CN111682924B - Bidirectional frequency domain Turbo equalization method adopting expected propagation - Google Patents

Bidirectional frequency domain Turbo equalization method adopting expected propagation Download PDF

Info

Publication number
CN111682924B
CN111682924B CN202010263763.0A CN202010263763A CN111682924B CN 111682924 B CN111682924 B CN 111682924B CN 202010263763 A CN202010263763 A CN 202010263763A CN 111682924 B CN111682924 B CN 111682924B
Authority
CN
China
Prior art keywords
external information
information
mean
decoding
equalization
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010263763.0A
Other languages
Chinese (zh)
Other versions
CN111682924A (en
Inventor
姜斌
唐禹
包建荣
朱芳
唐向宏
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Hangzhou Dianzi University
Original Assignee
Hangzhou Dianzi University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Hangzhou Dianzi University filed Critical Hangzhou Dianzi University
Priority to CN202010263763.0A priority Critical patent/CN111682924B/en
Publication of CN111682924A publication Critical patent/CN111682924A/en
Application granted granted Critical
Publication of CN111682924B publication Critical patent/CN111682924B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045—Arrangements at the receiver end
    • H04L1/0047—Decoding adapted to other signal detection operation
    • H04L1/005—Iterative decoding, including iteration between signal detection and decoding operation
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/29—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
    • H03M13/2957—Turbo codes and decoding
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045—Arrangements at the receiver end
    • H04L1/0052—Realisations of complexity reduction techniques, e.g. pipelining or use of look-up tables
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045—Arrangements at the receiver end
    • H04L1/0055—MAP-decoding
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0059—Convolutional codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0064—Concatenated codes
    • H04L1/0066—Parallel concatenated codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03159—Arrangements for removing intersymbol interference operating in the frequency domain
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention discloses a bidirectional frequency domain Turbo equalization method adopting expected propagation, which comprises the following steps: s1, receiving a transmission signal of underwater sound or a wireless channel, and approximately deducing posterior distribution characteristics of a symbol bit of the received signal by adopting an EP soft mapping method; s2, processing the received signal by adopting a bidirectional frequency domain soft equalization method to obtain equalization external information; s3, combining bidirectional balanced external information by using a bidirectional combination method assisted by covariance; s4, inputting the combined external information into a Log-MAP decoding judgment method to obtain decoded external information, inputting the decoded external information into an EP soft mapping method as prior, and repeatedly executing steps S1-S4; s5, judging whether the iteration times reach the preset iteration times or not, if not, continuing to execute the steps S1-S4; if yes, judging decoding by using a Log-MAP decoding judgment method, and outputting a decoding code word.

