Method and device for joint blind estimation of dual synchronous sequences in PCMA system

Abstract

The present invention discloses a method and device for joint blind estimation of dual synchronization sequences in a PCMA system. Targeting amplitude-phase modulated PCMA signals, the method utilizes the structural characteristics of communication system data frames, employs the concept of subspace decomposition, and focuses on analyzing the singular value decomposition results of the signal correlation matrix under different conditions, achieving accurate estimation of the synchronization waveforms and sequences of the two signals. Simulation results demonstrate that the present invention is widely applicable to the blind estimation of synchronization waveforms and synchronization sequences for amplitude-phase modulated PCMA signals. Under low signal-to-noise ratio conditions, the algorithm outperforms the maximum likelihood estimation method. As the signal-to-noise ratio increases and the amount of data used increases, the estimation performance continues to improve, enabling high-precision estimation of the dual synchronization sequences of PCMA signals. This method provides a prerequisite for the application of data-assisted parameter estimation methods in engineering practice and lays an important foundation for PCMA signal modulation parameter estimation and subsequent blind separation technology research.

Description

Technical Field

[0001] The present invention relates to the technical field of PCMA signal blind estimation, and in particular to a method and device for joint blind estimation of dual synchronization sequences of a PCMA system. Background Art

[0002] Paired Carrier Multiple Access (PCMA) is a frequency-domain multiple access technology for satellite communications proposed by ViaSat. In a PCMA system, a satellite ground station receives a mixed signal consisting of a local signal (self-interference) and a remote ground station signal (useful signal) on the same frequency. In cooperative communication, the ground station knows the full content and parameters of the transmitted signal, enabling interference cancellation to achieve normal communication. In blind signal reception scenarios, the receiver lacks prior information and can only use single-channel blind separation to obtain the communication content.

[0003] Traditional blind separation techniques for PCMA mixed signals primarily rely on particle filtering and per-survivor processing (PSP). To reduce separation algorithm complexity, Gibbs sampling, iterative quantum genetic optimization, and stacking algorithms have been applied to PCMA signal blind separation. These traditional algorithms require accurate parameter estimates as initialization parameters, otherwise their performance will be severely impacted. With the advancement of deep learning technology, neural networks have also been applied to PCMA signal demodulation. These deep learning-based blind separation methods also require accurate parameter estimates as network initialization parameters.

[0004] In PCMA signal parameter estimation algorithms, methods that use synchronization sequences as data aids offer significant advantages over non-data-aided methods, such as higher accuracy and greater robustness. However, these data-aided parameter estimation methods often assume the synchronization sequence as a known condition, without providing an estimation method. Therefore, obtaining an accurate blind estimation of the synchronization sequence remains a pressing challenge for data-aided blind estimation of PCMA signal modulation parameters. Currently, no relevant literature has been found addressing this issue, so this paper focuses on blind synchronization sequence estimation for PCMA signals.

[0005] For traditional single-carrier signals, blind demodulation algorithms are relatively mature, and the demodulation results can be used to estimate the synchronization sequence. However, PCMA signals are co-frequency aliasing signals formed by the linear superposition of two amplitude-phase modulation (APM) signals. These signals differ in frequency, phase, delay, and amplitude, and therefore lack a mature blind separation scheme. This is especially true for high-order modulated PCMA signals, which are currently difficult to achieve blind separation and present significant challenges in estimating the synchronization sequence. Summary of the Invention

[0006] The present invention addresses the problem that in blind reception of PCMA signals, the synchronization sequence is often unpredictable, and the estimation of the two-way synchronization sequence must be obtained under the condition that separation and demodulation cannot be completed, which is a relatively difficult problem. A method and device for joint blind estimation of dual synchronization sequences in a PCMA system are proposed. Under the condition that the modulation rate is known, the relationship between the PCMA signal symbol frame length and the signal autocorrelation function is derived. By searching for the peak of the autocorrelation function, the symbol frame lengths of the two-way APM signals are estimated. The autocorrelation matrix is ​​decomposed using the singular value decomposition (SVD) theory, and the corresponding relationship between the matrix eigenvectors and the signal synchronization waveforms is derived. The differences in the decomposition results under different signal parameters are analyzed, and a synchronization waveform estimation method is given in each case. The synchronization waveform of the two-way APM signal is estimated. Based on this premise, under the condition that the synchronization waveform position is determined, local SVD processing is performed on the mixed signal at the synchronization waveform position to obtain a more accurate synchronization waveform estimate. The synchronization waveform is demodulated to obtain a synchronization sequence estimate, and the algorithm performance is evaluated by comparing it with an estimation method using the maximum likelihood (ML) principle.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] In one aspect, the present invention provides a method for joint blind estimation of dual synchronous sequences in a PCMA system, comprising:

[0009] Search the peak value of the signal autocorrelation function to estimate the frame length of the two-way amplitude-phase modulation PCMA signal;

[0010] The oversampled PCMA signal is segmented according to the frame length, and the autocorrelation matrix is ​​subjected to overall singular value decomposition to obtain a preliminary estimate of the synchronization waveform;

[0011] Perform local singular value decomposition on the mixed signal at the synchronous waveform position;

[0012] Demodulate the synchronization waveform to obtain the synchronization sequence estimate.

