An iterative equalization method for AFDM systems

Abstract

The application discloses an iterative equalization method for an AFDM system, and belongs to the field of physical layer low-complexity signal processing of wireless communication. The application solves the problem of high complexity of the traditional iterative equalization method in the AFDM system. The application is adapted to the AFDM system, selects optimal Chirp parameters matched with a channel to transmit an AFDM signal, and after receiving the signal, expands the time domain according to a channel matrix to perform iterative equalization, wherein the external soft information output of the previous iteration is used as prior information for the next iteration, and different low-complexity operations are performed on the first iteration and the subsequent iterations according to different iteration numbers. The application effectively improves transmission reliability by using optimal Chirp parameter transmission and iterative equalization, and designs low-complexity strategies for different iteration numbers to ensure that the big matrix inversion operation is avoided, thereby overcoming the problem of high computational complexity of the traditional iterative equalization method in the AFDM system. The application can be applied to the field of signal processing of wireless communication.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of low-complexity signal processing in the physical layer of wireless communication, and particularly relates to an iterative equalization method for an AFDM (Affine Fourier Division Multiplexing) system. BACKGROUND

[0002] In the upcoming 6G communication, the application scenarios such as vehicle-to-everything, unmanned aerial vehicle communication and high-speed rail communication can be summarized as wireless communication scenarios under high-speed movement. When the communication device presents a high-speed movement state, the wireless channel presents a time-frequency double selection characteristic. The mainstream OFDM (Orthogonal Fourier Division Multiplexing) system at present will introduce subcarrier interference under the time-frequency double selection channel, which greatly reduces the transmission reliability. The AFDM communication system as a new emerging robust communication system can be regarded as a multi-carrier communication system composed of orthogonal Chirp signals, and shows excellent anti-interference performance in the double selection channel. The AFDM communication system can also quickly change the affine Fourier transform by adjusting the Chirp parameter, helping the communication system to better match the channel.

[0003] Excellent transmission performance needs not only excellent communication system, but also excellent signal processing technology. As a commonly used means to improve transmission reliability, the introduction of iterative equalization technology can further reduce the influence of subcarrier interference and noise. The soft information output by each equalizer is used as the input of the next equalizer, and through multiple soft information iterations, significant performance improvement can be brought. However, the traditional LMMSE (Linear Minimum Mean Square Error) iterative equalization method faces the challenge of high complexity of large matrix inversion when applied to the AFDM system, which is not conducive to the actual deployment and application of the receiver. Therefore, a low-complexity iterative equalization method for the AFDM system under the double selection channel is needed to effectively avoid the direct inversion of the matrix and better adapt to the AFDM system to ensure excellent performance. SUMMARY

[0004] The purpose of the present application is to solve the problem of high complexity of the traditional iterative equalization method in the AFDM system, and an iterative equalization method for the AFDM system is proposed.

[0005] The technical solution adopted by the present application to solve the above technical problems is:

[0006] An iterative equalization method for an AFDM system, the method specifically comprises the following steps:

[0007] At the transmitting end

[0008] Step one, modulate the input data with length of Nxl, get the affine field modulation sequence x;

[0009] Step two, select Chirp parameters c1 and c2, then based on Chirp parameters c1 and c2, perform the affine Fourier inverse transform on sequence x, get the time domain sequence s with length of Nxl;

[0010] Step three, perform the insertion of cyclic prefix processing on time domain sequence s, then transmit the processed time domain sequence to wireless channel via radio frequency link;

[0011] At the receiving end

[0012] Step four, perform the radio frequency processing and the removal of cyclic prefix operation on the signal received from wireless channel, get the sequence y with length of Nxl and time domain channel matrix H t ;

[0013] Step five, calculate the equivalent channel matrix H based on time domain channel matrix H t , and initialize the prior information m [1] =0 N×1 , diag(η [1] )=I N , I N is the unit matrix;

[0014] Step six, take m [1] and diag(η [1] )=I N as the input of the first iteration equalization, get the posterior information μ [1] =H H (Ψ [1] ) -1 y, Σ [1] =I N -H H (Ψ [1] ) -1 H, intermediate variable matrix represents the power of white noise, the superscript -1 represents the inverse of the matrix;