Description

Bidirectional frequency domain Turbo equalization method adopting expected propagation
Technical Field
The invention relates to the technical field of digital communication, in particular to a bidirectional frequency domain Turbo equalization method adopting expectation propagation.
Background
With the ever-increasing demand for communication during marine operations, there is a continuing need for improvements in marine communication technologies. The transmission medium for underwater acoustic communication is sound waves. Due to the limitation of sound waves, an underwater sound channel has the characteristics of serious selective fading, extremely long time delay expansion and the like, so that the problem of extremely serious intersymbol interference of received signals is caused. In order to solve the problems, a Turbo equalization structure is introduced to process the received signals. The Turbo equalization can effectively solve the problem of crosstalk between signals through soft information iteration between the equalization module and the decoding module, so that the Turbo equalization method is widely applied to underwater robots, unmanned aerial vehicles and signal receiving modules of underwater sensor networks.
Turbo equalization using Maximum a posteriori probability (MAP) is one of the currently best performance equalizers, also called BCJR equalization. The state and the transition probability are calculated by adopting a grid, but the calculation complexity is exponentially increased along with the increase of the modulation order, and the requirement on the channel estimation precision is higher. Although the subsequent simplification and improvement are carried out, the problems that the equalization effect is weakened greatly and the like easily occur if the channel order exceeds the number of grid states. The Turbo equalizer adopting the Minimum Mean Square Error (MMSE) and the confidence method has greater application potential under the condition of a long time delay time-varying channel.
The Turbo equalizer using MMSE criterion can be classified as time domain or frequency domain Turbo equalization according to the difference of signal processing signal domains. When the former processes data with a long frame length, the data is processed in batches by a sliding window, so that the complexity can be effectively reduced. However, in practical applications, the size of the sliding window is set to have a large influence on the equalization receiving performance, so that the method is not suitable for time-varying underwater sound and wireless channel environments. The Turbo equalization in frequency domain can be approximately regarded as single-tap Turbo equalization in time domain, and the computation complexity of the time domain equalizer can be represented by O (N) through Fast Fourier Transform (FFT) 2 L) is reduced to O (NlogN), and the method has the advantages of low computational complexity, stable performance and the like. But both of the above equalizers perform far worse than BCJR equalization. The confidence balance mainly comprises BP (belief propagation), GMP (Gaussian mean propagation) and BP processing signals by using a factor graph model, the application of the BP processing signals is limited to sparse channels, and the confidence iteration cycle edge number is more than 6 to ensure better convergence performance. GMP mainly adopts a tree graph to process confidence information, effectively solves the problem of short loop, but has the problems of excessive iteration times and the like, improves the calculation complexity because the calculation complexity and the channel length form a square relation, and is not suitable for long-delay high-order underwater sound and wireless channels;
the EP method comprises the following steps:
the EP method is a deterministic approximation method in approximation inference. Which approximates the posterior distribution of the difficult-to-compute parameter with a simple distribution pair. The basic principle of the method is that the posterior distribution is approximated by iteration through factorization of target distribution. In one example, assuming that q (x) is a gaussian distribution N (x | μ, Σ), p (x) is a complex distribution, EP minimizes divergence KL (p | q) by iteratively equalizing the mean and variance of μ, Σ and p (x), and when the iterations converge, q (x) can be considered to be approximately equal to p (x), which is also referred to as Moment Matching.
Bayesian formula:
the Bayes theorem is based on a conditional probability formula to solve the following problem: suppose event H 1 、H 2 、...、H n Mutually exclusive and constitute a complete event, the probability P (H) of which is known i ) N occurs with an observed event a, and the conditional probability P (a | H) is known i ) Solving for P (H) using the following equation i |A)：
Figure BDA0002440426100000021
The above equation is called Bayesian equation.
The Log-MAP decoding method comprises the following steps:
MAP decoding, also known as BCJR decoding, is a maximum a posteriori decoding method for error correcting codes defined on a trellis. However, the computation complexity is too high due to the large number of exponents and multiplications of the MAP. Therefore, logarithm operation is introduced, multiplication operation can be effectively converted into addition operation, and therefore the calculation complexity is reduced.
The Log-MAP decoding judgment method comprises the following steps:
obtaining a conditional probability by using the received channel output sequence, and calculating a conditional LLR:
Figure BDA0002440426100000022
the upper type
Figure BDA0002440426100000023
For an input sequence of length N the input sequence,
Figure BDA0002440426100000024
Figure BDA0002440426100000025
in order to receive the information bits, the receiver,
Figure BDA0002440426100000026
is the received check bit.
Figure BDA0002440426100000027
Is about decoding bit u k The Log-MAP decoder task is to solve the decision symbols of the above LLR:
Figure BDA0002440426100000031
the Turbo equalization method comprises the following steps: in digital communication, Turbo equalization is a method for processing intersymbol interference and noise interference existing between received signals, and by transmitting iterative information between a soft-in soft-out equalizer and a decoder, the receiving performance can be effectively improved. In terms of method structure, the method is related to Turbo codes, a channel can be regarded as a non-redundant convolutional code encoder, and Turbo equalization is correspondingly regarded as an iterative decoding method. Turbo can only be used to suppress intersymbol interference and noise, since there is no addition of information redundancy in the signal passing through the channel.
Disclosure of Invention
The invention aims to provide a bidirectional frequency domain Turbo equalization method adopting expected propagation aiming at the defects of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a bidirectional frequency domain Turbo equalization method adopting expected propagation comprises the following steps:
