Carrier estimation and decoding cooperation method based on residual phase deviation tolerance threshold

Abstract

The invention discloses a carrier estimation and decoding cooperation method based on a residual phase deviation tolerance threshold, and belongs to the field of communication signal processing. According to the method, the weighted normalized check node satisfaction probability under the action of each phase compensation factor is designed as a metric value, and the accuracy and adaptability of carrier parameter estimation are improved in combination with soft information generated by the check node and the variable node in each iterative decoding process. According to the method, the phase estimator is embedded in the iterative decoding process, and a structure without a feedback loop is adopted, so that efficient cooperation of phase estimation and signal decoding is realized. According to the method, the tolerance range of phase estimation error deviation is introduced, the synchronization performance and the decoding performance of the algorithm are comprehensively considered by calculating the cmMSE, and the requirement for independent evaluation of signal synchronization and decoding performance in a traditional method is simplified. The method has universality, can adapt to wider and more complex communication scenes, and is not limited by specific signal-to-noise ratio conditions. Meanwhile, the method has no constraint on a modulation mode and a phase offset estimation range, and is wide in application.

Description

Technical Field

[0001] The present invention relates to a carrier estimation and decoding cooperation method based on a residual phase deviation tolerance threshold, and belongs to the field of communication signal processing. Background Art

[0002] In a complex border communication environment, due to the influence of various adverse factors such as extreme climate, electromagnetic interference, and complex terrain, signal transmission is easily interfered by multipath effects, terrain blockage, and Doppler effects, which significantly increases the difficulty of maintaining the stability and reliability of the communication link under low signal-to-noise ratio conditions, and the synchronous demodulation of signals becomes extremely difficult. To achieve high-reliability reception of signals under complex conditions, carrier phase recovery and efficient demodulation reception become key technical problems in designing high-performance communication receivers.

[0003] Existing carrier phase recovery methods are mainly divided into two categories: data-aided method (Data-aided, abbreviated as DA) and non-data-aided method (Non-data-aided, abbreviated as NDA). The data-aided method usually relies on pilot signals for channel parameter estimation and synchronization optimization, but this method will additionally increase the consumption of bandwidth and energy, and with the improvement of the information transmission speed, the additional pilot signals will lead to a reduction in the transmission rate of effective data, which is not suitable for communication application scenarios with tight resources and high efficiency requirements. In contrast, the traditional non-data-aided method directly estimates carrier parameters by performing non-linear transformation on the received data without relying on prior information. However, the synchronization performance of this method is poor under low signal-to-noise ratio conditions, especially in a complex border communication environment, this problem is more prominent.

[0004] In this context, the non-data-aided method introduced by channel coding technology has become a new way to achieve high-reliability signal synchronization in a low signal-to-noise ratio environment. As an efficient channel coding method, low density parity check code (LDPC code) has been widely used in modern communication systems due to its error correction performance close to the Shannon limit. The LDPC code-assisted NDA synchronization method uses the soft information generated during the iterative decoding process to improve the carrier estimation performance and signal demodulation performance. Existing methods focus on using hard decision signals or log-likelihood ratio information for phase estimation in the framework of iterative decoding. However, since most of them adopt a feedback mechanism, that is, the input of this iteration needs to use the carrier estimation result of the previous iteration, the system structure tends to be complex, and in the face of a complex and changeable border communication environment, the system stability and adaptability are insufficient. At the same time, there are also certain limitations in the accuracy and estimation range of existing technologies. In addition, current technologies mostly focus on the separate evaluation of synchronization performance or decoding performance, and the joint performance analysis of the two is still insufficient and requires further in-depth research. Summary of the Invention

[0005] To solve the problems of insufficient signal synchronization performance and poor data demodulation reliability of communication receivers in complex communication environments, the purpose of the present invention is to provide a carrier estimation and decoding cooperation method based on the residual phase offset tolerance threshold. This method performs multi-path compensation and parallel decoding on signals with residual phase offsets, conducts iterative probabilistic message passing based on the factor graph model, and maximizes the metric values under various phase compensation factors to obtain phase estimates, thereby achieving high-precision estimation of carrier parameters and highly reliable reception of received signals, realizing efficient cooperation between carrier recovery and demodulation decoding, with a simple system structure and strong anti-interference ability.

