A communication signal carrier frequency estimation method based on cyclic modulation spectrum

Abstract

The application discloses a communication signal carrier frequency estimation method based on cyclic modulation spectrum, comprising the following steps: discretizing a communication signal received by a receiving end to obtain a discrete real signal; windowing the discrete real signal and calculating the modulo-2 norm of the window function; performing short-time Fourier transform on the windowed discrete real signal and performing modulo value square calculation on the short-time Fourier transform signal; performing discrete Fourier transform on the signal after the modulo value square calculation to obtain the cyclic modulation spectrum of the discrete real signal; calculating the cyclic frequency corresponding to the maximum amplitude of the cyclic modulation spectrum on the positive frequency axis; bringing the cyclic frequency corresponding to the maximum amplitude into the cyclic modulation spectrum to obtain a function about the discrete frequency; calculating the discrete frequency corresponding to the maximum modulo value of the function about the discrete frequency, and taking the discrete frequency as the carrier frequency of the communication signal. The application has better generalization and strong application value in various practical scenarios.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a method for estimating the carrier frequency of a communication signal based on a cyclic modulation spectrum, which is suitable for estimating the carrier frequency of a communication signal in a non-cooperative communication scenario. Background Art

[0002] Carrier frequency estimation is crucial in wireless communication systems, especially in non-cooperative communication environments. Accurate carrier frequency estimation can effectively compensate for frequency offset, ensure signal demodulation accuracy, reduce bit error rates, and improve the system's frequency synchronization capabilities.

[0003] Currently available communication signal carrier frequency estimation methods are based on frequency domain analysis methods, mainly including frequency domain estimation methods, including frequency centering method and phase difference method. These methods make rough or precise estimates by analyzing the spectral characteristics of the signal. For example, the frequency centering method is suitable for processing the main frequency offset problem of the signal, which is common in high-noise environments. Time domain estimation methods include zero-crossing detection method, instantaneous frequency mean method, etc. These methods estimate the carrier frequency by the change of the signal in the time domain and are generally more robust to low signal-to-noise ratio environments. The instantaneous frequency mean method is particularly suitable for multipath propagation. Spectral correlation estimation methods mainly include cyclic spectrum method and autocorrelation method. These methods use the periodic characteristics of the signal to estimate the carrier frequency. For example, the cyclic spectrum method can effectively process the periodic characteristics of the signal and can work under low signal-to-noise ratio conditions.

[0004] In non-cooperative environments, the receiver cannot obtain the transmitter's frequency information in advance. Accurately estimating the carrier frequency is essential for ensuring correct signal demodulation and avoiding interference. This is particularly important under complex conditions such as high-speed motion and multipath propagation. Traditional cyclic spectrum-based carrier frequency estimation uses a different method for each modulated signal, reducing its generalizability. Summary of the Invention

[0005] In view of the fact that traditional cyclic spectra have weak generalization for signals of each modulation type, the purpose of the present invention is to provide a communication signal carrier frequency estimation method based on cyclic modulation spectrum, which extracts the modulation features of the signal by frequency band, calculates the spectrum correlation function, and finds the carrier frequency of the signal through spectrum peak search.

[0006] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0007] A communication signal carrier frequency estimation method based on cyclic modulation spectrum, comprising:

[0008] Discretize the communication signal received by the receiving end to obtain a discrete real signal; add a window to the discrete real signal and calculate the modulo-2 norm of the window function;

[0009] Perform short-time Fourier transform on the discrete real signal after windowing, and perform modulus square calculation on the signal after short-time Fourier transform;

[0010] The signal after the square of the modulus value is used to perform discrete Fourier transform to obtain the cyclic modulation spectrum of the discrete real signal;

[0011] Calculate the cyclic frequency corresponding to the maximum amplitude of the cyclic modulation spectrum on the positive frequency axis;

[0012] Substituting the cyclic frequency corresponding to the maximum amplitude into the cyclic modulation spectrum to obtain a function related to discrete frequencies;

[0013] The discrete frequency corresponding to the maximum modulus value of the function about the discrete frequency is calculated, and the discrete frequency is used as the carrier frequency of the communication signal.

[0014] Furthermore, the discretization of the communication signal received by the receiving end to obtain a discrete real signal; windowing the discrete real signal and calculating the modulo-2 norm of the window function includes:

[0015] Discretize x(t) to obtain a discrete real signal x[n]=s[n]+u[n], where n represents the nth sampling point, s[n] and u[n] represent the modulated signal after discretization and Gaussian white noise; let the length of x[n] be L, first add a window to the discrete real signal x[n], the window function is w[n], and the window function length is N w ; Calculate the modulo 2 norm of the window function, ||·|| 2 represents the modulo 2 norm of .