s1, receiving a transmission signal of underwater sound or a wireless channel, and approximately deducing posterior distribution characteristics of a symbol bit of the received signal by adopting an EP soft mapping method;
s2, processing the received signal by adopting a bidirectional frequency domain soft equalization method to obtain equalization external information;
s3, combining bidirectional balance external information by using a bidirectional combination method assisted by covariance;
s4, inputting the combined external information into a Log-MAP decoding judgment method to obtain decoded external information, inputting the decoded external information into an EP soft mapping method as prior, and repeatedly executing steps S1-S4;
s5, judging whether the iteration times reach the preset iteration times or not, if not, continuing to execute the steps S1-S4; if yes, judging decoding by using a Log-MAP decoding judgment method, and outputting a decoding code word.
Further, the step S1 specifically includes:
s11, receiving transmission signals of underwater sound or wireless channels;
s12, respectively transmitting the sequence and the outer decoding information in the received signal to a forward Turbo equalization method and a reverse Turbo equalization method for processing;
s13, generating decoded external information L from the processed information by using a Log-MAP decoding method d,k ；
S14, the posterior probability is subjected to Bayesian formula
Figure BDA0002440426100000032
Calculating;
s15, according to the posterior probability
Figure BDA0002440426100000041
Mean value of posterior distribution at current time
Figure BDA0002440426100000042
Sum variance mean gamma d Calculating;
s16, obtaining posterior extrinsic information edge probability distribution q by using a moment matching method E (s k ) And calculating the feedback symbol of the edge distribution of the external information by using a Gaussian decomposition method
Figure BDA0002440426100000043
Sum variance mean v new ；
S17, for the feedback symbol
Figure BDA0002440426100000044
Sum variance mean v new Updating to obtain updated feedback symbol
Figure BDA0002440426100000045
Sum variance mean v d 。
Further, the step S2 specifically includes:
s21, according to the updated feedback symbol
Figure BDA0002440426100000046
Sum mean of variance v d Calculating a pre-filter coefficientf k 、ξ；
S22, adopting a feedback symbol
Figure BDA0002440426100000047
Sum variance mean v d Equalizing the received signal to obtain equalized symbol
Figure BDA0002440426100000048
Sum variance v e 。
Further, the step S3 specifically includes:
s31, according to the posterior probability
Figure BDA0002440426100000049
And outer information of decoding L d，k Respectively calculating forward balanced external information L 1，k And reverse equalizing the extrinsic information
Figure BDA00024404261000000410
S32, balancing the reverse direction external information
Figure BDA00024404261000000411
The reverse extrinsic information L obtained by performing a time reversal operation 2，k ；
S33, according to the forward direction balance external information L 1，k And reverse extrinsic information L 2，k And merging the external information.
Further, the step S12 further includes performing a time reversal operation before transmitting to the reverse Turbo equalization end, which is represented as:
Figure BDA00024404261000000412
wherein the content of the first and second substances,
Figure BDA00024404261000000413
and
Figure BDA00024404261000000414
and the real number respectively represents the received signal after time reversal and the decoded extrinsic information.
Further, in the step S15
Figure BDA00024404261000000415
Mean value of posterior distribution at current time
Figure BDA00024404261000000416
Sum variance mean gamma d A calculation was performed, expressed as:
Figure BDA00024404261000000417
Figure BDA00024404261000000418
further, the feedback sign of the edge distribution of the extrinsic information is calculated in the step S16
Figure BDA00024404261000000419
Sum variance mean v new Expressed as:
Figure BDA00024404261000000420
Figure BDA0002440426100000051
wherein the content of the first and second substances,
Figure BDA0002440426100000052
and v new Are all real numbers.
Further, the pre-filter coefficient is calculated in the step S21f k ξ, expressed as:
Figure BDA0002440426100000053
Figure BDA0002440426100000054
wherein the content of the first and second substances,h k is a complex number, which represents the k-th value of the channel after FFT with length of N points,
Figure BDA0002440426100000055
is a real number, representing the noise variance.
Further, in step S22, a feedback symbol is specifically adopted
Figure BDA0002440426100000056
Sum variance mean v d Andh k equalizing the received signal to obtain equalized symbol
Figure BDA0002440426100000057
Sum variance v e Expressed as:
Figure BDA0002440426100000058
v e ＝ξ -1 -v d
wherein the content of the first and second substances,
Figure BDA0002440426100000059
y k indicating the k-th value of the feedback symbol and the received signal after the FFT with N points.
Further, step S33 is preceded by: calculating the forward balance outer information L 1，k And reverse extrinsic information L 2，k Represented as:
Figure BDA00024404261000000510
wherein the content of the first and second substances,
Figure BDA00024404261000000511
for real numbers, covariance is indicated. m is 1 And m 2 The symbol mean value of soft mapping of soft information output by the forward equalizer and the reverse equalizer is respectively expressed as a real number;
in step S33, the external information is merged, which is represented as:
Figure BDA00024404261000000512
wherein L is e，k Is a real number and represents the combined equalized extrinsic information.
Compared with the prior art, the method utilizes the EP to approximate the posterior probability of the symbols, has lower calculation complexity compared with the prior BCJR method, and has lower signal-to-noise ratio threshold compared with the traditional frequency domain Turbo equalization method. In addition, the bidirectional frequency domain equalization structure is adopted, so that the characteristics of low correlation degree and the like are achieved, the error propagation problem can be effectively inhibited, and the error rate is further reduced. The method is very suitable for receiving signals with intersymbol interference, such as underwater sound, wireless signals and the like, and can effectively improve the communication performance.
Drawings
FIG. 1 is a flow chart of a bi-directional frequency domain Turbo equalization method using expectation propagation according to an embodiment;
fig. 2 is a structural diagram of a downlink throughput enhancement system of a bidirectional transmission network based on an exclusive-or operation according to an embodiment;
FIG. 3 is a flowchart of a method for soft mapping using EP according to an embodiment;
fig. 4 is a flowchart of a frequency domain soft equalization method according to an embodiment;
FIG. 5 is a flowchart of a covariance-assisted two-way merge method according to an embodiment;
FIG. 6 is an EXIT diagram of different equalization methods provided in one embodiment;
FIG. 7 is an EXIT-based iteration trace diagram of different equalization methods provided by an embodiment;