[0006] The purpose of the present invention is achieved through the following technical solutions.

[0007] A carrier estimation and decoding cooperation method based on the residual phase offset tolerance threshold disclosed by the present invention includes the following steps:

[0008] Step 1: The transmitting end generates an original information sequence, completes encoding and modulation processing, and generates a transmitted signal.

[0009] The transmitting end generates an original information sequence b = [b(1) b(2)... b(k)... b(K)], performs LDPC encoding with a code rate of N / K on it to obtain an encoded signal c = [c(1) c(2)... c(n)... c(N)]; performs MPSK modulation on c, where M represents the modulation order, to obtain a modulated signal d = χ(c), where d = [d(1) d(2)... d(n d )... d(N d )], and χ(·) represents the mapping function corresponding to MPSK modulation, represents the ceiling operation, that is, every adjacent k = log2(M) bits are mapped to 1 MPSK symbol d(n d ), as shown in Equation (1):

[0010]

[0011] Among them, (·) 10 represents the decimal representation of the binary sequence, and d is used as the transmitted signal;

[0012] Step 2: Receive the transmitted signal in Step 1, and complete phase compensation and bit transformation to obtain a compensated sequence.

[0013] The transmitted signal passes through a Gaussian channel to obtain a baseband signal with residual phase offset, which is called the received signal r = [r(1) r(2)... r(n d )... r(N d )],

[0014]

[0015] Among them, is the residual phase deviation, and z(n d ) is complex noise that follows a Gaussian distribution (0, σ 2 ). The residual phase interval of the received signal is evenly divided into L points, and a total of L equally spaced phase values are obtained where l is the phase value index. The complex number corresponding to the phase value is defined as the phase compensation factor. That is, the l-th phase compensation factor after the interval is evenly divided is expressed as The L phase compensation factors are respectively conjugated and multiplied with the received signal to obtain L received sequences after phase compensation; then, bit transformation is realized through Equation (3) to obtain L compensation sequences

[0016]

[0017] Among them, χ -1 (·) represents the demapping function and is the inverse function of the mapping function χ(·);

[0018] Step 3: Input the compensation sequences obtained in Step 2 into L parallel decoders in sequence to complete the initialization of variable nodes;

[0019] The received signal after being compensated in the l-th path is received by the decoder and is called the decoding input signal; the prior information of the decoding input signal is corrected through Equation (4) to obtain the corrected channel prior information, that is, the l-th decoding input h l The information passed to the variable node v,

[0020]

[0021] where P is the probability and the value of c is 0 or 1; initialize the variable node information,

[0022]

[0023] where m is the index of the check node f, and the superscript (1) represents the first iteration process of the decoder;

[0024] Step 4: Construct a factor graph model according to the parity-check matrix and perform iterative decoding until candidate decoding results are respectively output by each decoder

[0025] Construct a factor graph model with parity-check constraints according to the parity-check matrix H where V represents the set of variable nodes v, F represents the set of check nodes f, represents the set of edges connecting variable nodes and check nodes; update the check nodes according to the factor graph model constraints;

[0026]

[0027] Superscript (i) represents the i-th iteration process of the decoder; represents the sum of values excluding the value corresponding to index n, κ f (m) represents the constraint relationship characterized by the m-th check equation corresponding to the factor graph, R f (m) represents the set of check node indices connected to the m-th check node f, R f (m)\{n} represents the set R f removing index n;

[0028]

[0029] m is the index of the check node f, R v (n) represents the set of check node indices connected to the n-th variable node v, R v (n)\{m} represents the set R v removing index m;

[0030] The check node unidirectionally transmits information to the estimation node, that is, in the l-th decoder, the m-th check node f unidirectionally transmits information to the estimation node o l unidirectionally transmits information;

[0031]

[0032] Among them, for the decoding result generated in the i-th iteration process there is that is represents that the m-th check equation in the i-th iteration process is valid; represents that the m-th check equation in the i-th iteration process is invalid, is the weighting factor of the m-th check node in the i-th iteration process,

