A signal processing optimization method and system for training BCJR using least squares method

Abstract

The present invention discloses a signal processing optimization method and system for training BCJR using the least squares method, which belongs to the technical field of short-distance high-speed optical communication signal processing. At the receiving end, the signal is processed by a feedforward filter FFE and then processed by a feedback filter PF; the output of the feedback filter PF and the training sequence are used to perform channel estimation using the least squares LS algorithm; based on the channel response estimated by the least squares LS algorithm, the BCJR algorithm is used for soft decision decoding to calculate the maximum a posteriori probability MAP of each symbol; based on the maximum a posteriori probability MAP of each symbol, the bit-by-bit log-likelihood ratio is calculated; and the signal is restored based on the obtained log-likelihood ratio. The present invention can solve the problem that the performance of the traditional BCJR algorithm is significantly reduced when facing severe inter-symbol interference. By optimizing the coefficients of the BCJR algorithm, it is made closer to the original channel response, thereby effectively reducing the bit error rate and improving system performance.

Description

Technical Field

[0001] The present invention relates to the technical field of short-distance high-speed optical communication signal processing, and more particularly to a signal processing optimization method and system using least squares method to train BCJR. 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 optical communication channel environments, the decoding accuracy of the BCJR algorithm in practical applications may be limited. To improve 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 achieving more accurate decoding results in complex optical communication environments.

[0003] The BCJR algorithm calculates the forward probability and backward probability of each symbol through a forward-backward recursive method to achieve optimal decoding. However, due to the following factors, the accuracy of the BCJR algorithm in certain channel environments may be affected: 1. Channel noise: The noise in optical communication systems usually comes from thermal noise, light source noise, and channel attenuation. 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, thereby affecting the decoding accuracy. 3. Non-ideal channel: In actual optical communication systems, the channel is often not completely ideal, and there are 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 categories:

[0005] 1. Improved soft decision strategy

[0006] The BCJR algorithm uses soft decisions to obtain symbol probability information to achieve more accurate decoding. In some optical communication systems, improved soft decision strategies can help improve decoding accuracy. In order to improve the accuracy of the decision, the BCJR algorithm can combine the prior information of the channel to reduce the occurrence of symbol decision errors and improve accuracy under low signal-to-noise ratio (SNR) conditions. Dynamic soft decision based on signal-to-noise ratio: Under low signal-to-noise ratio conditions, the soft decision of the BCJR algorithm may be inaccurate, resulting in decoding errors. To this end, the researchers proposed a dynamic soft decision method based on signal-to-noise ratio, which adjusts the decision strategy according to different channel qualities and enhances the reliability of soft decisions under poor channel conditions.

[0007] 2. Iterative decoding and joint signal detection

[0008] By combining it with other decoding algorithms, the BCJR algorithm's decoding accuracy can be significantly improved. Low-Density Parity-Check (LDPC) codes are combined with BCJR decoding: LDPC codes are powerful error-correcting codes. When used in conjunction with the BCJR algorithm, they can continuously improve decoding results through a soft input and output update process, thereby increasing the system's bit error rate (BER). This joint decoding approach leverages the error correction capabilities of LDPC codes and combines them with the maximum likelihood decoding properties of the BCJR algorithm, significantly improving decoding accuracy.

[0009] However, in the above existing technologies, the memory length of BCJR is fixed at 2. When the inter-symbol interference is relatively serious, there is a significant loss in performance because the fixed memory length discards information other than the actual channel response memory length. This causes the BCJR algorithm to lose part of the channel response in the process of compensating for signal damage, thereby affecting the overall performance of the algorithm. Therefore, further improvement is necessary.

[0010] Therefore, how to provide a signal processing optimization method and system using the least squares method to train BCJR is a problem that needs to be solved urgently 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 is significantly reduced when facing severe inter-symbol interference. By optimizing the coefficients of the BCJR algorithm, it is made closer to the original channel response, thereby effectively reducing the bit error rate and improving system performance. The least squares method (LS) is used for channel estimation, which is simpler and more efficient than other channel estimation algorithms. Although this method increases the computational complexity, this additional computational burden is reasonable in view of its ability to significantly improve system performance. In this way, the shortcomings of the BCJR algorithm in signal recovery accuracy can be effectively solved, bringing significant performance improvements to the system.

