阅读说明：本技术 一种采用期望传播的双向频域Turbo均衡方法 (Bidirectional frequency domain Turbo equalization method adopting expected propagation ) 是由 姜斌 唐禹 包建荣 朱芳 唐向宏 于 2020-04-07 设计创作，主要内容包括：本发明公开了一种采用期望传播的双向频域Turbo均衡方法,包括步骤：S1.接收水声或无线信道的传输信号,并采用EP软映射方法近似推断接收到的信号的符号比特的后验分布特征；S2.采用双向频域软均衡方法对接收到的信号进行处理,得到均衡外信息；S3.利用协方差辅助的双向合并方法合并双向均衡外信息；S4.将所述合并的外信息输入到Log-MAP译码判决方法中,得到译码外信息,并将所述译码外信息作为先验输入到EP软映射方法中,重复执行步骤S1-S4；S5.判断迭代次数是否达到预设的迭代次数,若否,则继续执行步骤S1-S4；若是,则利用Log-MAP译码判决方法判决译码,输出译码码字。(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.)

1. A bidirectional frequency domain Turbo equalization method adopting expectation 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.

2. The bi-directional frequency domain Turbo equalization method using expectation propagation according to claim 1, wherein the 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 subjected to Bayesian formulaCalculating;

s15, according to the posterior probability

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 methodSum variance mean v^new；

S17, for the feedback symbolSum variance mean v^newUpdating to obtain updated feedback symbolSum variance mean v^d。

3. The bi-directional frequency domain Turbo equalization method using expectation propagation according to claim 2, wherein the step S2 specifically includes:

s21, according to the updated feedback symbolSum variance mean v^dCalculating a pre-filter coefficientf _k、ξ；

S22, adopting a feedback symbol

4. The bi-directional frequency domain Turbo equalization method using expectation propagation according to claim 3, wherein the step S3 specifically includes:

s31, according to the posterior probabilityAnd outer information L of decoding_d,kRespectively calculating forward balanced external information L_1，kAnd reverse equalizing the extrinsic information

S32, the reverse balance external information is subjected to

S33, according to the forward direction balance external information L_1，kAnd reverse extrinsic information L_2，kAnd merging the external information.

5. The bi-directional frequency-domain Turbo equalization method with desired propagation according to claim 2, wherein said step S12 further includes performing a time reversal operation before transmitting to the reverse Turbo equalization end, which is expressed as:

wherein the content of the first and second substances,

6. The bi-directional frequency-domain Turbo equalization method with desired propagation according to claim 2, wherein said step S15 is executedMean value of posterior distribution at current timeSum variance mean gamma^dA calculation is performed, expressed as:

7. the bi-directional frequency-domain Turbo equalization method using expectation propagation as claimed in claim 2, wherein the step S16 is performed to calculate the feedback symbols of the outer information edge distribution

wherein the content of the first and second substances,and v^newAre all real numbers.

8. The bi-directional frequency-domain Turbo equalization method using expectation propagation as claimed in claim 3, wherein the pre-filtering coefficients are calculated in step S21f _kξ, expressed as:

wherein the content of the first and second substances,h _kis a complex number, which represents the k-th value of the channel after FFT with length of N points,

9. The bi-directional frequency-domain Turbo equalization method using expectation propagation as claimed in claim 8, wherein the step S22 is implemented by using feedback symbols

v^e＝ξ^-1-v^d

wherein the content of the first and second substances,

10. The bi-directional frequency domain Turbo equalization method with desired propagation according to claim 4, wherein said step S33 is preceded by the steps of: calculating forward balanced extrinsic information L_1，kAnd reverse extrinsic information L_2，kRepresented as:

wherein the content of the first and second substances,

in step S33, the external information is merged, which is represented as:

wherein L is_e，kIs a real number and represents the combined equalized extrinsic information.

