A method for blind separation of joint frequency offset estimation of paired carrier multiple access signals in a single channel

Abstract

The application provides a kind of joint frequency offset estimation paired carrier multiple access signal single channel blind separation method, first using received signal to estimate each signal parameter, the initialization of channel filter is realized;Symbol sequence is searched, and the sampling waveform is reconstructed based on the current channel filter;Through the reconstructed sampling waveform and actual sampling waveform, the cumulative metric of survivor path is calculated and the update of survivor path is carried out based on cumulative metric;Based on the error model of frequency offset and channel filter coefficient, the channel estimation is updated path by path using extended Kalman filter;Finally, the channel filter coefficient of next symbol time is predicted through the optimal estimation of channel parameter.The application establishes the error transfer model of frequency offset and channel filter coefficient, separates the frequency offset error, carries out joint estimation with time invariant channel filter coefficient, fully utilizes the prior information that channel filter coefficient produces deterministic change under the driving of frequency offset error, and realizes the optimal estimation of channel parameter.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and more specifically, to a single-channel blind separation method for paired carrier multiple access signals based on joint frequency offset estimation. Background Technology

[0002] Single-channel blind separation of paired carrier multiple access (PCMA) signals is a special type of blind signal separation problem. A single-channel received signal is obtained by mixing two digitally modulated signals at the same frequency. This is a typical two-input, one-output model. It mainly utilizes the differences in frequency deviation, amplitude deviation, phase deviation, and timing deviation between the two source signals to achieve source signal separation through joint symbol detection and channel tracking.

[0003] Single-channel blind separation methods for PCMA signals can be divided into two categories based on their technical approach: one is separation followed by demodulation, with Independent Component Analysis (ICA) being a typical algorithm; the other is joint separation and demodulation, with Per-Survivor Processing (PSP) being a representative method. Joint separation and demodulation is based on the idea of ​​data recovery and, compared to separation followed by demodulation, can better utilize the relationship between symbols, channel parameters, and signal waveforms, exhibiting a significant performance advantage. The basic idea of ​​the PSP algorithm is to use the combined influence of signal parameters such as frequency offset, time delay, initial phase, and shaping filter coefficients as equivalent channel parameters. By embedding data-aided unknown channel parameter estimation techniques into the Viterbi algorithm structure, joint estimation of signal parameters and symbol sequences is achieved. In existing PSP-type methods, channel parameter tracking and estimation often employ adaptive filtering algorithms such as RLS and LMS, which mainly have the following drawbacks:

[0004] 1. In a constant-parameter channel, the effects of time delay, initial phase, and shaping filter coefficient errors on the equivalent channel parameters are static and do not change with time. They can be estimated as random constants. Although frequency offset error causes channel parameters to change with time, its time-varying nature can be described by a deterministic model. The adaptive filters in existing blind separation methods uniformly treat channel parameters as time-varying parameters for unconstrained free estimation, failing to fully utilize the intrinsic relationship between frequency offset error and equivalent channel parameters. This results in the inability to obtain the optimal estimate of signal parameters and poor estimation accuracy of channel parameters.

[0005] 2. When there is an error in the initial signal parameter estimation, the existing methods do not fully utilize the above-mentioned constraint relationship to take into account the frequency offset error estimation, resulting in an inaccurate error propagation model for the channel parameters and poor convergence ability of the blind separation algorithm.

[0006] 3. The tracking accuracy of channel parameters directly affects the cumulative measurement of surviving paths, which in turn affects the search for symbol sequences, ultimately leading to a discrepancy between the separation bit error rate and the theoretical value.

[0007] The key to solving the above problems and defects lies in constructing a rigorous error propagation model based on the PCMA signal model to describe the relationship between frequency offset error and equivalent channel filter coefficients, separating the frequency offset error from signal parameters that have static effects such as initial phase and time delay, and making full use of prior constraint information to carry out joint estimation.

[0008] The significance of solving the above problems and defects lies in making full use of the inherent constraints between signal parameters, obtaining the optimal estimate of signal parameters, improving the convergence ability of the algorithm and the estimation accuracy of channel parameters, and thus improving the performance of blind separation and demodulation. Summary of the Invention

[0009] The present invention aims to provide a single-channel blind separation method for paired carrier multiple access signals based on joint frequency offset estimation, so as to solve the above-mentioned problems.