[0016] Furthermore, the window function takes the form of a Hamming window function.

[0017] Furthermore, the performing of short-time Fourier transform on the windowed discrete real signal and performing modulus square calculation on the short-time Fourier transformed signal comprises:

[0018] Perform short-time Fourier transform on the windowed discrete real signal, which is expressed as:

[0019]

[0020] In the above formula, e is a natural constant, j is an imaginary unit, and F s is the sampling frequency, the i-th discrete frequency is f i =iΔf, R represents the time step of the window function, x[kR+n] is the discrete real signal at the sampling position kR+n, X STFT (k,f i ) is the signal after short-time Fourier transform;

[0021] To X STFT (k,f i ) is used to calculate the square of the modulus value, which is expressed as follows:

[0022] X′ STFT (k,f i )=|X STFT (k,f i )| 2

[0023] Here, |·| represents calculating the modulus of a complex number.

[0024] Furthermore, the cyclic modulation spectrum is expressed as follows:

[0025]

[0026] In the above formula, α is the cycle frequency of the window function, K is the number of symbols received, that is, the total step length of the window function moving on the discrete real signal length L; K = floor(|(LN w ) / R|)+1, floor() represents the floor function, and M represents the middle value of the window function w[n].

[0027] Furthermore, M satisfies w[Mn]=w[M+n], when N w When it is an even number, M=N w / 2, when N w When it is an odd number, M=(N w +1) / 2.

[0028] Furthermore, the positive frequency axis is α≥0,f i ≥0.

[0029] Furthermore, for the function S with respect to discrete frequencies CMS (α max ,f i ) Calculate the discrete frequency f corresponding to the maximum value of its modulus i , expressed as where |·| represents the modulus of ·.

[0030] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, the communication signal carrier frequency estimation method based on cyclic modulation spectrum is implemented.

[0031] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the communication signal carrier frequency estimation method based on cyclic modulation spectrum is implemented.

[0032] Compared with the prior art, the present invention has the following technical features:

[0033] The present invention can perform effective carrier frequency estimation under a variety of modulation signal types, and is not limited to a specific modulation method. Compared with the traditional method, which requires designing and implementing different carrier frequency estimation algorithms for each modulation method, this method is not only complicated, but also easily leads to over-design of the system, increasing the diversity of algorithms and the complexity of hardware implementation in actual engineering. Compared with other methods, the present invention has better generalization and is more valuable in a variety of practical scenarios. The present invention is applicable to technical fields such as non-cooperative signal analysis, intelligent communication, spectrum monitoring, and spectrum sensing. The present invention does not involve complex algorithms, is convenient for hardware deployment, and has a wider range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of the process of the present invention;

[0035] Figure 2 is the 2PSK cyclic modulation spectrum and α=α max Cross-sectional diagram of carrier frequency estimation;

[0036] Figure 3 is the 4QAM cyclic modulation spectrum and α=α max Cross-sectional diagram of carrier frequency estimation;

[0037] Figure 4 is the 2ASK cyclic modulation spectrum and α=α max Cross-sectional diagram of carrier frequency estimation;

[0038] Figure 5 The normalized mean square error of various modulation signals varies with the signal-to-noise ratio;

[0039] Figure 6 The normalized mean square error of various modulation signals varies with symbol length. DETAILED DESCRIPTION

[0040] The present invention provides a communication signal carrier frequency estimation method based on cyclic modulation spectrum, which is applicable to most modulation type signals, especially to single-carrier digital modulation signals, and has strong engineering universality; especially for high-order modulation signals, the method of the present invention is still applicable.

[0041] During the signal transmission process, the communication signal received by the receiving end is a continuous real signal x(t) contaminated by Gaussian noise, x(t) = s(t) + u(t), where s(t) is the modulated signal. u(t) is zero-mean Gaussian white noise and is independent of s(t), where: A k is the modulation amplitude, θ k is the modulation phase, f c is the carrier frequency, is the carrier phase, g(t) is the shaped pulse function, T is the symbol period, K is the number of symbols received, and k represents the kth symbol.

[0042] See attached Figure 1 The present invention provides a communication signal carrier frequency estimation method based on cyclic modulation spectrum, comprising the following steps:

[0043] Step 1: discretize the communication signal received by the receiving end to obtain a discrete real signal; add a window to the discrete real signal, and calculate the modulo-2 norm of the window function.

