Single-channel mixed signal demodulation method based on oversampling

Abstract

This invention discloses a single-channel mixed signal demodulation method based on oversampling. First, the mixed signal of BPSK and 16QAM signals received in a PCMA communication system is processed to construct a multi-channel blind source separation model. The signal from the multi-channel blind source separation model is then centered and whitened to reduce the computational cost of FastICA. Then, FastICA is used to extract independent components. Finally, based on the obtained independent components, a phase-locked loop is used to extract baseband information to obtain the baseband signal. This invention effectively solves the problem of high bit error rate after separating and demodulating mixed signals in a single-channel environment. This invention utilizes the orthogonality of carriers, which further improves the demodulation performance of single-channel mixed signals when the sampling factor is increased. Compared with time-domain filtering methods, frequency-domain notch filtering methods, empirical mode decomposition methods, and wavelet decomposition methods, this method has better demodulation performance and a lower bit error rate.

Description

Technical Field

[0001] This invention belongs to the field of signal processing, specifically relating to a single-channel mixed signal demodulation method based on oversampling. Background Technology

[0002] With the development of communication technology, the modern electromagnetic environment is becoming increasingly complex, and multi-channel signal separation may not be able to cope with some channel scenarios or receiving environments. In some communication environments, such as paired carrier multiple access (PCMA) communication systems and spaceborne automatic identification systems for ships, only a single receiving antenna can be used to receive signals. Therefore, it is of great significance to study methods for separating single-channel mixed signals and achieving good performance after demodulation.

[0003] Mingxiang Guan et al. in the paper [1] The paper "Adaptive Separation of Subcarrier for Wireless Link of Satellite Communication" uses filters to separate signals. Since the signals do not overlap in the frequency domain, filters can be used to individually filter out the source signals. However, the performance is poor when the spectra of the mixed signals overlap. (Yao Junyong et al., in their paper...) [2] The paper "Research on the Filtering Threshold Problem in Frequency Domain Anti-interference Algorithms" uses a frequency domain notch filter algorithm to obtain the target signal spectrum, and then performs an inverse Fourier transform to obtain the target signal. However, this method suffers from signal spectrum overlap, as the frequency domain notch filter affects the target signal, leading to signal corruption and a high bit error rate after demodulation. Fang Xiaoli et al., in their paper... [3] The paper "GNSS Frequency Anti-interference Algorithm Based on Spectral Symmetry" utilizes spectral symmetry to separate signals with overlapping spectra. Specifically, after obtaining the target signal through notch filtering in the frequency domain, the unelectdated spectral lines are recovered using the unaffected portion of the target signal's spectrum, based on spectral symmetry, thus obtaining the complete spectrum of the target signal. However, this method cannot recover the spectral lines using symmetry when the spectral overlap is too large. (Liu Pei's paper...) [4] The paper "Research and Implementation of Blind Separation Algorithm for PCMA Signals" uses a particle filtering algorithm for single-channel signal separation. However, when processing high-order signals such as 16QAM signals, the large symbol space necessitates a large number of particles for iteration, leading to particle degeneration. This degeneration results in errors in the separation results, resulting in a high bit error rate after demodulation. He Ji'ai et al., in their paper... [5]The paper "Research on Blind Separation Algorithm for Single-Channel Communication Signals Based on EMD" constructs multi-channel signals using Empirical Mode Decomposition (EMD) and then performs independent component analysis to separate mixed signals. When the frequency components in the signals are similar, mode aliasing occurs, meaning the decomposed components contain elements from other components, leading to a degraded demodulation performance. Wang Jiao et al., in their paper... [6] The paper "A Single-Channel Blind Separation Interference Suppression Method Based on Wavelet Decomposition" constructs multi-channel signals using wavelet decomposition and combines it with independent component analysis to separate single-channel signals. However, due to its frequency resolution, wavelet decomposition's ability to separate signals with severe frequency domain aliasing is reduced, leading to a decrease in demodulation performance.

[0004] The above algorithm performs poorly in demodulating mixed signals with severe time-frequency aliasing after separation, resulting in a high bit error rate.

[0005] References:

[0006] [1]Guan M, Wang L, Peng B. Adaptive separation of subcarrier for wireless link of satellite communication [J]. Wireless Personal Communications, 2018, 103: 159-166.

[0007] [2] Yao Junyong, Zheng Linhua. Research on filtering threshold problem in frequency domain anti-interference algorithm [J]. Modern Electronics Technology, 2007, 30(1):1-2,8. DOI:10.3969 / j.issn.1004-373X.2007.01.001.

