A message passing method based on an exponential damping factor

Abstract

The application discloses a message passing method based on an exponential damping factor, and belongs to the technical field of wireless communication.The application solves the problems of high calculation complexity of a damping factor determined by an existing MP algorithm and poor stability and reliability of the existing MP algorithm.In the process of running the algorithm, the relationship between the damping factor and a probability mass function is described according to an exponential, and the probability mass function value can be updated.The correctness of the probability mass function value calculation can be continuously improved along with the iteration process, the optimal performance of the MP algorithm under different channel conditions is obtained, the stability of the MP algorithm is further improved, and more reliable transmission performance is obtained.The application uses a suitable exponential to replace a static damping factor, and the optimal damping factor does not need to be searched, so that the MP algorithm has lower complexity, stronger environmental adaptability and more stable and reliable detection performance.The application can be applied to the technical field of wireless communication.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to a message transmission method based on an exponential damping factor. Background Technology

[0002] Future B5G and 6G wireless communication systems will face numerous demands in highly mobile scenarios. Orthogonal Frequency Division Multiplexing (OFDM) modulation technology, widely used in 4G and 5G communications, is susceptible to time-frequency dispersion caused by time-varying channels in highly mobile scenarios, resulting in severe inter-carrier interference (ICI) or inter-symbol interference (ISI), leading to a significant degrade in communication performance. To effectively address these challenges, Orthogonal Time Frequency Space (OTFS) and Affine Frequency Division Multiplexing (AFDM) technologies have emerged as promising new modulation techniques. Unlike OFDM technology, which transmits information in the frequency domain, OTFS or AFDM technologies use novel modulation methods to modulate information into the time-delay-Doppler domain (or affine Fourier domain) for transmission. This characteristic allows them to better resist interference caused by time-frequency dispersion in highly dynamic scenarios, demonstrating higher reliability transmission potential compared to traditional modulation techniques.

[0003] Signal detection technology plays a crucial role in fully realizing the potential of OTFS or AFDM technologies. Signal detection technology aims to enable signal receivers to accurately detect signals from complex noise and interference and effectively extract the transmitted information. Currently common detection techniques include minimum mean square error (MMSE), zero-forcing (ZF) detection, maximum likelihood (ML) detection, and message passing algorithm (MP) detection. Among these, MMSE and ZF detection algorithms have the advantage of lower complexity, but their bit error rate performance is poor. Maximum likelihood detection theoretically has the best performance, but its extremely high complexity makes it difficult to apply in practice. Compared with maximum likelihood detection, the MP algorithm has relatively lower complexity and far surpasses the performance of ZF and MMSE, showing great potential in the field of detection algorithms for next-generation waveform modulation technologies.

[0004] The MP algorithm is an iterative signal detection algorithm that uses a damping factor to regulate the convergence speed of the iterative process to obtain optimal results. Currently, most MP algorithms employ a constant damping factor. The determination of this constant damping factor typically involves either selecting a fixed value empirically for different channels, or conducting Monte Carlo simulations with multiple candidate values ​​under specific channel conditions and selecting the optimal damping factor based on bit error rate performance. However, the optimal damping factor value varies significantly under different channel conditions, and determining this value for each channel condition is often cumbersome and complex. Therefore, current MP algorithms lack a stable and low-complexity damping factor control algorithm to address the poor stability and reliability issues of the MP algorithm while reducing computational complexity. Summary of the Invention

[0005] The purpose of this invention is to address the problems of high computational complexity in determining the damping factor using the existing MP algorithm, as well as the poor stability and reliability of the existing MP algorithm, and to propose a message passing method based on an exponential damping factor.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is: a message passing method based on an exponential damping factor, the method specifically including the following steps:

[0007] At the sending end:

[0008] Step 1: In the time-delay Doppler domain, map the information bits through a constellation of Q symbols to obtain a time-delay Doppler domain signal x with a signal dimension of MN×1; and then map the Q symbols a1, a2, ..., a... Q Let A be the set formed by them;

[0009] The time-delay Doppler domain signal x is then transformed to obtain a time-domain signal s with dimension MN×1. The time-domain signal s is then converted from parallel to serial and sent to the time-varying channel.

[0010] At the receiving end:

[0011] Step 2: The time-domain signal s arrives at the receiver through the time-varying channel. The time-domain received signal r is received at the receiver. After processing the time-domain received signal r, the time-delay Doppler domain discrete received signal y is obtained.

