Symbol Rate Estimation Method for QPSK Baseband Signal Based on Constellation Variance

Abstract

The present invention discloses a QPSK baseband signal symbol rate estimation method based on constellation diagram variance, the steps of which are as follows: obtaining baseband signal sequences of different lengths; obtaining constellation diagrams corresponding to baseband signal sequences of different lengths; calculating the mean of constellation points in each quadrant of the constellation diagram; obtaining a mean residual diagram of each constellation diagram; calculating the total variance of each mean residual diagram; determining a sampling invariant point; and estimating the symbol rate of the QPSK baseband signal. The present invention uses the total variance of the mean residual diagram to determine the sampling invariant point, and the number of total variances of the calculated mean residual diagram is the number of sampling points in one symbol period. The sampling invariant point is used to estimate the symbol rate of the QPSK baseband signal, thereby avoiding the influence of the band-limited filter and being applicable to the symbol rate estimation of the baseband signal using a band-limited shaping filter. The present invention has the advantages of high flexibility, low computational complexity, and high engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of communications technology, and more specifically, relates to a method for estimating the symbol rate of a quaternary phase-shift keying (QPSK) baseband signal based on constellation variance in wireless communications. This invention can be used in the field of signal processing to estimate the symbol rate of a QPSK baseband signal using constellation variance. Background Art

[0002] In digital signal processing, the symbol rate, also known as the symbol rate, is one of the fundamental parameters for identifying digital signals. In cooperative communications, the receiver can typically obtain this information from pilot signals, enabling accurate signal sampling decisions. However, in non-cooperative communications, the symbol rate is often not directly available and requires effective estimation at the receiver. Therefore, symbol rate estimation plays a crucial role in non-cooperative communications. Existing methods based on wavelet analysis leverage the ability of wavelet analysis to simultaneously obtain information in both the time and frequency domains. They combine the wavelet transform with the autocorrelation function and utilize fast Fourier transforms and interpolation algorithms to estimate the symbol rate. While these methods offer high estimation accuracy, they require complex continuous wavelet transforms and interpolation operations, resulting in high time complexity. Furthermore, these methods fail to account for the effects of band-limited filters, limiting their applicability. Furthermore, existing methods based on cyclostationary characteristics calculate the signal's cyclic autocorrelation function and extract these cyclostationary features to estimate the symbol rate.

[0003] Chengdu Eagle Information Technology Co., Ltd., in its patent application, "A Method for Estimating Symbol Rate of Digital Baseband Signals Based on Wavelet Transform" (Patent Application No. 202211251389.8, Publication No. CN 115622841 A), discloses a symbol rate estimation method based on wavelet analysis. This method leverages the ability of wavelet analysis to simultaneously obtain both time and frequency domain information. It analyzes the bilateral power spectrum of the modulus sequence of wavelet transform coefficients of a multi-bit digital baseband waveform and detects discrete spectral lines at integer multiples of the symbol rate to estimate the symbol rate of the digital baseband signal. The method defines the intercepted digital baseband signal whose symbol rate is to be estimated as the intercepted signal. A wavelet with instantaneous amplitude characteristics similar to those of the intercepted signal at symbol transitions is selected. A continuous wavelet transform is performed on the intercepted signal, and the bilateral power spectrum of the modulus sequence of the wavelet transform coefficients is calculated. Furthermore, the bilateral power spectrum of the modulus sequence of the wavelet transform coefficients of the multi-bit digital baseband waveform is analyzed, and the symbol rate of the digital baseband signal is estimated by detecting discrete spectral lines at integer multiples of the symbol rate. Although this method has high estimation accuracy, it still has some shortcomings: it relies on discrete spectral lines at integer multiples of the symbol rate to estimate the symbol rate. The discrete spectral lines are easily interfered by noise under high signal-to-noise ratio. In addition, the methods based on wavelet transform all assume that the signal passes through a rectangular pulse shaping filter and is obtained by the receiver after passing through a flat fading channel. However, in practice, in order to improve frequency band utilization, band-limited pulse shaping filters are usually used, such as raised cosine pulse shaping filters and root raised cosine pulse shaping filters. The methods based on wavelet transform do not consider the influence of band-limited filters, and their application scope has certain limitations.