[0033]

[0034] Among them, LLR( i-1) [Q(n)] is the log-likelihood ratio of the posterior probability output by the n-th variable node in the (i - 1)-th iteration process. The estimation node o l outputs the information generated in each iteration Repeat step four until the preset maximum number of iterations I is reached, and each decoder outputs a candidate decoding result

[0035] Step 5: According to the information output by the estimation node, calculate the metric values of the bit compensation factors corresponding to each decoder, and use the phase compensation value corresponding to the maximum metric value as the phase estimation value, and the candidate decoding result corresponding to the maximum metric value as the final decoding result, thus completing the collaborative processing of carrier estimation and decoding.

[0036] Take the average value of all the iterative processes output by the estimation node o l and perform normalization processing to obtain the weighted normalized check node satisfaction probability which is called the metric value;

[0037]

[0038] where α is the normalization factor. Further, according to the maximum likelihood criterion, take the phase compensation value corresponding to the maximum metric value as the phase estimation value, and the candidate decoding result corresponding to the maximum metric value as the final decoding result;

[0039]

[0040] It further includes Step 6: Based on the weighted normalized check node satisfaction probability, calculate the code-assisted modified mean square error (Code-modified mean square error, abbreviated as cmMSE) to predict the collaborative performance.

[0041] Through Equation (12), take the decoder corresponding to the phase estimation value to obtain the weighted normalized check node satisfaction probability generated in its last iteration

[0042]

[0043] Set the tolerance threshold th(σ 2 ), and calculate the code-assisted modified mean square error through Equation (13);

[0044]

[0045] When the weighted normalized check node satisfaction probability generated in the last iteration falls within the tolerance threshold range, the modified mean square error is regarded as zero, and it is determined that its collaborative performance is excellent; when the weighted normalized check node satisfaction probability generated in the last iteration exceeds this threshold, the modified mean square error is the square of the deviation between the estimated phase and the actual phase, and it is determined that its collaborative performance is poor.

[0046] ​Through the above six steps, the present invention uses the probability that the weighted normalized check node generated in the iterative process satisfies as a metric value to estimate the residual phase offset to complete carrier recovery, and at the same time uses the channel prior information and the check matrix information to obtain the approximate posterior probability of the original information sequence, realizing demodulation and decoding.

[0047] Advantages:

[0048] 1. A carrier estimation and decoding cooperation method based on the residual phase offset tolerance threshold disclosed by the present invention designs the probability that the weighted normalized check node under the action of each phase compensation factor satisfies as a metric value, effectively combines the soft information generated by the check node and the variable node in each iterative decoding process, and improves the accuracy and adaptability of carrier parameter estimation. Compared with the traditional method, it can effectively eliminate the influence of residual phase offset on the demodulation performance under low signal-to-noise ratio conditions, thereby improving the anti-interference ability and data transmission quality of the overall communication system.

[0049] 2. A carrier estimation and decoding cooperation method based on the residual phase offset tolerance threshold disclosed by the present invention embeds a phase estimator in the iterative decoding process and adopts a structure design without a feedback loop to realize the efficient cooperation of phase estimation and signal decoding, while effectively improving the phase estimation accuracy and simplifying the system architecture.

[0050] 3. A carrier estimation and decoding cooperation method based on the residual phase offset tolerance threshold disclosed by the present invention introduces a tolerance range for the phase estimation error deviation. By calculating cmMSE, it comprehensively considers the synchronization performance and decoding performance of the algorithm, and simplifies the independent evaluation requirements for signal synchronization and decoding performance in the traditional method.