[0013] Furthermore, the estimation of the signal autocorrelation function Expressed as:

[0014]

[0015] where k = 0, 1, ..., K r , K r is less than N r And any number much greater than 1, that is, 1<<K r <N r , N r represents the length of the oversampled PCMA signal sample; ω i is the residual carrier angular frequency of the two-channel amplitude-phase modulated PCMA signals, i = 1 or 2. When i = 1, ω1 represents the residual carrier angular frequency of the first channel amplitude-phase modulated PCMA signal. When i = 2, ω2 represents the residual carrier angular frequency of the second channel amplitude-phase modulated PCMA signal. p is the oversampling multiple. h i is the instantaneous amplitude of the two-channel amplitude-phase modulation PCMA signals. When i=1, h1 represents the instantaneous amplitude of the first channel amplitude-phase modulation PCMA signal. When i=2, h2 represents the instantaneous amplitude of the second channel amplitude-phase modulation PCMA signal. Respectively represent the equivalent filter impulse response vector of the i-th APM signal under the oversampling multiples of l1 and l2; Respectively represent the symbol vectors of the i-th amplitude and phase modulated PCMA signal at time k1 and k2; T s represents the sampling interval, T s =T / p, where T is the symbol period and the two signals are the same; k1 represents the k1th symbol of the first amplitude-phase modulated PCMA signal, l1 represents the l1th sampling point of the k1th symbol of the first amplitude-phase modulated PCMA signal, k2 represents the k2th symbol of the second amplitude-phase modulated PCMA signal, and l2 represents the l2th sampling point of the k2th symbol of the second amplitude-phase modulated PCMA signal.

[0016] Furthermore, the two-way amplitude-phase modulation PCMA signal frame lengths are equal, and the estimation of the two-way amplitude-phase modulation PCMA signal frame lengths is for:

[0017]

[0018] in Indicates the peak position corresponding to the first frame length, and all peaks of the autocorrelation function are its multiples. is the estimation of the modulation rate of two-way amplitude-phase modulated PCMA signals, f s is the sampling rate, [·] means rounding to the nearest integer.

[0019] Furthermore, the estimation of the autocorrelation matrix Expressed as:

[0020] When (ω1-ω2)NT s =2mπ

[0021]

[0022] When (ω1-ω2)NT s ≠2mπ

[0023]

[0024] Where Λ′ is a diagonal matrix, σ v represents the standard deviation of Gaussian white noise, I represents the unit matrix, and there is

[0025]

[0026] Where N is the oversampling frame length; m = 0, ±1, ±2…; data matrix A = [y0, y1,…, y P-1 ],y0,y1,…,y P-1 is the observation set; g 1,0 、g 2,0 They represent the equivalent filter impulse response vectors of the first and second channel amplitude and phase modulated PCMA signals under 0 oversampling multiple respectively; g 1,p-1 、g 2,p-1 They represent the equivalent filter impulse response vectors of the first and second channel amplitude and phase modulated PCMA signals under the p-1 oversampling multiple respectively; Respectively The symbol vector of the first amplitude-phase modulated PCMA signal at time t; Respectively The symbol vector of the second amplitude-phase modulated PCMA signal at time t; Respectively represent the initial phases of the two-way amplitude-phase modulation PCMA signal carriers; Respectively represent the start and end positions of the first channel amplitude and phase modulation PCMA signal synchronization waveform; They respectively represent the start and end positions of the second amplitude-phase modulation PCMA signal synchronization waveform.

[0027] Furthermore, the overall singular value decomposition of the autocorrelation matrix is ​​performed, and three decomposition results are obtained under different conditions:

[0028] When (ω1-ω2)NT s =2mπ, the autocorrelation matrix Can be decomposed into

[0029]

[0030] in Ignoring the influence of the last two terms, we can assume that the eigenvalue λ and eigenvector u correspond to The first eigenvalue of and the first eigenvector Then the estimate of (b1+b2) is

[0031] When (ω1-ω2)NT s ≠2mπ, and When the autocorrelation matrix Can be decomposed into

[0032]

[0033] And a1=b1 / h1, a2=b2 / h2, η=h2 / h1, At this time, it can be considered that the eigenvalues ​​λ1, λ2 and the eigenvectors u1, u2 correspond to The eigenvalue of and eigenvectors Then the estimate of b1 is The estimate of b2 is

[0034] When (ω1-ω2)NT s ≠2mπ, and When the autocorrelation matrix Can be decomposed into

[0035]

[0036] In the formula At this point, it can be considered that the eigenvalue λ and the eigenvectors u1 and u2 correspond to The eigenvalue of and eigenvectors If u1 and In the same direction and u2 and In the same direction, the estimate of b1 is The estimate of b2 is

[0037] Furthermore, a preliminary estimate of the synchronization waveform is expressed as:

[0038]

[0039] In the formula l=0,...,p-1;

[0040] The value of the PCMA signal in the n-th frame synchronization waveform interval of the i-th signal can be expressed as

[0041]

[0042] Where n=0,1,2,…, is the Gaussian white noise sampling value. Since the two APM-type PCMA signals are statistically independent, z i,k (l) and The cross-correlation can be calculated as follows

[0043]

[0044] In the formula Synchronous waveform estimation z obtained by SVD decomposition i,k (l) and The phase difference of the real synchronous waveform contained in Approximate calculation, the true synchronization waveform of the n-th frame signal is estimated to be

[0045]

[0046] Where angle is the angle function.

[0047] Furthermore, when η≈1 and the total energy of the two synchronous waveforms is not equal, the vector The non-zero position waveform in the vector is obtained by the i-th signal Amplitude estimation in Then the true amplitude estimate of the i-th signal is Will Multiply the synchronous waveform by the coefficient A synchronous waveform estimate with true amplitude can be obtained; is the tth eigenvalue, is the t-th eigenvector, Indicates that the i-th signal is in the vector The amplitude estimate in Indicates that the i-th signal is in the vector Amplitude estimation in .