[0012] The equivalent time-delay Doppler domain channel matrix H is calculated based on the time-varying channel matrix H. eff H∈C MN×MN H eff ∈C MN×MN C is a complex number;

[0013] Step 3: Nodeize the transmitting signal x, and denote the c-th variable node of the transmitting signal x as x[c], 1≤c≤MN; Nodeize the receiving signal y, and denote the d-th observation node of the receiving signal y as y[d], 1≤d≤MN;

[0014] The c-th variable node x[c] and the d-th observation node y[d] are placed in the time-delay Doppler domain channel matrix H eff The corresponding element is denoted as H. eff [d,c],H eff [d,c] represents the time-delay Doppler domain channel matrix H. eff The element in the d-th row and c-th column;

[0015] Step 4: Initialize message passing method parameters: Initialize the maximum number of iterations n iter The probability that the initial variable node x[c] sends a symbol to the observation node y[d] via the path c→d. Initialize exponential damping factor α is a constant; and η is initialized. (0) The value;

[0016] Step 5: Initialize the iteration count i = 1;

[0017] Step 6: The observation node y[d] transmits information to the variable node x[c] that established the channel. and

[0018] Step 7: Variable node x[c] is based on... and Calculate the probability of transmitting back to the observation node y[d] in the (i-1)th iteration.

[0019] Based on the exponential damping factor f(Δ) and probability Calculate the probability that variable node x[c] sends a symbol to observation node y[d] via path c→d. And based on probability Update the damping factor f(Δ);

[0020] Step 8: Calculate the iteration indicator function η based on the messages received by all variable nodes. (i) Then determine whether η is satisfied. (i) >η (i-1) :

[0021] If η (i) >η (i-1) ,make Then proceed to step nine;

[0022] Otherwise, let η (i) =η (i-1)Then proceed to step nine;

[0023] Step 9: Determine whether the judgment conditions (1), (2), or (3) are met;

[0024] Judgment condition (1): η (i) =1;

[0025] Judgment condition (2): η (i) <max(η) (k) )-ε, k=1,...,i-1, ε is the set threshold;

[0026] Judgment condition (3): i = n iter ;

[0027] If judgment conditions (1), (2), or (3) are met, then This is the final detected value of the transmitted signal x;

[0028] If the judgment conditions (1), (2), and (3) are not met, then let i = i + 1 and return to step six.

[0029] Furthermore, in step one, the time-delay Doppler domain signal x is transformed, specifically as follows:

[0030] Perform an inverse sine Fourier transform on the time-delayed Doppler domain signal x, and then perform a Heisenberg transform on the result of the inverse sine Fourier transform. The result of the Heisenberg transform is the time-domain signal s.

[0031] Further, after processing the time-domain received signal r, the time-delay Doppler domain discrete received signal y is obtained; specifically:

[0032] After performing serial-to-parallel conversion on the time-domain received signal r, a Wigner transform is performed on the result of the serial-to-parallel conversion, and a Syn-Fourier transform is performed on the result of the Wigner transform to obtain a time-delay Doppler domain discrete received signal y with dimension MN×1.

[0033] Furthermore, the information for:

[0034]

[0035] in, H represents the probability calculated in the (i-1)th iteration that the variable node x[e] sends a symbol to the observation node y[d] through the path e→d. eff [d,e] represents the time-delay Doppler domain channel matrix H. eff The element in row d and column e, Ro(d), represents the set of all variable nodes that have a transmission path with the observation node y[d].

[0036] Furthermore, the information for:

[0037]

[0038] Where |·| represents calculating the absolute value, σ 2 This represents the noise variance of the channel.

[0039] Furthermore, the specific process of step seven is as follows:

[0040]

[0041] Where Cl(c) represents the set of all observation nodes that have a transmission path with variable node x[c], y[e′] represents the e′-th observation node, and H eff [e′,c] represents the time-delay Doppler domain channel matrix H. eff The element in row e′ and column c.

[0042] Furthermore, the statement based on the exponential damping factor f(Δ) and probability... Calculate the probability that variable node x[c] sends a symbol to observation node y[d] via path c→d. Specifically:

[0043]

[0044] Where Q represents the total number of symbols in set A.

[0045] Furthermore, the step of calculating the iteration indicator function η based on the messages received by all variable nodes... (i) Specifically:

[0046]

[0047] in, As an intermediate variable, Let be a function, and γ be a constant.