[0008] [3] Fang Xiaoli, Wu Lijie, Peng Hui. Anti-interference algorithm for GNSS frequency based on spectrum symmetry [J]. Journal of Terahertz Science and Electronic Information, 2022, 20(6): 590-594. DOI: 10.11805 / TKYDA2020164.

[0009] [4] Liu, Pei. Research and Implementation of PCMA Signal Blind Separation Algorithm [D]. Sichuan: University of Electronic Science and Technology of China, 2016. DOI:10.7666 / d.D00988517.

[0010] [5] He J.A., Li Y.F., Zhang X.J. Research on blind separation algorithm of single-channel communication signal based on EMD [J]. Journal of Gansu Science, 2015, 27(4):14-19. DOI:10.16468 / j.cnki.issn1004-0366.2015.04.004.

[0011] [6] Wang Jiao, Liu Yulin, He Wei, et al. A method for suppressing interference by single-channel blind separation in wavelet decomposition[J]. Journal of Chongqing University of Posts and Telecommunications (Natural Science Edition), 2014, 26(5):648-653.DOI:10.3979 / j.issn.1673-825X.2014.05.015.

[0012] [7] Hyvarinen, Aapo. "Fast and robust fixed-point algorithms for independent component analysis." IEEE transactions onNeuralNetworks 10.3(1999):626-634. Summary of the Invention

[0013] The purpose of this invention is to improve the demodulation performance of mixed signals in a single channel. A single-channel mixed signal demodulation method based on oversampling is proposed. This invention is used to demodulate mixed signals of BPSK (Binary Phase Shift Keying) and 16QAM (Quadrature Amplitude Modulation) signals received in a PCMA communication system. The method first constructs a multi-channel data mixing matrix model of the received signal. This data matrix is ​​the projection of the data symbols of different signals onto their corresponding orthogonal carrier sequences, which can be regarded as a MIMO (Multiple-Input Multiple-Output) model. Then, Fast Independent Component Analysis (FastICA) is used to separate the signals and demodulate them to obtain the baseband data codes of different signals. Since different carrier frequencies are orthogonal, according to the method of constructing the data matrix according to this invention, as the sampling multiple increases, the orthogonality of the carrier sequences becomes stronger, and the bit error rate decreases with the increase of the sampling multiple. When the sampling multiple reaches a certain level, the decrease in bit error rate slows down. Experimental results show that the method proposed in this paper for constructing multi-channel fast independent component analysis to separate mixed signals and perform demodulation has good performance, with an average bit error rate lower than that of wavelet decomposition, empirical mode decomposition, and filtering separation methods.

[0014] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0015] Step 1: Process the mixed signal of BPSK (Binary Phase Shift Keying) and 16QAM (Quadrature Amplitude Modulation) signals received in the PCMA communication system to construct a multi-channel blind source separation model.

[0016] Step 2: Center and whiten the multi-channel blind source separation model signal to reduce the computational cost of FastICA, and then use FastICA to extract independent components.

[0017] Step 3: Based on the obtained independent components, use a phase-locked loop to extract baseband information and obtain the baseband signal.

[0018] Furthermore, the method for constructing the multi-channel blind source separation model described in step one is as follows:

[0019] The complex baseband time-domain expression of the mixed signal of BPSK and 16QAM signals received by a single antenna is as follows:

[0020]

[0021] In equation (1), the signal with k=1 represents the BPSK signal, the signal with k=2 represents the 16QAM signal, n(t) is additive white Gaussian noise, and the noise variance is σ. 2 ω represents time, and i represents the imaginary unit. k Let A be the carrier frequency of the k-th signal. k,m , Let f be the amplitude and phase information corresponding to the m-th symbol of the k-th signal. The code rate of both signals is R. This signal is oversampled at an oversampling frequency of f. s f s The relationship with the code rate R is as follows:

[0022] f s =L*R (2)

[0023] Where L is the oversampling factor. The signal expression, or signal model, after oversampling the signal y(t) is:

[0024]

[0025] In equation (3), n represents the number of sampling points, and n(n) represents the additive white Gaussian noise after sampling. Analyzing the real part of the signal model using equation (3), the real part of the signal model can be obtained as follows:

[0026]

[0027] y I (n) is the real part of y(n), nI (n) is the real part of n(n). For y I (n), where L consecutive points form an observation vector. Since there is a delay when observing the signal, let τ... k The delay is the delay of the k-th signal.