[0051] 4. A carrier estimation and decoding cooperation method based on the residual phase offset tolerance threshold disclosed by the present invention has universality and can adapt to a wider and more complex communication scenario without being restricted by specific signal-to-noise ratio conditions. At the same time, this method has no constraints on the modulation method and the phase offset estimation range, making its application potential in diverse communication environments more extensive. Description of the Drawings

[0052] Figure 1 is the flowchart of a carrier estimation and decoding cooperation method based on the residual phase offset tolerance threshold described in the present invention;

[0053] Figure 2 is the factor graph model of LDPC iterative decoding and carrier recovery based on the iterative probability message passing algorithm described in the present invention;

[0054] Figure 3 is the (1944,972) LDPC code type in the IEEE 802.11n standard described in the embodiment of the present invention under different E b / N0 and different The ε simulation curve under;

[0055] Figure 4 is the mean square error (MSE) / cmMSE curve of the (1944,972) LDPC code type in the IEEE 802.11n standard described in the embodiments of the present invention under different estimation algorithms;

[0056] Figure 5 is the bit error rate BER curve of the (1944,972) LDPC code type in the IEEE 802.11n standard described in the embodiments of the present invention under different estimation algorithms. Detailed implementation manners

[0057] To make the above objects, features, and advantages of the present invention more understandable, the following further detailed description is provided in conjunction with the accompanying drawings and specific implementation manners. In this embodiment, the (1944,972) LDPC code in the IEEE 802.11n standard is used, and the system parameters are shown in the following table:

[0058]

[0059] The LDPC iterative decoding and carrier recovery factor graph model based on the iterative probability message passing algorithm according to this embodiment is as Figure 1 shown, and the overall flowchart of the carrier estimation and decoding cooperation method proposed in this embodiment is as Figure 2 shown.

[0060] As Figure 2 shown, a carrier estimation and decoding cooperation method based on the residual phase offset tolerance threshold disclosed in this embodiment specifically includes the following implementation steps:

[0061] Step 1: The transmitting end generates an original information sequence, completes encoding and modulation processing, and generates a transmitted signal;

[0062] The transmitting end generates an original information sequence b = [b(1) b(2)... b(k)... b(972)], performs LDPC encoding with a code rate of N / K on it to obtain an encoded signal c = [c(1) c(2)... c(n)... c(1944)]; performs MPSK modulation on c, where M represents the modulation order. For BPSK modulation, M = 2, and further obtains a modulated signal d = χ(c), where d = [d(1) d(2)... d(n d )... d(1944)], and χ(·) represents the mapping function corresponding to MPSK modulation, represents the ceiling operation, that is, every adjacent k = log2(M) = log2(2) = 1 bit is mapped to 1 BPSK symbol d(nd ) as shown in Equation (1):

[0063]

[0064] where (·) 10 represents the decimal representation of a binary sequence, and d is used as the transmitted signal;

[0065] Step 2: Receive the signal transmitted in Step 1, and complete phase compensation and bit transformation to obtain a compensated sequence;

[0066] The transmitted signal passes through a Gaussian channel to obtain a baseband signal with residual phase offset, which is called the received signal r = [r(1) r(2)... r(n d )... r(N d )],

[0067]

[0068] where is the residual phase offset, and z(n d ) is complex noise that follows a Gaussian distribution (0, σ 2 ). The residual phase interval of the received signal is evenly divided into 31 points, and a total of L equally spaced phase values are obtained, where l is the phase value index. The complex number corresponding to the phase value is defined as the phase compensation factor. That is, the l-th phase compensation factor after the interval is evenly divided is expressed as The 31 phase compensation factors are respectively multiplied conjugately with the received signal to obtain 31 phase-compensated received sequences; then bit transformation is achieved through Equation (3) to obtain 31 compensated sequences

[0069]

[0070] where χ -1 (·) represents the demapping function, which is the inverse function of the mapping function χ(·);

[0071] Step 3: Input the compensated sequences obtained in Step 2 into 31 parallel decoders in sequence to complete variable node initialization;

[0072] The l-th phase-compensated received signal is received by the decoder, which is called the decoding input signal; the prior information of the decoding input signal is corrected through Equation (4) to obtain the corrected channel prior information, that is, the information h l transmitted to the variable node v,

[0073]

[0074] Where P is the probability and the value of c is 0 or 1; initialize the variable node information,

[0075]

[0076] where m is the index of the check node f, and the superscript (1) represents the first iteration process of the decoder;

[0077] Step 4: Construct a factor graph model according to the parity-check matrix and perform iterative decoding;

