calculate the amplitude of the FFT result. For bandwidth estimation tasks, the frequency distribution and energy characteristics of the signal are very important. The amplitude information in the frequency domain reflects the energy distribution of the signal at different frequencies and can reveal the signal's bandwidth characteristics.

[0195] The formula for calculating the amplitude |X(k)| is:

[0196]

[0197] In the formula, Re(X(k)) and Im(X(k)) are the real and imaginary parts of X(k), respectively.

[0198] Convert the signal amplitude to a logarithmic scale, i.e., the bandwidth is expressed in 20log. 10 The signal strength is represented by |X(k)|, which more intuitively indicates the changes in signal strength.

[0199] This approach is commonly used in signal processing, especially when analyzing the magnitude of frequency domain amplitudes. In practical applications, signal amplitudes span a wide dynamic range, with differences reaching several orders of magnitude. When using a linear scale to represent amplitude, these variations are very difficult to simultaneously display and analyze. By taking the logarithm of the amplitude, the dynamic range of the signal can be compressed, allowing for a more intuitive display and processing of significantly different amplitudes, thus extracting the energy intensity of each frequency in the frequency domain.

[0200] 4) Normalize the bandwidth values ​​of the input signals in the training set and divide them by the maximum bandwidth value in the training set.

[0201] To prevent excessively large data ranges from causing model training to become extremely slow or even fail to converge, normalize and scale the data to a smaller range, which then serves as the label for the input data. Perform the same operation on the signals of the validation and test sets.

[0202] Step 2: Construct a Roinformer network to perform regression learning on the input spectral features, namely frequency domain amplitude and frequency.

[0203] Specifically:

[0204] First, Roinformer is a deep learning network architecture based on a multi-head probabilistic sparse self-attention mechanism. This network architecture adopts an encoder architecture, which is responsible for mapping the input sequence to a continuous representation space. It consists of multiple Informer modules, each of which contains a self-attention mechanism and a distillation operation, responsible for extracting features from historical time series.

[0205] Unlike traditional Q, K, V matrix calculation methods, Roinformer calculates the correlation between each time point in the sequence and other time points within the same time interval by comparing each time point with a uniform distribution. The more significant the difference, the higher the correlation of that time point within the interval. Different attention modules perform feature downsampling through convolution and pooling operations, and extract important features through distillation.

[0206] Roinformer uses the ProbSparse self-attention mechanism. Traditional self-attention is defined as a probabilistic kernel smoothing method:

[0207]

[0208] The difference between the distribution of the query vector and a uniform distribution can be measured by the KL divergence:

[0209]

[0210] By removing the constant term, the sparsity metric of the i-th query vector can be defined as:

[0211]

[0212] The query matrix Q, key matrix K, and value matrix V are three identical matrices obtained by linearly transforming the same input sequence. Attention weights are obtained by calculating the correlation between Q and K. These weights are then weighted and summed with V to obtain the result of the attention mechanism, which represents the degree of attention given to different parts of the input sequence. The process of the ProbSparse self-attention mechanism is represented as follows:

[0213]

[0214] In the formula, This indicates that the dimension of the query matrix Q in the real number field is L. Q ×d; The dimension of the key matrix K in the real number field is L. K ×d; The dimension of the value matrix V in the real number field is L. V ×d; d represents the characteristic dimension (number of columns) of the matrix; d k It is the characteristic dimension (number of columns) of the key matrix K. T represents the transpose of the matrix.

[0215] Multi-head attention mechanisms allow networks to simultaneously focus on multiple different parts of the input sequence, effectively capturing global dependencies in long sequences. Due to the characteristics of self-attention mechanisms, they possess high parallelism, with the output at each position being computed independently, giving them a significant advantage when processing long sequences.

[0216] Rotary Position Embedding (ROPE) is a positional encoding method in natural language processing that introduces relative positional information into self-attention mechanisms while preserving the ability to model sequence order. Compared to traditional absolute positional encoding methods, ROPE uses a rotational approach to directly embed positional information into the self-attention computation. This method is particularly suitable for models with multi-head attention mechanisms, such as Informer networks. ROPE achieves positional information modeling by embedding the positional encoding as a rotation matrix into the vector space of the self-attention computation.

