CN113078983B - A LLR Calculation Method Based on Double Gaussian Approximation - Google Patents

Abstract

The invention discloses an LLR (log likelihood ratio) calculation method based on double-Gaussian approximation, belonging to the field of channel decoding; the method comprises the following steps: in a multi-user interference scenario, the received signal is simultaneously subjected to the signal from unknown numbersFirstly, using receiving end to receive and store receiving signal y corresponding to complete code word₁,y₂,…,y_N(ii) a Then, calculating the statistical average equivalent as the statistical characteristic of the received signal, and further calculating the statistical characteristic of the total noise; meanwhile, calculating the statistical characteristics of double Gaussian distribution according to the probability density function; calculating parameters mu and sigma under the condition of ensuring that the total noise is the same as the statistical characteristics of double-Gaussian distribution; finally, the receiving end carries out soft demodulation on the received signal, substitutes the parameters mu and sigma into LLR, and calculates to obtain the result lambda corresponding to the received signal₁,λ₂,…,λ_NAnd inputting the signal into a decoder for channel decoding to obtain the expected signal. The invention effectively improves the channel decoding performance under multi-user interference with minimum cost.

Description

A LLR Calculation Method Based on Double Gaussian Approximation

technical field

The invention belongs to the field of channel decoding, and relates to the LLR (Log-Likelihood Ratio) calculation problem in channel decoding in a multi-user interference scenario, in particular to an LLR calculation method based on double Gaussian approximation.

Background technique

In recent years, wireless communication technology has developed rapidly, and the fifth-generation mobile communication technology has also been put into use. As a key technology that can effectively improve channel reliability, channel coding plays an important role in wireless communication systems. Turbo codes and LDPC codes widely used in 3G and 4G systems, as well as Polar codes introduced in 5G, all have performance close to the limit of Shannon's theory, which is largely due to the decoding method that uses soft information transfer.

The calculation of soft information LLR is an important link in the communication process. As shown in Figure 1, in the physical layer of today's mobile communication, the information bits are channel-coded by the encoder, and then sent after BPSK modulation. After demodulation, it is input to the decoder for channel decoding, thereby recovering the information bits. Since the modern channel coding adopts the decoding method of soft information transmission, it is necessary to soft demodulate the channel output, output the LLR, and then input it to the decoder for decoding. The calculation of LLR has a direct impact on the accuracy and complexity of channel decoding.

In order to solve the calculation of LLR in different scenarios, there have been many research results, such as simplified calculation of LLR under high-order modulation, LLR calculation in pulsed interference scenarios such as PLC (Power Line Communication), and wireless fading channels, MIMO (Multiple-Input Multiple-Output, Multiple-Input Multiple-Output), NOMA (Non-Othogonal Multiple Access, Non-Othogonal Multiple Access) and other scenarios LLR calculation.

For today's mobile communication, the multi-user interference scenario also has important research significance.

In the multi-user interference scenario, the total noise includes interference and channel noise, which is non-Gaussian distribution, and its probability density distribution is usually difficult to know. To accurately write the probability density function of the total noise, it is necessary to measure the channel of all interference sources. With the substantial growth of mobile communication users and the isomerization of communication networks, the interference of communication may be the interference in different cells or the interference between different systems, such as the interference of different operators, the interference of WiFi to the cellular network Wait. Therefore, it is not easy to ask the receiver to measure the channel gain from each interferer to the receiver, and even the number of interferers is difficult to know.

For multi-user interference scenarios, existing technologies such as multi-user joint detection and soft interference cancellation are all performed on the basis that the receiver knows all the interference source information. For the case where the interference source is unknown, methods such as adding a probability density estimator to the decoder have been studied, but the iterative calculation of the probability density estimator also leads to a significant increase in complexity.

The LLR calculation problem in the multi-user interference scenario is particularly important for today's mobile communication. The receiver can reasonably improve the accuracy of its LLR calculation for a single desired signal, that is, the channel decoding performance can be improved with the minimum cost. It is inspired by this: extracting information from the received signal and reasonably optimizing the calculation of LLR can effectively improve the decoding performance under multi-user interference.

SUMMARY OF THE INVENTION

In order to reasonably optimize the calculation of LLR and effectively improve the channel decoding performance under multi-user interference with the minimum cost, the present invention proposes an LLR calculation method based on double Gaussian approximation.

The described LLR calculation method based on double Gaussian approximation, in the multi-user interference scenario, the received signal is simultaneously interfered by an unknown number of unknown interference sources, and the sum of all interference signals and channel noise is the total noise. The specific steps are: as follows:

Step 1: For a complete codeword of length N, use the receiving base station to receive signals y ₁ , y ₂ , ..., y _N to calculate the statistical average, which is equivalent to the statistical characteristics of the received signals, and further calculate the statistical characteristics of the total noise z;

The received signal of the receiving base station is:

g_k是第k个干扰用户到对应的接收端的路径增益；K为干扰用户个数，w是高斯噪声。Among them, g ₀ is the path gain from the target user U ₀ to the receiving base station B ₀ ; x ₀ is the desired signal sent by the target user U ₀ ; x _k is the interference signal sent by the k-th interfering user, satisfying

g _k is the path gain from the k-th interfering user to the corresponding receiver; K is the number of interfering users, and w is Gaussian noise.