[0004] In their paper "Blind symbol rate estimation by exploiting cyclostationary features in the wavelet domain," published at the 2016 International Conference on Advances in Computing, Communications and Informatics (ICACCI) IEEE, 2016, Kumar S et al. proposed a symbol rate estimation method based on cyclostationary features. This method performs discrete wavelet denoising on the signal, calculates the signal's cyclic autocorrelation function, extracts the signal's cyclostationary features in the wavelet domain, constructs cyclic autocorrelation feature vectors for the same cyclic frequency but different delays, and determines a cyclic frequency search interval such that the frequency with the maximum norm of the feature vector is the symbol rate. This method utilizes cyclostationary features to extract symbol rate information, resulting in high estimation accuracy. However, this method still has drawbacks: it requires selecting a suitable cyclic frequency interval to search for the symbol rate, and the calculation of the cyclic autocorrelation function requires the use of a large number of sample points and the construction of a large-dimensional feature vector, resulting in high computational complexity. Summary of the Invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a QPSK baseband signal symbol rate estimation method based on constellation diagram variance, which is used to solve the problems that the prior art does not consider the influence of band-limited filters and has a certain limitation in application scope, as well as the high computational complexity of using more sample points for cyclic autocorrelation calculation and constructing large-dimensional feature vectors.

[0006] The basic idea for achieving the purpose of the present invention is that the present invention utilizes the characteristics of the constellation diagram that can reflect the information carried by various types of signals and is not affected by band-limited filters. It can be applied to the symbol rate estimation of various modulation types of baseband signals using raised cosine shaping filters, overcoming the shortcomings of the existing wavelet transform-based methods that do not consider the influence of band-limited filters and have a certain limited scope of application. In addition, the present invention utilizes the characteristics of the QPSK baseband signal constellation diagram that can reflect the sampling point information to calculate the total variance of the mean residual diagram and determine the sampling invariant points. The number of total variances of the mean residual diagram that need to be calculated is the number of sampling points within a symbol period, and the time complexity of the variance calculation is low. This overcomes the shortcomings of the existing methods based on cyclostationary characteristics that require a large number of sample points for cyclic autocorrelation calculation and construct large-scale feature vectors, resulting in high computational complexity. This makes the present invention highly flexible and applicable to various types of signals.

[0007] The specific steps for achieving the purpose of the present invention are as follows:

[0008] Step 1: Taking each sampling point in the QPSK discrete baseband signal sequence as a starting point, baseband signal sequences of different lengths are obtained;

[0009] Step 2: convert each baseband signal sequence into a two-dimensional scattered point image to obtain a constellation diagram consisting of four quadrants corresponding to the baseband signal sequence;

[0010] Step 3, calculating the mean of the in-phase component and the orthogonal component of the constellation points in each quadrant of each constellation diagram, and taking the mean of the two in the quadrant of the constellation diagram as the mean of the constellation points in the quadrant;

[0011] Step 4, calculating the mean residual point value of the constellation points in each quadrant of each constellation diagram;

[0012] Step 5, calculate the total variance of each mean residual map:

[0013] Step 6: Select two adjacent sampling points that meet the sampling invariant point condition from the sampling points corresponding to all total variance values ​​as sampling invariant points;

[0014] Step 7: Estimate the symbol rate of the QPSK baseband signal using the sampling invariant point.

[0015] Compared with the prior art, the present invention has the following advantages:

[0016] First, the present invention uses sampling invariant points to estimate the code element rate of the QPSK baseband signal, which is not affected by the band-limited filter and can be applied to the code element rate estimation of the baseband signal using the band-limited shaping filter. It overcomes the shortcomings of the wavelet transform-based method in the prior art that does not consider the influence of the band-limited filter and has a certain limitation in the scope of application. This makes the present invention highly flexible and applicable to various types of signals.

[0017] Second, the present invention uses the total variance of the mean residual graph to determine the sampling invariant points. The number of times the total variance of the mean residual graph needs to be calculated is the number of sampling points in one code element period, and the calculation time complexity of the variance is low. This overcomes the shortcomings of the existing method based on cyclostationary characteristics, which requires the use of more sample points for cyclic autocorrelation calculation and the construction of large-dimensional feature vectors, and has high computational complexity. This makes the present invention have the advantages of low computational complexity and high engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a flow chart of the present invention;

[0019] Figure 2 It is the constellation diagram of the simulation experiment of the present invention;

[0020] Figure 3 This is the mean residual graph of the simulation experiment of the present invention. DETAILED DESCRIPTION

[0021] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0022] Reference Figure 1 , further describing the implementation steps of the embodiment of the present invention.