[0048] Another aspect of the present invention provides a device for joint blind estimation of dual synchronous sequences in a PCMA system, comprising:

[0049] The frame length estimation module is used to search for the peak of the signal autocorrelation function to estimate the frame length of the two-channel amplitude-phase modulation PCMA signal;

[0050] The synchronization waveform estimation module is used to segment the oversampled PCMA signal according to the frame length, perform overall singular value decomposition on the autocorrelation matrix, and obtain a preliminary estimate of the synchronization waveform;

[0051] Local singular value decomposition module, used to perform local singular value decomposition on the mixed signal at the synchronous waveform position;

[0052] The synchronization waveform demodulation module is used to demodulate the synchronization waveform and obtain the synchronization sequence estimation.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] This invention targets amplitude-phase modulation (APM)-type PCMA signals, utilizing the structural characteristics of communication system data frames and employing the concept of subspace decomposition. It focuses on analyzing the singular value decomposition results of the signal correlation matrix under different conditions, achieving accurate estimation of the synchronization waveforms and sequences of the two signals. Simulation results demonstrate that the invention is widely applicable to the blind estimation of synchronization waveforms and synchronization sequences of APM-type PCMA signals. Under low signal-to-noise ratio conditions, the algorithm outperforms the maximum likelihood estimation method. As the signal-to-noise ratio increases and the amount of data used increases, the estimation performance continues to improve, enabling high-precision estimation of the dual synchronization sequences of PCMA signals. This provides a prerequisite for the application of data-assisted parameter estimation methods in engineering practice and an important foundation for PCMA signal modulation parameter estimation and subsequent blind separation technology research. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a basic flow chart of a method for joint blind estimation of dual synchronization sequences in a PCMA system according to an embodiment of the present invention;

[0056] Figure 2 Schematic diagram of the PCMA mixed signal symbol frame structure according to an embodiment of the present invention;

[0057] Figure 3 This is a correlation matrix energy isolinear distribution diagram according to an embodiment of the present invention;

[0058] Figure 4 It is a local expansion of the time domain autocorrelation of a mixed signal of equal frame length according to an embodiment of the present invention;

[0059] Figure 5 It is a local expansion of the time domain autocorrelation of mixed signals with different frame lengths according to an embodiment of the present invention;

[0060] Figure 6 It is a local expansion of the time domain autocorrelation of the mixed modulation signal according to an embodiment of the present invention;

[0061] Figure 7 is the mean square error of frame length estimation under different data amounts in the embodiment of the present invention;

[0062] Figure 8 The embodiment of the present invention is an SVD decomposition of the main eigenvector envelope under the condition of unequal frequency difference amplitudes;

[0063] Figure 9 The embodiment of the present invention is an SVD decomposition of the main eigenvector envelope under the condition of equal frequency difference amplitude;

[0064] Figure 10 The main eigenvector envelope of the SVD decomposition under the condition of no frequency difference in the embodiment of the present invention;

[0065] Figure 11 This is the waveform recovery result of the embodiment of the present invention;

[0066] Figure 12 This is a constellation diagram for synchronous waveform demodulation of different modulation modes according to an embodiment of the present invention;

[0067] Figure 13 This is the 8PSK / 8QAM hybrid PCMA synchronous waveform demodulation constellation diagram of the embodiment of the present invention;

[0068] Figure 14 The demodulation bit error rate curve of the second 16QAM signal synchronization waveform under different signal-to-noise ratios in an embodiment of the present invention is shown;

[0069] Figure 15 The demodulation bit error rate curve of the second 16QAM signal synchronization waveform under different data amounts in the embodiment of the present invention is shown;

[0070] Figure 16 The present invention is a structural diagram of a device for joint blind estimation of dual synchronization sequences in a PCMA system. DETAILED DESCRIPTION

[0071] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments:

[0072] like Figure 1 As shown, a joint blind estimation method for dual synchronous sequences in a PCMA system includes:

[0073] Search the peak value of the signal autocorrelation function to estimate the frame length of the two-way amplitude-phase modulation PCMA signal;

[0074] The oversampled PCMA signal is segmented according to the frame length, and the autocorrelation matrix is ​​subjected to overall singular value decomposition to obtain a preliminary estimate of the synchronization waveform;

[0075] Perform local singular value decomposition on the mixed signal at the synchronized waveform position to further improve the estimation performance;

[0076] Demodulate the synchronization waveform to obtain the synchronization sequence estimate.

[0077] Specifically, the signal model of two-channel amplitude-phase modulation PCMA signals can be constructed as follows:

[0078] The complex baseband model of the PCMA signal using two amplitude and phase modulated signals can be expressed as

[0079]

[0080] Where h1(t) and h2(t) are the instantaneous amplitudes of the two APM signals, ω1 and ω2 are the residual carrier angular frequencies of the two signals, θ1 and θ2 are the initial phases of the two signals, and v(t) is the additive white Gaussian noise with independent real and imaginary parts, and the variance is a1(t) and a2(t) are the baseband modulation signals of the two APM signals, which can be expressed as

[0081]

[0082] Where α i (n) represents the nth symbol sent by the i-th APM signal; g i (t) is the impulse response of the equivalent channel filter including the shaping filter, channel filter and matched filter; T is the symbol period, and the two signals are the same; τ i (t) is the relative time delay between the i-th signal and the local reference clock.

[0083] Assume that the equivalent channel filter response has a finite duration [-L1T, L2T], L = L1 + L2 + 1, and the instantaneous amplitude and relative delay of each signal are constant over a period of time, that is, h i (t) = h i , τ i (t) = τ i The mixed signal y(t) is measured at a time interval T s =T / p for sampling, where p is the oversampling multiple, which is a positive integer, and its oversampling discrete form can be obtained.

[0084]

[0085] Where l = 0, ..., p-1, y k (l) = y[(k+l / p)T], Gaussian white noise sampling value v k (l) = v[(k+l / p)T].

[0086] The useful signal sampling value can be expressed as

[0087]

[0088] Define the symbol vector of the i-th APM signal at time k as

[0089] s i,k =[α i (k-L1),…,α i (k+L2)] T (5)

[0090] The equivalent filter impulse response vector of the i-th APM signal is

[0091] g i,l =[g i (L1T+lT / p-τ i ),...,g i (-L2T+lT / p-τ i )] T (6)

[0092] Then x k (l) can be expressed as vector multiplication

[0093]

[0094] 1 frame length estimation

[0095] When the bit stream data transmitted by both parties in satellite communication has a frame structure, it generally has a fixed synchronization bit and data frame length. Then the baseband symbol obtained after APM modulation also has a fixed synchronization symbol and symbol frame length, and then the oversampling form of the signal also has a synchronization waveform and oversampling frame length. The PCMA mixed signal symbol frame structure is as follows: Figure 2 As shown, H i is the length of the synchronization symbol of the APM-type PCMA signal of the i-th channel, n i It is the starting position of the synchronization symbol of the i-th APM-type PCMA signal.