The total noise is expressed as:

近似计算公式为：2nd and 4th order moments in the statistical characteristics of the received signal

The approximate calculation formula is:

Then, the calculation formulas of the second and fourth moments in the statistical characteristics of the total noise z are:

Step 2: Calculate the statistical characteristics of the double Gaussian distribution according to the probability density function of the double Gaussian distribution;

First, the probability density function of the double Gaussian distribution is

μ is the absolute value of the approximate interference signal, σ ² is the variance of the approximate Gaussian noise;

Then, according to the target probability density p _BG (z), the 2nd and 4th order moments in the statistical characteristics of the double Gaussian distribution are calculated;

The calculation result is:

Step 3: Calculate the parameters μ and σ in the double Gaussian distribution under the condition that the statistical characteristics of the total noise z and the double Gaussian distribution are the same;

从而计算得到双高斯分布的参数μ和σ：The statistical characteristics are the same: the first four moments of the total noise z of the received signal are the same as the first four moments of the target probability density p _BG (z); since the first and third moments of the target probability density p _BG (z) are zero, That is, the 2nd and 4th order moments of the two are the same. That is to satisfy:

Thus, the parameters μ and σ of the double Gaussian distribution are calculated:

Step 4: The receiving end performs soft demodulation on the received signals y ₁ , y ₂ ,...,y _N , substitutes the parameters μ and σ in the double Gaussian distribution into the LLR, and calculates the corresponding results of the received signals λ ₁ , λ ₂ ,... , λ _N and input to the decoder for channel decoding to obtain the desired signal.

If the desired signal x ₀ is modulated by BPSK, the LLR calculation formula based on the double Gaussian approximation is:

表示λ的修正项。Pr{·|·} represents the conditional probability; where,

Represents the correction term for λ.

The advantages of the present invention are:

1), an LLR calculation method based on double Gaussian approximation. Compared with the traditional multi-user joint detection and interference cancellation, the LLR calculation based on double Gaussian approximation does not need to know the channel gain of the interferer, the number of interferers, or even the number of interferers. The distribution parameters can be estimated by statistical observation of the received signal without knowing the constellation of the interfering signals x _k , k=1, 2, . . .

2), an LLR calculation method based on double Gaussian approximation. Compared with the LLR calculation based on Gaussian approximation, the double Gaussian distribution better matches the true probability density of noise and interference, and the added correction term makes the LLR more accurate, which can reduce translation. Therefore, the double Gaussian approximation is superior to the ordinary Gaussian approximation in terms of bit error rate and decoding complexity.

Description of drawings

Fig. 1 is the calculation communication flow of soft information LLR in the prior art of the present invention;

Fig. 2 is a kind of LLR calculation method flow chart based on double Gaussian approximation of the present invention;

3 is a schematic diagram of a communication scenario in which an interfering user and a target user constructed according to the present invention correspond to respective base stations;

FIG. 4 is a schematic diagram of a probability density curve of double Gaussian distribution according to the present invention.

Detailed ways

In order to further illustrate the implementation method of the present invention, an example of implementation is given below. This example is only meant to illustrate the principle of the present invention and does not represent any limitation of the present invention.

In the multi-user interference scenario, the received signal at the receiving end contains interference from an unknown number of unknown interference sources, the LLR calculation method based on double Gaussian approximation proposed by the present invention can effectively reduce the bit error rate and complexity of channel decoding. degree; the LLR calculation is applicable to all channel decoding that requires soft information, and the present invention does not specifically limit the specific encoding and decoding methods used.

As shown in Figure 2, the specific steps are as follows:

Step 1, constructing a communication scenario in which K interfering users and one target user correspond to their respective base stations;

As shown in FIG. 3 , the target user U ₀ corresponds to the base station B ₀ , the interfering users U ₁ and U ₂ correspond to the respective base stations B ₁ and B ₂ , respectively; and unknown interference sources, such as the interference access points B ₃ and B 2 in the WiFi network Terminal U ₃ ; the unknown interference source means that the receiver does not need to perform channel measurement on the interference source, and the LLR can be obtained by calculating the received signal.