[0078] Construct a factor graph model with parity-check constraint relationships according to the parity-check matrix H where V represents the set of variable nodes v and F represents the set of check nodes f, represents the set of edges connecting variable nodes and check nodes; update the check nodes according to the factor graph model constraint relationships;

[0079]

[0080] The superscript (i) represents the i-th iteration process of the decoder; represents the sum of values excluding the value corresponding to index n, κ f (m) represents the constraint relationship characterized by the m-th parity-check equation corresponding to the factor graph, R f (m) represents the set of indices of check nodes connected to the m-th check node f, R f (m)\{n} represents the set R f (m) removing index n;

[0081]

[0082] m is the index of the check node f, R v (n) represents the set of indices of check nodes connected to the n-th variable node v, R v (n)\{m} represents the set R v (n) removing index m;

[0083] The check node unidirectionally transmits information to the estimation node, that is, in the l-th decoder, the m-th check node f unidirectionally transmits information to the estimation node o l Unidirectionally transmit information;

[0084]

[0085] Among them, for the decoding result generated in the i-th iteration process there is that is indicates that the m-th parity-check equation in the i-th iteration process is valid; Indicate that the m-th check equation in the i-th iteration process is invalid, is the weighting factor of the m-th check node in the i-th iteration process,

[0086]

[0087] where LLR( i-1) [Q(n)] is the log-likelihood ratio of the posterior probability output by the n-th variable node in the (i - 1)-th iteration process. The estimation node o l outputs the information generated in each iteration Repeat step four until the preset maximum number of iterations 20 is reached, and each decoder outputs a candidate decoding result

[0088] Step five, according to the information output by the estimation node, calculate the metric values of the phase compensation factors corresponding to each decoder, and use the phase compensation value corresponding to the maximum metric value as the phase estimation value, and the candidate decoding result corresponding to the maximum metric value as the final decoding result to complete the cooperative processing of carrier estimation and decoding.

[0089] Take the estimation node o l outputs all the information generated in the iteration process and take the average value, and perform normalization processing to obtain the weighted normalized check node satisfaction probability Call it the metric value;

[0090]

[0091] where α is the normalization factor. Further, according to the maximum likelihood criterion, take the phase compensation value corresponding to the maximum metric value as the phase estimation value, and the candidate decoding result corresponding to the maximum metric value as the final decoding result;

[0092]

[0093] Step six, based on the normalized check node satisfaction probability, calculate the code-aided modified mean square error to verify the cooperative performance;

[0094] Through Equation (12), take the decoder corresponding to the phase estimation value, and obtain the normalized check node satisfaction probability generated in its last iteration

[0095]

[0096] Set the tolerance threshold th(σ 2 ) = 0.8, and calculate the code-aided modified mean square error through Equation (13);

[0097]

[0098] When the satisfaction probability of the normalized check node generated by the last iteration falls within the tolerance threshold range, the corrected mean square error is regarded as zero, and it is determined that its cooperation performance is excellent; when the satisfaction probability of the normalized check node generated by the last iteration exceeds this threshold, the corrected mean square error is the square of the deviation between the estimated phase and the actual phase, and it is determined that its cooperation performance is poor. Figure 3 The satisfaction probability simulation curves of the LDPC code type adopted in this embodiment for the normalized check node under different signal-to-noise ratios and different phase compensation factors are given.

[0099] In this embodiment, a phase estimation metric is constructed by weighting the satisfaction probability of the normalized check node and is used for residual phase deviation estimation to complete carrier recovery. At the same time, the approximate posterior probability of the original information sequence is deduced by combining the channel prior information and the characteristics of the parity-check matrix, realizing the joint processing of synchronization and decoding.

