Signal processing optimization method and system for training BCJR by using least square method

Abstract

The invention discloses a signal processing optimization method and system for training a BCJR by using a least square method, and belongs to the technical field of short-distance high-speed optical communication signal processing. At a receiving end, the signal is processed by a feed-forward filter (FFE) and then processed by a feed-back filter (PF); channel estimation is carried out through a least square (LS) algorithm by using the output of a feedback filter (PF) and a training sequence; based on channel response estimated by a least square (LS) algorithm, soft decision decoding is carried out by using a BCJR algorithm, and the maximum posterior probability MAP of each symbol is calculated; according to the maximum posterior probability MAP of each symbol, calculating a bit-by-bit log-likelihood ratio; and recovering the signal according to the obtained log-likelihood ratio. The method can solve the problem that the performance of a traditional BCJR algorithm is remarkably reduced when the traditional BCJR algorithm faces serious inter-symbol interference. By optimizing the coefficient of the BCJR algorithm, the BCJR algorithm is closer to the original channel response, so that the bit error rate is effectively reduced, and the system performance is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of short - distance high - rate optical communication signal processing, and more specifically, to a signal processing optimization method and system for training BCJR using the least - squares method. Background Art

[0002] The maximum a posteriori probability (Bahl - Cocke - Jelinek - Raviv, BCJR) algorithm is widely used in optical communication systems because it can provide signal decoding performance close to the maximum likelihood solution. However, due to factors such as multipath fading, noise interference, and frequency offset in the optical communication channel environment, the decoding accuracy of the BCJR algorithm may be limited in practical applications. To improve the decoding accuracy and enhance the robustness and adaptability of the BCJR algorithm, many studies have proposed different optimization strategies. These strategies focus on enhancing the algorithm's tolerance to channel noise and interference, thereby obtaining more accurate decoding results in complex optical communication environments.

[0003] The BCJR algorithm calculates the forward probability and backward probability of each symbol through forward - backward recursion to achieve optimal decoding. However, due to the following factors, the accuracy of the BCJR algorithm may be affected in some channel environments: 1. Channel noise: The noise in an optical communication system usually comes from thermal noise, light source noise, and channel attenuation, etc. The intensity of the noise directly affects the decoding accuracy of the signal. 2. Multipath effect: In optical fiber communication, due to the multipath propagation of optical signals, the signal may experience different propagation paths, resulting in signal distortion and interference, thus affecting the decoding accuracy. 3. Non - ideal channel: In an actual optical communication system, the channel is often not completely ideal, with problems such as signal distortion and frequency offset. These factors will affect the accuracy of the BCJR algorithm.

[0004] Currently, the existing technologies for improving the accuracy of the BCJR algorithm are divided into the following several types:

[0005] 1. Improved soft - decision strategy

[0006] The BCJR algorithm obtains the probability information of symbols through soft - decision to achieve more accurate decoding. In some optical communication systems, the improved soft - decision strategy helps to improve the decoding accuracy. To improve the accuracy of the decision, the BCJR algorithm can combine the prior information of the channel. The decision can reduce the occurrence of symbol decision errors and improve the accuracy under lower signal - to - noise ratio (SNR) conditions. Dynamic soft - decision based on SNR: In the case of low SNR, the soft - decision of the BCJR algorithm may be inaccurate, leading to decoding errors. For this reason, researchers have proposed a dynamic soft - decision method based on SNR, which adjusts the decision strategy according to different channel qualities to enhance the reliability of the soft - decision under poor channel conditions.

[0007] 2. Iterative Decoding and Joint Signal Detection

[0008] By combining with other decoding algorithms, the decoding accuracy of the BCJR algorithm can be significantly improved. The joint decoding of Low-Density Parity-Check (LDPC) codes and BCJR: LDPC codes are a powerful error-correcting code. When used in conjunction with the BCJR algorithm, they can continuously improve the decoding result through the update process of soft input and output, and improve the Bit Error Rate (BER) of the system. This joint decoding method utilizes the error-correcting ability of LDPC codes and combines the maximum likelihood decoding characteristics of the BCJR algorithm, thus significantly improving the decoding accuracy.