[0096] Take the length N r Oversampled PCMA mixed signal sample y k (l), when the data length N r When it is large enough, its autocorrelation function R y The estimate of (k) can be expressed as

[0097]

[0098] Where k = 0, 1, ..., K r , 1<<K r <N r Substitute equation (7) into equation (8), and take into account the vector s i,k The elements in obey the uniform distribution with mean zero, and the two APM-like PCMA signals are independent of each other.

[0099]

[0100] Assume that the number of frames of the two APM-type PCMA signals contained in the PCMA signal sample is much greater than 1. From formula (9), it can be seen that if the sequence and sequence sequence and sequence are unrelated to each other, then If sequence and sequence or sequence and sequence If there is a correlation between The stronger the correlation The larger the value of k is, the greater the correlation is. When k aligns the synchronization symbols of the first signal or the second signal, the correlation is the greatest. A maximum value appears. Assume that the symbol frame length of the i-th signal is Two-way APM type PCMA signal modulation rate R B are equal and their estimates are The sampling rate is f s , exist The maximum value appears at the integer multiple position. Therefore, by searching the correlation function, it is estimated The peak value of the two-way APM-type PCMA signal symbol frame length can be estimated

[0101]

[0102] The symbol [·] indicates rounding to the nearest integer. PCMA signal modulation rate estimation It can be obtained using the cyclic correlation method. In this paper, the modulation rate is taken as a known condition.

[0103] 2 Synchronous sequence estimation

[0104] For structures such as Figure 2 The PCMA signal shown is generally considered to have the same symbol frame length as the two APM-type PCMA signals. Oversampling frame length N = pN s , the oversampled signal vector of the nth frame can be expressed as

[0105] y n =x n +v n (11)

[0106] Where n = 0, 1, ...; is the useful signal vector of the nth frame, where is the Gaussian white noise vector of the nth frame, where

[0107] Define vector y n The autocorrelation matrix is

[0108]

[0109] For an observation set The data matrix is ​​defined as A = [y0,y1,…,y P-1], according to the singular value decomposition theory, the data matrix A N×P It can be decomposed into A=UΣV H , where U N×N and V P×P is an orthogonal normalized matrix, that is, U -1 =U H , V -1 =V H , the matrix Σ has the following form

[0110]

[0111] Where m≤min(P,N), σ1≥σ2≥...≥σ m are the singular values ​​of the data matrix A and are real numbers greater than zero. The estimate of the correlation matrix R is

[0112]

[0113] in is a diagonal square matrix; is the correlation matrix estimate The characteristic value of is the column vector of U, which is the orthogonal normalized left singular vector or correlation matrix estimate of the data matrix A The eigenvector of .

[0114]

[0115] in

[0116]

[0117] Substituting formula (7) into the above formula, we can get

[0118]

[0119] Where 0≤l1,l2≤p-1,0≤k1,k2≤N s -1.

[0120] Assume that the two APM-type PCMA signals are asynchronous, that is, the synchronization symbols do not overlap in time. In one frame of data, the synchronization symbol position interval of the two signals is k1∈[r1 (1) ,r2 (1) ],k2∈[r1 (2) ,r2 (2) ], and r2 (2) >r1 (2) >r2 (1) >r1 (1) >0.

[0121] when or And pk1+l1≠pk2+l2, that is, k1≠k2 or l1≠l2, since the asynchronous part of the data is randomly distributed, for different frame numbers n, There is no correlation between them. When the amount of data P is large enough

[0122]

[0123] when or And pk1+l1=pk2+l2, that is, k1=k2 and l1=l2

[0124]

[0125] When k1,k2∈[r1 (1) ,r2 (1) ]∪[r1 (2) ,r2 (2) ], expand and simplify formula (17) and define Define p1 to p4 as

[0126]

[0127] at this time

[0128]

[0129] Substitute (20) into the above equation and note that due to the existence of the synchronization sequence, when k i ∈[r1 (i) ,r2 (i) ] can be approximately considered

[0130] It can be proved that when pk1+l1=pk2+l2, that is, k1=k2 and l1=l2, the same result as formula (19) can be obtained.

[0131] When pk1+l1≠pk2+l2, that is, k1≠k2 or l1≠l2

[0132]

[0133] If (ω1-ω2)NT s =2mπ, m=0,±1,±2…

[0134]

[0135] If (ω1-ω2)NT s ≠2mπ, m=0,±1,±2…

[0136]

[0137] Substituting equations (16) to (24) into equation (15), we can obtain the equation (ω1-ω2)NT s =2mπ, it is approximately considered

[0138]

[0139] When (ω1-ω2)NT s ≠2mπ, it is approximately considered

[0140]

[0141] Where Λ′ is a diagonal matrix. And

[0142]

[0143] In the formula Then, we can get an estimate of b1 and b2, and thus an estimate of the synchronous waveforms of the two signals and their locations.

[0144] In formula (11) and the above derivation, it is assumed that the data starting point k = 0, l = 0. In fact, when the data is segmented according to the frame length, the starting point position is changed under the premise of ensuring that a frame of data contains a complete synchronization waveform, and the derivation results are similar.

[0145] When (ω1-ω2)NT s =2mπ, the autocorrelation matrix The energy distribution of Figure 3 As shown in (a), the main energy is concentrated in the matrix diagonal and the position of the autocorrelation operation and cross-correlation operation of the two-way APM-type PCMA signal synchronization waveform; when (ω1-ω2)NT s ≠2mπ, the autocorrelation matrix The energy distribution of Figure 3 As shown in (b), the main energy is concentrated on the matrix diagonal and the position of the autocorrelation operation of the synchronous waveform of the two APM-like PCMA signals.