[0015] Step seven, calculate the input m [1] and η [1] of the second iteration equalization based on m [1] , η [1] , μ [2] and Σ [2] , calculate the posterior information μ [2] and Σ [2] of the output of the second iteration equalization based on m [2] and η [2] ;

[0016] The input m [1] and η [1] of the second iteration equalization are calculated according to m [1] , η [1] , μ [2] and Σ [2] , and the specific process is as follows:

[0017]

[0018] wherein subscript (n) represents the nth element of the vector, and (n, n) represents the element of the matrix in the nth row and the nth column;

[0019] Step eight, let the iteration number l=3;

[0020] Step nine, the input m [l-1] and η [l-1] of the lth iteration equalization are calculated according to m [l-1] , η [l-1] , μ [l] and Σ [l] ;

[0021]

[0022] wherein, is the average value of all elements in the vector η [l-1] ;

[0023] The posterior information μ [l] and Σ [l] of the lth iteration equalization output are calculated according to m [l] and η [l] ;

[0024] Step ten, judge whether the iteration number l reaches the set maximum iteration number or not;

[0025] If the set maximum iteration number is reached, the posterior information μ [l] output by the last iteration is used to make a decision output;

[0026] If the set maximum iteration number is not reached, let l=l+1, and then return to execute step nine.

[0027] Preferably, in the step one, the modulation mode adopted is PSK or QAM.

[0028] Preferably, the specific process of selecting Chirp parameters c1 and c2 is as follows:

[0029] 1) In the double-selected channel state, the Chirp parameter c1 is:

[0030]

[0031] wherein, denotes a floor operation, l p is the maximum delay tap of channel multipath propagation;

[0032] In the dual-selected channel state, the Chirp parameter c2 is arbitrarily selected;

[0033] 2) In the frequency-selected channel state, the Chirp parameter c1 is:

[0034]

[0035] wherein, k odd denotes an arbitrary odd number;

[0036] In the frequency-selected channel state, the Chirp parameter c2 is arbitrarily selected.

[0037] Preferably, the time-domain sequence s is:

[0038]

[0039] wherein, Λ c represents a diagonal matrix with as diagonal elements, i.e. c = c1 or c2, e is the base of natural logarithm, j is the imaginary unit, the upper index H represents the conjugate transpose, A H is the N x N affine inverse Fourier transform matrix, and F is the Fourier transform matrix.

[0040] Preferably, the specific process for calculating the equivalent channel matrix H t is as follows:

[0041] H = H t A H

[0042] Preferably, the calculation method of the posterior information μ [1] is as follows:

[0043] Ψ [1] is subjected to block matrix decomposition, is an (N-l p ) x (N-l p ) submatrix, is an l p x (N-l p ) submatrix, is an (N-l p ) x l p submatrix, is an l p x l psub-matrices of L Ψ [1] = L [1] U [1] , where L [1] and U [1] are lower and upper triangular matrices respectively, and are sub-matrices of L [1] , and are sub-matrices of U [1] ;

[0044] μ [1] is calculated according to the following numerical order:

[0045]

[0046] Preferably, the calculation method of the posterior information Σ [1] is:

[0047] Diag(H H (Ψ [1] ) -1 H) is approximated as (H H (Ψ [1] ) -1 H) (n,n) I N , then Σ [1] is:

[0048]

[0049] wherein, denotes the nth column of A H .

[0050] Preferably, the posterior information μ [l′] and Σ [l′] are:

[0051] μ [l′] = m [l′] + diag(η [l′] )H H (Ψ [l′] ) -1 (y-Hm [l′] )

[0052] Σ [l′] = diag(η [l′] )-diag(η [l′] )H H (Ψ [l′] ) -1 Hdiag(η[l′] )

[0053] wherein l' >= 2, the intermediate variable matrix is a vector [l′] is the average of all elements.