[0048] Furthermore, the intermediate variable for:

[0049]

[0050] Furthermore, the function The definition is: if but otherwise

[0051] The beneficial effects of this invention are:

[0052] The exponential damping factor of this invention iteratively changes with the message passing algorithm. During algorithm execution, the relationship between the damping factor and the probability quality function is described by the exponent, allowing the probability quality function value to be updated. As the iteration process progresses, the accuracy of the probability quality function value calculation is continuously improved, enabling the MP algorithm to achieve optimal performance under different channel conditions. This further enhances the stability of the MP algorithm, resulting in more reliable transmission performance. This invention uses a suitable exponent to replace the static damping factor without searching for the optimal damping factor, giving the MP algorithm lower complexity, stronger environmental adaptability, and more stable and reliable detection performance. Compared to MP algorithms based on static damping factors, the damping factor of this invention can automatically adjust during algorithm execution to further improve the accuracy of the probability quality function value calculation. Compared to traditional MP algorithms based on static damping factors, this invention's method has a higher performance limit. Attached Figure Description

[0053] Figure 1 This is a flowchart of a message passing method based on an exponential damping factor according to the present invention;

[0054] Figure 2 This is a comparison chart of the bit error rate performance of the method of this invention and the traditional MP algorithm at different moving speeds;

[0055] In the figure, FD-MP represents the method of the present invention, and MP represents the conventional method;

[0056] Figure 3 This is a comparison chart of the bit error rate performance of the method of this invention and the traditional MP algorithm under different maximum number of iterations. Detailed Implementation

[0057] Specific implementation method one: Combining Figure 1 This embodiment describes a message passing method based on an exponential damping factor, which specifically includes the following steps:

[0058] At the sending end:

[0059] Step 1: In the time-delay Doppler domain, map the information bits through a constellation of Q symbols to obtain a time-delay Doppler domain signal x with a signal dimension of MN×1; and then map the Q symbols a1, a2, ..., a... Q Let A be the set formed by them;

[0060] The time-delay Doppler domain signal x is then transformed to obtain a time-domain signal s with dimension MN×1. The time-domain signal s is then converted from parallel to serial and sent to the time-varying channel.

[0061] At the receiving end:

[0062] Step 2: The time-domain signal s arrives at the receiver through the time-varying channel. The time-domain received signal r is received at the receiver. After processing the time-domain received signal r, the time-delay Doppler domain discrete received signal y is obtained.

[0063] The equivalent time-delay Doppler domain channel matrix H is calculated based on the time-varying channel matrix H. eff H∈C MN×MN H eff ∈C MN×MN C is a complex number;

[0064] Step 3: Nodeize the transmitting signal x, and denote the c-th variable node of the transmitting signal x as x[c], 1≤c≤MN; Nodeize the receiving signal y, and denote the d-th observation node of the receiving signal y as y[d], 1≤d≤MN;

[0065] The c-th variable node x[c] and the d-th observation node y[d] are placed in the time-delay Doppler domain channel matrix H eff The corresponding element is denoted as H. eff [d,c],H eff [d,c] represents the time-delay Doppler domain channel matrix H. eff The element in the d-th row and c-th column;

[0066] If H eff If [d,c] are non-zero, then a transmission path is established between y[d] and x[c] to transmit information (i.e., the probability density function calculated in subsequent steps); otherwise, no transmission path is established between y[d] and x[c].

[0067] Step 4: Initialize message passing method parameters: Initialize the maximum number of iterations n iter The probability that the initial variable node x[c] sends a symbol to the observation node y[d] via the path c→d. Initialize exponential damping factor α is a constant (which can be set empirically); and η is initialized. (0) The value;

[0068] Step 5: Initialize the iteration count i = 1;

[0069] Step 6: The observation node y[d] transmits information to the variable node x[c] that established the channel. and

[0070] Step 7: Variable node x[c] is based on... and Calculate the probability of transmitting back to the observation node y[d] in the (i-1)th iteration.

[0071] Based on the exponential damping factor f(Δ) and probability Calculate the probability that variable node x[c] sends a symbol to observation node y[d] via path c→d. And based on probability Update the damping factor f(Δ), i.e.

[0072] Step 8: Calculate the iteration indicator function η based on the messages received by all variable nodes. (i) Then determine whether η is satisfied. (i) >η (i-1) :

[0073] If η (i) >η (i-1) ,make Then proceed to step nine;

[0074] Otherwise, let η (i) =η (i-1) Then proceed to step nine;

[0075] Step 9: Determine whether the judgment conditions (1), (2), or (3) are met;

[0076] Judgment condition (1): η (i) =1;

[0077] Judgment condition (2): η (i) <max(η) (k) )-ε, k=1,...,i-1, ε is the set threshold;

[0078] Judgment condition (3): i = n iter ;

[0079] If judgment conditions (1), (2), or (3) are met, then This is the final detected value of the transmitted signal x;

[0080] If the judgment conditions (1), (2), and (3) are not met, then let i = i + 1 and return to step six.