[0146] According to the singular value decomposition theory, the autocorrelation matrix By performing singular value decomposition, three decomposition results can be obtained under different conditions.

[0147] Decomposition result 1 when (ω1-ω2)NT s =2mπ, according to matrix decomposition theory, there is the following relationship

[0148] (b1+b2)(b1+b2) H (b1+μb2)=λ(b1+μb2) (28)

[0149] Where λ is the matrix (b1+b2)(b1+b2) HThe eigenvalues ​​of the matrix are the linear combinations of b1 and b2 (b1+μb2), where μ is a real number. Let h2=ηh1, b1=h1a1, b2=h2a2, λ=λ′h1 2 , μ = ημ′, then Equation (28) can be re-expressed as

[0150] (a1+ηa2)(a1+ηa2) H (a1+μ′a2)=λ′(a1+μa2) (29)

[0151] Note that the two signals are asynchronous, so there is an approximate equality relationship Simplifying equation (29) yields the following equation:

[0152]

[0153] Solving the above equation we get

[0154]

[0155] So the matrix (b1+b2)(b1+b2) H Only one eigenvalue Corresponding to the only normalized eigenvector

[0156] At this time, the autocorrelation matrix Can be decomposed into

[0157]

[0158] in Ignoring the influence of the last two terms, we can assume that the eigenvalue λ and eigenvector u correspond to The first eigenvalue of and the first eigenvector Then the estimate of (b1+b2) is

[0159] When (ω1-ω2)NT s When ≠2mπ, according to matrix decomposition theory, the following relationship exists

[0160]

[0161] Similarly, the equation can be simplified to

[0162]

[0163] Solving the above equation, we can get two situations.

[0164] Decomposition result 2 When μ′=0, Since μ′=0, it is easy to get another eigenvalue by symmetry At this time the matrix There are two eigenvalues and The corresponding two normalized eigenvectors are and

[0165] At this time, the autocorrelation matrix Can be decomposed into

[0166]

[0167] and At this time, it can be considered that the eigenvalues ​​λ1, λ2 and the eigenvectors u1, u2 correspond to The eigenvalue of and eigenvectors Then the estimate of b1 is The estimate of b2 is

[0168] Decomposition result 3 When , the eigenvalue λ′ is a double characteristic root, And the two corresponding eigenvectors are orthogonal, μ=±η. Then the matrix There are two equal eigenvalues The corresponding orthogonal normalized eigenvectors are and In actual signal processing This is a special case. A common case is when the amplitude ratio η=1 and the total energy of the two synchronization waveforms is equal. For MPSK signals, that is, the synchronization symbol lengths are equal; for QAM signals, it is very likely that the synchronization symbols of the two signals are the same.

[0169] At this time, the autocorrelation matrix Can be decomposed into

[0170]

[0171] In the formula At this point, it can be considered that the eigenvalue λ and the eigenvectors u1 and u2 correspond to The eigenvalue of and eigenvectors If u1 and In the same direction and u2 and In the same direction, the estimate of b1 is The estimate of b2 is

[0172] In actual signals, this situation usually occurs when η≈1 and the total energy of the two synchronous waveforms is equal, but due to the influence of the matrix The last two terms Λ′ and Due to the influence of , the matrix decomposition may not get completely equal double roots, the eigenvalues ​​and eigenvectors have greater randomness, and the above method is no longer valid, but it still satisfies

[0173]

[0174] Substituting equation (37) into equation (36) yields

[0175]

[0176] Arranged x1x2=-y1y2, ρ1, ρ2>0. Since the eigenvector The direction problem is that the signs of the coefficients x1, x2, y1, and y2 are difficult to determine, which can be solved by the vector The amplitude of the waveform at non-zero position in the The i-th signal in the vector The amplitude estimation in the ith channel is Will Multiply the synchronous waveform by the coefficient A synchronous waveform estimate with true amplitude can be obtained.

[0177] The above method can be used to obtain the synchronous waveforms of two APM-type PCMA signals respectively.

[0178]

[0179] In the formula l=0,...,p-1.

[0180] The value of the PCMA signal in the n-th frame synchronization waveform interval of the i-th signal can be expressed as

[0181]

[0182] Where n=0,1,2,…. Since the two APM-like PCMA signals are statistically independent, z i,k (l) and The cross-correlation can be calculated as follows

[0183]

[0184] In the formula From Equation (41), we can see that the synchronization waveform estimate z obtained by SVD decomposition is i,k (l) and The phase difference of the real synchronous waveform contained in Approximate calculation, the true synchronization waveform of the n-th frame signal is estimated to be

[0185]

[0186] In summary, by decomposing the data autocorrelation matrix using SVD and solving for vectors b1 and b2, we can estimate the synchronization waveforms of the two APM signals and their positions in the data frame. The synchronization waveform is estimated to be a conventional single-carrier signal, which is easy to demodulate. By demodulating the synchronization waveform, we can obtain an estimate of the dual-path synchronization sequence.

[0187] In the above derivation, a large number of approximate calculations are used, so the synchronization waveform estimation obtained using the above SVD decomposition method has a certain performance loss. Therefore, after obtaining the estimation of the positions of the two synchronization waveforms, the mixed signals of the synchronization waveform positions can be taken out respectively, and the correlation matrix can be constructed for SVD decomposition to obtain a more accurate synchronization waveform estimation. The derivation process is similar and will not be proved in this article.

[0188] 3 Simulation Analysis

[0189] To verify the effectiveness of the algorithm in this paper, experiments are designed to estimate the frame length and synchronization waveform of the PCMA signal, demodulate the synchronization waveform to obtain a dual synchronization sequence, and estimate the bit error rate through the synchronization sequence to verify the estimation performance.

[0190] Experiment 1 takes the QPSK modulated PCMA mixed signal as an example. The simulation conditions are: sampling rate 20MHz, symbol rate 5MBd, raised cosine filter roll-off coefficient 0.35, two-way QPSK signal symbol frame length 1046, synchronization symbol length 52, amplitude h1 = 0.5, h2 = 0.4, frequency offset f1 = 500Hz, f2 = -500Hz, delay τ1 = 0.1T, τ2 = 0.5T, and the mixed signal signal-to-noise ratio E s When / N0=12dB, the mixed signal is autocorrelated at 20,000 sampling points. The simulation results are as follows: Figure 4 shown.