[0044] Discretize x(t) to obtain a discrete real signal x[n]=s[n]+u[n], where n represents the nth sampling point, s[n] and u[n] represent the modulated signal and Gaussian white noise after discretization; assuming that the length of x[n] is L, first add a window to the discrete real signal x[n], the window function is w[n] (in the form of a Hamming window function), and the window function length is N w ; Calculate the modulo 2 norm of the window function, ||·|| 2 represents the modulo 2 norm of .

[0045] Step 2: Perform short-time Fourier transform on the windowed discrete real signal, and perform modulus square calculation on the signal after short-time Fourier transform.

[0046] Among them, the short-time Fourier transform of the windowed discrete real signal is expressed as:

[0047]

[0048] In the above formula, e is a natural constant, j is an imaginary unit, and F s is the sampling frequency, the i-th discrete frequency is f i =iΔf, R represents the time step of the window function, x[kR+n] is the discrete real signal at the sampling position kR+n, X STFT (k,f i ) is the signal after short-time Fourier transform.

[0049] To X STFT (k,f i ) is used to calculate the square of the modulus value, which is expressed as follows:

[0050] X′ STFT (k,f i )=|X STFT (k,f i )| 2

[0051] Here, |·| represents calculating the modulus of a complex number.

[0052] Step 3: Perform discrete Fourier transform on the signal after the modulus square calculation to obtain the cyclic modulation spectrum of the discrete real signal.

[0053] Wherein, the cyclic modulation spectrum S CMS (α,f i ) is represented as follows:

[0054]

[0055] In the above formula, α is the cycle frequency of the window function, K is the number of symbols received, that is, the total step length of the window function moving on the discrete real signal length L; K = floor(|(LN w ) / R|)+1, floor(·) represents the floor rounding function, M represents the middle value of the window function w[n], satisfying w[Mn]=w[M+n], that is, when N w When it is an even number, M=N w / 2, when N w When it is an odd number, M=(N w +1) / 2.

[0056] Step 4: On the positive frequency axis (α≥0,f i ≥0)) to calculate the cyclic modulation spectrum S CMS (α,f i ) corresponds to the maximum amplitude of the cycle frequency α max , which is expressed as follows:

[0057]

[0058] Among them, ~ means taking any f i .

[0059] Step 5: The cycle frequency α corresponding to the maximum amplitude max Substitute α into the cyclic modulation spectrum S CMS (α,f i ), we get the discrete frequency f i Function S CMS (α max ,f i ).

[0060] Step 6: For the function S CMS (α max ,f i ) Calculate the discrete frequency f corresponding to the maximum value of its modulus i , the discrete frequency f i As the carrier frequency of the communication signal Indicates calculation

[0061] Modulus value.

[0062] The carrier frequency obtained by this solution can be used in practical applications to estimate signal parameters in non-cooperative communication scenarios, mainly including:

[0063] Frequency offset correction: Carrier frequency estimation enables effective frequency offset correction. In communication systems, received signals often exhibit carrier frequency offset due to factors such as equipment accuracy and channel conditions. Accurate carrier frequency estimation allows frequency offset compensation and improves demodulation accuracy. Signal demodulation: Carrier frequency is a key parameter in signal demodulation. By estimating the carrier frequency, the receiver can determine the correct frequency reference point, enabling accurate downconversion of the received signal. Accurate carrier frequency estimation is crucial for signals using phase modulation (such as PSK) and amplitude modulation (such as ASK). Frequency synchronization: In multi-user communication or frequency division multiplexing (FDM) systems, carrier frequency estimation enables system-wide frequency synchronization. This effectively reduces interference (i.e., crosstalk) from adjacent channels, improving system capacity and spectrum utilization. Furthermore, for communication systems requiring spectrum sensing and monitoring, accurate carrier frequency estimation helps improve spectrum sensing efficiency, enabling spectrum sharing and dynamic spectrum allocation.

[0064] Example:

[0065] This embodiment uses a 2PSK signal as an example to verify the above carrier frequency estimation method. The simulation parameters are: symbol rate 0.4Mbps; carrier rate 1Mbps; sampling rate 4Msps; number of symbols 1024; signal-to-noise ratio range -15 to 20dB; window function length 64, step size 16. According to the above steps, an experiment is carried out to obtain the following: Figures 2 to 4 The cyclic modulation spectrum shown and the corresponding (α=α max ) cross-sectional diagram, it can be seen that its maximum value is the carrier frequency of the corresponding real signal.

[0066] Since the baseband symbols are randomly generated, different results may be obtained in each experiment. In order to test the performance of the method from a statistical perspective, the experiment was repeated 100 times under the same parameter conditions. The modulation signal types of the experiment were 2PSK, 4PSK, 8PSK, 2ASK, 4ASK, 4QAM, 16QAM, and 64QAM signals. The simulation parameters were the same as the above 2PSK single simulation parameters, see Figure 5 and Figure 6 The normalized mean square error of the carrier frequency estimation value of 1000 trials is within 10 -3 The estimated accuracy for 2ASK, 4ASK, and 2PSK is about 10 -6 It can be seen that this method has a wide range of applications and can estimate the carrier frequency of most modulation type signals.

[0067] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A communication signal carrier frequency estimation method based on cyclic modulation spectrum, characterized in that: include: Discretize the communication signal received by the receiving end to obtain a discrete real signal; Window the discrete real signal and calculate the modulo-2 norm of the window function; Perform short-time Fourier transform on the discrete real signal after windowing, and perform modulus square calculation on the signal after short-time Fourier transform; The signal after the square of the modulus value is used to perform discrete Fourier transform to obtain the cyclic modulation spectrum of the discrete real signal; Calculate the cyclic frequency corresponding to the maximum amplitude of the cyclic modulation spectrum on the positive frequency axis; Substituting the cyclic frequency corresponding to the maximum amplitude into the cyclic modulation spectrum to obtain a function related to discrete frequencies; The discrete frequency corresponding to the maximum modulus value of the function about the discrete frequency is calculated, and the discrete frequency is used as the carrier frequency of the communication signal.

2. The method for estimating carrier frequency of a communication signal based on cyclic modulation spectrum according to claim 1, wherein: The discretization of the communication signal received by the receiving end to obtain a discrete real signal; windowing the discrete real signal and calculating the modulo-2 norm of the window function includes: Discretize x(t) to obtain a discrete real signal x[n]=s[n]+u[n], where n represents the nth sampling point, s[n] and u[n] represent the modulated signal after discretization and Gaussian white noise; let the length of x[n] be L, first add a window to the discrete real signal x[n], the window function is w[n], and the window function length is N w ; Calculate the modulo 2 norm of the window function, ||·|| 2 represents the modulo 2 norm of .

3. The communication signal carrier frequency estimation method based on cyclic modulation spectrum according to claim 1, characterized in that: The window function is in the form of a Hamming window function.

4. The method for estimating carrier frequency of a communication signal based on cyclic modulation spectrum according to claim 1, wherein: The method of performing short-time Fourier transform on the windowed discrete real signal and performing modulus square calculation on the short-time Fourier transformed signal comprises: Perform short-time Fourier transform on the windowed discrete real signal, which is expressed as: In the above formula, e is a natural constant, j is an imaginary unit, and F s is the sampling frequency, the i-th discrete frequency is f i =iΔf, R represents the time step of the window function, x[kR+n] is the discrete real signal at the sampling position kR+n, X STFT (k,f i ) is the signal after short-time Fourier transform; To X STFT (k,f i ) is used to calculate the square of the modulus value, which is expressed as follows: X′ STFT (k,f i )=|X STFT (k,f i )| 2 Here, |·| represents calculating the modulus of a complex number.

5. The communication signal carrier frequency estimation method based on cyclic modulation spectrum according to claim 1, characterized in that: The cyclic modulation spectrum is expressed as follows: In the above formula, α is the cycle frequency of the window function, K is the number of symbols received, that is, the total step length of the window function moving on the discrete real signal length L; K = floor(|(LN w ) / R|)+1, floor(·) represents the floor function, and M represents the middle value of the window function w[n].

6. The communication signal carrier frequency estimation method based on cyclic modulation spectrum according to claim 1, characterized in that: M satisfies w[Mn]=w[M+n], when N w When it is an even number, M=N w / 2, when N w When it is an odd number, M=(N w +1) / 2.

7. The method for estimating carrier frequency of a communication signal based on cyclic modulation spectrum according to claim 1, wherein: The positive frequency axis is α≥0,f i ≥0.

8. The communication signal carrier frequency estimation method based on cyclic modulation spectrum according to claim 1, characterized in that: For the function S with respect to discrete frequencies CMS (α max ,f i ) Calculate the discrete frequency f corresponding to the maximum value of its modulus i , expressed as where |·| represents the modulus of ·.

9. A terminal device comprising a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the communication signal carrier frequency estimation method based on cyclic modulation spectrum according to any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program; wherein: When the computer program is executed by a processor, the communication signal carrier frequency estimation method based on cyclic modulation spectrum according to any one of claims 1 to 8 is implemented.

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