[0217] Following feature extraction, a regression task is performed to establish a relationship model between features and continuous numerical targets, which is used to predict numerical targets for unknown samples. Regression is a supervised learning task; unlike classification tasks, the goal of regression is to predict continuous values ​​rather than discrete categories. Regression tasks are commonly used to estimate continuous numerical attributes of radio frequency signals, such as signal bandwidth, center frequency, and direction of arrival.

[0218] Unlike classification tasks, regression tasks typically output a scalar or one-dimensional vector, with values ​​that are continuous within a certain range, without requiring probability distribution mapping through the Softmax function.

[0219] Step 3: Conduct experimental simulations to obtain the bandwidth estimation results under different network models, and then comprehensively evaluate each model.

[0220] Specifically:

[0221] 1) Experimental simulation platform

[0222] The experimental simulation platform is a Windows 10 64-bit operating system, the programming environment is Python 3.9, the integrated development environment is PyCharm 2020.3.5, and the model building is mainly implemented using deep learning frameworks such as PyTorch.

[0223] 2) Model evaluation indicators

[0224] To comprehensively evaluate model performance, we introduce two evaluation metrics: mean absolute error loss function (MAE) and mean absolute percentage error (MAPE), i.e., error rate. The smaller the MAE and error rate, the better the model's predictive performance.

[0225] MAE and error rate are defined as follows.

[0226]

[0227] In the formula, Represents the predicted value, y i This represents the true value, and N represents the number of predicted samples.

[0228] 3) Simulation Experiment Design

[0229] Experimental simulations demonstrate the model's effectiveness. The training set contains 50,000 data points, the validation set contains 1,000 data points, and the test set contains 1,000 data points. The batch size is set to 64. The number of training epochs is set to 200. The learning rate is 1 × 10⁻⁶. -3 The loss function is the mean absolute error loss (MAE). The model convergence criterion is that training stops and the model is saved when the MAE metric on the validation set no longer decreases for ten consecutive times.

[0230] 4) Experimental Results

[0231] The loss function curves during training and validation are as follows: Figure 6 As shown in (a), the error rates on the training and validation sets are as follows: Figure 6As shown in (b). Experimental results using Roinformer and Transformer networks are shown in the table below. The Roinformer prediction network achieved an optimal training batch validation set error rate of 7.09%. Experimental results for different networks are shown in Table 1:

[0232] Table 1

[0233]

[0234] Scatter plot of estimated and true values ​​in the test set as follows Figure 7 As shown, scatter plots can visually demonstrate the relationship between true and estimated values, helping to identify the model's prediction accuracy, potential systematic biases, nonlinear relationships, and outliers. Ideally, the relationship between the estimated and true values ​​should be close to linear, meaning the data points should be close to the diagonal of y = x. In the image, the data points (blue scatter dots) are tightly clustered around the red dashed line, showing a good linear trend. This indicates that the error between the model's estimates and the true values ​​is very small, and the model's estimation performance is good. The degree of agreement between the estimated and true values ​​remains consistent, even for larger true values ​​(top right) and smaller true values ​​(bottom left), indicating that the model's estimation ability is balanced across the entire data range.