[0028] From equation (4), the observation vector r can be... m,I Represented as Equation (5):

[0029]

[0030] In equation (5), y k,m Let N be the m-th observation vector of the k-th signal. m Let be the noise vector obtained after sampling the Gaussian white noise in the m-th observation vector through L consecutive points. The m-th observation vector of the k-th signal can be expressed as Equation (6):

[0031] y k,m =h k,1 +h k,2 (6)

[0032] In equation (6), h k,1 and h k,2 For y k,m The first and second piecewise vectors can be represented as:

[0033]

[0034]

[0035] Among them, C I,k,1 for h k,1 The in-phase component, C I,k,2 for h k,1 The orthogonal components of C. I,k,3 for h k,2 The in-phase component, C I,k,4 for h k,2 The orthogonal components. In equations (7) and (8), we have:

[0036]

[0037]

[0038] Therefore, from equations (6), (7), and (8), we can obtain equation (11):

[0039] y k,m =[b k,m,1 C I,k,1 +b k,m,2 C I,k,2 +bk,m,3 C I,k,3 +b k,m,4 C I,k,4 ] L×1 (11)

[0040] From equations (5) and (11), we can determine r m,I Represented as equation (12):

[0041]

[0042] In equation (12), N m Let G be the noise vector obtained after sampling the Gaussian white noise in the m-th observation vector through L consecutive points. Equation (12) is the multi-channel blind source separation model. G and B I,m It can be represented as:

[0043]

[0044]

[0045] In equation (13), G is the channel matrix, and the column vectors of the channel matrix are shown in equation (9). In equation (14), B I,m Let be the data sequence vector in the m-th observation vector.

[0046] Furthermore, step two is implemented as follows:

[0047] For r m,I After centralization, calculate r. m,I The covariance matrix is ​​then subjected to singular value decomposition, and the result is as follows:

[0048]

[0049] Among them, R rr Let M be the covariance matrix, and M be the total number of symbols in the mixed signal.

[0050] The signal and noise are uncorrelated, and due to the weak correlation between different carriers, y 1,m and y 2,m Since they can be considered unrelated, we can obtain the following from equations (7), (8), and (15):

[0051]

[0052] In equation (16), Let μ be the variance of the information code of the k-th signal. I,k,j =C I,k,j / ||C I,k,j || represents the column vector of the normalized channel matrix, and j is the index of the column vector of the channel matrix G, j = 1, 2, 3, 4. EI,k,j E represents the energy of the column vectors of the channel matrix G. I,k,j =||C I,k,j ||, ||·|| are the 2-norm of the orientation quantity. I is the identity matrix. Signal subspace U S The column vectors represent the signal components. Its conjugate transpose. N The column vectors represent the noise components. It is its conjugate transpose. The eigenvalue matrix corresponding to the signal subspace is D. S D S The values ​​on the diagonal represent the eigenvalues ​​corresponding to the signal components, arranged in descending order. The eigenvalue matrix corresponding to the noise subspace is D. N D N The values ​​on the diagonal are the eigenvalues ​​corresponding to the noise components. O is an all-zero matrix. According to equation (16), the first 8 eigenvalues ​​of the covariance matrix are called the principal eigenvalues, which can be approximately expressed as:

[0053]

[0054] In equation (17), λ I,k,· These represent the four principal eigenvalues ​​of the k-th signal. Since k = 1, 2, there are a total of eight principal eigenvalues. Projecting the received signal onto a signal subspace for dimensionality reduction can reduce the complexity of the Fast Independent Component Analysis (FIC). A whitening matrix is ​​used. After whitening, the observation signal z of the real part I path is obtained. m , z m With a size of 8×1, it can be represented by equation (18):

[0055]

[0056] From equations (12) and (18), we get: P is a mixing matrix.

[0057] In blind source separation, the inverse matrix P of the mixing matrix is ​​calculated. -1 Equation (19) can be obtained.

[0058]

[0059] This invention calculates the inverse matrix P using FastICA iteration. -1 Due to the presence of errors, the inverse matrix is ​​approximated as W. T The matrix W is also called the unmixing matrix. After obtaining the unmixing matrix, the data sequence vector B can be obtained by equation (19). I,m Estimate That is, the independent components extracted after FastICA. The expression is as shown in equation (20):

[0060]

[0061] Similarly, after the same processing, the data sequence vector of the received Q-channel data can be obtained. That is, the independent components extracted after FastICA.