[0054] Preferably, the calculation method of the posterior information [l′] is:

[0055] diag(η [l′] ) is replaced by decomposition to obtain [l′] = L [l′] U [l′] , L [l′] and U [l′] are lower triangular matrix and upper triangular matrix obtained after LU decomposition, respectively, then [l′] is calculated according to the following numerical order:

[0056]

[0057] Preferably, the calculation method of the posterior information [l′] is:

[0058] diag(η [l′] ) is replaced by Diag(H H (Ψ [l′] ) -1 H) is approximated as (H H (Ψ [l′] ) -1 H) (n,n) I N , then

[0059]

[0060] The beneficial effects of the present application are:

[0061] The present application is adapted to the AFDM system, selects the optimal Chirp parameter of the matched channel to transmit the AFDM signal, and according to the iterative equalization of the time domain when the channel matrix is unfolded, the external information output of the previous iteration is output as the prior information of the next iteration, and different low complexity operations are performed on the first iteration and the subsequent iterations according to the different iteration numbers. The method of the present application effectively improves the transmission reliability by using the optimal Chirp parameter transmission and iterative equalization, and designs a low complexity strategy for different iteration numbers to ensure that it avoids the inverse operation of a large matrix, and overcomes the problem of high computational complexity of the traditional iterative equalization method in the AFDM system. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 This is a flowchart of an iterative equalization method for an AFDM system according to the present invention;

[0063] Figure 2 This is a comparison chart of the bit error rate between the low-complexity iterative equalization method proposed in this invention and other methods;

[0064] Figure 3 The bit error rate diagrams for the low-complexity iterative equalization method proposed in this invention under different modulation schemes and signal-to-noise ratios are shown. Detailed Implementation

[0065] Specific Implementation Method 1: Combination Figure 1 This embodiment describes an iterative equalization method for AFDM systems. The specific process of the method is as follows:

[0066] At the launch end

[0067] Step 1: Modulate the input data of length N×1 to obtain the affine domain modulation sequence x;

[0068] Step 2: Select Chirp parameters c1 and c2, and then perform an inverse affine Fourier transform on the sequence x based on the Chirp parameters c1 and c2 to obtain a time-domain sequence s of length N×1.

[0069] Step 3: Insert a cyclic prefix into the time-domain sequence s, and then transmit the processed time-domain sequence into the wireless channel via the radio frequency link;

[0070] At the receiving end

[0071] Step 4: Perform radio frequency processing and cyclic prefix removal on the signal received from the wireless channel to obtain a sequence y of length N×1 and a time-domain channel matrix H. t ;

[0072] Step 5: Based on the time-domain channel matrix H t Calculate the equivalent channel matrix H and initialize the prior information m of the modulation sequence x. [1] =0 N×1 ,diag(η [1] ) = I N I N It is the identity matrix;

[0073] Step Six: Place m [1] and diag(η) [1] ) = I N As input to the first iterative equalization, the posterior information μ of the first iterative equalization output is obtained. [1] =H H (Ψ [1] )-1 y,∑ [1] =I N -H H (Ψ [1] ) -1 H, intermediate variable matrix denotes the power of white noise, the upper index -1 represents the inverse of matrix;

[0074] Step seven, according to m [1] , η [1] , μ [1] and ∑ [1] , calculate the input m [2] and η [2] of the second iteration equalization (m [2] and η [2] are the external information passed from the first iteration to the second iteration), according to m [2] and η [2] , calculate the posterior information μ [2] and ∑ [2] of the second iteration equalization output;

[0075] The specific process of said according to m [1] , η [1] , μ [1] and ∑ [1] , calculate the input m [2] and η [2] of the second iteration equalization is:

[0076]

[0077] Wherein, the subscript (n) represents the nth element of the vector, (n, n) represents the element of the nth row and the nth column of the matrix;

[0078] Step eight, let the iteration number l=3;

[0079] Step nine, according to m [l-1] , η [l-1] , μ [l-1] and ∑ [l-1] , calculate the input m [l] and η [l] of the lth iteration equalization;

[0080]

[0081] Wherein, is the average value of all elements in the vector η [l-1] ;

[0082] According to m [l] and η [l] , calculate the posterior information μ[l] and∑ [l] ;

[0083] Step ten, judge whether the iteration number l reaches the set maximum iteration number or not;

[0084] If the set maximum iteration number is reached (the maximum iteration number can be set according to actual situation), the posterior information μ [l] outputted in the last iteration is used to make decision output;

[0085] If the set maximum iteration number is not reached, then let l = l + 1, and return to execute step nine.