[0023] Step 1: Taking each sampling point in the QPSK discrete baseband signal sequence as a starting point, baseband signal sequences of different lengths are obtained;

[0024] In a quadrature modulation scheme, a baseband signal whose digital modulation scheme is quaternary phase shift keying (QPSK) is divided into an in-phase component and a quadrature component. Assume that both the in-phase component and the quadrature component of the QPSK baseband signal are discrete sequences of length n = 100, where each element in the sequence is a sampling point value of the baseband signal, and the subscripts of the sampling points in the sequence are i = 0, 1, 2, ..., 100. Sequences of sampling points in the baseband signal sequence with subscripts from i to 100 are intercepted to obtain baseband signal sequences of different lengths intercepted at different starting sampling points.

[0025] Step 2: convert each baseband signal sequence into a two-dimensional scattered point image to obtain a constellation diagram consisting of four quadrants corresponding to the baseband signal sequence;

[0026] The constellation diagram has an abscissa representing the in-phase component of the QPSK baseband signal and an ordinate representing the quadrature component of the QPSK baseband signal. The in-phase component and the quadrature component of the baseband signal are used as the abscissa value and the ordinate value, respectively, to convert the constellation diagram into a two-dimensional scattered point constellation diagram with four quadrants.

[0027] Step 3, calculating the mean of the in-phase component and the orthogonal component of the constellation points in each quadrant of each constellation diagram, and taking the mean of the two in the quadrant of the constellation diagram as the mean of the constellation points in the quadrant;

[0028] The mean of the in-phase component and the orthogonal component of each quadrant in the constellation diagram of baseband signal sequences of different lengths is calculated respectively, and the mean of the constellation point is obtained by combining the two.

[0029] Step 4: Calculate the mean residual point value of the constellation points in each quadrant of each constellation diagram according to the following formula:

[0030]

[0031]

[0032] in, Represents the mean residual value of the in-phase component of the j-th constellation point in the i-th quadrant of the k-th constellation diagram, Represents the mean residual value of the orthogonal components of the j-th constellation point in the i-th quadrant of the k-th constellation diagram, represents the in-phase component of the j-th constellation point in the i-th quadrant of the k-th constellation diagram, represents the orthogonal component of the jth constellation point in the i-th quadrant of the k-th constellation diagram, represents the mean of the in-phase components of all constellation points in the i-th quadrant of the k-th constellation diagram, It represents the mean of the orthogonal components of all constellation points in the i-th quadrant of the k-th constellation diagram, and all mean residual points in the four quadrants form a mean residual diagram.

[0033] Step 5, calculate the total variance of each mean residual map:

[0034] Combine the mean residual points from the four quadrants of the constellation to create the mean residual map. Calculate the variance of each constellation point in each of the four quadrants of the mean residual map. The variance of a constellation point is the sum of the variance of the in-phase component and the variance of the orthogonal component. Sum the variances of the four quadrants of the mean residual map to obtain the total variance of the mean residual map.

[0035] Step 6: Determine the sampling invariant point:

[0036] Two adjacent starting sampling points that meet the sampling invariant point condition are selected from the starting sampling points corresponding to the total variance values ​​of all mean residual graphs as sampling invariant points.

[0037] The sampling invariant point condition refers to a situation where one of the following conditions is met:

[0038] Condition 1: The sampling point corresponding to the minimum total variance value among all total variance values;

[0039] Condition 2: The difference between the total variance value and the minimum total variance value is less than the sampling point of the threshold value; the threshold value is set based on experience.

[0040] Step 7: Estimate the symbol rate of the QPSK baseband signal using the sampling invariant point.

[0041] The number of sampling points included between the sampling invariant points is taken as the number of sampling points in a symbol period, the sampling frequency is set to 5 to 8 times the carrier frequency, and the sampling frequency is divided by the number of sampling points in a symbol period to obtain the symbol rate.

[0042] The technical effects of the present invention are further illustrated below in conjunction with simulation experiments.

[0043] 1. Simulation experiment conditions:

[0044] The hardware platform of the simulation experiment of the present invention is: the processor is Intel(R) Core(TM) i5-10210U CPU, the main frequency is 1.60GHz, and the memory is 12GB.

[0045] The software platforms for the simulation experiment of the present invention are: Windows 10 operating system and Visual Studio 2019 software.