[0009] However, in the above prior art, the memory length of BCJR is fixed at 2. When the inter-symbol interference is relatively severe, there is a significant loss in performance because the fixed memory length discards the information outside the memory length of the true channel response. This causes the BCJR algorithm to miss part of the channel response during the process of compensating for signal damage, thus affecting the overall performance of the algorithm. Therefore, it is necessary to further improve it.

[0010] Therefore, how to provide a signal processing optimization method and system for training BCJR using the least squares method is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0011] In view of this, the present invention provides a signal processing optimization method and system for training BCJR using the least squares method, aiming to solve the problem that the performance of the traditional BCJR algorithm significantly degrades when facing severe inter-symbol interference. By optimizing the coefficients of the BCJR algorithm to make it closer to the original channel response, the bit error rate can be effectively reduced and the system performance can be improved. The least squares (LS) method is used for channel estimation. Compared with other channel estimation algorithms, this method is more concise and efficient. Although the computational complexity of this method increases, considering that it can significantly improve the system performance, this additional computational burden is reasonable. In this way, the deficiency of the BCJR algorithm in the accuracy of signal recovery can be effectively solved, bringing a significant performance improvement to the system.

[0012] To achieve the above object, the present invention provides the following technical solutions:

[0013] A signal processing optimization method for training BCJR using the least squares method, comprising:

[0014] At the receiving end, after the signal is processed by the Feed-Forward Equalizer (FFE), it is processed by the Posteriori Filter (PF);

[0015] Channel estimation is performed by the least squares (LS) algorithm using the output of the post-filter PF and the training sequence.

[0016] Based on the channel response estimated by the least squares (LS) algorithm, soft decision decoding is performed using the BCJR algorithm to calculate the maximum a posteriori probability (MAP) of each symbol.

[0017] According to the maximum a posteriori probability (MAP) of each symbol, the bit-by-bit log-likelihood ratio is calculated.

[0018] The signal is recovered according to the obtained log-likelihood ratio.

[0019] Furthermore, the transfer function of the post-filter PF is:

[0020] H(z) = 1 + alph * z -1 ;

[0021] Where alph represents the tap coefficient of the post-filter PF, and z represents the Laplace transform.

[0022] Furthermore, the output of the post-filter PF is expressed as:

[0023] Y(i) = r(i) + alph * r(i + 1);

[0024] Where i represents the current time, and r(i) represents the signal received by the post-filter PF.

[0025] Furthermore, the channel estimation by the least squares (LS) algorithm includes:

[0026] Form a Toeplitz matrix using the training sequence:

[0027]

[0028] Where N is the number of rows of the training matrix, p is the number of columns, and the channel response re-estimated according to the least squares (LS) algorithm is:

[0029] w = (X T X) -1 X T Y;

[0030] Furthermore, based on the channel response estimated by the least squares (LS) algorithm, soft decision decoding is performed using the BCJR algorithm to calculate the maximum a posteriori probability (MAP) of each symbol, including:

[0031] Calculate the state transition metric of BCJR:

[0032] γ(p,n) = lnP(x) - (Y - (x n *w n +x n-1 *wn-1 +...x n-L *w n-L )) 2 / N0;

[0033] Calculate the forward recursion parameters:

[0034] α n+1 (n)=max{a n (p)+γ(p,n)};

[0035] Calculate the backward recursion parameters:

[0036] b n (p)=max{b n+1 (n)+γ(p,n)};

[0037] Calculate the posterior probability of each symbol, expressed as:

[0038] Ρ(χ)=Sexp{a n (p)+γ(p,n)+b n+1 (n)};

[0039] Where x represents a possible symbol, p represents the state at the previous moment, n represents the state at the next moment, P(x) represents the prior probability of the symbol, N0 represents the noise power, and L represents the memory length of BCJR.