[0010] This invention provides a single-channel blind separation method for paired carrier multiple access signals based on joint frequency offset estimation, comprising the following steps:

[0011] Step 1, Channel filter initialization: Estimate the signal parameters of the two source signals using the mixed signal, and convert the signal parameters into equivalent channel filter coefficients using the PCMA signal generation model;

[0012] Step 2, Symbol Sequence Search and Waveform Reconstruction: Based on the modulation scheme, a set of all symbol pairs is predefined. Within each symbol period, all possibilities of the current symbol are searched. The sampled waveform is reconstructed by combining the symbol sequence and the channel filter coefficients at the current moment.

[0013] Step 3, Survivor Path Update: For each currently retained surviving path, calculate the cumulative metric by comparing the reconstructed sampled waveform with the original sampled waveform, and delete or add surviving paths based on the cumulative metric;

[0014] Step 4, frequency offset error and signal parameter estimation for each path: Configure a channel estimator based on extended Kalman filter for each surviving path. The parameters to be estimated include the channel filter coefficients and frequency offset error of the two signals. Based on the error propagation model and observation error model of the parameters to be estimated, channel estimation and tracking are realized by Kalman filtering.

[0015] Step 5, Channel filter prediction based on frequency offset error: Correct the frequency offset of the two signals using the estimated value of the frequency offset error, and predict the channel filter coefficients at all sampling points in the next symbol period based on the corrected frequency offset, which are used for waveform reconstruction and surviving path update in the next symbol period.

[0016] Furthermore, in step 1, the channel filter initialization includes:

[0017] By sampling the PCMA signal y(t) at an oversampling rate of P, the baseband discrete-time model of the single-channel PCMA signal is obtained, which is expressed as:

[0018]

[0019] Where the superscript i represents the source signal number, i = 1, 2; h, ω, θ, τ represent amplitude, frequency offset, initial phase, and time delay, respectively; s m This represents the modulation symbol at time m, where the symbol rates of the two signals are assumed to be equal. Let i and k represent the phase of the i-th signal at the k-th sampling point within the n-th symbol period, respectively, and the equivalent pulse shaping filter be:

[0020]

[0021] T is the symbol period of the digital modulation signal; the frequency offset is decomposed as follows:

[0022]

[0023] in, The frequency offset estimate is Δω. i This is frequency offset error. By pre-estimating, the baseband discrete-time model of the single-channel separation of the PCMA signal can be rewritten in a simpler matrix form:

[0024] Y i (n)=F i (n)B i (n)S i (n)+v(n)

[0025] Where v(n) is additive white Gaussian noise, F i (n) represents the frequency offset estimate. Impact on signal sampling:

[0026]

[0027] S i (n) represents the symbol sequence at time n when the channel length is L:

[0028]

[0029] B i (n) is a P×L channel filter coefficient matrix, containing Impact on signal sampling dynamics The dimension is P×P, and h i ,θ i ,τ i and shaping filter g i static effects The dimension is P×L:

[0030]

[0031] After initial value estimation of h, ω, θ, τ, we obtain... Then, the channel filter coefficient matrix B is calculated and initialized according to the above formula. i (0).

[0032] Furthermore, in step 2, the symbol sequence search and waveform reconstruction include:

[0033] Let S be the set of all possible symbol pairs corresponding to the modulation scheme of the source signal, and let n be the current time. Then the symbol state of the j-th surviving path retained at time n-1 is: If the symbol being traversed is Then the symbol sequence within the channel length at time n is:

[0034]

[0035] Based on the above symbol sequence and the predicted value of the channel filter coefficient matrix at the current time. Substitute into the following formula to reconstruct the sampled waveform

[0036]

[0037] Furthermore, in step 3, the survivor path update includes:

[0038] Based on step 2, calculate the cumulative metric for the j-th path in a given symbolic traversal:

[0039]

[0040] If the currently retained path contains a sequence of symbols identical to the one traversed in this iteration, compare the cumulative metrics and keep the path with the smaller cumulative metric value; otherwise, check if there exists a value greater than M. j If the cumulative metric of (n) exists, the path corresponding to the largest cumulative metric found will be deleted, and the path currently traversed will be added as the surviving path.