[0046] The digital signal modulation mode used in the simulation experiment of the present invention is quaternary phase shift keying QPSK, the baseband signal sequence length is 20000, the modulation signal amplitude is 100V, the carrier frequency is 2kHz, the root raised cosine shaping filter order is 16, the roll-off coefficient is 0.25, the low-pass filter order is 12, the modulation signal code element rate is 2000Buad, the receiving signal sampling frequency is 16kHz, and the number of sampling points in one code element period is 8. It is assumed that the receiving end has down-converted the time domain high-frequency digital signal to a time domain baseband signal, and the down-converted baseband signal is divided into an in-phase component and an orthogonal component, which are discrete signal sequences with a length of 10000 respectively.

[0047] 2. Simulation content and results analysis:

[0048] The simulation experiment of the present invention uses the present invention to convert 9 QPSK baseband signal sequences of different lengths intercepted at different starting sampling points into corresponding 9 different constellation diagrams, calculates the total variance of the mean residual diagram corresponding to each generated constellation diagram, determines the sampling invariant point, and performs code rate estimation.

[0049] Figure 2 This is the constellation diagram of the baseband signal sequence intercepted at 9 different starting sampling points. Figure 2 The horizontal axis represents the amplitude value of the sampling point of the in-phase component of the baseband signal, the unit is v, and the vertical axis represents the amplitude value of the sampling point of the orthogonal component of the baseband signal, the unit is v. Figure 2 (a) is the constellation diagram with the starting sampling subscript 0 in the simulation experiment of the present invention, Figure 2 (b) is the constellation diagram with the starting sampling subscript 1 in the simulation experiment of the present invention, Figure 2 (c) is the constellation diagram with the starting sampling subscript 2 in the simulation experiment of the present invention, Figure 2 (d) is the constellation diagram with the starting sampling subscript 3 in the simulation experiment of the present invention, Figure 2 (e) is the constellation diagram with the starting sampling subscript 4 in the simulation experiment of the present invention, Figure 2 (f) is the constellation diagram with the starting sampling subscript 5 in the simulation experiment of the present invention, Figure 2 (g) is the constellation diagram with the starting sampling subscript 6 in the simulation experiment of the present invention, Figure 2 (h) is the constellation diagram with the starting sampling subscript 7 in the simulation experiment of the present invention, Figure 2 (i) is the constellation diagram with the starting sampling subscript 8 in the simulation experiment of the present invention.

[0050] Depend on Figure 2 It can be seen that the constellation diagrams of the QPSK baseband signal intercepted at different starting sampling points have different degrees of dispersion. When the starting sampling points are 0 and 8, the constellation diagrams are similar, and the constellation points in each quadrant are the most concentrated.

[0051] Figure 3 is the mean residual graph of the baseband signal sequence intercepted at 9 different starting sampling points, Figure 3 The mean residual graph in is composed of the mean residual graphs of the four quadrants of the constellation diagram under the corresponding starting sampling point. The horizontal axis represents the mean residual point value of the amplitude value of the in-phase component sampling point of the baseband signal in each quadrant, and the unit is v. The vertical axis represents the mean residual point value of the amplitude value of the orthogonal component sampling point of the baseband signal in each quadrant, and the unit is v. Figure 3 (a) is the mean residual graph with the initial sampling subscript 0 in the simulation experiment of the present invention, Figure 3 (b) is the mean residual graph of the initial sampling subscript 1 in the simulation experiment of the present invention, Figure 3 (c) is the mean residual graph of the starting sample with the subscript 2 in the simulation experiment of the present invention, Figure 3 (d) is the mean residual graph of the starting sample with the subscript 3 in the simulation experiment of the present invention, Figure 3 (e) is the mean residual graph of the starting sample with the subscript 4 in the simulation experiment of the present invention, Figure 3 (f) is the mean residual graph of the starting sample with the subscript 5 in the simulation experiment of the present invention, Figure 3 (g) is the mean residual graph of the starting sample with the subscript 6 in the simulation experiment of the present invention, Figure 3 (h) is the mean residual graph of the starting sample with the subscript 7 in the simulation experiment of the present invention, Figure 3 (i) is the mean residual graph of the starting sample with the subscript 8 in the simulation experiment of the present invention.

[0052] Depend on Figure 3 It can be seen that the constellation points in each quadrant of the baseband signal constellation diagram intercepted at different starting sampling points have different dispersion levels, and the mean residual diagram amplifies the distribution of the constellation points.

[0053] Table 1 shows the variance and total variance of each quadrant of the mean residual graph corresponding to the baseband signal sequence intercepted at 9 different starting sampling points, respectively. Figure 3 The variance of the constellation points in the four quadrants of the mean residual plot is calculated. The variance of the constellation points in each quadrant is the sum of the variance of the in-phase component and the variance of the orthogonal component. The total variance of each mean residual plot is the sum of the variances of the four quadrants of the mean residual plot.