[0081] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that, in step one, the time-delay Doppler domain signal x is transformed, specifically as follows:

[0082] Perform an inverse sine Fourier transform on the time-delayed Doppler domain signal x, and then perform a Heisenberg transform on the result of the inverse sine Fourier transform. The result of the Heisenberg transform is the time-domain signal s.

[0083] The other steps and parameters are the same as in Specific Implementation Method 1.

[0084] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that, after processing the time-domain received signal r, a time-delay Doppler domain discrete received signal y is obtained; specifically:

[0085] After performing serial-to-parallel conversion on the time-domain received signal r, a Wigner transform is performed on the result of the serial-to-parallel conversion, and a Syn-Fourier transform is performed on the result of the Wigner transform to obtain a time-delay Doppler domain discrete received signal y with dimension MN×1.

[0086] Other steps and parameters are the same as in specific implementation method one or two.

[0087] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the information... for:

[0088]

[0089] in, H represents the probability calculated in the (i-1)th iteration that the variable node x[e] sends a symbol to the observation node y[d] through the path e→d. eff [d,e] represents the time-delay Doppler domain channel matrix H. eff The element in the d-th row and e-th column, Ro(d), represents the set of all variable nodes (i.e., H) that have a transmission path with the observation node y[d]. eff (The set of variable nodes corresponding to the non-zero elements in the d-th row).

[0090] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0091] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the information... for:

[0092]

[0093] Where |·| represents calculating the absolute value, σ 2 This represents the noise variance of the channel.

[0094] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0095] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the specific process of step seven is as follows:

[0096]

[0097] Where Cl(c) represents the set of all observation nodes that have a transmission path with variable node x[c], y[e′] represents the e′-th observation node, and H eff [e′,c] represents the time-delay Doppler domain channel matrix H. eff The element in row e′ and column c is represented by Π, which indicates cumulative multiplication.

[0098] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0099] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that the step of basing the calculation on the exponential damping factor f(Δ) and probability... Calculate the probability that variable node x[c] sends a symbol to observation node y[d] via path c→d. Specifically:

[0100]

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

[0102] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One through Seven in that the step of calculating the iteration indicator function η based on the messages received by all variable nodes is... (i) Specifically:

[0103]

[0104] in, As an intermediate variable, Let be a function, and γ be a constant.

[0105] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0106] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that the intermediate variable... for:

[0107]

[0108] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0109] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that the function... The definition is: if otherwise

[0110] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0111] The feasibility and effectiveness of this invention are verified through simulation experiments below:

[0112] The message passing algorithm of this invention is applicable to various transmission modulation techniques and various channel conditions, such as modulation techniques OTFS and AFDM, time-varying channels, and multipath quasi-static channels; this invention takes OTFS block transmission technology and time-varying channels as examples.

[0113] like Figure 2 and Figure 3 The figure shows the bit error rates of the MP algorithm of this invention and the traditional static damping factor algorithm when α = 0.45 under different channel conditions with varying mobility. Figure 2 and Figure 3 As can be seen, compared with the MP algorithm based on static damping factor, the method of this invention has better transmission performance than the traditional static damping factor because it dynamically changes the damping factor during iteration.