[0012] In order 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, the signal is processed by the feedforward filter FFE and then processed by the feedback filter PF;

[0015] Channel estimation is performed using the least squares LS algorithm using the output of the feed-back filter PF and the training sequence;

[0016] Based on the channel response estimated by the least squares LS algorithm, the BCJR algorithm is used for soft decision decoding to calculate the maximum a posteriori probability MAP of each symbol;

[0017] Calculate the bit-by-bit log-likelihood ratio based on the maximum a posteriori probability MAP of each symbol;

[0018] The signal is recovered based on 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 shift.

[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 moment, and r(i) represents the signal received by the post-filter PF.

[0025] Furthermore, the channel estimation is performed using the least squares LS algorithm, including:

[0026] Use the training sequence to form the Toeplitz matrix:

[0027]

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

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

[0030] Furthermore, the channel response estimated based on the least squares LS algorithm is soft-decided 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] Compute the forward recursive 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] The posterior probability of each symbol is calculated 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, the bit-by-bit log-likelihood ratio is calculated based on the maximum a posteriori probability MAP of each symbol. 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 bit is 1 at the current moment, and x=0 is the probability that the bit is 0 at the current moment.

[0043] A signal processing optimization system for training BCJR using the least squares method includes 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, which are 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 feedforward filter FFE, it is processed by the feedback filter PF;

[0047] Channel estimation is performed using the least squares LS algorithm using the output of the feed-back filter PF and the training sequence;

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

[0049] Calculate the bit-by-bit log-likelihood ratio based on the maximum a posteriori probability MAP of each symbol;

[0050] The signal is recovered based on the obtained log-likelihood ratio.

[0051] Through the above technical solution, it can be seen that compared with the existing technology, the present invention discloses a signal processing optimization method and system for training BCJR using the least squares method. After the post-filter processing, the LS algorithm is introduced for secondary channel estimation to optimize the coefficients of the BCJR algorithm so that it more accurately reflects the original channel response. With the reasonable increase in the memory length of the BCJR algorithm, the system performance is significantly improved, while ensuring that the length of the original channel response is not exceeded. Unlike traditional methods, which directly use the tap coefficients of the post-filter as BCJR coefficients, our improved solution 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 easy implementation. Therefore, although our improved solution introduces additional calculation steps, the overall computational complexity is not significantly increased compared to the original system. Such a design not only maintains the high 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 embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0053] Figure 1 Schematic diagram of the method principle of the present invention;

[0054] Figure 2 This is a system block diagram of the present invention. DETAILED DESCRIPTION

[0055] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

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

[0057] At the receiver, after processing by the linear equalizer, the FFE algorithm effectively mitigates most of the intersymbol interference. However, this process inevitably amplifies the noise. To effectively suppress the noise enhanced by equalization, the signal is further processed by the postfilter. The transfer function of the postfilter is:

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

[0059] Where, alph represents the tap coefficient of PF, z represents the Laplace change;

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

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

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

[0063] Specifically, after obtaining the output of PF, the LS algorithm is used to perform channel estimation. The 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 of the training sequence is first taken out as the least squares training sequence. After the BCJR coefficients are obtained by the least squares estimation, the soft information is calculated based on the maximum a posteriori probability starting from the extracted sequence. The response length calculated by LS corresponds to the BCJR memory length. First, the state transition metric of BCJR is calculated:

[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] Where x represents the possible state value (-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 lengths are different for different channel response conditions. After obtaining the first parameter, calculate the forward recursive parameters:

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

[0072] Specifically, the backward recursive parameters:

[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-wise log-likelihood ratio (LLR) can be obtained from the posterior probability of each symbol:

[0077]

[0078] Where x = 1 is the probability that the bit is 1 at the current moment, and x = 0 is the probability that the bit is 0 at the current moment. Finally, the signal is restored based on the obtained LLR information.