[0040] Furthermore, according to the maximum a posteriori probability MAP of each symbol, calculate the bit-by-bit log-likelihood ratio, and the formula is:

[0041] L(x)=max x＝1 {a n (p)+γ(p,n)+b n+1 (n)}-max x＝0 {a n (p)+γ(p,n)+b n+1 (n)};

[0042] Where x = 1 is the probability that the current bit is 1, and x = 0 is the probability that the current bit is 0.

[0043] A signal processing optimization system for training BCJR using the least squares method, including a first data signal processing module, an arbitrary waveform generator, an electro-absorption modulator, a Mach-Zehnder modulator, a variable optical attenuator, a photodiode, an analog-to-digital converter, and a second digital signal processing module connected in sequence.

[0044] Furthermore, the Mach-Zehnder modulator is connected to a laser.

[0045] Furthermore, the second digital signal processing module includes:

[0046] After the signal is processed by the feed - forward filter FFE, it is processed by the feedback filter PF;

[0047] Using the output of the feedback filter PF and the training sequence, channel estimation is performed by the least - squares LS algorithm;

[0048] Based on the channel response estimated by the least - squares LS algorithm, soft - decision decoding is performed using the BCJR algorithm to calculate the maximum a posteriori probability MAP of each symbol;

[0049] According to the maximum a posteriori probability MAP of each symbol, the bit - by - bit log - likelihood ratio is calculated;

[0050] The signal is recovered according to the obtained log - likelihood ratio.

[0051] As can be seen from the above - mentioned technical solutions, compared with the prior art, the present invention discloses a signal - processing optimization method and system for training BCJR using the least - squares method. After post - filter processing, the LS algorithm is introduced for secondary channel estimation to optimize the coefficients of the BCJR algorithm, making it more accurately reflect the original channel response. With a reasonable increase in the memory length of the BCJR algorithm, the system performance is significantly improved, while ensuring that it does not exceed the length of the original channel response. Different from the traditional method, which directly uses the tap coefficients of the post - filter as the BCJR coefficients, our improved scheme significantly enhances the system performance by recalculating the BCJR coefficients. In addition, since the least - squares method is a basic algorithm in the field of channel estimation, it is known for its low complexity, simple structure, stable performance, and ease of implementation. Therefore, although our improved scheme introduces additional calculation steps, the overall computational complexity does not increase significantly compared with the original system. Such a design not only maintains the efficiency of the system but also achieves a significant improvement in performance. Brief Description of the Drawings

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on the provided drawings.

[0053] Figure 1 It is a schematic diagram of the method principle of the present invention;

[0054] Figure 2 It is a block diagram of the system of the present invention. Detailed Embodiments

[0055] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0056] See Figure 1 , an embodiment of the present invention discloses a signal processing optimization method for training BCJR using the least squares method, including:

[0057] At the receiving end, after being processed by a linear equalizer, the FFE algorithm effectively reduces most of the inter-symbol interference. However, this process inevitably amplifies the noise. To effectively suppress the noise enhanced by equalization, the signal is then further processed by PF, and the transfer function of the post-filter is:

[0058] H(z) = 1 + alph*z -1 (1)

[0059] In the formula, alph represents the tap coefficient of PF, and z represents the Laplace transform;

[0060] Specifically, the output of PF can be expressed as:

[0061] Y(i) = r(i) + alph*r(i + 1) (2)

[0062] In the formula, i represents the current moment, and r(i) represents the signal received by PF;

[0063] Specifically, after obtaining the output of PF, the LS algorithm is used for channel estimation. A Toeplitz matrix is formed using the training sequence:

[0064]

[0065] Specifically, according to the LS algorithm formula, the re-estimated channel response is:

[0066] w = (X T X) -1 X T Y (4)

[0067] Specifically, when performing the least squares estimation, a part is taken from the training sequence as the training sequence for the least squares method. After obtaining the coefficients of BCJR through the least squares estimation, the soft information is calculated based on the maximum a posteriori probability starting from after the taken sequence. The response length calculated by LS corresponds to the memory length of BCJR. First, calculate the state transition metric of BCJR:

[0068] γ(p,n) = lnP(x) - (Y - (x n *w n +x n-1 *w n-1 +...x n-L *w n-L )) 2 / N0 (5)

[0069] Wherein, x represents possible state values (-3, -1, 1, 3), p represents the state at the previous moment, n represents the state at the next moment, P(x) represents the prior probability of the symbol, N0 represents the noise power, and L represents the memory length of BCJR.