[0114] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A message passing method based on an exponential damping factor, characterized in that, The method specifically includes the following steps: At the sending end: Step 1: In the time-delay Doppler domain, map the information bits through a constellation of Q symbols to obtain a time-delay Doppler domain signal x with a signal dimension of MN×1; and then map the Q symbols a1, a2, ..., a... Q Let A be the set formed by them; The time-delay Doppler domain signal x is then transformed to obtain a time-domain signal s with dimension MN×1. The time-domain signal s is then converted from parallel to serial and sent to the time-varying channel. At the receiving end: Step 2: The time-domain signal s arrives at the receiver through the time-varying channel. The time-domain received signal r is received at the receiver. After processing the time-domain received signal r, the time-delay Doppler domain discrete received signal y is obtained. The equivalent time-delay Doppler domain channel matrix H is calculated based on the time-varying channel matrix H. eff H∈C MN×MN H eff ∈C MN ×MN C is a complex number; Step 3: Nodeize the transmitting signal x, and denote the c-th variable node of the transmitting signal x as x[c], 1≤c≤MN; Nodeize the receiving signal y, and denote the d-th observation node of the receiving signal y as y[d], 1≤d≤MN; The c-th variable node x[c] and the d-th observation node y[d] are placed in the time-delay Doppler domain channel matrix H eff The corresponding element is denoted as H. eff [d,c],H eff [d,c] represents the time-delay Doppler domain channel matrix H. eff The element in the d-th row and c-th column; Step 4: Initialize message passing method parameters: Initialize the maximum number of iterations n iter The probability that the initial variable node x[c] sends a symbol to the observation node y[d] via the path c→d. Initialize exponential damping factor α is a constant; and η is initialized. (0) The value; Step 5: Initialize the iteration count i = 1; Step 6: The observation node y[d] transmits information to the variable node x[c] that established the channel. and Step 7: Variable node x[c] is based on... and Calculate the probability of transmitting back to the observation node y[d] in the (i-1)th iteration. Based on the exponential damping factor f(Δ) and probability Calculate the probability that variable node x[c] sends a symbol to observation node y[d] via path c→d. And based on probability Update the damping factor f(Δ); Step 8: Calculate the iteration indicator function η based on the messages received by all variable nodes. (i) Then determine whether η is satisfied. (i) >η (i-1) : If η (i) >η (i-1) ,make Then proceed to step nine; Otherwise, let η (i) =η (i-1) Then proceed to step nine; Step 9: Determine whether the judgment conditions (1), (2), or (3) are met; Judgment condition (1): η (i) =1; Judgment condition (2): η (i) <max(η) (k) )-ε, k=1,...,i-1, ε is the set threshold; Judgment condition (3): i = n iter ; If judgment conditions (1), (2), or (3) are met, then This is the final detected value of the transmitted signal x; If the judgment conditions (1), (2), and (3) are not met, then let i = i + 1 and return to step six.

2. The message passing method based on an exponential damping factor according to claim 1, characterized in that, In step one, the time-delayed Doppler domain signal x is transformed, specifically as follows: Perform an inverse sine Fourier transform on the time-delayed Doppler domain signal x, and then perform a Heisenberg transform on the result of the inverse sine Fourier transform. The result of the Heisenberg transform is the time-domain signal s.

3. The message passing method based on an exponential damping factor according to claim 1, characterized in that, After processing the time-domain received signal r, the time-delay Doppler domain discrete received signal y is obtained; specifically: After performing serial-to-parallel conversion on the time-domain received signal r, a Wigner transform is performed on the result of the serial-to-parallel conversion, and a Syn-Fourier transform is performed on the result of the Wigner transform to obtain a time-delay Doppler domain discrete received signal y with dimension MN×1.

4. The message passing method based on an exponential damping factor according to claim 1, characterized in that, The information for: in, H represents the probability calculated in the (i-1)th iteration that the variable node x[e] sends a symbol to the observation node y[d] through the path e→d. eff [d,e] represents the time-delay Doppler domain channel matrix H. eff The element in row d and column e, Ro(d), represents the set of all variable nodes that have a transmission path with the observation node y[d].

5. The message passing method based on an exponential damping factor according to claim 4, characterized in that, The information for: Where |·| represents calculating the absolute value, σ 2 This represents the noise variance of the channel.

6. The message passing method based on an exponential damping factor according to claim 5, characterized in that, The specific process of step seven is as follows: Where Cl(c) represents the set of all observation nodes that have a transmission path with variable node x[c], y[e′] represents the e′-th observation node, and H eff [e′,c] represents the time-delay Doppler domain channel matrix H. eff The element in row e′ and column c.

7. The message passing method based on an exponential damping factor according to claim 6, characterized in that, The above is based on the exponential damping factor f(Δ) and probability. Calculate the probability that variable node x[c] sends a symbol to observation node y[d] via path c→d. Specifically: Where Q represents the total number of symbols in set A.

8. The message passing method based on an exponential damping factor according to claim 7, characterized in that, The iterative indicator function η is calculated based on the messages received by all variable nodes. (i) Specifically: in, As an intermediate variable, Let be a function, and γ be a constant.

9. A message passing method based on an exponential damping factor according to claim 8, characterized in that, The intermediate variable for:

10. A message passing method based on an exponential damping factor according to claim 9, characterized in that, The function The definition is: if but otherwise

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