[0100] For this embodiment, cmMSE and bit error rate simulation analyses are carried out, and the simulation results are as Figure 4 and Figure 5 shown. Figure 4 The simulation results of several phase estimation algorithms under different signal-to-noise ratios are shown. First, for comparison, a phase estimation algorithm based on data-aided correlation accumulation (denoted as "pilot method" in the legend) is used for simulation, and Barker codes of different lengths are specifically used as data pilots. The simulation results show that as the pilot length increases from 5 bits to 11 bits, the estimation performance of the algorithm is significantly improved. However, when the pilot length further increases from 11 bits to 13 bits, the improvement of the estimation accuracy tends to level off, showing a saturation trend in performance. After introducing LDPC codes, the assisted phase estimation shows obvious performance advantages in high signal-to-noise ratio scenarios. In the comparison, four existing metrics are selected for comparison. The simulation results show that in the low to medium signal-to-noise ratio region, the weighted satisfaction probability metric of the normalized check node in this embodiment shows the best estimation performance. Compared with the four existing metrics NSSP, GAMMA, El, and CSVP, its performance improvement is between 0.5 and 0.8 dB. In the higher signal-to-noise ratio region, the cmMSE results obtained by the four metrics tend to be close. The reason for this phenomenon is that when the signal-to-noise ratio is relatively high, the influence of noise on phase estimation decreases, and the effects of various metrics tend to be the same. Generally speaking, the LDPC iterative decoding strategy for joint phase estimation effectively improves the accuracy of phase estimation, especially in a harsh noise environment, and its advantages are more obvious.

[0101] Figure 5The LDPC decoding bit error rate curves of different estimation algorithms are shown. Introducing LDPC coding greatly improves the anti-noise robustness of the system, and verifies the cooperative optimization effect of LDPC coding combined with phase estimation. Specifically, at a relatively low signal-to-noise ratio, the algorithm of the present invention has comparable performance to the El algorithm and has the best bit error rate performance, with a performance advantage of about 0.15 dB compared to the NSSP and GAMMA algorithms. However, the CSVP algorithm has poor performance, with a performance decline of 0.5 dB at about Eb / N0 = 0 dB compared to other metrics, which is consistent with the cmMSE simulation results. It is worth noting that as the signal-to-noise ratio is further increased, although there are differences in the residual phase error among the algorithms, since the phase compensation factors within a certain range of the ideal phase deviation are sufficient to meet the demodulation requirements, in the high signal-to-noise ratio region, their bit error rate performances tend to be consistent. This phenomenon indicates that under high signal-to-noise ratio conditions, the influence of phase estimation accuracy on the decoding performance gradually weakens, and the bit error rate is mainly limited by the threshold characteristics of the LDPC coding itself.