[0041] Furthermore, in step 4, the path-by-path frequency offset error and signal parameter estimation include:

[0042] First, the channel response state vector corresponding to the i-th source signal is constructed as follows:

[0043]

[0044] in, Representation matrix The element at row P and column P, the channel response state vector X at different times, has the following recurrence relation:

[0045] X i (n)=Γ i X i (n-1)

[0046] in, Let be an LP+1 order symmetric matrix; by linearly expanding the above recurrence relation, taking the first-order part and considering the system noise W, we obtain the error propagation model of the state vector:

[0047] δX i (n)=Φ i (n)δX i (n-1)+W i (n)

[0048] Where, Φ i For an LP+1 order square matrix:

[0049]

[0050] Where, δX i (n) represents the error state, the superscript ~ represents the estimated value, and the superscript ∧ represents the predicted value. The column vector representing the first LP elements of the predicted channel response state is interposed with the channel filter coefficient matrix. Equivalent, O 1×LP It is a zero matrix of 1×LP;

[0051] By transforming the matrix form of the baseband discrete-time model of a single-channel PCMA signal, the observation error model is obtained:

[0052] Y i (n)=F i (n)D i (n)X i (n)=H i (n)X i (n)

[0053] in:

[0054]

[0055] in,[] P Let P be the p-th repeating term. Considering the observation noise V, the observation error model is expressed as:

[0056] δY i (n)=H i (n)δX i (n)+V i (n)

[0057] Based on the surviving path update completed in step 3, the symbol sequence of all paths is obtained. Substituting the estimated channel response state from the previous time step into the above equation, the coefficient matrix Φ in the observation error model is obtained. i (n), H i (n), and then the channel response state is estimated and tracked according to the classical formula of Kalman filtering to obtain the estimated value of the channel response state of the j-th path. right The channel filter coefficient matrix is ​​obtained by rearranging the first L×P terms.

[0058] Furthermore, in step 5, the channel filter prediction based on frequency offset error includes:

[0059] The optimal estimate of the channel filter coefficient matrix obtained at time n Based on this, combined with the optimal estimation of frequency offset error The prediction of the channel filter coefficient matrix at time n+1 is achieved according to the following formula.

[0060]

[0061] In obtaining Then, jump to step 2 to continue the symbol traversal and survivor path update at time n+1.

[0062] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0063] 1. This invention exhibits superior convergence performance in scenarios with significant frequency offset errors. Frequency offset errors cause the equivalent channel response to change over time. When the frequency offset error is large, the channel filter coefficients change rapidly, making it impossible for existing methods to track accurately. This invention, however, considers the impact of frequency offset in the channel state and tracks it in real time, demonstrating excellent frequency offset tracking and channel parameter convergence capabilities even in scenarios with large frequency offsets or frequency drift.

[0064] 2. This invention achieves accurate estimation of channel parameters. Channel filter coefficients estimated by existing algorithms generally do not satisfy the constraints inherent in the signal model, resulting in low parameter estimation accuracy. This invention establishes an error propagation model for frequency offset and channel filter coefficients, obtaining an accurate and complete description of the channel model and improving the estimation accuracy of channel parameters.

[0065] 3. This invention achieves a performance improvement in bit error rate for blind separation demodulation. The core of the PSP blind separation algorithm demodulation based on the data recovery concept lies in the accurate estimation and tracking of channel parameters. The more accurate the channel parameter estimation, the closer the distribution of the reconstructed sampled waveform is to the actual sampling, and the closer the bit error rate of separation demodulation is to the performance limit. Attached Figure Description

[0066] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0067] Figure 1 This is a flowchart of a single-channel blind separation method for paired carrier multiple access signals based on joint frequency offset estimation in an embodiment of the present invention. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0069] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0070] Example

[0071] like Figure 1 As shown, this embodiment proposes a single-channel blind separation method for paired carrier multiple access signals with joint frequency offset estimation, including:

[0072] Channel filter initialization: The signal parameters of the two source signals are estimated using the mixed signal, and the signal parameters are transformed into equivalent channel filter coefficients through the PCMA signal generation model;

[0073] Symbol sequence search and waveform reconstruction: Based on the modulation scheme, a set of all symbol pairs is predefined. Within each symbol period, all possibilities of the current symbol are searched. The sampled waveform is reconstructed by combining the symbol sequence and the channel filter coefficients at the current moment.

