Variable damping factor message passing method based on affine frequency division multiplexing

Abstract

The present application belongs to the field of signal detection in signal processing, and particularly relates to a variable damping factor message passing method based on affine frequency division multiplexing (AFDM). The present application initiatively designs a message passing method for solving an optimal variable damping factor in view of the problem that the damping factor is a fixed value in a traditional message passing method; the damping factor is generated at equal intervals L between 0 and 1, the AFDM signal is detected, each damping factor is detected, the optimal damping factor is obtained by taking the average bit error rate (BER) performance as the first weight and combining the average iteration number as the second weight according to the bit error rate obtained after detection, and the average BER and the average iteration number are considered; then the best damping factor is brought into the message passing method, and finally the output signal is obtained. The present application simultaneously meets the requirements of low complexity, high BER performance and global optimization.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of signal detection in signal processing, and particularly relates to a variable damping factor message passing method based on affine frequency division multiplexing (AFDM). BACKGROUND

[0002] Generally, wireless signals are contaminated by noise during propagation. After receiving the signals at the receiving end, signal detection is usually needed to restore the original signals. Existing AFDM signal detection methods, such as maximum likelihood-based signal detection method, minimum mean square error-based signal detection method, maximum ratio combining-based signal detection method and message passing-based signal detection method, have poor detection effects on AFDM signals.

[0003] The maximum likelihood-based signal detection method and the minimum mean square error-based signal detection method have high complexity and very limited performance; the maximum ratio combining-based signal detection method reduces the complexity, but its performance is similar to that of the minimum mean square error-based signal detection method; the message passing-based signal detection method has low complexity and good performance, but the damping factor in the method is a given constant, and global optimization cannot be achieved. Table 1 below shows the characteristics of the existing signal detection methods for AFDM signal detection:

[0004] Existing signal detection method name Complexity Feature Based on maximum likelihood (ML) High Low bit error rate performance Based on minimum mean square error (MMSE) High Low bit error rate performance Based on maximum ratio combination (MRC) Low Low bit error rate performance Based on message passing (MP) Low High bit error rate performance, unable to achieve global optimization

[0005] As can be seen from the above, there is currently a lack of a signal detection method for AFDM signals that can achieve low complexity, high bit error rate performance and global optimization. SUMMARY

[0006] In view of the above problems or deficiencies, in order to simultaneously meet the three requirements of low complexity, high bit error rate performance and global optimization, the present application provides a variable damping factor message passing method based on affine frequency division multiplexing (AFDM).

[0007] A variable damping factor message passing method based on affine frequency division multiplexing (AFDM) includes the following steps:

[0008] Step 1: For the received AFDM demodulated signal, generate damping factors with an interval L between 0 and 1, and number them as Δ(u), u = 1, 2,..., N L , where N L represents the number of damping factors generated under the condition of interval L.

[0009] Step 2: Bring Δ(u) into the message passing method for iteration to calculate the corresponding average bit error rate BER(u) and average iteration number

[0010] Furthermore, the calculation formula of the BER(u) is as follows:

[0011]

[0012] in, The symbol represents the XOR operation, N represents the number of AFDM symbols, n iter represents the number of times the Monte Carlo method is repeated, Q represents the order of quadrature amplitude modulation (QAM), that is, the length of the QAM alphabet, and a (t) [c] and Represents the cth element of the message signal and the estimated signal respectively, t is in n iter Take the value in.

[0013] Furthermore, the average number of iterations The calculation formula is as follows:

[0014]

[0015] in Represents the number of iterations of the message passing method.

[0016] Step 3: Find the minimum average bit error rate BER min .

[0017] Furthermore, BER min The calculation formula is as follows:

[0018]

[0019] Step 4: Find the damping factor Δ(u) that can achieve the best BER and average number of iterations.

[0020] Initialize the optimal damping factor Δ(u) with the number TminT=1 and the average number of iterations T min for Traverse Δ(u); when |BER min -BER(u)|<γ, 0<γ<1, and renew minT=u.

[0021] Since BER performance is more important than the average number of iterations in communication, the average number of iterations should be kept as small as possible while ensuring the optimal BER performance. Therefore, the relationship between BER(u) and BER(u) is not considered. min The difference is large.

[0022] Step 5: The optimal damping factor selected in step 4 is Δ(minT), which is substituted into the message passing method to obtain the BER.