fig. 8 is a schematic diagram comparing bit error rate curves of different equalization methods according to an embodiment.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict.
The invention aims to provide a bidirectional frequency domain Turbo equalization method adopting expected propagation aiming at the defects of the prior art.
(1) Firstly, the EP soft mapping method approximately deduces the posterior distribution characteristics of the symbol bit; (2) secondly, processing the received signal by using a bidirectional frequency domain soft equalization method; (3) then, combining bidirectional balance external information by using a bidirectional combination method assisted by covariance; (4) and finally, inputting the combined external information into a Log-MAP decoding method of the background technology to obtain decoded external information, inputting the decoded external information into an EP soft mapping method as prior, repeating the methods (1) to (4), judging decoding by using a decoding judgment method of the background technology after the preset maximum iteration times are reached, and outputting decoded code words.
Principle of covariance auxiliary external information merging method
The joint forward and reverse equalization extrinsic information has the following formula:
Figure BDA0002440426100000071
L e,k is a real number, representing the combined equalized extrinsic information, a k Denotes the k-th code word, a k ＝{0，1}，L e,1 (a k ) Representing the first bit of forward balanced extrinsic information, L e,2 (a k ) Represents the kth reverse equalized extrinsic information, P (L) e,1 (a k ),L e,2 (a k )|a k 0) represents a codeword a k When equal to 0, the external information L e,1 (a k 0) and L e,2 (a k 0) probability of occurrence, P (L) e,1 (a k ),L e,2 (a k )|a k 1) represents a codeword a k When 1, the external information L e,1 (a k 1) and L e,2 (a k 1) probability of occurrence.
Since the probability distribution of the output of the equalization method is generally assumed to be gaussian distribution, although the reverse equalization method processes a signal that is time-reversed, the forward equalization method and the reverse equalization method essentially process the same received signal in the same channel, and therefore P (L) can be assumed e,1 (a k ),L e,2 (a k )|a k ) For a joint gaussian distribution, there are therefore:
Figure BDA0002440426100000072
in the above formula, L k ＝[L e,1 (a k ),L e,2 (a k )]，
Figure BDA0002440426100000073
μ k ＝a k [γ 1 ,γ 2 ]，ρ,γ 1 ,σ 1 ,γ 2 ,σ 2 Are all real numbers, ρ is the correlation coefficient, γ 1 ,σ 1 Is L e,1 Mean and variance of γ 2 ,σ 2 Is L e,1 Mean and variance of
Figure BDA0002440426100000074
Substituting the formula into a formula, simplifying, and solving a merged extrinsic information expression as follows:
L e,k ＝λ 1 L e,1 (a k )+λ 2 L e,2 (a k )
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002440426100000075
since the bi-directional and reverse equalization are independent of the input signal y, the forward and reverse equalization filter parameters can be approximately considered the same, and thus there is γ 1 ≈γ 2 ，σ 1 ≈σ 2 And since the modulation is BPSK, there are
Figure BDA0002440426100000076
Therefore, there are:
Figure BDA0002440426100000081
thus, there is merged extrinsic information
Figure BDA0002440426100000082
Example one
The embodiment provides a bidirectional frequency domain Turbo equalization method using expected propagation, as shown in fig. 1, including the steps of:
s1, receiving a transmission signal of underwater sound or a wireless channel, and approximately deducing posterior distribution characteristics of a symbol bit of the received signal by adopting an EP soft mapping method;
s2, processing the received signal by adopting a bidirectional frequency domain soft equalization method to obtain equalization external information;
s3, combining bidirectional balanced external information by using a bidirectional combination method assisted by covariance;
s4, inputting the combined external information into a Log-MAP decoding judgment method to obtain decoded external information, inputting the decoded external information into an EP soft mapping method as a priori, and repeatedly executing steps S1-S4:
s5, judging whether the iteration times reach the preset iteration times or not, if not, continuing to execute the steps S1-S4; if yes, judging decoding by using a Log-MAP decoding judgment method, and outputting a decoding code word.
In step S1, the EP soft mapping approximation is used to infer the symbol bits of the received signal, and the method flow is shown in fig. 2, and specifically includes:
s11, receiving transmission signals of underwater sound or wireless channels;
the mathematics of transmission of a hydroacoustic or wireless channel are described as follows:
Figure BDA0002440426100000083
wherein h is a vector with length L, which represents the impulse response of underwater sound or wireless channel, and the expression is: h ═ h 1 ，h 2 ，h 3 ，...，h L ](ii) a L is an integer and represents the number of taps of the channel impulse response, h i Is the ith tap coefficient, and i is an integer, and the value range is: 1, …, L; x is a vector of length N, representing a symbol of the data bit vector u after encoding, interleaving, modulation mapping, and is expressed as x ═ x 1 ，x 2 ，x 3 ，...，x N ]，x j Is the jth modulation symbol, and N, j is an integer, and the value range of j is: j is 1, …, N, x j E.g. a, where a is the set of mapping symbols, and for BPSK, a { -1, 1 }. N and y are each a vector of length N + L-1, representing the additive noise and the received signal, N ═ N 1 ，n 2 ，n 3 ，…，n N+L-1 ]，y＝[y 1 ，y 2 ，y 3 ，...，y N+L-1 ]，n k And y k Respectively for the kth noise and received signal, and k is the integer, and the value range is: 1, N + L-1.
Figure BDA0002440426100000084
Representing a convolution operation.
S12, respectively transmitting the sequence and the outer decoding information in the received signal to a forward Turbo equalization method and a reverse Turbo equalization method for processing;
receiving signal sequence y and outer decoding information L d，k The data are respectively transmitted to the forward Turbo equalization method and the reverse Turbo equalization method mentioned in the background technology. Before transmitting to the reverse Turbo equalization end, time reversal operation is required, namely:
Figure BDA0002440426100000091
wherein the content of the first and second substances,
Figure BDA0002440426100000092
and
Figure BDA0002440426100000093
and the real number respectively represents the received signal after time reversal and the decoded extrinsic information.
S13, generating decoded external information L from the processed information by using a Log-MAP decoding method d，k ；
Method for generating decoding external information L by Log-MAP decoding method d，k And L is d，k Is a real number, k is the current time, is an integer, and is represented by the following formula for the prior probability P k (α i ) The calculation, expressed as:
Figure BDA0002440426100000094
wherein, P k (α i ) Is a real number and has a value range of [0, 1 ]](ii) a M is a modulation order; alpha is alpha i Mapping set A for modulation symbolsThe ith mapping symbol;