[0086] Specific implementation two, different from the specific implementation one, in the step one, the modulation mode adopted is PSK or QAM.

[0087] The other steps and parameters are the same as the specific implementation one.

[0088] Specific implementation three, different from the specific implementation one or two, the specific process of selecting the Chirp parameters c1 and c2 is as follows:

[0089] 1) In the double-selected channel state, the Chirp parameter c1 is:

[0090]

[0091] wherein, represents the floor operation, l p is the maximum time delay tap of channel multipath propagation;

[0092] In the double-selected channel state, the Chirp parameter c2 is selected arbitrarily, that is, there is no constraint on the selection of the Chirp parameter c2.

[0093] 2) In the frequency-selected channel state with no obvious Doppler shift, the Chirp parameter c1 is:

[0094]

[0095] wherein, k odd represents any odd number;

[0096] In the frequency-selected channel state with no obvious Doppler shift, the Chirp parameter c2 is selected arbitrarily, that is, there is no constraint on the selection of the Chirp parameter c2.

[0097] The other steps and parameters are the same as the specific implementation one or two.

[0098] Specific implementation four, different from any one of the specific implementations one to three, the time domain sequence s is:

[0099]

[0100] Among them, Λ c Representative with A diagonal matrix with diagonal elements, i.e. c = c1 or c2, e is the base of the natural logarithm, j is the imaginary unit, the superscript H represents the conjugate transpose, A H Let F be the N×N affine Fourier inverse transform matrix, and F be the Fourier transform matrix.

[0101] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0102] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the step of using the time-domain channel matrix H... t The specific process for calculating the equivalent channel matrix H is as follows:

[0103] H = H t A H

[0104] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0105] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the posterior information μ... [1] The calculation method is as follows:

[0106] against Ψ [1] Perform block matrix decomposition. For (Nl) p )×(Nl p The submatrix of ) For l p ×(Nl p The submatrix of ) For (Nl) p )×l p submatrix, For l p ×l p The submatrix is ​​obtained by LU decomposition. Then Ψ [1] =L [1] U [1] , where L [1] and U [1] These are the lower triangular matrix and the upper triangular matrix obtained after LU decomposition, respectively. and For L [1] submatrix, and For U [1] submatrices;

[0107] Then μ [1] Calculate according to the following numerical labeling order:

[0108]

[0109] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0110] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that the posterior information Σ... [1] The calculation method is as follows:

[0111] Diag(H) H (Ψ [1] ) -1 H) is approximately equal to (H) H (Ψ [1] ) -1 H) (n,n) I N , then Σ [1] for:

[0112]

[0113] in, A represents H The nth column.

[0114] In this embodiment, n can be any value chosen from {1,2,..,N}.

[0115] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0116] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One through Seven in that the posterior information μ... [l′] and Σ [l′] for:

[0117]

[0118] Where l′≥2, the intermediate variable matrix For vector η [l′] The average value of all elements in the matrix.

[0119] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0120] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that the posterior information μ... [l′] The calculation method is as follows:

[0121] diag(η) [l′] Replace with Using a decomposition method similar to that used in the first iteration, Ψ is obtained. [l′] =L [l′] U [l′] L [l′] and U [l′] Let μ be the lower triangular matrix and the upper triangular matrix obtained after LU decomposition, respectively. [l′] Calculate according to the following numerical labeling order:

[0122]

[0123] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0124] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that the a posteriori information Σ... [l′] The calculation method is as follows:

[0125] diag(η) [l′] Replace with Diag(H) H (Ψ [l′] ) -1 H) is approximately equal to (H) H (Ψ [l′] ) -1 H) (n,n) I N ,but

[0126]

[0127] In this embodiment, n can be any value chosen from {1,2,..,N}.