[0023] Further, the interval L of the generated damping factor is adjusted in size according to the actual application scenario; if the performance requirement is high and the computing resource is rich, it is adjusted to be small; otherwise, it is adjusted to be large.

[0024] To sum up, the present application designs a message passing method for solving the optimal variable damping factor for the problem that the damping factor is a fixed value in the traditional message passing method, performs signal detection on the AFDM signal, and sequentially performs according to steps 1-5 to obtain the optimal damping factor with the best BER and the least average iteration number; then the optimal damping factor is brought into the message passing method, and finally the output signal is obtained, which meets the requirements of high bit error rate performance and global optimization. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1 The flowchart of the present application;

[0026] Figure 2 The BER performance comparison chart of the comparative example message passing method and the embodiment variable damping factor message passing method. DETAILED DESCRIPTION

[0027] The present application will be further described in detail below in combination with the drawings and embodiments.

[0028] EMBODIMENT

[0029] A variable damping factor message passing method based on affine frequency division multiplexing (AFDM), the flowchart is as shown in Figure 1 .

[0030] First, set the number of AFDM symbols N = 256, use 4-QAM modulation, i.e. Q = 4. Then, use MATLAB software to randomly generate Nlog2(Q) bit data with values of 0 or 1, and use QAM modulation on it to obtain an AFDM message signal. The AFDM message signal is modulated, then passes through a channel, and the channel parameters are set as: the number of paths P = 4, the normalized Doppler shift and time delay corresponding to each path are set as [0, 1, 2, 3] and [0, 1, 2, 3] respectively, and the channel gain is generated by using a random variable with a mean of 0 and a variance of 1 / P of an independent complex Gaussian distribution. After receiving the signal at the receiving end, it is demodulated to obtain an AFDM demodulation signal.

[0031] Step 1: For the received AFDM demodulation signal, generate damping factors between 0 and 1 with an interval of 0.1, and number them as Δ(u), u = 1, 2,..., 10.

[0032] Step 2: Bring Δ(u) into the message passing method for iteration, calculate the average bit error rate BER(u) and the average iteration number This embodiment sets the number of repeated calculations n of the Monte Carlo method iter is 10000.

[0033] The calculation formula for BER(u) is as follows:

[0034]

[0035] Average number of iterations The calculation formula is as follows:

[0036]

[0037] Step 3: Find the minimum average bit error rate BER min , the calculation formula is as follows:

[0038]

[0039] Step 4: Find the damping factor Δ(u) that can achieve the optimal average bit error rate BER and average number of iterations;

[0040] Initialize the optimal damping factor Δ(u) with the number minT=1 and the average number of iterations T min for Traverse Δ(u); when |BER min -BER(u)|<1×10 -5 ,and When, update minT=u.

[0041] Step 5: The optimal damping factor selected in step 4 is Δ(minT), which is substituted into the message passing method to obtain the BER. The specific existing message passing method is shown in the comparative example.

[0042] Comparative Example

[0043] The AFDM demodulated signal used in the embodiment is directly post-processed using an existing AFDM-based message passing method, specifically including the following steps:

[0044] Step 1: Calculate the average value of interference in the channel and variance

[0045]

[0046] Among them, H eff represents the channel matrix, I(d) is the index value corresponding to the non-zero element in the dth row of the channel matrix, and a j is the jth element in the QAM alphabet A, σ 2 Represents the power of the noise.

[0047] Step 2: Update the probability mass function

[0048]

[0049] where Δ ∈ (0, 1] is a damping factor used to improve performance by controlling the convergence speed, and:

[0050]

[0051] where X is the message signal, y is the demodulated signal, and has:

[0052]

[0053] Step 3: Calculate the convergence indicator η (i) .

[0054]

[0055] where γ is a number greater than 0 and less than 1, which is set to 0.05 in this example, is an indicator function that gives a value of 1 if the expression in the argument is true, and 0 otherwise, and:

[0056]

[0057] where J(c) represents the index of the non-zero elements in the c-th column of the channel matrix.

[0058] Step 4: Update the decision.

[0059] If η (i) > η (i-1) , the decision of the transmitted symbol is updated as:

[0060]

[0061] Step 5: Stopping condition. The message passing method stops when at least one of the following conditions is met:

[0062] (1) η (i) = 1,

[0063] (2) where i * ∈ {1, …, i-1} is the iteration index that maximizes .