[0191] from Figure 4 It can be seen from Figure 1 that the autocorrelation function of the mixed signal has a peak near the integer multiple of the oversampling frame length.

[0192] Adjust the symbol frame length of the second QPSK signal to 900, and keep the other signal parameters unchanged. The simulation results are as follows: Figure 5 As shown. Figure 5 It can be seen from FIG that the mixed signal autocorrelation function has a peak near the integer multiple of the first signal oversampling frame length, and also has a peak near the integer multiple of the second signal oversampling frame length.

[0193] Adjust the modulation mode of the second signal to BPSK, keep the symbol frame length to 900, and keep other parameters unchanged. The simulation results are as follows Figure 6 As shown. Figure 6 It can be seen that the peak position of the mixed signal autocorrelation function and Figure 5 Consistent in.

[0194] The results of Experiment 1 show that regardless of whether the frame lengths and modulation modes of the two signals contained in the PCMA mixed signal are the same, the autocorrelation function peak search method can effectively estimate the symbol frame length.

[0195] Experiment 2 is to verify the autocorrelation length K r The impact of frame length estimation performance, taking the QPSK modulated PCMA mixed signal as an example, uses data with different frame numbers for autocorrelation. The simulation conditions are: sampling rate 20MHz, symbol rate 5MBd, raised cosine filter roll-off coefficient 0.35, two-way QPSK signal symbol frame length 1046, synchronization symbol length 52, amplitude h1 = 0.5, h2 = 0.4, frequency offset f1 = 500Hz, f2 = -500Hz, delay τ1 = 0.1T, τ2 = 0.5T, mixed signal signal-to-noise ratio E s / N0=6dB.k n Indicates the position of the nth peak of the autocorrelation function, 1 <n<N e , then the estimation of the oversampling frame length N can be expressed as The mean square error of frame length estimation can be expressed as The estimated mean square error obtained using different data amounts is as follows: Figure 7 shown.

[0196] from Figure 7 It can be seen from the figure that with the increase of autocorrelation length, the mean square error of frame length estimation continues to decrease. When using more than 60 frames of data under low signal-to-noise ratio, the mean square error reaches below 0.2, and the correct frame length estimation can be obtained.

[0197] Experiment 3 takes 8PSK modulated PCMA signal as an example, with sampling rate of 125MHz, symbol rate of 5MBd, raised cosine filter roll-off coefficient of 0.35, duration of 8 symbol lengths, two-way 8PSK signal symbol frame length of 700, synchronization symbol length of 16, synchronization symbol starting position of 20th symbol and 100th symbol respectively, amplitude of h1=0.5, h2=0.4 respectively, frequency deviation of f1=500Hz, f2=-500Hz respectively, delay of τ1=0.1T, τ2=0.5T respectively, mixed signal signal-to-noise ratio E s / N0=15dB, take 200 frames of data, the SVD decomposition result is as follows Figure 8 shown.

[0198] Figure 8 middle They are equal to the square root of the first and second eigenvalues ​​of the data autocorrelation matrix multiplied by the eigenvector, corresponding to (ω1-ω2)NT s ≠2mπ and The amplitude envelope plot shows that f1 and f2 exhibit high amplitudes of approximately 0.5 and 0.4, respectively, in the synchronization waveforms of the two 8PSK signals, which are close to the original signal envelope amplitudes. This indicates that the vectors derived from SVD decomposition can be used to estimate the synchronization waveform positions and the amplitudes of the two signals.

[0199] The amplitude condition is set to h1=h2=1.0, and the decomposition result is as follows Figure 9 shown. Figure 9 The amplitude envelope in corresponds to (ω1-ω2)NT s ≠2mπ and Situation. Figure 9 It can be seen that b1 and b2 have energy distribution in f1 and f2, and ρ1≈0.8 and ρ2≈0.6, which meets the above derivation. In fact, this is also a manifestation of the law of conservation of energy. The sum of the energies of b1 and b2 distributed in f1 and f2 is equal to their respective total energies.

[0200] Adjust the two frequency deviations f1 = f2 = 0Hz, and the decomposition results are as follows Figure 10 shown. Figure 10 Medium amplitude envelope corresponds to (ω1-ω2)NT s =2mπ, then f1=b1+b2, and all the synchronization waveforms are contained in vector f1.

[0201] Under the initial conditions, the phase of the synchronous waveform is corrected and compared with the original signal waveform. The simulation results are as follows Figure 11 shown. Figure 11 The dotted line is the real signal waveform, and the solid line is the waveform restored according to the algorithm in this paper. Figure 11 It can be seen that the synchronous waveform can be effectively restored by using the method in this paper.

[0202] Experiment 4 uses the proposed method to obtain the synchronization waveform and demodulate the PCMA mixed signal using 8PSK, 16QAM and other modulation modes. The simulation conditions are: sampling rate 20MHz, symbol rate 5MBd, raised cosine filter roll-off coefficient 0.35, amplitude h1 = 1.0, h2 = 0.8, frequency offset f1 = 500Hz, f2 = -500Hz, delay τ1 = 0.1T, τ2 = 0.5T, all modulation signal frame lengths are set to 1024, synchronization symbol length 52, mixed signal signal-to-noise ratio E s / N0=10dB. SVD decomposition uses data frame number P=200, and the synchronous waveform demodulation constellation diagram is as follows Figure 12 shown.

[0203] It can be seen from the demodulated constellation diagram that the synchronization waveform estimated by the proposed method can effectively recover the synchronization sequence.

[0204] The PCMA signal is changed to 8PSK / 8QAM mixed modulation mode, and other conditions remain unchanged. The simulation results are as follows Figure 13 As shown in Figure 2, the synchronous waveform demodulation constellation diagram shows that the proposed algorithm is also effective for PCMA signals using hybrid modulation.