[0054] Table 1. Total variance of the mean residual graph at different starting sampling points in the simulation experiment

[0055]

[0056]

[0057] Combining Table 1, we can see that when the starting sampling point is subscripted 0, the total variance of the mean residual graph is minimum. When the starting sampling point is subscripted 8, the difference between the total variance of the mean residual graph and the minimum total variance is less than the threshold value of 0.1. Therefore, the sampling points with subscripts 0 and 8 are sampling invariant points. The number of sampling points between sampling invariant points is 8, so the number of sampling points in one symbol period is 8. Given that the carrier frequency is 2 kHz, the sampling frequency is set to 5 to 8 times the carrier frequency, and the sampling frequency is set to 16 kHz. The sampling frequency is divided by the number of sampling points in one symbol period, and the estimated symbol rate is 2000 Buad.

Claims

1. A QPSK baseband signal symbol rate estimation method based on constellation diagram variance, characterized in that: The QPSK baseband signal constellation diagram is used to generate a mean residual diagram, the total variance of the mean residual diagram is calculated, and the sampling invariant point is determined. The steps of the symbol rate estimation method include the following: Step 1: Taking each sampling point in the QPSK discrete baseband signal sequence as a starting point, baseband signal sequences of different lengths are obtained; Step 2: convert each baseband signal sequence into a two-dimensional scattered point image to obtain a constellation diagram consisting of four quadrants corresponding to the baseband signal sequence; Step 3, calculating the mean of the in-phase component and the orthogonal component of the constellation points in each quadrant of each constellation diagram, and taking the mean of the two in the quadrant of the constellation diagram as the mean of the constellation points in the quadrant; Step 4, calculating the mean residual point value of the constellation points in each quadrant of each constellation diagram; Step 5, calculating the total variance of each mean residual map: using the mean residual value of the in-phase component in the mean residual point value of each constellation point as the horizontal coordinate and the mean residual value of the orthogonal component as the vertical coordinate, the mean residual points corresponding to all constellation points in the four quadrants of each constellation map form a mean residual map; calculating the variance of the constellation points in the four quadrants of the mean residual map respectively, summing the variances of the four quadrants of the mean residual map to obtain the total variance of the mean residual map; Step 6: Select two adjacent sampling points that meet the sampling invariant point condition from the sampling points corresponding to all total variance values ​​as sampling invariant points; The sampling invariant point condition refers to a situation where one of the following conditions is met: Condition 1: The sampling point corresponding to the minimum total variance value among all total variance values; Condition 2: The difference between the total variance value and the minimum total variance value is less than the sampling point threshold; The threshold is set based on experience; Step 7: Add 1 to the number of sampling points between the sampling invariant points as the number of sampling points within a symbol period, and use the sampling invariant points to estimate the symbol rate of the QPSK baseband signal.

2. The QPSK baseband signal symbol rate estimation method based on constellation diagram variance according to claim 1, wherein The horizontal axis of the constellation diagram in step 2 represents the in-phase component of the QPSK baseband signal, and the vertical axis represents the orthogonal component of the QPSK baseband signal.

3. The QPSK baseband signal symbol rate estimation method based on constellation diagram variance according to claim 1, wherein The mean residual point value of the constellation point in each quadrant of each constellation diagram in step 4 is obtained by the following formula: in, Represents the mean residual value of the in-phase component of the j-th constellation point in the i-th quadrant of the k-th constellation diagram, Represents the mean residual value of the orthogonal components of the j-th constellation point in the i-th quadrant of the k-th constellation diagram, represents the in-phase component of the j-th constellation point in the i-th quadrant of the k-th constellation diagram, represents the orthogonal component of the jth constellation point in the i-th quadrant of the k-th constellation diagram, represents the mean of the in-phase components of all constellation points in the i-th quadrant of the k-th constellation diagram, It represents the mean of the orthogonal components of all constellation points in the i-th quadrant of the k-th constellation diagram, and all mean residual points in the four quadrants form a mean residual diagram.

4. The QPSK baseband signal symbol rate estimation method based on constellation diagram variance according to claim 1, wherein The use of sampling invariant points in step 7 to estimate the symbol rate of the QPSK baseband signal refers to dividing the sampling frequency by the number of sampling points in one symbol period to obtain the symbol rate.

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