[0128] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0129] In this invention, the posterior information is calculated in ascending order of numerical labels.

[0130] The iterative equalization algorithm of this invention ensures that multiple iterative equalizations in the AFDM system can be performed with low computational complexity, with a main complexity of O(l[P 2 +(2l p +1) 2 +log2(N)]N), where l is the number of iterations and P is the total number of multipath paths. Compared to the traditional iterative equilibrium method, which requires direct matrix inversion operations requiring O(lN) operations, this method achieves a higher efficiency. 3 The complexity is significantly reduced, which is more conducive to the deployment of hardware devices with low computing power.

[0131] The low-complexity iterative equalization method provided by the present application is compared with other methods in terms of bit error rate through Monte Carlo simulation, and a comparison chart is shown in FIG. Figure 2 The comparison between the iterative equalization of the OFDM system and the AFDM system is given in the chart, and it can be seen that after the fifth iteration, the low-complexity method of the present application slightly sacrifices part of the performance compared with the iterative equalization method without low-complexity processing. Considering the significant saving of computational complexity of the present application, the slight performance loss is acceptable. Compared with the curve of the iterative equalization of the AFDM system for one time and the curve of the iterative equalization of the OFDM system for five times, the performance is better, and there is a significant improvement. This shows that the low-complexity iterative equalization method provided by the present application has the advantages of low complexity and high performance in the AFDM system.

[0132] The convergence of the method provided by the present application is verified through Monte Carlo simulation, and the convergence of the low-complexity iterative equalization method provided by the present application under different modulation modes and different signal-to-noise ratios is shown in FIG. Figure 3 Three modulation modes of QPSK, 16QAM and 64QAM are selected, and the signal-to-noise ratios correspond to 5dB, 15dB and 25dB respectively. It can be seen from the chart that the performance improvement of the low-complexity iterative equalization method is more significant in the early stage of iteration, and the performance tends to be flat after five iterations, and the convergence is guaranteed, which shows that the low-complexity strategy provided by the present application will not deteriorate the convergence of the traditional iterative equalization method.

[0133] The above examples of the present application are only to illustrate the calculation model and calculation process of the present application, and are not limited to the embodiments of the present application. Based on the above description, other different forms of changes or variations can be made by those skilled in the art, and it is impossible to enumerate all the embodiments here. Any obvious changes or variations derived from the technical solutions of the present application are still within the protection scope of the present application.

Claims

1. An iterative equalization method for an AFDM system, characterized in that, The method specifically comprises the following steps: At the transmitting end Step one, modulating the input data with length of N*1 to obtain an affine field modulation sequence x; Step two, selecting Chirp parameters c1 and c2, and then performing affine Fourier inverse transform on the sequence x based on the Chirp parameters c1 and c2 to obtain a time domain sequence s with length of N*1; Step three, performing cyclic prefix insertion processing on the time domain sequence s, and then transmitting the processed time domain sequence to a wireless channel through a radio frequency link; At the receiving end Step four, radio frequency processing and removing cyclic prefix operation are performed on the signal received from the wireless channel to obtain a sequence y with length of Nxl and a time domain channel matrix H t ; Step five, compute the equivalent channel matrix H according to the time domain channel matrix H t Compute the equivalent channel matrix H, and initialize the prior information m of the modulation sequence x [1] = 0 N×1 , diag(η [1] ) = I N , I N is a unit matrix; Step six, m [1] and diag(η [1] ) N As the input of the first iteration equalization, the posteriori information μ [1] = H H (Ψ [1] ) -1 y,∑ [1] = I N - H H (Ψ [1] ) -1 H, the intermediate variable matrix denotes the power of white noise, and the superscript -1 represents the inverse of the matrix; Step 7: Based on m [1] η [1] μ [1] and Σ [1] Calculate the input m for the second iteration of the equilibrium. [2] and η [2] According to m [2] and η [2] Calculate the posterior information μ of the equalization output in the second iteration. [2] and Σ [2] ; According to m [1] η [1] μ [1] and Σ [1] Calculate the input m for the second iteration of the equilibrium. [2] and η [2] The specific process is as follows: Wherein, subscript (n) represents the nth element of a vector, and (n, n) represents the element in the nth row and the nth column of a matrix; Step eight, setting the iteration number l=3; Step nine, compute the input m [l-1] , η [l-1] , μ [l-1] , and Σ [l-1] to the lth iteration of the equalization [l] and η [l] ; wherein is the vector η [l-1] the average of all elements in the vector According to m [l] And η [l] Calculate the posterior information μ of the lth iteration of the equalization output [l] And Σ [l] ; Step ten, judging whether the iteration number l reaches the set maximum iteration number; If the set maximum number of iterations is reached, the posterior information μ [l] decision output is made; If the set maximum iteration number is not reached, then setting l=l+1, and returning to execute step nine.