[0205] To verify the performance of the algorithm, taking the 16QAM modulated PCMA signal as an example, 100 frames of data are used to estimate the synchronization sequence of the PCMA mixed signal under different signal-to-noise ratios. First, the signal is segmented by frame and the overall SVD decomposition is performed to obtain the synchronization waveform position estimation. Then, the SVD decomposition method and the maximum likelihood method are used to perform local processing on the mixed data of the synchronization waveform position to obtain the synchronization waveform, and then the synchronization sequence estimation is obtained by demodulation. The bit error rate curve of the synchronization sequence estimation of one signal with amplitude h2 = 0.8 is shown as follows Figure 14 shown. Figure 14 Middle horizontal coordinate The amplitude h2 = 0.8 represents the ratio of the energy per bit of the signal to the power density of Gaussian white noise.

[0206] from Figure 14 It can be seen that the local SVD decomposition method and the local maximum likelihood method have significantly improved estimation performance compared with the overall SVD decomposition method; under low signal-to-noise ratio conditions, the local SVD decomposition method is better than the local maximum likelihood method, and under high signal-to-noise ratio conditions, the performance of the two methods is similar.

[0207] In order to verify the impact of data volume on algorithm performance, we still take the 16QAM modulated PCMA signal as an example. Under different signal-to-noise ratio conditions, we use data of different frame numbers and obtain the synchronization waveform according to the method of first global and then local SVD decomposition. The synchronization sequence estimation is obtained by demodulation. The bit error rate curve of the synchronization sequence estimation of one channel with amplitude h2 = 0.8 is shown as follows: Figure 15 shown.

[0208] The signal with amplitude h1 = 1.0 has a higher signal-to-noise ratio than the signal with amplitude h2 = 0.8, and can obviously achieve a better estimation effect.

[0209] The results of Experiment 4 show that the proposed method can effectively estimate the synchronization waveform of PCMA signals using single APM modulation and mixed APM modulation, and thus obtain dual synchronization sequence estimation. Moreover, the proposed method performs better than the maximum likelihood estimation method under low signal-to-noise ratio conditions. As the signal-to-noise ratio improves and the amount of data used increases, the estimated bit error rate continues to decrease, and high-precision dual synchronization sequence estimation of PCMA signals can be obtained.

[0210] Based on the above embodiments, Figure 16 As shown, the present invention also proposes a PCMA system dual synchronization sequence joint blind estimation device, comprising:

[0211] The frame length estimation module is used to search for the peak of the signal autocorrelation function to estimate the frame length of the two-channel amplitude-phase modulation PCMA signal;

[0212] The synchronization waveform estimation module is used to segment the oversampled PCMA signal according to the frame length, perform overall singular value decomposition on the autocorrelation matrix, and obtain a preliminary estimate of the synchronization waveform;

[0213] The local singular value decomposition module is used to perform local singular value decomposition on the mixed signal at the synchronous waveform position to further improve the estimation performance;

[0214] The synchronization waveform demodulation module is used to demodulate the synchronization waveform and obtain the synchronization sequence estimation.

[0215] In summary, in the PCMA signal blind separation scenario, the present invention proposes a joint blind estimation method and device for dual synchronization sequences of PCMA system on the basis of known modulation rate, derives the relationship between the PCMA signal symbol frame length and the PCMA mixed signal autocorrelation function, and obtains the estimation of the symbol frame length of the two-way APM signal by searching the peak of the autocorrelation function; applies the singular value decomposition theory to the PCMA signal blind separation problem, derives the corresponding relationship between the eigenvector of the autocorrelation matrix and the signal synchronization waveform, focuses on analyzing the influence of parameters such as frequency deviation and total energy of the synchronization waveform on the decomposition result, and obtains the synchronization waveform of the two-way APM signal under different conditions. The proposed method is used to estimate the shape of the synchronous waveform, and the synchronous sequence is estimated by demodulating the synchronous waveform under different signal-to-noise ratio and data volume conditions, and then compared with the maximum likelihood estimation method. From the simulation results, it can be seen that the proposed method is better than the maximum likelihood estimation method under low signal-to-noise ratio conditions, and the effect is similar to the maximum likelihood estimation method under high signal-to-noise ratio conditions. With the improvement of signal-to-noise ratio and the increase of data volume, the estimated bit error rate continues to decrease, and a high-precision estimation of the dual synchronization sequence of the PCMA signal can be obtained, which provides a prerequisite for the application of data-assisted parameter estimation methods in engineering practice, and provides an important foundation for the research on PCMA signal modulation parameter estimation and subsequent blind separation technology.

[0216] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for joint blind estimation of dual synchronous sequences in a PCMA system, characterized by: include: Search the peak value of the signal autocorrelation function to estimate the frame length of the two-way amplitude-phase modulation PCMA signal; The oversampled PCMA signal is segmented according to the frame length, and the autocorrelation matrix is ​​subjected to overall singular value decomposition to obtain a preliminary estimate of the synchronization waveform; Perform local singular value decomposition on the mixed signal at the synchronous waveform position; Demodulate the synchronization waveform to obtain the synchronization sequence estimate.