[0079] On the other hand, see Figure 2An embodiment of the present invention also discloses a signal processing optimization system for training BCJR using the least squares method, comprising 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 transmitter, a 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). The electrical signal is then 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 over standard single-mode fiber (SSMF). The optical signal transmission distance varies at different system rates, as detailed in the experimental results. At the receiver, the received optical power (ROP) is adjusted using a variable optical attenuator (VOA). Signal detection is performed using a PD (FINRSAR XPDV2120ra), and the analog-to-digital converter (ADC) is implemented using a real-time oscilloscope (UXR 0334A) to capture the signal. The speed of the real-time oscilloscope is 128GSa / s, and the cutoff bandwidth is 33GHz. The end-to-end channel frequency response is measured. The channel response is not stable. Due to the low-cost transceiver, the 3dB bandwidth of the system is approximately 19GHz. The digital signal processing process at the receiving end first uses the digital square technology after normalization and resampling to achieve accurate timing recovery, and uses the multi-tap FFE algorithm to eliminate the inter-symbol interference caused by bandwidth limitation and dispersion effect. After FFE processes the signal, a post filter (PF) is introduced. Its function is to solve the noise enhancement problem that may be caused by FFE. At the same time, it also introduces known inter-symbol interference. The BCJR algorithm is used to deal with the introduced inter-symbol interference. In the optimized BCJR algorithm, the LS algorithm is further introduced to pre-process the signal before BCJR estimation. The algorithm principle is as follows: Figure 2 As shown in Figure 2, the maximum a posteriori-based BCJR can more accurately handle the residual intersymbol interference that FFE cannot completely eliminate and the known intersymbol interference introduced by the post-filter. Finally, the system's bit error rate is calculated to comprehensively evaluate the algorithm's performance.

[0081] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0082] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one 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. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A signal processing optimization method for training BCJR using the least squares method, characterized in that: include: At the receiving end, the signal is processed by the feedforward filter FFE and then processed by the feedback filter PF; Channel estimation is performed using the least squares LS algorithm using the output of the feed-back filter PF and the training sequence; Based on the channel response estimated by the least squares LS algorithm, the BCJR algorithm is used for soft decision decoding to calculate the maximum a posteriori probability MAP of each symbol; Calculate the bit-by-bit log-likelihood ratio based on the maximum a posteriori probability MAP of each symbol; Recover the signal based on the obtained log-likelihood ratio; The channel response estimated based on the least squares LS algorithm uses the BCJR algorithm for soft decision decoding 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: Compute the forward recursive parameters: a n+1 (n)=max{a n (p)+γ(p,n)}; Calculate the backward recursion parameters: b n (p)=max{b n+1 (n)+γ(p,n)}; The posterior probability of each symbol is calculated as: P(x)=Sexp{a n (p)+γ(p,n)+b n+1 {noun}; 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.

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 feedback filter PF is: H(z)=1+alpha*z -1 ; Wherein, alph represents the tap coefficient of the feed-back filter PF, and z represents the Laplace change.

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 feed-back filter PF is expressed as: Y(i)=r(i)+alph*r(i+1); Where i represents the current moment, and r(i) represents the signal received by the feed-back 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 is performed using the least squares LS algorithm, comprising: Use the training sequence to form the Toeplitz matrix: Where N is the number of rows in the training matrix and p is the number of columns. 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 PF.

5. 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, the bit-by-bit log-likelihood ratio is calculated as follows: 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 bit is 1 at the current moment, and x=0 is the probability that the bit is 0 at the current moment.

6. A signal processing optimization system for training BCJR using the least squares method, applying the signal processing optimization method for training BCJR using the least squares method according to any one of claims 1 to 5, characterized in that: The device comprises 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 which are connected in sequence.

7. The signal processing optimization system for training BCJR using the least squares method according to claim 6, characterized in that: The Mach-Zehnder modulator is connected to a laser.

8. The signal processing optimization system for training BCJR using the least squares method according to claim 6, characterized in that: The second digital signal processing module includes: After the signal is processed by the feedforward filter FFE, it is processed by the feedback filter PF; Channel estimation is performed using the least squares LS algorithm using the output of the feed-back filter PF and the training sequence; Based on the channel response estimated by the least squares LS algorithm, the BCJR algorithm is used for soft decision decoding to calculate the maximum a posteriori probability MAP of each symbol; Calculate the bit-by-bit log-likelihood ratio based on the maximum a posteriori probability MAP of each symbol; The signal is recovered based on the obtained log-likelihood ratio.

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