[0102] The above specific description further details the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A carrier estimation and decoding cooperation method based on a residual phase deviation tolerance threshold, characterized in that: It includes the following steps: Step 1: The transmitting end generates an original information sequence, completes encoding and modulation processing, and generates a transmitted signal. The transmitting end generates an original information sequence b = [b(1) b(2)... b(k)... b(K)], performs LDPC encoding with a code rate of N / K on it to obtain an encoded signal c = [c(1) c(2)... c(n)... c(N)]; performs MPSK modulation on c, where M represents the modulation order, to obtain a modulated signal d = χ(c), where d = [d(1) d(2)... d(n d )... d(N d )], and χ(·) represents the mapping function corresponding to MPSK modulation, denotes the ceiling operation, that is, every adjacent k = log2(M) bits are mapped to 1 MPSK symbol d(n d ), as shown in Equation (1): where (·) 10 represents the decimal representation of the binary sequence, and d is used as the transmitted signal; Step 2: Receive the transmitted signal in Step 1, and complete phase compensation and bit transformation to obtain a compensated sequence. The transmitted signal passes through a Gaussian channel to obtain a baseband signal with residual phase offset, which is called the received signal r = [r(1) r(2)... r(n d )... r(N d )]. Among them, is the residual phase deviation, and z(n d ) is complex noise obeying the Gaussian distribution (0, σ 2 ); the residual phase interval of the received signal is evenly divided into L points, and a total of L phase values with equal intervals are obtained where l is the phase value index, and the complex number corresponding to the phase value is defined as the phase compensation factor, that is, the l-th phase compensation factor after the interval is evenly divided is expressed as The L phase compensation factors are respectively conjugated and multiplied with the received signal to obtain L received sequences after phase compensation; then the bit transformation is realized through Equation (3) to obtain L compensation sequences Among them, χ -1 (·) represents a demapping function, which is the inverse function of the mapping function χ(·); Step 3: Input the compensated sequence obtained in Step 2 into L parallel decoders in sequence to complete variable node initialization. The received signal after the l-th path compensation is received by the decoder and is called the decoding input signal; the prior information of the decoding input signal is corrected by Equation (4) to obtain the corrected channel prior information, that is, the l-th path decoding input h l the information passed to the variable node v where P is the probability, and the value of c is 0 or 1; initialize the variable node information. where m is the index of the check node f, and the superscript (1) represents the first iteration process of the decoder; Step 4: Construct a factor graph model based on the parity-check matrix and perform iterative decoding until the candidate decoding results are respectively output by each decoder Construct a factor graph model O=(V∪F,K) with parity check constraint relationships according to the parity check matrix H, where V represents the set of variable nodes v, F represents the set of parity check nodes f, and K represents the set of edges connecting variable nodes and parity check nodes; update the parity check nodes according to the factor graph model constraint relationships. Superscript (i) represents the i-th iteration process of the decoder; represents the summation of values other than the value corresponding to index n, and κf(m) represents the constraint relationship characterized by the m-th parity-check equation corresponding to the factor graph, R f (m) represents the set of parity-check node indices connected to the m-th parity-check node f, R f (m)\{n} represents the set R f (m) removing index n; m is the index of the check node f, R v R(n) represents the set of indices of check nodes connected to the n-th variable node v, R v R(n)\{m} represents the set R v R(n) removing the index m; The check node unidirectionally transmits information to the estimation node, that is, in the l-th decoder, the m-th check node f unidirectionally transmits information to the estimation node o l transmits information unidirectionally; Among them, for the decoding result generated in the i-th iteration process there is that is indicating that the m-th check equation in the i-th iteration process is valid; indicating that the m-th check equation in the i-th iteration process is invalid, and it is the weighting factor of the m-th check node in the i-th iteration process, Among them, LLR (i-1) [Q(n)] is the log-likelihood ratio of the posterior probability output by the nth variable node in the (i - 1)th iteration process; Estimation node o l Outputs the information generated in each iteration Repeat step four until the preset maximum number of iterations I is reached, and each decoder outputs a candidate decoding result respectively Step 5: According to the information output by the estimation node, calculate the metric values of the bit compensation factors corresponding to each decoder, and use the phase compensation value corresponding to the maximum metric value as the phase estimation value, and the candidate decoding result corresponding to the maximum metric value as the final decoding result to complete the cooperative processing of carrier estimation and decoding. Take the estimated node o l Generated by all iterations of the output The average value of, and perform normalization processing to obtain the weighted normalized check node satisfaction probability Call it the metric value; where α is the normalization factor. Further, according to the maximum likelihood criterion, the phase compensation value corresponding to the maximum metric value is taken as the phase estimation value, and the candidate decoding result corresponding to the maximum metric value is taken as the final decoding result; 2. The method according to claim 1, characterized in that: It also includes Step 6: Calculate the code-aided corrected mean square error based on the normalized parity check node satisfaction probability to predict the cooperative performance. Through formula (12), the decoder corresponding to the phase estimation value is taken, and the normalized check node satisfaction probability generated by its last iteration is obtained Set the tolerance threshold th(σ 2 ), and calculate the code-assisted modified mean square error through Equation (13); When the normalized parity check node satisfaction probability generated in the last iteration falls within the tolerance threshold range, the corrected mean square error is regarded as zero, and its cooperative performance is determined to be excellent; when the normalized parity check node satisfaction probability generated in the last iteration exceeds this threshold, the corrected mean square error is the square of the deviation between the estimated phase and the actual phase, and its cooperative performance is determined to be poor.

3. The method according to claim 2, characterized in that: Through the above six steps, the residual phase deviation is estimated by using the satisfaction probability of the weighted normalized parity check nodes generated in the iterative process as a metric to complete carrier recovery, and at the same time, the approximate posterior probability of the original information sequence is obtained by using the channel prior information and the parity check matrix information to realize demodulation and decoding.

Images