[0062] Furthermore, step three is implemented as follows:

[0063] The data sequence vector separated by the FastICA algorithm needs to be subjected to carrier recovery using a phase-locked loop (PLL) to obtain baseband information. The PLL used in this invention is a Costas loop. A suitable phase detector is selected based on the signal type: for mixed signals including BPSK and 16QAM signals, the arctangent phase detector method is selected for BPSK signals, and the d-power decision loop method is selected for 16QAM signals.

[0064] Furthermore, the specific method for centering the observation vector is as follows:

[0065] The formula for centering the observation vector is shown in equation (21):

[0066] r m,I ←r m,I -E{r m,I}(twenty one)

[0067] Among them, E{r m,I} represents the observation vector r m,I The mean of the observed vectors is zero after centering.

[0068] Furthermore, the specific method for calculating the unmixing matrix is ​​as follows:

[0069] The unmixing matrix is ​​W = [w1, w2, w3, w4, w5, w6, w7, w8]. 8×8 The column vectors of the unmixing matrix are random vectors with unit norm, which serve as the initial separating vectors. This is achieved through w... p This indicates that the range of values ​​for p is [1, 8]. First, let p = 1, and then for w... p The iteration is performed, and the iteration formula is:

[0070]

[0071] Wherein, the function g(x) = x 3 , where g'(·) is the derivative of g(·). After each iteration, w... p Perform Schmidt orthogonalization. The orthogonalization formula is shown in equation (23).

[0072]

[0073] Where j' represents the index of the column vector of the unmixing matrix. Then normalization is performed by equation (24).

[0074]

[0075] If w p If convergence is not achieved, continue iterating using equations (22), (23), and (24) until w is reached. p Convergence. When w p After convergence, update p by executing p←p+1. Then continue updating w. p The iteration continues until p = 8. At this point, the iterative calculation is complete, and the unmixing matrix W is obtained.

[0076] The beneficial effects of this invention are as follows:

[0077] 1. Effectively solves the problem of high bit error rate after separating and demodulating mixed signals in a single-channel environment.

[0078] 2. By utilizing the orthogonality of the carrier waves, the demodulation performance of single-channel mixed signals is further improved when the sampling multiple is increased.

[0079] 3. Compared with time-domain filtering, frequency-domain notch filtering, empirical mode decomposition, and wavelet decomposition, this method has better demodulation performance and a lower bit error rate.

[0080] In summary, this invention has advantages such as low bit error rate and strong robustness. Attached Figure Description

[0081] Figure 1 This is a diagram showing the observation vector structure of an embodiment of the present invention;

[0082] Figure 2 This is a structural diagram of the Costas ring according to an embodiment of the present invention;

[0083] Figure 3 Bit error rate curves at different sampling multiples;

[0084] Figure 4 Bit error rate curves of different BPSK signal algorithms;

[0085] Figure 5 shows the bit error rate curves of different algorithms for 16QAM signals. Detailed Implementation

[0086] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0087] Example 1:

[0088] The technical solution adopted in this invention:

[0089] Step 1. Signal Generation

[0090] The BPSK and 16QAM signals were generated using Matlab software, and then the two signals were mixed using random weights to obtain a mixed signal.

[0091] Step 2. Construction method of multi-channel blind source separation model

[0092] Based on the sampling factor, each set of L points forms an observation vector. Figure 1 This refers to the specific method for constructing the observation vector;

[0093] The complex baseband time-domain expression of the mixed signal of BPSK and 16QAM signals received by a single antenna is as follows:

[0094]

[0095] In equation (1), the signal with k=1 represents the BPSK signal, the signal with k=2 represents the 16QAM signal, n(t) is additive white Gaussian noise, and the noise variance is σ. 2 ω represents time, and i represents the imaginary unit. k Let A be the carrier frequency of the k-th signal. k,m , Let f be the amplitude and phase information corresponding to the m-th symbol of the k-th signal. The code rate of both signals is R. This signal is oversampled at an oversampling frequency of f. s f s The relationship with the code rate R is as follows:

[0096] f s =L*R (2)

[0097] Where L is the oversampling factor. The signal expression, or signal model, after oversampling the signal y(t) is:

[0098]

[0099] In equation (3), n represents the number of sampling points, and n(n) represents the additive white Gaussian noise after sampling. Analyzing the real part of the signal model using equation (3), the real part of the signal model can be obtained as follows:

[0100]

[0101] y I (n) is the real part of y(n), n I(n) is the real part of n(n). For y I (n), where L consecutive points form an observation vector. Since there is a delay when observing the signal, let τ... k The delay is the delay of the k-th signal.