Figure BDA0002440426100000095
and the q-th bit code word is the ith mapping symbol of the A. In the first iteration, the decoding module does not generate the decoding external information, and then the decoding external information L d，k The initial values of (a) are: l is d，k ＝0。
S14, the posterior probability is subjected to Bayesian formula
Figure BDA0002440426100000096
Calculating;
using Bayes formula in background technique to pair posterior probability
Figure BDA0002440426100000097
The calculation, expressed as:
Figure BDA0002440426100000098
wherein the content of the first and second substances,
Figure BDA0002440426100000099
is a real number and has a value range of [0, 1 ]]The likelihood probability representing the extrinsic information is calculated by the following equation (5):
Figure BDA00024404261000000910
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00024404261000000911
and v e And is a real number, representing the equalized symbols and the mean of variance of the equalizer output. When the equalization is to be initialized, the equalization is started,
Figure BDA00024404261000000912
has a value of 0, i.e.
Figure BDA00024404261000000913
v e Inf, Inf denotes infinityIs large.
Figure BDA00024404261000000914
Is a real number with a value range of [0, 1]To equalize the symbols as
Figure BDA00024404261000000915
The sum of the probabilities of the events is calculated by the following equation (6):
Figure BDA00024404261000000916
s15, according to posterior probability
Figure BDA00024404261000000917
Mean value of posterior distribution at current time
Figure BDA00024404261000000918
Sum variance mean gamma d An estimate is made, expressed as:
Figure BDA0002440426100000101
Figure BDA0002440426100000102
s16, obtaining posterior extrinsic information edge probability distribution q by using a moment matching method E (s k ) And calculating the feedback symbol of the edge distribution of the external information by using a Gaussian decomposition method
Figure BDA0002440426100000103
Sum variance mean v new ；
Obtaining posterior information outer edge probability distribution q by using Moment Matching method mentioned in background technology E (s k ) As shown in formula (9):
Figure BDA0002440426100000104
the feedback symbols of the edge distribution of the obtained extrinsic information are calculated according to the Gaussian decomposition method described in the literature ("T.P.Minka", "A family of algorithms for improving Bayesian reference", "Ph.D.Disservation, depth.electric.Eng.Compout.Sci., MIT, Cambridge, MA, USA, Jan.2001.")
Figure BDA0002440426100000105
Sum variance v new Respectively expressed as:
Figure BDA0002440426100000106
Figure BDA0002440426100000107
wherein the content of the first and second substances,
Figure BDA0002440426100000108
and v new Are all real numbers.
S17, for the feedback symbol
Figure BDA0002440426100000109
Sum mean of variance v new Updating to obtain updated feedback symbol
Figure BDA00024404261000001010
Sum variance mean v d 。
To avoid the confidence information from being locked to local minimum, the feedback symbols are expressed by the following equations (12) and (13)
Figure BDA00024404261000001011
Sum variance mean v d Update, represented as:
v d(next) ＝(1-β)ν new +βv d(prev) (12)
Figure BDA00024404261000001012
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00024404261000001013
v d for real numbers, superscripts (next) and (prev) represent the next and previous states, respectively. β is an adjustment parameter, is a real number, and for Phase Shift Key (PSK) modulation, β is 0.7 × 0.9 s And S is an integer and is the self-iteration number, S belongs to {1, 2,. and S }, S is an integer and represents the maximum self-iteration number, and the convergence of the EP equalization method can be guaranteed by taking the value as 3. At the first iteration, since there is no previous state, at this time
Figure BDA00024404261000001014
v d(prev) ＝1。
In step S2, the received signal is processed by using a bidirectional frequency domain soft equalization method to obtain the information outside the equalization. As shown in fig. 3, the method specifically includes:
s21, feedback sign obtained by S17
Figure BDA0002440426100000111
Sum variance mean v d Calculating a pre-filter coefficientf k ξ, expressed as:
Figure BDA0002440426100000112
Figure BDA0002440426100000113
wherein the content of the first and second substances,h k is a complex number, which represents the k-th value of the channel h after FFT with the length of N points,
Figure BDA0002440426100000114
is a real number, representing the noise variance.
S22, adopting the inverse methodFeed symbol
Figure BDA0002440426100000115
Sum variance mean v d Equalizing the received signal to obtain equalized symbol
Figure BDA0002440426100000116
Sum variance v e 。
Using feedback symbols
Figure BDA0002440426100000117
Sum variance mean v d Andh k for received signal y k Performing equalization processing to obtain equalized symbol
Figure BDA0002440426100000118
Sum variance v e Expressed as:
Figure BDA0002440426100000119
v e ＝ξ -1 -v d (17)
wherein the content of the first and second substances,
Figure BDA00024404261000001110
y k the k-th value after the feedback symbol xd and the received signal y are subjected to FFT with the length of N points is represented; x is the number of d Is a vector of length N and,
Figure BDA00024404261000001111
Figure BDA00024404261000001112
the k-th feedback symbol is represented, k is an integer, and the value range of k is as follows: k ═ 1,2,., N }.
And repeating the steps S13-S17 and S21-S22 until the set maximum number S of self-iterations is reached, wherein S is an integer. In this embodiment, the performance can be converged by iterating 3 times with the EP equalization method, with S set to 3.
In step S3, the bi-directional equalization extrinsic information is merged using a covariance-aided bi-directional merging method. As shown in fig. 4, the method specifically includes:
s31, according to the posterior probability
Figure BDA00024404261000001113
And outer information L of decoding d，k Respectively calculating forward balanced external information L 1，k And reverse equalizing the extrinsic information
Figure BDA00024404261000001114
According to the posterior
Figure BDA00024404261000001115
And outer information L of decoding d，k Respectively calculate forward balanced extrinsic information L by using the following formula (18) 1，k And reverse equalizing the extrinsic information
Figure BDA00024404261000001116
Expressed as:
Figure BDA00024404261000001117
wherein L is k And the number is real, and the equalization extrinsic information is represented.
S32, the reverse balance external information is subjected to
Figure BDA0002440426100000125
The reverse extrinsic information L obtained by performing a time reversal operation 2，k (ii) a Expressed as:
Figure BDA0002440426100000121
s33, according to the forward direction balance external information L 1，k And reverse extrinsic information L 2，k And merging the external information.
Step S33 is preceded by: calculating forward balanced extrinsic information L 1，k And converselyOutgoing information L 2，k Represented as:
Figure BDA0002440426100000122