[0074] Survivor path update: For each currently retained survivor path, the cumulative metric is calculated by comparing the reconstructed sampled waveform with the original sampled waveform, and survivor paths are deleted or added based on the cumulative metric;

[0075] Path-by-path frequency offset error and signal parameter estimation: Configure a channel estimator based on extended Kalman filter for each surviving path. The parameters to be estimated include the channel filter coefficients and frequency offset error of the two signals. Based on the error propagation model and observation error model of the parameters to be estimated, channel estimation and tracking are realized by Kalman filtering.

[0076] Channel filter prediction based on frequency offset error: The frequency offset of the two signals is corrected by the estimated value of the frequency offset error. Based on the corrected frequency offset, the channel filter coefficients at all sampling points in the next symbol period are predicted and used for waveform reconstruction and surviving path update in the next symbol period.

[0077] Specifically, a single-channel blind separation method for paired carrier multiple access signals based on joint frequency offset estimation includes the following steps:

[0078] Step 1, Channel filter initialization:

[0079] By sampling the PCMA signal y(t) at an oversampling rate of P, the baseband discrete-time model of the single-channel PCMA signal is obtained, which is expressed as:

[0080]

[0081] Where the superscript i represents the source signal number, i = 1, 2; h, ω, θ, τ represent amplitude, frequency offset, initial phase, and time delay, respectively; s m This represents the modulation symbol at time m, where the symbol rates of the two signals are assumed to be equal. Let i and k represent the phase of the i-th signal at the k-th sampling point within the n-th symbol period, respectively, and the equivalent pulse shaping filter be:

[0082]

[0083] T is the symbol period of the digital modulation signal; the frequency offset is decomposed as follows:

[0084]

[0085] in, The frequency offset estimate is Δω. i This is frequency offset error. By pre-estimating, the baseband discrete-time model of the single-channel separation of the PCMA signal can be rewritten in a simpler matrix form:

[0086] Y i (n)=Fi (n)B i (n)S i (n)+v(n)

[0087] Where v(n) is additive white Gaussian noise, F i (n) represents the frequency offset estimate. Impact on signal sampling:

[0088]

[0089] S i (n) represents the symbol sequence at time n when the channel length is L:

[0090]

[0091] B i (n) is a P×L channel filter coefficient matrix, containing Impact on signal sampling dynamics The dimension is P×P, and h i ,θ i ,τ i and shaping filter g i static effects The dimension is P×L:

[0092]

[0093] After initial value estimation of h, ω, θ, τ, we obtain... Then, the channel filter coefficient matrix B is calculated and initialized according to the above formula. i (0).

[0094] Step 2, Symbol Sequence Search and Waveform Reconstruction:

[0095] Let S be the set of all possible symbol pairs corresponding to the modulation scheme of the source signal, and let n be the current time. Then the symbol state of the j-th surviving path retained at time n-1 is: If the symbol being traversed is Then the symbol sequence within the channel length at time n is:

[0096]

[0097] Based on the above symbol sequence and the predicted value of the channel filter coefficient matrix at the current time. Substitute into the following formula to reconstruct the sampled waveform

[0098]

[0099] Step 3, Survivor path update includes:

[0100] Based on step 2, calculate the cumulative metric for the j-th path in a given symbolic traversal:

[0101]

[0102] If the currently retained path contains a sequence of symbols identical to the one traversed in this iteration, compare the cumulative metrics and keep the path with the smaller cumulative metric value; otherwise, check if there exists a value greater than M. j If the cumulative metric of (n) exists, the path corresponding to the largest cumulative metric found will be deleted, and the path currently traversed will be added as the surviving path.

[0103] Step 4, path-by-path frequency offset error and signal parameter estimation includes:

[0104] First, the channel response state vector corresponding to the i-th source signal is constructed as follows:

[0105]

[0106] in, Representation matrix The element at row P and column P, the channel response state vector X at different times, has the following recurrence relation:

[0107] X i (n)=Γ i X i (n-1)

[0108] in, It is an LP+1 order symmetric matrix; the above recursive formula contains nonlinear components, due to Δω i Since the magnitude is very small, a linear expansion of the above recurrence relation, taking the first-order part and considering the system noise W, yields the error propagation model of the state vector:

[0109] δX i (n)=Φ i (n)δX i (n-1)+W i (n)

[0110] Where, Φ i For an LP+1 order square matrix:

[0111]