2. The iterative equalization method for AFDM system according to claim 1, wherein, In the step one, the modulation mode is PSK or QAM.

3. The method of claim 1, wherein the AFDM system is a single carrier system. The specific process of selecting the Chirp parameters c1 and c2 is as follows: 1) In a dual-selected channel state, the Chirp parameter c1 is: wherein denotes a floor operation, l p is the maximum delay tap of the channel multipath propagation; In the dual-selected channel state, the Chirp parameter c2 is selected at will; 2) In a frequency-selected channel state, the Chirp parameter c1 is: wherein k odd represents any odd integer; In the frequency-selected channel state, the Chirp parameter c2 is selected at will.

4. The method of claim 1, wherein the AFDM system is a single carrier system. The time domain sequence s is: where Λ c represents a diagonal matrix with as diagonal elements, i.e. c = cl or c2, e is the base of the natural logarithm, j is the imaginary unit, the upper index H represents the conjugate transpose, A H is the N x N affine inverse Fourier transform matrix, and F is the Fourier transform matrix.

5. The method for iterative equalization for AFDM systems according to claim 4, wherein, The time-domain channel matrix H t The specific process of calculating the equivalent channel matrix H is as follows: H = H t A H .

6. The method for iterative equalization for AFDM system according to claim 5, wherein, The posterior information μ [1] The calculation method is: Ψ [1] is decomposed into block matrices, is an (N-l p ) x (N-l p ) submatrix, l p is the maximum delay tap of channel multipath propagation, is an l p x (N-l p ) submatrix, is an (N-l p ) x l p submatrix, is an l p x l p submatrix, and is obtained by LU decomposition Ψ [1] = L [1] U [1] , where L [1] and U [1] are lower triangular matrix and upper triangular matrix obtained by LU decomposition, and are submatrices of L [1] , and are submatrices of U [1] . then μ [1] The calculations are made in the following order of numerical labels:

7. The iterative equalization method for an AFDM system according to claim 6, characterized in that, The posterior information Σ [1] The calculation method is: Diag(H H (Ψ [1] ) -1 H) is approximated by (H H (Ψ [1] ) -1 H) (n,n) I N , then ∑ [1] is: wherein represents A H the nth column of A.

8. The method of claim 7, wherein the AFDM system is a single carrier frequency domain equalization (SC-FDE) system. The posterior information μ [l′] and∑ [l′] is: μ [l′] = m [l′] + diag(η [l′] )H H (Ψ [l′] ) -1 (y-Hm [l′] ) Σ [l′] = diag(η [l′] ) - diag(η [l′] ) H (Ψ [l′] ) -1 Hdiag(η [l′] ) where l'≥ 2, the intermediate variable matrix is a vector η [l′] the average of all elements.

9. The method of claim 8, wherein the AFDM system is a single carrier AFDM system. The posterior information μ [l′] The calculation method is: replace diag(η [l′] ) with decomposition to get Ψ [l′] = L [l′] U [l′] , L [l′] and U [l′] are lower and upper triangular matrix respectively after LU decomposition, then μ [l′] is calculated according to the following numerical label order:

10. The method of claim 9, wherein the AFDM system is a single carrier system. The posterior information Σ [l′] The calculation method is: replace diag(η [l′] ) by replace Diag(H H (Ψ [l′] ) -1 H) by (H H (Ψ [l′] ) -1 H) (n,n) I N then

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