wherein the content of the first and second substances,
Figure BDA0002440426100000126
for real numbers, covariance is indicated. m is 1 And m 2 The symbol mean value of soft mapping of soft information output by the forward equalizer and the reverse equalizer is respectively expressed as a real number; the calculation formula is m i ＝1/2tanh(L k /2)，i＝1,2，L k And the number is real, and the equalization extrinsic information is represented. Sign [. to]"denotes a symbolic function.
According to forward direction external information L 1,k And reverse extrinsic information L 2,k The external information is merged using the following formula (21):
Figure BDA0002440426100000123
wherein L is e，k Is a real number and represents the combined equalized extrinsic information.
In step S4, the merged extrinsic information is input into a Log-MAP decoding decision method to obtain decoded extrinsic information, and the decoded extrinsic information is input as a priori into an EP soft mapping method, and steps S1-S4 are repeatedly performed. The method specifically comprises the following steps:
s41, generating a decoding posterior probability P (u) by using Log-MAP decoding method k |y k )。
S42, the method uses the following formula to obtain the decoded extrinsic information L d,k
Figure BDA0002440426100000124
S43, inputting the decoded information as a priori to the method (1).
In step S5, it is determined whether the iteration count reaches the preset iteration count, and if not, the steps S1-S4 are continuously performed; if yes, judging decoding by using a Log-MAP decoding judgment method, and outputting a decoding code word.
When the maximum Turbo iteration times T is reached, the iterative computation is stopped, a Log-MAP decoding method is used to generate a decoding posterior probability, and after a decoding judgment method mentioned in the background technology is executed, the decoding posterior probability is used as a final output result of the embodiment, and the embodiment is ended.
Fig. 5 is a schematic diagram of a bi-directional frequency domain Turbo equalization structure using EP according to this embodiment, which mainly includes a forward and reverse frequency domain equalization module, a soft mapping module using EP, and a bi-directional external information combining module. The receiving quality of the signals is ensured by adopting the modules to work together.
Fig. 6 and 7 are graphs comparing EXIT performance and iterative convergence trajectories of a Bi-directional frequency-domain Turbo equalization (Bi-EP-SFDE) method using EP, a Turbo equalization (MAP) method using MAP, a frequency-domain Turbo equalization (EP-SFDE) method using EP, a soft frequency-domain Turbo equalization (SFDE) method, and a Bi-directional soft feedback Turbo equalization (Bi-SDFE) method according to this embodiment. The intersymbol interference channel used for the simulation was the Proakis C channel ═ 0.227,0.460,0.688,0.460,0.227, with a signal-to-noise ratio set at 6 dB. It can be seen from fig. 6 that the mutual information output by the bidirectional frequency domain Turbo equalization method using EP is greater than the extrinsic information output by other methods. The larger the mutual information is, the higher the quality of signal recovery of the corresponding equalization method is, so the bit error rate of the Bi-EP-SFDE method is lower than that of other methods, as can be seen from the iteration track in fig. 7, the equalization method outputs the same mutual information, the Bi-EP-SFDE only needs 2 iterations, the Bi-SDFE needs 4 iterations, and the MAP needs 5 iterations, so the Bi-EP-SFDE has the advantage of fast convergence speed.
Table 1 below shows the computational complexity of different equalization methods, where T is an integer, the number of iterations S of Turbo equalization is an integer, the maximum number of self-iterations of the EP equalization method is used, N is an integer, the length of the received signal, β is an integer, and represents the decoding complexity of the decoder, and M is 2 q Is an integer representing the number of modulation mapped symbols, q is an integer representing the order of modulation, and L is an integer representing the order of the channel. As can be seen from the table below, the MAP equalization method calculationThe complexity is exponentially related to the modulation order and the channel length, and the SDFE calculation complexity is squared related to the signal length and linearly related to the channel length. Because the underwater acoustic channel environment channel has the characteristic of long time delay, the MAP and the Bi-SDFE have the defect of high calculation complexity in the underwater acoustic environment, and the calculation complexity of the Bi-EP-SFDE is only in a linear relation with the signal length and the modulation order, so the Bi-EP-SFDE has the advantage of lower calculation complexity compared with the MAP and the Bi-SDFE.
Figure BDA0002440426100000141
TABLE 1
As shown in FIG. 8, it is a bit error curve diagram of Bi-EP-SFDE, Bi-SFDE without EP module, MAP, Bi-SDFE provided by the implementation, where the signal-to-noise ratio range is 0-12 dB, the signal frame length is 512, the frame number is 800 frames, the coding rate is 1/2, and the generated matrix is [5, 7]]After coding, using BPSK to modulate code words to obtain mapping symbols, setting the maximum iteration number to be 5, wherein '—' is a performance curve under the condition of no iteration, '- -' is an error rate curve of one iteration, and '- -' is an error rate curve of five iterations. As can be seen from the figure, the MAP equalization method has better performance than other methods in the initialization iteration, but the Bi-EP-SFDE has obvious performance improvement along with the iteration, and when the iteration number of the equalization method reaches the fifth time, the error rate is also 10 -3 The signal-to-noise ratio is required to be reduced by 2.5dB by adopting a Bi-EP-SFDE method compared with the traditional SFDE method and reduced by 0.5dB and 0.4dB by adopting a MAP method and a Bi-SDFE respectively, and the Bi-EP-SFDE method for analyzing the mutual information has lower error rate performance. In summary, the frequency domain Turbo equalization using EP proposed by the present invention not only has low computational complexity and fast convergence speed, but also can effectively eliminate error transfer and realize low error rate transmission, thereby having high application value.
It is to be noted that the foregoing is only illustrative of the preferred embodiments of the present invention and the technical principles employed. It will be understood by those skilled in the art that the present invention is not limited to the particular embodiments described herein, but is capable of various obvious changes, rearrangements and substitutions as will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, although the present invention has been described in greater detail by the above embodiments, the present invention is not limited to the above embodiments, and may include other equivalent embodiments without departing from the spirit of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims (1)