[0112] Where, δX i (n) represents the error state, the superscript ~ represents the estimated value, and the superscript ∧ represents the predicted value. The column vector representing the first LP elements of the predicted channel response state is interposed with the channel filter coefficient matrix. Equivalent (mutual conversion through element rearrangement), O 1×LP It is a zero matrix of 1×LP;

[0113] By transforming the matrix form of the baseband discrete-time model of a single-channel PCMA signal, the observation error model is obtained:

[0114] Y i (n)=F i (n)D i (n)X i (n)=H i (n)X i (n)

[0115] in:

[0116] D i (n)=diag({[S i (n)0]1,[S i (n)0]2,…,[S i (n)0] P-1 ,[S i (n)0] P})

[0117] in,[] P Let P be the p-th repeating term. Considering the observation noise V, the observation error model is expressed as:

[0118] δY i (n)=H i (n)δX i (n)+V i (n)

[0119] Based on the surviving path update completed in step 3, the symbol sequence of all paths is obtained. Substituting the estimated channel response state from the previous time step into the above equation, the coefficient matrix Φ in the observation error model is obtained. i (n), H i (n), and then the channel response state is estimated and tracked according to the classical formula of Kalman filtering to obtain the estimated value of the channel response state of the j-th path. right The channel filter coefficient matrix is ​​obtained by rearranging the first L×P terms.

[0120] Step 5, Channel filter prediction based on frequency offset error:

[0121] The optimal estimate of the channel filter coefficient matrix obtained at time n Based on this, combined with the optimal estimation of frequency offset error The prediction of the channel filter coefficient matrix at time n+1 is achieved according to the following formula.

[0122]

[0123] In obtaining Then, jump to step 2 to continue the symbol traversal and survivor path update at time n+1.

[0124] As described above, this invention proposes a single-channel blind separation method for paired carrier multiple access signals based on joint frequency offset estimation. The first step involves initializing the channel filter by estimating various signal parameters, including amplitude, frequency offset, initial phase, and time delay, using the received signal. The second step involves searching for the symbol sequence and reconstructing the sampled waveform based on the current channel filter. The third step calculates the cumulative metric of the surviving path using the reconstructed and actual sampled waveforms and updates the surviving path based on this cumulative metric. The fourth step uses an extended Kalman filter to update the channel estimation path path by path based on the error model of the frequency offset and channel filter coefficients. Finally, the optimal estimation of the channel parameters is used to predict the channel filter coefficients at the next symbol time, providing the necessary conditions for symbol search and waveform reconstruction at the next time step.

[0125] This invention differs from existing PSP blind separation methods based on RLS or LMS, which transform all signal parameters, including frequency offset, into equivalent channel response filter coefficients, treating them as time-varying parameters for free estimation and tracking. This invention establishes an error propagation model for frequency offset and channel filter coefficients, separating the frequency offset error and jointly estimating it with time-invariant channel filter coefficients (under constant-parameter channels). By fully utilizing the prior information of deterministic changes in channel filter coefficients driven by frequency offset error, optimal estimation of channel parameters is achieved.

[0126] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A single-channel blind separation method for paired carrier multiple access signals with joint frequency offset estimation, characterized in that, Includes the following steps: Step 1, Channel filter initialization: Estimate the signal parameters of the two source signals using the mixed signal, and convert the signal parameters into equivalent channel filter coefficients using the PCMA signal generation model; Step 2, Symbol Sequence Search and Waveform Reconstruction: Based on the modulation scheme, a set of all symbol pairs is predefined. Within each symbol period, all possibilities of the current symbol are searched. The sampled waveform is reconstructed by combining the symbol sequence and the channel filter coefficients at the current moment. Step 3, Survivor Path Update: For each currently retained surviving path, calculate the cumulative metric by comparing the reconstructed sampled waveform with the original sampled waveform, and delete or add surviving paths based on the cumulative metric; Step 4, frequency offset error and signal parameter estimation for each path: Configure a channel estimator based on extended Kalman filter for each surviving path. The parameters to be estimated include the channel filter coefficients and frequency offset error of the two signals. Based on the error propagation model and observation error model of the parameters to be estimated, channel estimation and tracking are realized by Kalman filtering. Step 5, Channel filter prediction based on frequency offset error: Correct the frequency offset of the two signals using the estimated value of the frequency offset error, and predict the channel filter coefficients at all sampling points in the next symbol period based on the corrected frequency offset, which are used for waveform reconstruction and surviving path update in the next symbol period. In step 1, the channel filter initialization includes: PCMA signal by By sampling at a multiple of the oversampling rate, the baseband discrete-time model of the PCMA signal single-channel separation is obtained, expressed as: Among them, superscript i Indicates the source signal number. i =1,2; These represent amplitude, frequency offset, initial phase, and time delay, respectively. express The modulation symbol at the specified time, here we assume the symbol rates of the two signals are equal; , They represent the first The road signal is in the first Within the nth symbol period, the first The phase and equivalent pulse shaping filter for each sampling point are as follows: Let be the symbol period of the digital modulation signal; the frequency offset is decomposed as follows: in, This is the frequency offset estimate. This is frequency offset error. By pre-estimating, the baseband discrete-time model of the single-channel separation of the PCMA signal can be rewritten in a simpler matrix form: in, It is additive white Gaussian noise. Indicates the frequency offset estimate Impact on signal sampling: Indicates the channel length is hour, The symbol sequence of time: for The channel filter coefficient matrix contains Impact on signal sampling dynamics , The dimension is ,as well as and shaping filter static effects , The dimension is : In the After completing the initial value estimation, we obtain Then, the channel filter coefficient matrix is ​​calculated and initialized according to the above formula. .