[0102] From equation (4), the observation vector r can be... m,I Represented as Equation (5):

[0103]

[0104] In equation (5), y k,m Let N be the m-th observation vector of the k-th signal. m Let be the noise vector obtained after sampling the Gaussian white noise in the m-th observation vector through L consecutive points. The m-th observation vector of the k-th signal can be expressed as Equation (6):

[0105] y k,m =h k,1 +h k,2 (6)

[0106] In equation (6), h k,1 and h k,2 For y k,m The first and second piecewise vectors can be represented as:

[0107]

[0108]

[0109] Among them, C I,k,1 for h k,1 The in-phase component, C I,k,2 for h k,1 The orthogonal components of C. I,k,3 for h k,2 The in-phase component, C I,k,4 for h k,2 The orthogonal components. In equations (7) and (8), we have:

[0110]

[0111]

[0112] Therefore, from equations (6), (7), and (8), we can obtain equation (11):

[0113] y k,m =[b k,m,1 C I,k,1 +b k,m,2 C I,k,2 +b k,m,3 CI,k,3 +b k,m,4 C I,k,4 ] L×1 (11)

[0114] From equations (5) and (11), we can determine r m,I Represented as equation (12):

[0115]

[0116] In equation (12), N m Let G be the noise vector obtained after sampling the Gaussian white noise in the m-th observation vector through L consecutive points. Equation (12) is the multi-channel blind source separation model. G and B I,m It can be represented as:

[0117]

[0118]

[0119] In equation (13), G is the channel matrix, and the column vectors of the channel matrix are shown in equation (9). In equation (14), B I,m Let be the data sequence vector in the m-th observation vector.

[0120] Step 3. Extract independent components using the rapid independent component analysis method:

[0121] The formula for centering the observation vector is shown in equation (15):

[0122] r m,I ←r m,I -E{r m,I} (15)

[0123] Among them, E{r m,I} represents the observation vector r m,I The mean of the observed vectors is zero after centering.

[0124] For r m,I After centralization, calculate r. m,I The covariance matrix is ​​then subjected to singular value decomposition, and the result is as follows:

[0125]

[0126] Among them, R rr Let M be the covariance matrix, and M be the total number of symbols in the mixed signal.

[0127] The signal and noise are uncorrelated, and due to the weak correlation between different carriers, y 1,m and y 2,mSince they can be considered unrelated, we can obtain the following from equations (7), (8), and (16):

[0128]

[0129] In equation (17), Let μ be the variance of the information code of the k-th signal. I,k,j =C I,k,j / ||C I,k,j || represents the column vector of the normalized channel matrix, and j is the index of the column vector of the channel matrix G, j = 1, 2, 3, 4. E I,k,j E represents the energy of the column vectors of the channel matrix G. I,k,j =||C I,k,j ||, ||·|| are the 2-norm of the orientation quantity. I is the identity matrix. Signal subspace U S The column vectors represent the signal components. Its conjugate transpose. N The column vectors represent the noise components. It is its conjugate transpose. The eigenvalue matrix corresponding to the signal subspace is D. S D S The values ​​on the diagonal represent the eigenvalues ​​corresponding to the signal components, arranged in descending order. The eigenvalue matrix corresponding to the noise subspace is D. N D N The values ​​on the diagonal are the eigenvalues ​​corresponding to the noise components. O is an all-zero matrix. According to equation (16), the first 8 eigenvalues ​​of the covariance matrix are called the principal eigenvalues, which can be approximately expressed as:

[0130]

[0131] In equation (18), λ I,k,· These represent the four principal eigenvalues ​​of the k-th signal. Since k = 1, 2, there are a total of eight principal eigenvalues. Projecting the received signal onto a signal subspace for dimensionality reduction can reduce the complexity of the Fast Independent Component Analysis (FIC). A whitening matrix is ​​used. After whitening, the observation signal z of the real part I path is obtained. m , z m With a size of 8×1, it can be represented by equation (18):

[0132]

[0133] From equations (12) and (19), we get: P is a mixing matrix.

[0134] In blind source separation, the inverse matrix P of the mixing matrix is ​​calculated. -1 Equation (20) can be obtained.

[0135]

[0136] This invention calculates the inverse matrix P using FastICA iteration. -1 Due to the presence of errors, the inverse matrix is ​​approximated as W. T The matrix W is also called the unmixing matrix.