1. A bidirectional frequency domain Turbo equalization method adopting expected propagation is characterized by comprising the following steps:
s1, receiving a transmission signal of underwater sound or a wireless channel, and approximately deducing posterior distribution characteristics of a symbol bit of the received signal by adopting an EP soft mapping method;
s2, processing the received signal by adopting a bidirectional frequency domain soft equalization method to obtain equalization external information;
s3, combining bidirectional balanced external information by using a bidirectional combination method assisted by covariance;
s4, inputting the combined external information into a Log-MAP decoding judgment method to obtain decoded external information, inputting the decoded external information into an EP soft mapping method as prior, and repeatedly executing steps S1-S4;
s5, judging whether the iteration times reach the preset iteration times or not, if not, continuing to execute the steps S1-S4; if yes, judging decoding by using a Log-MAP decoding judgment method, and outputting a decoding code word;
step S1 specifically includes:
s11, receiving transmission signals of underwater sound or wireless channels;
s12, respectively transmitting the sequence and the decoded external information in the received signal to a forward Turbo equalization method and a reverse Turbo equalization method for processing;
s13, generating decoded external information L from the processed information by using a Log-MAP decoding method d，k ；
S14, the posterior probability is compared by utilizing a Bayesian formula
Figure FDA0003720616090000011
Calculating;
s15, according to the posterior probability
Figure FDA0003720616090000012
Mean value of posterior distribution at current time
Figure FDA0003720616090000013
Sum variance mean gamma d Calculating;
s16, obtaining posterior extrinsic information edge probability distribution q by using a moment matching method E (s k ) And calculating the feedback symbol of the edge distribution of the external information by using a Gaussian decomposition method
Figure FDA0003720616090000014
Sum variance mean v new ；
S17, for the feedback symbol
Figure FDA0003720616090000015
Sum variance mean v new Updating to obtain updated feedback symbol
Figure FDA0003720616090000016
Sum mean of variance v d ；
In step S12, before transmitting to the reverse Turbo equalization end, the method further includes performing a time reversal operation, which is represented as:
Figure FDA0003720616090000017
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003720616090000018
and
Figure FDA0003720616090000019
are real numbers, representing time reversals, respectivelyThen receiving the signal and the outer information of the decoding;
in step S15
Figure FDA00037206160900000110
Mean value of posterior distribution at current time
Figure FDA00037206160900000111
Sum variance mean gamma d A calculation was performed, expressed as:
Figure FDA0003720616090000021
Figure FDA0003720616090000022
feedback sign for calculating edge distribution of extrinsic information in step S16
Figure FDA0003720616090000023
Sum mean of variance v new Expressed as:
Figure FDA0003720616090000024
Figure FDA0003720616090000025
wherein the content of the first and second substances,
Figure FDA0003720616090000026
and v new Are all real numbers;
step S2 specifically includes:
s21, according to the updated feedback symbol
Figure FDA0003720616090000027
Sum variance mean v d Calculating a pre-filter coefficientf k 、ξ；
S22, adopting a feedback symbol
Figure FDA0003720616090000028
Sum mean of variance v d Equalizing the received signal to obtain equalized symbol
Figure FDA0003720616090000029
Sum variance v e ；
In step S21, a pre-filter coefficient is calculatedf k ξ, expressed as:
Figure FDA00037206160900000210
Figure FDA00037206160900000211
wherein the content of the first and second substances,h k is a complex number, which represents the k-th value of the channel after FFT with length of N points,
Figure FDA00037206160900000212
is a real number, representing the variance of the noise;
in step S22, a feedback symbol is used
Figure FDA00037206160900000213
Sum variance mean v d Andh k equalizing the received signal to obtain equalized symbol
Figure FDA00037206160900000214
Sum variance v e Expressed as:
Figure FDA00037206160900000215
v e ＝ξ -1 -v d
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00037206160900000216
y k the k-th value after the feedback symbol and the received signal are subjected to FFT with the length of N points is represented;
step S3 specifically includes:
s31, according to the posterior probability
Figure FDA00037206160900000217
And outer information L of decoding d，k Respectively calculating forward balanced external information L 1，k And reverse equalizing the extrinsic information
Figure FDA00037206160900000218
S32, balancing the reverse direction external information
Figure FDA00037206160900000219
Performing a time reversal operation to obtain reversed extrinsic information L 2，k ；
S33, according to the forward direction balance external information L 1，k And reverse extrinsic information L 2，k Merging the external information;
step S33 is preceded by: calculating forward balanced extrinsic information L 1，k And reverse extrinsic information L 2，k Represented as:
Figure FDA0003720616090000031
wherein the content of the first and second substances,
Figure FDA0003720616090000032
is a real number, representing covariance; m is 1 And m 2 For real numbers, representing the forward and reverse equalizer outputs, respectivelyThe symbol mean value of the soft mapping of the soft information is obtained;
in step S33, the external information is merged, which is represented as:
Figure FDA0003720616090000033
wherein L is e，k Is a real number and represents the combined equalized extrinsic information.
CN202010263763.0A 2020-04-07 2020-04-07 Bidirectional frequency domain Turbo equalization method adopting expected propagation Active CN111682924B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010263763.0A CN111682924B (en) 2020-04-07 2020-04-07 Bidirectional frequency domain Turbo equalization method adopting expected propagation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010263763.0A CN111682924B (en) 2020-04-07 2020-04-07 Bidirectional frequency domain Turbo equalization method adopting expected propagation