2. The PCMA system dual synchronous sequence joint blind estimation method according to claim 1, characterized in that: Estimation of signal autocorrelation function Expressed as: where k = 0, 1, ..., K r , K r is less than N r And any number much greater than 1, that is, 1<<K r <N r , N r represents the length of the oversampled PCMA signal sample; ω i is the residual carrier angular frequency of the two-channel amplitude-phase modulated PCMA signals, i = 1 or 2. When i = 1, ω1 represents the residual carrier angular frequency of the first channel amplitude-phase modulated PCMA signal. When i = 2, ω2 represents the residual carrier angular frequency of the second channel amplitude-phase modulated PCMA signal. p is the oversampling multiple. h i is the instantaneous amplitude of the two-channel amplitude-phase modulation PCMA signals. When i=1, h1 represents the instantaneous amplitude of the first channel amplitude-phase modulation PCMA signal. When i=2, h2 represents the instantaneous amplitude of the second channel amplitude-phase modulation PCMA signal. Respectively represent the equivalent filter impulse response vector of the i-th APM signal under the oversampling multiples of l1 and l2; Respectively represent the symbol vectors of the i-th amplitude and phase modulated PCMA signal at time k1 and k2; T s represents the sampling interval, T s =T / p, where T is the symbol period and the two signals are the same; k1 represents the k1th symbol of the first amplitude-phase modulated PCMA signal, l1 represents the l1th sampling point of the k1th symbol of the first amplitude-phase modulated PCMA signal, k2 represents the k2th symbol of the second amplitude-phase modulated PCMA signal, and l2 represents the l2th sampling point of the k2th symbol of the second amplitude-phase modulated PCMA signal.

3. The PCMA system dual synchronous sequence joint blind estimation method according to claim 1, characterized in that: The two-way amplitude-phase modulation PCMA signal frame lengths are equal, and the estimation of the two-way amplitude-phase modulation PCMA signal frame lengths is performed. for: in Indicates the peak position corresponding to the first frame length, and all peaks of the autocorrelation function are its multiples; is the estimation of the modulation rate of two-way amplitude-phase modulated PCMA signals, f s is the sampling rate, [·] means rounding to the nearest integer.

4. The PCMA system dual synchronous sequence joint blind estimation method according to claim 2, characterized in that: Estimation of the autocorrelation matrix Expressed as: When (ω1-ω2)NT s =2mπ When (ω1-ω2)NT s ≠2mπ Where Λ′ is a diagonal matrix, σ v represents the standard deviation of Gaussian white noise, I represents the unit matrix, and there is Where N is the oversampling frame length; m = 0, ±1, ±2…; data matrix A = [y0, y1,…, y P-1 ],y0,y1,…,y P-1 is the observation set; g 1,0 、g 2,0 They represent the equivalent filter impulse response vectors of the first and second channel amplitude and phase modulated PCMA signals under 0 oversampling multiple respectively; g 1,p-1 、g 2,p-1 They represent the equivalent filter impulse response vectors of the first and second channel amplitude and phase modulated PCMA signals under the p-1 oversampling multiple respectively; Respectively represent r1 (1) 、 The symbol vector of the first amplitude-phase modulated PCMA signal at time t; Respectively represent r1 (2) 、 The symbol vector of the second amplitude-phase modulated PCMA signal at time t; Respectively represent the initial phases of the two amplitude-phase modulated PCMA signal carriers; r1 (1) 、 Respectively represent the start and end positions of the first channel amplitude and phase modulation PCMA signal synchronization waveform; r1 (2) 、 They respectively represent the start and end positions of the second amplitude-phase modulation PCMA signal synchronization waveform.

5. The PCMA system dual synchronous sequence joint blind estimation method according to claim 4, characterized in that: Performing overall singular value decomposition on the autocorrelation matrix, we can obtain three decomposition results under different conditions: When (ω1-ω2)NT s =2mπ, the autocorrelation matrix Can be decomposed into in Ignoring the influence of the last two terms, we can assume that the eigenvalue λ and eigenvector u correspond to The first eigenvalue of and the first eigenvector Then the estimate of (b1+b2) is When (ω1-ω2)NT s ≠2mπ, and When the autocorrelation matrix Can be decomposed into And a1=b1 / h1, a2=b2 / h2, η=h2 / h1, At this time, it can be considered that the eigenvalues ​​λ1, λ2 and the eigenvectors u1, u2 correspond to The eigenvalue of and eigenvectors Then the estimate of b1 is The estimate of b2 is When (ω1-ω2)NT s ≠2mπ, and When the autocorrelation matrix Can be decomposed into In the formula At this point, it can be considered that the eigenvalue λ and the eigenvectors u1 and u2 correspond to The eigenvalue of and eigenvectors If u1 and In the same direction and u2 and In the same direction, the estimate of b1 is The estimate of b2 is 6. The PCMA system dual-synchronous sequence joint blind estimation method according to claim 5, characterized in that: A preliminary estimate of the synchronization waveform is expressed as: In the formula The value of the PCMA signal in the n-th frame synchronization waveform interval of the i-th signal can be expressed as Where n=0,1,2,…, is the Gaussian white noise sampling value. Since the two APM-type PCMA signals are statistically independent, z i,k (l) and The cross-correlation can be calculated as follows In the formula Synchronous waveform estimation z obtained by SVD decomposition i,k (l) and The phase difference of the real synchronous waveform contained in Approximate calculation, the true synchronization waveform of the n-th frame signal is estimated to be Where angle is the angle function.

7. The PCMA system dual-synchronous sequence joint blind estimation method according to claim 5, characterized in that: When η≈1 and the total energy of the two synchronous waveforms is not equal, the vector The non-zero position waveform in the vector is obtained by the i-th signal Amplitude estimation in Then the true amplitude estimate of the i-th signal is Will Multiply the synchronous waveform by the coefficient A synchronous waveform estimate with true amplitude can be obtained; is the tth eigenvalue, is the t-th eigenvector, Indicates that the i-th signal is in the vector The amplitude estimate in Indicates that the i-th signal is in the vector Amplitude estimation in .

8. A joint blind estimation device for dual synchronous sequences in a PCMA system, characterized by: include: The frame length estimation module is used to search for the peak of the signal autocorrelation function to estimate the frame length of the two-channel amplitude-phase modulation PCMA signal; The synchronization waveform estimation module is used to segment the oversampled PCMA signal according to the frame length, perform overall singular value decomposition on the autocorrelation matrix, and obtain a preliminary estimate of the synchronization waveform; Local singular value decomposition module, used to perform local singular value decomposition on the mixed signal at the synchronous waveform position; The synchronization waveform demodulation module is used to demodulate the synchronization waveform and obtain the synchronization sequence estimation.

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