[0137] The specific method for calculating the unmixing matrix is ​​as follows:

[0138] The unmixing matrix is ​​W = [w1, w2, w3, w4, w5, w6, w7, w8]. 8×8 The column vectors of the unmixing matrix are random vectors with unit norm, which serve as the initial separating vectors. This is achieved through w... p This indicates that the range of values ​​for p is [1, 8]. First, let p = 1, and then for w... p Perform iterations, iteration formula [7] for:

[0139]

[0140] Wherein, the function g(x) = x 3 , where g'(·) is the derivative of g(·). After each iteration, w... p Perform Schmidt orthogonalization. The orthogonalization formula is shown in equation (22).

[0141]

[0142] Where j' represents the index of the column vector of the unmixing matrix. Then normalization is performed by equation (23).

[0143]

[0144] If w p If convergence is not achieved, continue iterating using equations (21), (22), and (23) until w is reached. p Convergence. When w p After convergence, update p by executing p←p+1. Then continue updating w. p The iteration continues until p = 8. At this point, the iterative calculation is complete, and the unmixing matrix W is obtained.

[0145] After obtaining the unmixing matrix, the data sequence vector B can be obtained from equation (20). I,m Estimate That is, the independent components extracted after FastICA. The expression is as shown in equation (24):

[0146]

[0147] Similarly, after the same processing, the data sequence vector of the received Q-channel data can be obtained. That is, the independent components extracted after FastICA.

[0148] Step 4. Baseband information extraction based on phase-locked loop:

[0149] This method uses Costas rings to extract baseband information. The structure of Costas is as follows: Figure 2 As shown. Costas, also known as in-phase quadrature loop, mainly consists of a low-pass filter, a phase detector loop filter, and a voltage-controlled oscillator. The input signal is divided into I-path and Q-path. The voltage a output by the voltage-controlled oscillator from the I-path is multiplied by a multiplier to obtain the voltage at point c. The voltage b output by a after a 90° phase shift from the Q-path is multiplied to obtain d. After passing through the low-pass filter, c and d are used to obtain e and f, where e is the output voltage of the Costas loop. After passing through the phase detector, e and f output the phase error voltage g. After being filtered by the loop, g can control and adjust the output carrier frequency of the voltage-controlled oscillator. Taking BPSK as an example, the independent components are obtained from equation (24) as follows: Since the signal includes a BPSK signal with frequency offset, this method extracts the carrier from the independent components through a Costas ring to obtain the baseband information of the signal. Let the expression of the BPSK signal input to the Costas ring be B(n) = A(n)cos(ωn+θ), where A(n) = ±1. Figure 2 The input voltages of the two voltage-controlled oscillators at points a and b are expressed as follows:

[0150]

[0151]

[0152] v a v b After multiplying the input signal by the multiplier, the output voltage v of the multiplier can be obtained. c v d .

[0153]

[0154]

[0155] These two voltages v c v d After low-pass filtering, we can obtain:

[0156]

[0157]

[0158] Two voltages v c v d After passing through a phase detector and loop filtering, a phase error signal is output, thereby extracting the signal carrier. An appropriate phase detector needs to be selected based on the signal type. Mixed signals include BPSK and 16QAM signals; for BPSK signals, the arctangent phase detector method is used, and for 16QAM signals, the d-power decision loop method is used.

[0159] a) The method of judging appearance by reverse tangent:

[0160] The phase detection algorithm used in the BPSK signal of this invention is the arctangent phase detection method, and the phase detection algorithm is shown in equation (32).

[0161] u d (n)=atan2(s q (n),s i (n)) (31)

[0162] In equation (31), s q (n) represents the sampled signal of the Q-channel after filtering, i.e. Figure 2 f, s i (n) represents the filtered I-channel sampled signal, i.e. Figure 2 e. u d (n) represents the output of the phase detector, i.e. Figure 2 The g in the image. This phase detector can extract unipolar or bipolar information of a signal.

[0163] b) d-th power decision ring method:

[0164] The phase detection algorithm used in the 16QAM signal of this invention is the d-th power decision loop method, as shown in equation (32).

[0165]

[0166] In equation (32), and These are the I-channel signal and Q-channel signal after being processed to the power of d, respectively. Figure 2 In the equation, e and f, d = 3.

[0167] When the output g of the phase detector converges and passes through the loop filter, the output of the voltage-controlled oscillator is point a. Point a is the carrier extracted from the signal by the Costas loop, and the loop output at point e is the baseband data code A(n) of the demodulated output.