2. The single-channel blind separation method for paired carrier multiple access signals based on joint frequency offset estimation according to claim 1, characterized in that, Step 2, symbol sequence search and waveform reconstruction, includes: Let the set of all possible symbol pairs corresponding to the modulation scheme of the source signal be . The current time is ,but The first time to keep j The symbolic state of the surviving paths is If the symbol being traversed is ,but The symbol sequence within the channel length at time point is: Based on the above symbol sequence and the predicted value of the channel filter coefficient matrix at the current time. Substitute into the following formula to reconstruct the sampled waveform ; 。 3. The single-channel blind separation method for paired carrier multiple access signals based on joint frequency offset estimation according to claim 2, characterized in that, In step 3, the survivor path update includes: Based on step 2, calculate the first symbolic traversal. Cumulative metric for each path: If the currently retained path contains a symbol sequence identical to the one traversed in this iteration, compare the cumulative metrics and keep the path with the smaller cumulative metric; otherwise, check if there exists a path with a cumulative metric greater than the current one. If the cumulative metric exists, the path corresponding to the largest cumulative metric found will be deleted, and the path currently being traversed will be added as the surviving path.

4. The single-channel blind separation method for paired carrier multiple access signals based on joint frequency offset estimation according to claim 3, characterized in that, In step 4, the path-by-path frequency offset error and signal parameter estimation include: First, construct the... The channel response state vector corresponding to the source signal is as follows: in, Representation matrix No. OK The elements at column positions represent the channel response state vectors at different times. The following recurrence relation exists: in, ,for First-order symmetric matrix; perform a linear expansion of the above recurrence relation, take the first-order part, and consider system noise. The error propagation model of the state vector is obtained as follows: in, for Square matrix: in, Indicates the error status, superscript Indicates an estimated value, indicated by a superscript. Indicates the predicted value. The first value of the channel response state prediction A column vector consisting of elements, and the channel filter coefficient matrix. equivalence, for The zero matrix; By transforming the matrix form of the baseband discrete-time model of a single-channel PCMA signal, the observation error model is obtained: in: in, Indicates the first One repeated term, considering observation noise. The observation error model is expressed as: Based on the surviving path update completed in step 3, the symbol sequence of all paths is obtained. Substituting this sequence with the estimated channel response state from the previous time step into the above equation, the coefficient matrix in the observation error model is obtained. , Then, the channel response state is estimated and tracked according to the classical formula of Kalman filtering to obtain the first... Estimates of the channel response state of each path ,right The former The channel filter coefficient matrix is ​​obtained by rearranging the terms. .

5. The single-channel blind separation method for paired carrier multiple access signals based on joint frequency offset estimation according to claim 4, characterized in that, In step 5, the channel filter prediction based on frequency offset error includes: exist Optimal estimation of the channel filter coefficient matrix obtained at time 1 Based on this, combined with the optimal estimation of frequency offset error Implemented according to the following formula Prediction of the channel filter coefficient matrix at time step ; In obtaining Then, proceed to step 2 to continue. Symbolic traversal and survival path update at each moment.

Images