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, the 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 system 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 confidence method has greater application potential under the condition of 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 longer 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 the Turbo equalization in single tap in time domain, and the computation complexity of the time domain equalizer can be represented by O (N) through Fast Fourier Transform (FFT)²L) is reduced to O (NlogN), and the method has the advantages of low computational complexity, stable performance and the like. But the two kinds mentioned aboveThe equalizer performance is much worse than BCJR equalization. The confidence equalization mainly comprises BP (belief propagation) and GMP (Gaussian mean Transmission), wherein the BP utilizes a factor graph model to process signals, the application of the BP 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:

bayes' theorem is based on the conditional probability formula to solve the following problems: suppose event H₁、H₂、...、H_nMutually 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)：

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:

the upper typeFor an input sequence of length N the input sequence,

in order to receive the information bits, the receiver,is the received check bit.Is about decoding bit u_kThe Log-MAP decoder task is to solve the decision symbols of the above LLR:

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. From the structural point of view of the method, 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 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.

Further, the 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 subjected to Bayesian formula

Calculating;

s15, according to the posterior probability

Mean value of posterior distribution at current timeSum variance mean gamma^dCalculating;

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 methodSum variance mean v^new；

S17, for the feedback symbol

Sum variance mean v^newUpdating to obtain updated feedback symbolSum variance mean v^d。

Further, the step S2 specifically includes:

s21, according to the updated feedback symbol

Sum variance mean v^dCalculating a pre-filter coefficientf _k、ξ；

S22, adopting a feedback symbol

Sum variance mean v^dEqualizing the received signal to obtain equalized symbolSum variance v^e。

Further, the step S3 specifically includes:

s31, according to the posterior probability

And outer information L of decoding_d，kRespectively calculating forward balanced external information L_1，kAnd reverse equalizing the extrinsic information

S32, the reverse balance external information is subjected to

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，kAnd reverse extrinsic information L_2，kAnd merging the external information.

Further, the step S12, before transmitting to the reverse Turbo equalization end, further includes performing a time reversal operation, which is represented as:

wherein the content of the first and second substances,and

and the real number respectively represents the received signal after time reversal and the decoded extrinsic information.

Further, in the step S15

Mean value of posterior distribution at current time

Sum variance mean gamma^dA calculation is performed, expressed as:

further, the feedback sign of the edge distribution of the extrinsic information is calculated in the step S16

Sum variance mean v^newExpressed as:

wherein the content of the first and second substances,

and v^newAre all real numbers.

Further, the pre-filter coefficient is calculated in the step S21f _kξ, expressed as:

wherein the content of the first and second substances,h _kis a complex number, which represents the k-th value of the channel after FFT with length of N points,is a real number, representing the noise variance.

Further, in step S22, a feedback symbol is specifically adoptedSum variance mean v^dAndh _kequalizing the received signal to obtain equalized symbol

Sum variance v^eExpressed as:

v^e＝ξ^-1-v^d

wherein the content of the first and second substances,

y _kindicating 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 forward balanced extrinsic information L_1，kAnd reverse extrinsic information L_2，kRepresented as:

wherein the content of the first and second substances,

for real numbers, covariance is indicated. m is₁And m₂The 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:

wherein L is_e，kIs 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 and the like in underwater sound, wireless 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 system for enhancing downlink throughput 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:

L_e,kis a real number, representing the combined equalized extrinsic information, a_kDenotes 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_k0) represents a codeword a_kWhen equal to 0, the external information L_e,1(a_k0) and L_e,2(a_k0) probability of occurrence, P (L)_e,1(a_k),L_e,2(a_k)|a_k1) represents a codeword a_kWhen 1, the external information L_e,1(a_k1) and L_e,2(a_k1) 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 subjected to time reversal, in essence, the forward equalization and the reverse equalization method 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:

in the above formula, L_k＝[L_e,1(a_k),L_e,2(a_k)]，μ_k＝a_k[γ₁,γ₂]，ρ,γ₁,σ₁,γ₂,σ₂Are all real numbers, ρ is the correlation coefficient, γ₁,σ₁Is L_e,1Mean and variance of γ₂,σ₂Is L_e,1Mean and variance of

Substituting the formula into a formula, simplifying, and solving a merged extrinsic information expression as follows:

L_e,k＝λ₁L_e,1(a_k)+λ₂L_e,2(a_k)

wherein the content of the first and second substances,

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 γ₁≈γ₂，σ₁≈σ₂And since the modulation is BPSK, there areTherefore, there are:

thus, there is merged extrinsic information