[0070] Specifically, the optimal BCJR memory length corresponding to different channel responses is different. After obtaining the first parameter, calculate the forward recursion parameter:

[0071] α n+1 (n) = max{a n (p) + γ(p,n)} (6)

[0072] Specifically, the backward recursion parameter:

[0073] b n (p) = max{b n+1 (n) + γ(p,n)} (7)

[0074] Specifically, after obtaining the three parameters, the posterior probability of each symbol is expressed as:

[0075] Ρ(χ) = Sexp{a n (p) + γ(p,n) + b n+1 (n)} (8)

[0076] Specifically, for PAM4 with two bits per symbol, the final bit-by-bit log-likelihood ratio (LLR) can be obtained from the posterior probability of each symbol:

[0077]

[0078] Wherein, x = 1 is the probability that the current bit is 1, and x = 0 is the probability that the current bit is 0. Finally, the signal is recovered according to the obtained LLR information.

[0079] On the other hand, referring to Figure 2, an embodiment of the present invention also discloses a signal processing optimization system for training BCJR using the least squares method, including a first data signal processing module, an arbitrary waveform generator, an electro-absorption modulator, a Mach-Zehnder modulator, a variable optical attenuator, a photodiode, an analog-to-digital converter, and a second digital signal processing module connected in sequence, wherein the Mach-Zehnder modulator is connected to a laser.

[0080] In a specific embodiment, at the transmitting end, the pseudo-random binary sequence is mapped to a PAM4 sequence. After the PAM4 signal is generated, pre-emphasis is performed using an AWG (Keysight M8196A). Then, the electrical signal is amplified by a linear EA (SHF 807) and used to generate an optical signal using a Mach-Zehnder modulator (MZM) (FTM 7937) driven by a C-band laser. The optical signal is transmitted in a standard single-mode fiber (SSMF), and the transmission distance of the optical signal is different at different system rates, which will be analyzed in detail in the experimental results. On the receiver side, the received optical power (ROP) is adjusted by a variable optical attenuator (VOA). The signal is detected by a PD (FINRSAR XPDV2120ra), and the function of the analog-to-digital converter is implemented by a real-time oscilloscope (RTO) (UXR 0334A) to capture the signal. The speed of the real-time oscilloscope is 128 GSa / s, and the cut-off bandwidth is 33 GHz. Measuring the end-to-end channel frequency response, the channel response is not stable. Due to the low-cost transceiver, the 3dB bandwidth of the system is approximately 19 GHz. The digital signal processing process at the receiving end first realizes accurate timing recovery through the digital square technique after normalization and resampling, and uses the multi-tap FFE algorithm to eliminate the inter-symbol interference caused by bandwidth limitation and dispersion effects. After the FFE processes the signal, a postfilter (PF) is introduced, whose function is to solve the problem of noise enhancement that may be caused by the FFE. At the same time, known inter-symbol interference is also introduced. The BCJR algorithm is used to process the introduced inter-symbol interference. In the optimized BCJR algorithm, the LS algorithm is further introduced for preprocessing before the BCJR estimates the signal, and the algorithm principle is as Figure 2 shown. In this way, the BCJR based on the maximum a posteriori can more accurately process the remaining inter-symbol interference that the FFE fails to completely eliminate and the known inter-symbol interference introduced by the postfilter, and finally calculate the bit error rate of the system to comprehensively evaluate the performance of the algorithm.

[0081] In the present specification, the various embodiments are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other. For the apparatuses disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple. For the relevant parts, reference can be made to the description in the method section.