[0168] Example 2:

[0169] 1. Signal Generation Parameters: In a Gaussian channel, BPSK and 16QAM signals are generated using Matlab. The basic parameters of the signals are: the code rate of both signals is R, where R = 10 Kbps. The carrier frequency f of the BPSK signal is... c1 =20000Hz, the carrier frequency f of the 16QAM signal c2 =30000Hz, sampling frequency f s =16*R=160Kbps, f s The sampling rate is 500. The number of generated information codes is 500. Because time-domain filtering and frequency-domain notch filtering methods have poor signal separation performance when there is significant spectral overlap, the carrier frequency of the BPSK signal is set to 20000Hz and the carrier frequency of the 16QAM signal is set to 60000Hz for simulation, with other conditions remaining unchanged.

[0170] 2. Simulation Result Analysis: Experiments were conducted at different oversampling factors when the signal-to-noise ratio was 15dB. The horizontal axis represents the oversampling factor, and the vertical axis represents the bit error rate (BER). 100 Monte Carlo experiments were performed for each sampling factor. The relationship between the sampling factor and the BER is shown below. Figure 3 .Depend on Figure 3 It can be seen that different oversampling factors have an impact on the bit error rate. As shown in Equation (9), when the sampling rate increases, the length of the carrier sequence contained in the symbol increases, and the correlation of the carrier sequence decreases, thereby improving the performance of independent component analysis. When the oversampling factor is about 24, the orthogonality of the carrier sequence increases slowly after the sampling factor increases. Therefore, as the sampling factor increases, the rate of decrease in bit error rate slows down.

[0171] The signal-to-noise ratio (SNR) ranged from 10 to 20 dB. For each SNR, 100 Monte Carlo simulations were performed on the proposed method, wavelet decomposition method, empirical mode decomposition method, time-domain filtering method, and frequency-domain notch filtering method. The simulation results from these 100 simulations were collected, and the average bit error rate (BER) was calculated. The BER curves for these five methods at different SNRs are shown below. Figure 4 , 5 As shown in the figure, comparing the bit error rate curves of the above methods under different signal-to-noise ratios, the bit error rate of the algorithm in this paper is significantly lower than that of wavelet decomposition, empirical mode decomposition, time-domain filtering and frequency-domain notch filtering methods for separating and demodulating mixed signals, and it has better performance.

[0172] Finally, it should be noted that the purpose of disclosing the embodiments is to help further understand the present invention. However, those skilled in the art will understand that various substitutions and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the content disclosed in the embodiments, and the scope of protection of the present invention is defined by the claims.

Claims

1. A method of single channel mixed signal demodulation based on oversampling, characterized in that, The steps include the following: Step 1: Process the mixed signal of BPSK and 16QAM received in the PCMA communication system to construct a multi-channel blind source separation model; Step 2: Center and whiten the signal of the multi-channel blind source separation model to reduce the computational cost of FastICA, and then use FastICA to extract independent components; Step 3: Based on the obtained independent components, use a phase-locked loop to extract baseband information and obtain the baseband signal; The method for constructing the multi-channel blind source separation model described in step one is as follows: The complex baseband time-domain expression of the mixed signal of BPSK and 16QAM signals received by a single antenna is as follows: (1) In equation (1), The signal represents the BPSK signal. The signal represents a 16QAM signal. It is additive white Gaussian noise with a noise variance of . , Indicates time, Represents the imaginary unit; For the first The carrier frequency of the signal; , Let be the amplitude and phase information corresponding to the m-th symbol of the k-th signal; the code rates of the two signals are . This signal is oversampled at a frequency of . , With code rate The relationship is as follows: (2) in, This is the oversampling factor; for the signal The oversampled signal expression, or signal model, is as follows: (3) In equation (3), For sampling points, Let represent the additive white Gaussian noise after sampling; by analyzing the real part of the signal model using equation (3), the signal model with the real part can be obtained as follows: (4) for The real part, for The real part; for ,continuous Each point forms an observation vector. Since there is a delay when observing the signal, let... For the first The delay of a signal; From equation (4), the observation vector can be... Represented as Equation (5): (5) In equation (5), Let m be the observation vector of the k-th signal. Let m be the noise vector obtained after sampling Gaussian white noise in the m-th observation vector through L consecutive points; the m-th observation vector of the k-th signal can be expressed as equation (6): (6) In equation (6), and for The first and second piecewise vectors can be represented as: (7) (8) in, for In-phase components, for orthogonal components; for In-phase components, for The orthogonal components; in equations (7) and (8), we have: (9) (10) Therefore, from equations (6), (7), and (8), we can obtain equation (11): (11) From equations (5) and (11), it is possible to... Represented as equation (12): (12) In equation (12), Let be the noise vector obtained after sampling the Gaussian white noise in the m-th observation vector through L consecutive points; Equation (12) is the multi-channel blind source separation model; and It can be represented as: (13) (14) In equation (13), Let be the channel matrix, and the column vectors of the channel matrix are shown in equation (9); in equation (14), Let be the data sequence vector in the m-th observation vector.