Claims

1. A deep learning bandwidth estimation method incorporating prior knowledge of the spectrum, characterized in that, This includes parameterizing and generating high-quality RF signal datasets covering various modulation schemes and bandwidth ranges, and achieving efficient and accurate bandwidth estimation through spectral feature extraction and the Roinformer network; the specific steps are as follows: Step 1: Generate diverse transmitter and receiver signal data using a parameterization method; Given the transmitter signal parameters, the transmitter's simulated signal is obtained through digital modulation; the receiver samples the transmitter by setting a sampling rate to obtain the receiver's simulated signal, and the transmitter and receiver's simulated signals are grouped together. Step 2: For each set of simulated signals from the transmitting and receiving ends, estimate the bandwidth and save the simulated signals of each set with acceptable bandwidth. The bandwidth of a set of simulated signals from both the transmitting and receiving ends is estimated, specifically as follows: First, for the simulated signal x[n] at the transmitting or receiving end, its length is N and its sampling frequency is f. s The power spectral density estimate is expressed as: In the formula, X(f) is the discrete Fourier transform of the simulated signal x[n]; Then, using the power spectral density estimates within the start and end frequency ranges of the simulated signal spectrum, the total power P of the signal is calculated. total : In the formula, f1 and f2 are the start and end frequencies of the signal spectrum, respectively; Finally, when the total signal power accumulates to 90%, the low-frequency and high-frequency boundary ranges of the simulated signal spectrum are calculated [f]. L ,f H The bandwidth B within ]; The following conditions must be met: B=f H -f L In the formula, f L and f H It is the low-frequency and high-frequency boundary when the signal power accumulates to 90%; Judge the bandwidth estimation results: Based on the estimated bandwidth of the transmitter, when the relative difference between the estimated bandwidth of the transmitter and the estimated bandwidth of the receiver exceeds 20%, the simulated signals of the transmitter and receiver are not saved. Otherwise, the data quality is considered good, the check is passed, and the simulated signals of the transmitter and receiver are saved. Step 3: Pass the qualified simulated signals from each group of transmitters and receivers through the IQ channels to obtain their respective two-dimensional real number arrays. Combine these arrays with their estimated bandwidths and write them into an h5 file to form a simulated radio frequency signal dataset. Step 4: Using Fast Fourier Transform, extract the spectral features of each simulated signal from the receiver in the simulated RF signal dataset to obtain their respective frequency domain amplitude and corresponding frequency. The specific extraction process is as follows: 1) Combine the two-dimensional real number array of the current received simulated signal s into a complex signal x′(n); The complex signal x′(n) is represented as follows: x′(n)=I(n)+jQ(n) In the formula, I(n) is the first dimension of the two-dimensional real number array, corresponding to the real part of the signal, and Q(n) is the second dimension of the two-dimensional real number array, corresponding to the imaginary part of the signal; 2) Perform a fast Fourier transform on the complex signal x′(n) to convert it from the time domain to the frequency domain, and obtain the complex representation of the frequency X(k); Its formula is expressed as: In the formula, M is the number of points in the FFT; 3) Calculate the amplitude |X(k)| in the complex representation of the frequency X(k); The calculation formula is: In the formula, Re(X(k)) and Im(X(k)) are the real and imaginary parts of the complex representation of frequency X(k), respectively; 4) Convert the amplitude |X(k)| to a logarithmic scale to obtain the frequency domain amplitude A of the simulated signal s. dB ; Its formula is expressed as: A dB =20·log 10 |X(k)| Step 5: Use the frequency domain amplitude and frequency of each signal as the training set, input them into the Roinformer neural network for regression task learning, output the estimated signal bandwidth of each signal, and compare it with the estimated bandwidth written into the h5 file. When the difference is within the threshold range, it means that the Roinformer neural network has completed learning. Specifically: First, the Roinformer neural network consists of multiple Informer modules connected through convolution, pooling, and downsampling operations. Each Informer module contains a ProbSparse self-attention mechanism and a distillation operation. The process of the ProbSparse self-attention mechanism can be represented as follows: Where, This indicates that the dimension of the query matrix Q in the real field is L. Q ×d; The dimension of the key matrix K in the real number field is L. K ×d; The dimension of the value matrix V in the real number field is L. V ×d; d represents the characteristic dimension of the matrix; d k It is the characteristic dimension of the key matrix K; Step 6: The transmitter transmits signals in real time, which are then input into the learned Roinformer neural network, directly outputting the corresponding bandwidth estimate.

2. The deep learning bandwidth estimation method incorporating prior spectrum knowledge as described in claim 1, characterized in that, In step one, the parameters of the transmitting signal include bandwidth, roll-off factor, and modulation method; Seven common digital modulation schemes were selected, including BASK, QASK, BFSK, QFSK, BPSK, QPSK, and 16QAM.

3. The deep learning bandwidth estimation method incorporating prior spectrum knowledge as described in claim 1, characterized in that, In step two, the formula for calculating X(f) is as follows: In the formula, f n It is the frequency value of the nth discrete frequency component in the frequency domain.

4. The deep learning bandwidth estimation method incorporating prior spectrum knowledge as described in claim 1, characterized in that, The third step is specifically as follows: the real part and imaginary part of the one-dimensional complex array of the transmitter signal data in the current group of simulation signals are split into I-path and Q-path respectively and stored to generate a two-dimensional real array; The same operation is performed on the received signal data. The real and imaginary parts of the one-dimensional complex array are split into I-path and Q-path respectively for storage, generating a two-dimensional real array.

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