[0064] (3) The maximum number of iterations n iter is reached.

[0065] Set ∈ = 0.2 to ignore small fluctuations in η.

[0066] Test analysis: In the computer MATLAB environment, for the received AFDM demodulated signal, the number of symbols, channel matrix, and noise power are input into the above method, and these parameters are brought into the formula of the variable damping factor message passing method of the above embodiment for calculation. Finally, the BER performance of the existing message passing method of the comparative example and the variable damping factor message passing method of the embodiment is obtained, as shown in FIG. Figure 2 As shown. Figure 2 It can be seen that under the signal-to-noise ratio condition of 14dB-20dB, the BER performance of the variable damping factor message passing method proposed in the present invention is better than that of the traditional message passing method.

[0067] It can be seen from the above embodiments that, in response to the problem that the damping factor in traditional message passing methods is a fixed value, the present invention has innovatively designed a message passing method for solving the optimal variable damping factor; by generating a damping factor at equal intervals L between 0 and 1, performing signal detection on the AFDM signal, and detecting each damping factor, according to the bit error rate obtained after the detection, taking the average bit error rate performance as the first weight and the average number of iterations as the second weight, the optimal damping factor that takes into account the average bit error rate BER and the average number of iterations is obtained; then the optimal damping factor is introduced into the message passing method to finally obtain the output signal. The present invention simultaneously meets the requirements of low complexity, high bit error rate performance and achieving global optimization.

Claims

1. A variable damping factor message transmission method based on RFDM, characterized in that: The following steps are involved: Step 1: For the received AFDM demodulated signal, generate damping factors at intervals L between 0 and 1 and number them as Δ(u), where u = 1, 2, ..., N L , where N L Represents the number of damping factors generated when the interval is L; Step 2: Substitute Δ(u) into the message passing method for iteration and calculate the corresponding average bit error rate BER(u) and average number of iterations Step 3: Find the minimum average bit error rate BER min ; Step 4: Find the damping factor Δ(u) that can achieve the optimal BER and average number of iterations; Initialize the optimal damping factor Δ(u) with the number min T=1 and the average number of iterations T min for Traverse Δ(u); when |BER min -BER(u)|<γ, 0<γ<1, and renew Step 5: The optimal damping factor selected in step 4 is Δ(min T), which is substituted into the message passing method to obtain the BER; The calculation formula of the average bit error rate BER(u) is as follows: in, The symbol represents the XOR operation, N represents the number of AFDM symbols, n iter represents the number of times the Monte Carlo method is repeated, Q represents the order of quadrature amplitude modulation (QAM), a (t) [c] and Represents the cth element of the message signal and the estimated signal respectively, t is in n iter The median value; The average number of iterations The calculation formula is as follows: in Represents the number of iterations of the message passing method; The BER min The calculation formula is: The message transmission method is specifically as follows: Step 1): Calculate the average value of interference in the channel and variance Among them, H eff represents the channel matrix, I(d) is the index value corresponding to the non-zero element in the dth row of the channel matrix, and a j QAM alphabet The jth element in σ 2 represents the power of the noise; Step 2): Update the probability mass function where Δ∈(0, 1] is a damping factor used to improve the performance by controlling the convergence speed, and: Where x is the message signal, y is the demodulated signal, and: Step 3): Calculate the convergence index η (i) ; Where γ is a number greater than 0 and less than 1, is an indicator function that gives the value 1 if the expression in the argument is true and 0 otherwise, and: Where J(c) represents the index of the non-zero element in the c-th column of the channel matrix; Step 4): Update decision; If η (i) >η (i-1) , then the decision of transmitting symbols is updated as: Step 5): The message delivery method stops when at least one of the following conditions is met: (1)the (i) =1; (2) where i * ∈{1,…,i-1} is such that Maximum iteration index; (3) Reach the maximum number of iterations n iter ; set up to ignore small fluctuations in η.

2. The variable damping factor message transmission method based on RFDM as claimed in claim 1, characterized in that: The interval L for generating the damping factor is adjusted according to the actual application scenario; If performance requirements are high and computing resources are abundant, adjust it to a smaller value; Otherwise, increase it.

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