[0082] The foregoing description of the disclosed embodiments enables those skilled in the art to practice or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An optimized signal processing method for training BCJR using the least squares method, characterized in that Including: At the receiving end, after the signal is processed by the feed-forward filter FFE, it is processed by the feed-back filter PF. Using the output of the feed-back filter PF and the training sequence, channel estimation is performed by the least squares LS algorithm. Based on the channel response estimated by the least squares LS algorithm, soft decision decoding is performed using the BCJR algorithm to calculate the maximum a posteriori probability MAP of each symbol. According to the maximum a posteriori probability MAP of each symbol, calculate the bit-by-bit log-likelihood ratio. Restore the signal according to the obtained log-likelihood ratio.

2. The signal processing optimization method for training BCJR using the least squares method according to claim 1, characterized in that, The transfer function of the post-filter PF is: H(z) = 1 + alph*z -1 ; Where alph represents the tap coefficient of the post-filter PF, and z represents the Laplace transform.

3. The signal processing optimization method for training BCJR using the least squares method according to claim 1, characterized in that, The output of the post-filter PF is expressed as: Y(i) = r(i) + alph * r(i + 1); Where i represents the current time, and r(i) represents the signal received by the post-filter PF.

4. The signal processing optimization method for training BCJR using the least squares method according to claim 1, characterized in that, The channel estimation performed by the least squares LS algorithm includes: Using the training sequence to form a Toeplitz matrix: Where N is the number of rows of the training matrix, p is the number of columns, and the channel response re-estimated by the LS algorithm is: w = ( X T X) -1 X T Y; Where w is the channel response re-estimated by the LS algorithm, X is the Toeplitz matrix, and Y is the output of the PF.

5. The signal processing optimization method for training BCJR using the least squares method according to claim 1, characterized in that, Based on the channel response estimated by the least squares LS algorithm, soft decision decoding is performed using the BCJR algorithm to calculate the maximum a posteriori probability MAP of each symbol, including: Calculate the state transition metric of BCJR: γ(p,n) = lnP(x) - (Y - (x n *w n + x n-1 *w n-1 +... x n-L *w n-L )) 2 / N0; Calculate the forward recursion parameter: α n+1 f(n) = max{a n (p) + γ(p, n)}; Calculate the backward recursion parameter: b n (p) = max{b n+1 (n) + γ(p, n)}; Calculate the posterior probability of each symbol, expressed as: Ρ(χ) = Sexp{a n (p) + γ(p,n) + b n+1 (n)}; Where x represents the possible symbol, p represents the state at the previous time, n represents the state at the next time, P(x) represents the prior probability of the symbol, N0 represents the noise power, and L represents the memory length of BCJR.

6. The signal processing optimization method for training BCJR using the least squares method according to claim 1, characterized in that According to the maximum a posteriori probability MAP of each symbol, calculate the bit-by-bit log-likelihood ratio, and the formula is: L(x) = max x＝1 {a n (p) + γ(p, n) + b n+1 (n)} - max x＝0 {a n (p) + γ(p, n) + b n+1 (n)}; Where x = 1 is the probability that the current bit is 1, and x = 0 is the probability that the current bit is 0.

7. A signal processing optimization system for training BCJR using the least squares method, characterized in that, Including a first data signal processing module, an arbitrary waveform generator, an electro-absorption modulator, a Mach-Zehnder modulator, a variable optical attenuator, a photodiode, an analog-to-digital converter, and a second digital signal processing module connected in sequence.

8. The signal processing optimization system for training BCJR using the least squares method according to claim 7, characterized in that The Mach-Zehnder modulator is connected to a laser.

9. The signal processing optimization system for training BCJR using the least squares method according to claim 7, characterized in that, The second digital signal processing module includes: After the signal is processed by the feed-forward filter FFE, it is processed by the feed-back filter PF. Using the output of the feed-back filter PF and the training sequence, channel estimation is performed by the least squares LS algorithm. Based on the channel response estimated by the least squares LS algorithm, soft decision decoding is performed using the BCJR algorithm to calculate the maximum a posteriori probability MAP of each symbol. According to the maximum a posteriori probability MAP of each symbol, calculate the bit-by-bit log-likelihood ratio. Restore the signal according to the obtained log-likelihood ratio.

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