2. The single-channel mixed signal demodulation method based on oversampling according to claim 1, characterized in that, Step two is implemented as follows: right After centralization, find The covariance matrix is ​​then subjected to singular value decomposition, and the result is as follows: (15) in, Let covariance matrix be the variance matrix. The total number of symbols in the mixed signal; The signal and noise are uncorrelated, and due to the weak correlation between different carriers, and Since they can be considered unrelated, we can obtain the following from equations (7), (8), and (15): (16) In equation (16), Let Variance be the information code variance of the k-th signal. The column vectors of the normalized channel matrix. Channel matrix The index of the column vector. ; Channel matrix Energy of column vectors , For the 2-norm of the orientation quantity; The identity matrix; signal subspace The column vectors represent the signal components. Its conjugate transpose; noise subspace The column vectors represent the noise components. Its conjugate transpose; the eigenvalue matrix corresponding to the signal subspace is , The values ​​on the diagonal represent the eigenvalues ​​corresponding to the signal components, arranged in descending order; the eigenvalue matrix corresponding to the noise subspace is... , The values ​​on the diagonal are the eigenvalues ​​corresponding to the noise components; The matrix is ​​composed entirely of zeros; according to equation (16), the first 8 eigenvalues ​​of the covariance matrix are called the principal eigenvalues, which can be approximately expressed as: (17) In equation (17), Indicates the first The four principal characteristic values ​​of the signal, due to Therefore, there are a total of 8 principal eigenvalues; the received signal is projected onto the signal subspace for data dimensionality reduction, using a whitening matrix. The whitening process is performed, and the observation signal of the real part I channel is obtained after the whitening process. , With a size of 8×1, it can be represented by equation (18): (18) From equations (12) and (18), we get: , It is a mixed matrix; In blind source separation, the inverse of the mixing matrix is ​​calculated. Equation (19) can be obtained; (19) The inverse matrix is ​​calculated using FastICA iteration. Due to the presence of errors, the inverse matrix is ​​approximated as follows: ,matrix Also known as the unmixing matrix; after obtaining the unmixing matrix, the data sequence vector can be obtained by equation (19). Estimate , that is, the independent components extracted after FastICA; The expression is as shown in equation (20): (20) Similarly, after the same processing, the data sequence vector of the received Q-channel data can be obtained. This refers to the independent components extracted after FastICA.

3. The single-channel mixed signal demodulation method based on oversampling according to claim 2, characterized in that, Step three is implemented as follows: The data sequence vector separated by the FastICA algorithm needs to be carrier recovered using a phase-locked loop (PLL) to obtain baseband information; the PLL used is a Costas loop; a suitable phase detector is selected according to the signal type: the mixed signal includes BPSK signal and 16QAM signal, the arctangent phase detector method is selected for BPSK signal, and the d-power decision loop method is selected for 16QAM signal.

4. The single-channel mixed signal demodulation method based on oversampling according to claim 2, characterized in that, The specific method for centering the observation vector is as follows: The formula for centering the observation vector is shown in equation (21): (21) in, Represents the observation vector The mean of the observed vectors is zero after centering.

5. The single-channel mixed signal demodulation method based on oversampling according to claim 2, characterized in that, The specific method for calculating the unmixing matrix is ​​as follows: The unmixing matrix is The column vectors of the unmixing matrix are random vectors with unit norm, which serve as the initial separating vectors. express, The range of values ​​is Firstly, let ,right The iteration is performed, and the iteration formula is: (22) Among them, the function , for The derivative function; after each iteration, the derivative function is... Perform Schmidt orthogonalization; the orthogonalization formula is shown in equation (23); (23) in, The index of the column vector of the unmixing matrix is ​​represented; then normalization is performed by equation (24); (24) like If convergence is not achieved, continue iterating using equations (22), (23), and (24) until the calculation is complete. Convergence; when After convergence, for To update, i.e., to execute Then continue with Iterate until... At this point, the iterative calculation is complete, and the unmixing matrix is ​​obtained. .

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