Publications (2)

Publication Number Publication Date
CN111682924A CN111682924A (en) 2020-09-18
CN111682924B true CN111682924B (en) 2022-09-09

Family

ID=72451410

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010263763.0A Active CN111682924B (en) 2020-04-07 2020-04-07 Bidirectional frequency domain Turbo equalization method adopting expected propagation

Country Status (1)

Country Link
CN (1) CN111682924B (en)

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103368885A (en) * 2013-07-29 2013-10-23 四川九洲电器集团有限责任公司 Fusion method of bidirectional iteration equilibriums of frequency domain
CN108270702A (en) * 2018-01-19 2018-07-10 中国民航大学 Turbo iteration equalizing detection methods based on MCMC
CN109246039A (en) * 2018-08-09 2019-01-18 华南理工大学 A kind of Soft Inform ation iteration receiving method based on two-way time domain equalization

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20190058529A1 (en) * 2017-04-08 2019-02-21 Yahong Rosa Zheng Turbo receivers for single-input single-output underwater acoustic communications

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103368885A (en) * 2013-07-29 2013-10-23 四川九洲电器集团有限责任公司 Fusion method of bidirectional iteration equilibriums of frequency domain
CN108270702A (en) * 2018-01-19 2018-07-10 中国民航大学 Turbo iteration equalizing detection methods based on MCMC
CN109246039A (en) * 2018-08-09 2019-01-18 华南理工大学 A kind of Soft Inform ation iteration receiving method based on two-way time domain equalization

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
时变水声信道下基于频域均衡的双向迭代接收算法;张硕;《中国优秀硕士论文电子期刊网》;20180715;第4章 *
短波通信中的均衡技术与调制识别;陈雨;《中国优秀硕士论文电子期刊网》;20200215;第5章 *

Also Published As

Publication number Publication date
CN111682924A (en) 2020-09-18

Similar Documents

Publication Publication Date Title
CN109246039B (en) Soft information iteration receiving method based on bidirectional time domain equalization
CN113242189B (en) Adaptive equalization soft information iteration receiving method combined with channel estimation
KR100651036B1 (en) Complexity-reduced iterative decoding receiver with partial sphere decoding in spatial multiplexing system and method thereof
CN108847848B (en) BP decoding algorithm of polarization code based on information post-processing
CN111106877B (en) Underwater acoustic communication transmission method based on Farrow filtering and code word matching
CN107124213A (en) Based on directly adaptive two-way turbo equalization methods in mimo systems
CN110572340A (en) turbo time domain equalization method for short wave communication
US20090310725A1 (en) Space Domain Filter Detecting Method In A Multi-Antenna Wireless Communication System
CN101119177A (en) Bit-symbol signal processing method for coherent communication machine
Xu et al. Spatial and time-reversal diversity aided least-symbol-error-rate turbo receiver for underwater acoustic communications
CN111682924B (en) Bidirectional frequency domain Turbo equalization method adopting expected propagation
CN112039809B (en) Block iterative equalizer based on mixed soft information and bidirectional block iterative equalizer
Zheng et al. Frequency domain direct adaptive turbo equalization based on block normalized minimum-SER for underwater acoustic communications
CN114244670B (en) Blind channel estimation method and system based on channel coding assistance
Abdulkader et al. Neural networks-based turbo equalization of a satellite communication channel
US8868019B2 (en) Forward filter training scheme
Iltis Iterative joint decoding and sparse channel estimation for single-carrier modulation
CN110912651A (en) FTN index modulation signal detection method
CN116016061B (en) Short wave double-selection channel double-iteration Turbo equalization method for high maneuvering platform
CN115225437B (en) Combined intelligent equalization and decoding method for underwater acoustic cooperative communication
CN115996065B (en) Robust adaptive turbo equalization method and apparatus applied to time-varying underwater acoustic channel
CN111314029B (en) Adaptive iterative receiving method based on prior information for underwater acoustic communication
CN116016061A (en) Short wave double-selection channel double-iteration Turbo equalization method for high maneuvering platform
Diouf et al. Iterative detection for MIMO systems associated with polar codes
CN117749579A (en) Single carrier frequency domain iterative equalization receiver based on expected propagation

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant