A Symbol Rate Estimation Method for Communication Signals Based on Enhanced Envelope Spectrum

Abstract

This invention discloses a method for estimating the symbol rate of a communication signal based on an enhanced envelope spectrum, comprising: discretizing the communication signal received at the receiver to obtain a discrete real signal; windowing the discrete real signal and calculating the modulo-2 norm of the window function; determining a phase correction factor based on the windowed discrete real signal; calculating an average cyclic periodic spectrum using the phase correction factor and the modulo-2 norm of the window function; determining a fast spectral correlation function based on the average cyclic periodic spectrum according to the cyclic frequency of the window function; normalizing the fast spectral correlation function to obtain a spectral coherence function; calculating the enhanced envelope spectrum based on the spectral coherence function; and determining the symbol rate of the communication signal using the enhanced envelope spectrum. This invention is applicable to the fields of non-cooperative signal analysis, intelligent communication, and spectrum monitoring. The method of this invention does not involve complex algorithms and is easy to implement in hardware.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology and mainly relates to a method for estimating the symbol rate of communication signals based on enhanced envelope spectrum, which is applicable to the estimation of symbol rate of communication signals in non-cooperative communication scenarios. Background Technology

[0002] In many non-cooperative communication scenarios, accurate reconstruction of the transmitted sequence is achieved through blind demodulation, which necessitates precise estimation of the signal's symbol rate. Existing methods for estimating the symbol rate vary depending on the modulation type, leading to decreased engineering applicability. Current symbol rate estimation methods include cyclic spectrum-based algorithms, wavelet transform-based algorithms, and nonlinear transformation-based algorithms.

[0003] In symbol rate estimation based on cyclic spectrum, since digital signals have cyclostationary characteristics and the symbol rate is one of their cyclic frequencies, the symbol rate can be estimated using these characteristics. In wavelet transform-based estimation, when the Haar wavelet is within a symbol, the wavelet coefficients have a fixed value; when the Haar wavelet is exactly between two symbols, the wavelet transform coefficients exhibit a jump. Therefore, the wavelet coefficients are periodic, and the symbol rate can be estimated by performing a Fourier transform on the wavelet coefficients. In nonlinear transform-based symbol rate estimation, a feature is constructed using a nonlinear transform, causing the spectrum of this feature to produce discrete spectral lines at integer multiples of the symbol rate.

[0004] The existing methods mentioned above are not applicable in practical applications and their estimation performance at low signal-to-noise ratios is poor, resulting in high deployment costs in practical applications. Summary of the Invention

[0005] The purpose of this invention is to provide a communication signal symbol rate estimation method based on enhanced envelope spectrum, which takes into account both low signal-to-noise ratio environments and universality, and achieves accurate estimation of communication signal symbol rate.

[0006] To achieve the above objectives, the present invention employs the following technical solution:

[0007] A method for estimating the symbol rate of a communication signal based on enhanced envelope spectrum includes the following steps:

[0008] The communication signal received by the receiver is discretized to obtain a discrete real signal; the discrete real signal is windowed, and the modulo-2 norm of the window function is calculated.

[0009] The phase correction factor is determined based on the windowed discrete real signal;

[0010] The average cyclic period spectrum is calculated using the phase correction factor and the modulo-2 norm of the window function.

[0011] Based on the cyclic frequency of the window function, the fast spectrum correlation function is determined according to the average cyclic period spectrum;

[0012] Normalize the fast spectral correlation function to obtain the spectral coherence function;

[0013] The enhanced envelope spectrum is calculated based on the spectral coherence function, and the symbol rate of the communication signal is determined using the enhanced envelope spectrum.

[0014] Further, 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] Discretizing x(t) yields the discrete real signal x[n] = s[n] + u[n], where n represents the nth sampling point, and s[n] and u[n] represent the discretized modulation signal and Gaussian white noise, respectively. Let the length of x[n] be L. First, window the discrete real signal x[n] using the window function w[n], with a length of N. w ; Calculate the modulo-2 norm of the window function, 2 This represents the modulo-2 norm of ·.

[0016] Further, determining the phase correction factor based on the windowed discrete real signal includes:

[0017] Calculate the phase correction factor Where F s It is the sampling frequency, and the discrete frequency is f. i =iΔf, i represents the i-th discrete frequency, and R represents the time step of the window function.

[0018] Furthermore, the calculation of the average cyclic periodic spectrum using the phase correction factor and the modulo-2 norm of the window function includes:

[0019] The formula for calculating the average cyclic period spectrum is:

[0020]

[0021] Where α is the cyclic frequency of the window function, k is the k-th symbol, and K is the total step size of the cyclic frequency, i.e., the total step size of the window function movement, K = floor((LN) w ) / R)+1, floor() represents the floor function, and the superscript * represents the conjugate complex number.

[0022] Further, determining the fast spectral correlation function based on the average cyclic periodic spectrum according to the cyclic frequency of the window function includes:

[0023] make p refers to the p-th discrete frequency. The fast spectrum correlation function is calculated as follows:

[0024]

[0025] Where e is the natural constant, j is the imaginary unit, and M represents the intermediate time value of the window function w[n], satisfying w[Mn] = w[M+n], that is, when N w When the number is even, M = N w / 2, when N w When M is an odd number, M = (N w +1) / 2.

[0026] Furthermore, the normalization of the fast spectral correlation function to obtain the spectral coherence function includes:

[0027]

[0028] Where S FSC (f i ) = S FSC (0,f i ), S FSC (f i -α)=S FSC (0,f i -α).

[0029] Furthermore, the step of calculating the enhanced envelope spectrum based on the spectral coherence function and using the enhanced envelope spectrum to determine the symbol rate of the communication signal includes:

[0030] Let f1 = 0, f2 = F s / 2 The enhanced envelope spectrum of the signal is calculated:

[0031]

[0032] Find the cycle frequency α that corresponds to the maximum value of the enhanced envelope spectrum, which is the symbol rate of the discrete real signal x[n].

[0033] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the communication signal symbol rate estimation method based on enhanced envelope spectrum.

[0034] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the method for estimating the symbol rate of a communication signal based on enhanced envelope spectrum.

[0035] Compared with the prior art, the present invention has the following technical features:

[0036] This invention exhibits strong noise resistance, does not rely on any threshold for decision-making, and can achieve good estimation performance under low signal-to-noise ratio and small sample conditions. It is suitable for various modulation types and has strong universality, especially for high-order modulation signals, where it demonstrates better performance compared to other methods. This invention is applicable to non-cooperative signal analysis, intelligent communication, spectrum monitoring, and other technical fields. The method does not involve complex algorithms, making it easy to implement in hardware. Attached Figure Description

[0037] Figure 1 This is a schematic flowchart of the method of the present invention;

[0038] Figure 2 The spectral correlation plot, spectral coherence plot, and enhanced envelope spectrum of 2PSK are shown.

[0039] Figure 3 The spectral correlation plot, spectral coherence plot, and enhanced envelope spectrum of 4PSK are shown.

[0040] Figure 4 The relationship between the normalized mean square error and the signal-to-noise ratio for signal symbol rate estimation;

[0041] Figure 5 The relationship between the normalized mean square error and symbol length for estimating the signal symbol rate. Detailed Implementation

[0042] During signal transmission, the receiving end receives a continuous real signal x(t) contaminated with Gaussian noise, x(t) = s(t) + u(t), where s(t) is the modulation signal. u(t) is zero-mean Gaussian white noise and is independent of s(t), where: A k For modulation amplitude, θ k For modulation phase, f c For carrier frequency, Let g(t) be the carrier phase, g(t) be the shaping pulse function, T be the symbol period, C be the number of received symbols, and k be the kth symbol.

[0043] See appendix Figure 1 The present invention provides a method for estimating the symbol rate of communication signals based on enhanced envelope spectrum, comprising the following steps:

[0044] Step 1: Discretize the communication signal received by the receiver to obtain a discrete real signal; window the discrete real signal and calculate the modulo 2 norm of the window function.

[0045] Discretizing x(t) yields the discrete real signal x[n] = s[n] + u[n], where n represents the nth sampling point, and s[n] and u[n] represent the discretized modulation signal and Gaussian white noise, respectively. Assuming x[n] has a length of L, the discrete real signal x[n] is first windowed with a window function w[n] (using the Hamming window function form), and the window function has a length of N. w ; Calculate the modulo-2 norm of the window function, 2 This represents the modulo-2 norm of ·.

[0046] Step 2: Determine the phase correction factor based on the windowed discrete real signal.

[0047] Calculate the phase correction factor Where F s It is the sampling frequency, and the discrete frequency is f. i =iΔf, i represents the i-th discrete frequency, R represents the time step of the window function, and n represents the n-th sampling point.

[0048] Step 3: Calculate the average cyclic periodic spectrum using the phase correction factor and the modulo 2 norm of the window function.

[0049] The formula for calculating the average cyclic period spectrum is:

[0050]

[0051] Where α is the cyclic frequency of the window function, k is the k-th symbol, and K is the total step size of the cyclic frequency, i.e., the total step size of the window function movement, K = floor((LN) w ) / R)+1, floor() represents the floor function, and the superscript * represents the conjugate complex number.

[0052] Step 4: Determine the fast spectrum correlation function based on the average cyclic period spectrum according to the cyclic frequency of the window function.

[0053] make p refers to the p-th discrete frequency. The fast spectrum correlation function is calculated as follows:

[0054]

[0055] Where e is the natural constant, j is the imaginary unit, and M represents the intermediate time value of the window function w[n], satisfying w[Mn] = w[M+n], that is, when N w When the number is even, M = N w / 2, when N w When M is an odd number, M = (N w +1) / 2.

[0056] Step 5: Normalize the fast spectral correlation function to obtain the spectral coherence function.

[0057]

[0058] Where S FSC (f i ) = S FSC (0,f i ), S FSC (f i -α)=S FSC (0,f i -α).

[0059] Step 6: Calculate the enhanced envelope spectrum based on the spectral coherence function, and use the enhanced envelope spectrum to determine the symbol rate of the communication signal.

[0060] Let f1 = 0, f2 = F s / 2 The enhanced envelope spectrum of the signal is calculated:

[0061]

[0062] Find the cycle frequency α that corresponds to the maximum value of the enhanced envelope spectrum; this is the symbol rate of the communication signal.

[0063]

[0064] The symbol rate obtained using the method of this invention can be used for signal parameter estimation in non-cooperative communication scenarios, mainly including the following scenarios:

[0065] Matched Filter Design: Based on the symbol rate, matched filters can be designed to maximize the signal-to-noise ratio, thereby enhancing signal detection and demodulation performance. Clock Recovery: The symbol rate is a key parameter for clock recovery. Using symbol rate information, the symbol clock at the transmitting end can be accurately recovered through a phase-locked loop (PLL) or other clock synchronization algorithms, providing a foundation for subsequent sampling and demodulation. Sampling Rate Conversion: At the receiving end, different signals may have different symbol rates. By estimating the symbol rate, the receiving system can dynamically adjust the sampling rate to achieve optimal matching with the signal and reduce sampling errors. Bandwidth Estimation and Resource Allocation: Based on the symbol rate, the signal bandwidth can be derived, thereby enabling optimized allocation of spectrum resources.

[0066] Example:

[0067] This embodiment uses a 2PSK signal as an example to verify the above symbol rate estimation algorithm. The simulation parameters are: symbol rate 0.4 Mbps; carrier rate 1 Mbps; sampling rate 4 Msps; number of symbols 1024; signal-to-noise ratio range -15 to 20 dB; window function length 64; and maximum cycle frequency F. s / 2. Conduct an experiment following the steps described above to obtain the following result. Figure 2 As shown and Figure 3 From the spectral correlation, spectral coherence, and enhanced envelope plots, we can see that the maximum value of the enhanced envelope spectrum is the symbol rate of the corresponding real signal.

[0068] Because the baseband symbol is randomly generated, different results may be obtained in each trial. To test the performance of the method from a statistical perspective, the trial was repeated 100 times under the same parameter conditions. (See Appendix) Figure 4 and Figure 5 The modulation signal types used in the experiment were 2PSK, 4PSK, 8PSK, 2ASK, 4ASK, 8ASK, 2FSK, 4FSK, 8FSK, 4QAM, 8QAM, 16QAM, 64QAM, and MSK signals. The simulation parameters were consistent with the simulation parameters for a single 2PSK test. The normalized mean square error of the symbol rate estimate after 100 trials was within 10. -8 The method yields good estimation results for most modulated signals under low signal-to-noise ratio conditions. Therefore, this method has a wide range of applications and can estimate the symbol rate of most modulation types (at least 14 types).

[0069] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for estimating the symbol rate of a communication signal based on enhanced envelope spectrum, characterized in that, include: The communication signal received by the receiving end is discretized to obtain a discrete real signal; Windowing is applied to discrete real signals, and the modulo-2 norm of the window function is calculated, including: right Discretization yields discrete real signals. , Indicates the first One sampling point, and Represents the discretized modulated signal and Gaussian white noise; denoted as Its length is First, for discrete real signals Windowing is applied, and the window function is: The window function length is ; Calculate the modulo-2 norm of the window function, , Indicates calculation The modulo-2 norm; Based on the windowed discrete real signal, determine the phase correction factor, including: Calculate the phase correction factor ,in It is the sampling frequency, and the discrete frequency is... , , Indicates the first A discrete frequency, The time step of the window function; The average cyclic period spectrum is calculated using the phase correction factor and the modulo-2 norm of the window function, including: The formula for calculating the average cyclic period spectrum is: in The loop frequency of the window function. k For the first k A symbol, This represents the total step size of the cycle frequency, i.e., the total step size of the window function movement. , Represents the floor function, superscript Represents the conjugate complex number; Based on the cyclic frequency of the window function, a fast spectral correlation function is determined according to the average cyclic period spectrum, including: make , It refers to the first For each discrete frequency, calculate the fast spectral correlation function: in, e It is a natural constant. j The imaginary unit, Representing window functions The intermediate time value satisfies That is, when When it is even, ,when When it is an odd number, ; Normalizing the fast spectral correlation function yields the spectral coherence function, which includes: in , ; The enhanced envelope spectrum is calculated based on the spectral coherence function, and the symbol rate of the communication signal is determined using the enhanced envelope spectrum, including: make , The enhanced envelope spectrum of the signal was calculated: Find the cycle frequency that corresponds to the maximum value of the enhanced envelope spectrum. That is, discrete real signal symbol rate .

2. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes the computer program, it implements the communication signal symbol rate estimation method based on enhanced envelope spectrum as described in claim 1.

3. A computer-readable storage medium storing a computer program; characterized in that, When the computer program is executed by the processor, it implements the communication signal symbol rate estimation method based on enhanced envelope spectrum as described in claim 1.

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