Step 2, the target user and all interfering users send signals to their corresponding base stations respectively;

The target user U ₀ sends an uplink signal to the base station B ₀ where it is located by wireless; at the same time, the interfering users U ₁ and U ₂ send signals to the base stations B ₁ and B ₂ respectively, and the access point B ₃ in the WiFi network sends a signal to the terminal U ₃ signal, all K interfering users send signals at the same time, and all wireless links can share the same frequency band;

The receiving end and the interference source refer to devices that can perform wireless transmission, and this scenario is also applicable to downlink communication: base station B ₀ sends downlink signals to its target user U ₀ wirelessly; base stations B ₁ and B ₂ respectively send downlink signals to the interfering user U1 and _U2 send downlink signals and so _on .

Step 3, the receiving base station B ₀ of the target user U ₀ receives the desired signal sent by the target user, and the signal is simultaneously interfered by the signals of the K interfering users, and the sum of all the interfering signals and the channel noise is called the total noise;

The received signal at the receiving end includes the desired signal, unknown interference and channel noise; the received signal of the receiving base station B ₀ is:

g_k是第k个干扰用户到对应的接收端的路径增益；w是高斯噪声。Among them, g ₀ is the path gain from the target user U ₀ to the receiving base station B ₀ ; x ₀ is the desired signal sent by the target user U ₀ ; x _k is the interference signal sent by the k-th interfering user, satisfying the energy

g _k is the path gain from the k-th interfering user to the corresponding receiver; w is Gaussian noise.

The total noise is expressed as:

In this embodiment, the receiving end can detect the path gain g ₀ . For the sake of simplicity, g ₀ is normalized to 1, and g _k , k=1, 2, . . . are not assumed to be known, K is not assumed to be known, or even It is assumed that the constellation diagrams of x _k , k=1, 2, . . . are known.

Step 4. Similarly, the receiving base station B ₀ receives a complete codeword of length N, and stores the corresponding received signals y ₁ , y ₂ , . . . , y _N ;

Step 5. Calculate the statistical average of the received signals y ₁ , y ₂ , ..., y _N , which is equivalent to the statistical characteristics of the received signals, and further calculate the statistical characteristics of the total noise z;

近似计算公式为：First, the 2nd and 4th order moments in the statistical characteristics of the received signal

The approximate calculation formula is:

Then, the calculation formulas of the second and fourth moments in the statistical characteristics of the total noise z are:

Step 6: Calculate the statistical characteristics of the double Gaussian distribution according to the probability density function of the double Gaussian distribution;

First, the probability density function of the double Gaussian distribution is

This double Gaussian distribution can be understood as the distribution of the random variable Z=X+Y, that is, the distribution of the sum of two random variables, where X is equal to the value ±μ; Y is a Gaussian random variable with zero mean and variance σ ² ;

In the present invention, μ is the approximate absolute value of the interference signal, and σ ² is the variance of the approximate Gaussian noise.

The double Gaussian distribution probability density curve used in this embodiment is shown in FIG. 4 .

Then, according to the target probability density p _BG (z), the 2nd and 4th order moments in the statistical characteristics of the double Gaussian distribution are calculated;

The calculation result is:

Step 7: Calculate the parameters μ and σ in the double Gaussian distribution under the condition that the statistical characteristics of the total noise z and the double Gaussian distribution are the same;

从而计算得到双高斯分布的参数μ和σ：The statistical characteristics are the same: the first fourth moment of the total noise z of the received signal is the same as the first fourth moment of the target probability density p _BG (z); analogous to the traditional Gaussian approximation, the traditional Gaussian approximation is to make the variance of the total noise and the Gaussian approximation The variance of the distribution is the same, that is, the first-order moment is zero, and the second-order moment is the same, because the Gaussian approximation only needs to calculate one parameter, which can be determined by the second-order moment; in this application, the double Gaussian approximation requires two parameters, so it is the first four-order Since the 1st and 3rd order moments of the target probability density p _BG (z) are zero, the 2nd and 4th order moments of the two are the same. That is to satisfy:

Thus, the parameters μ and σ of the double Gaussian distribution are calculated:

Step 8: The receiving end performs soft demodulation on the received signals y ₁ , y ₂ ,...,y _N , substitutes the parameters μ and σ in the double Gaussian distribution into the LLR, and calculates the corresponding results of the received signals λ ₁ , λ ₂ ,... , λ _N .

If the desired signal x ₀ is modulated by BPSK, the LLR calculation formula based on the double Gaussian approximation is:

表示λ的修正项；通过含有修正项的LLR计算式，使得LLR计算更加准确，在信道译码上的具体表现为更低的误码率及更低的译码复杂度。Pr{·|·} represents the conditional probability; where,

Represents the correction term of λ; the LLR calculation formula containing the correction term makes the LLR calculation more accurate, and the specific performance in channel decoding is lower bit error rate and lower decoding complexity.

Step 9: Input the LLR calculation results λ ₁ , λ ₂ ,...,λ _N into the decoder for channel decoding, and then the desired signal can be obtained.

Example:

Assuming that the sender uses Turbo code encoding, the length of the information bits is 1000 bits, the two sub-encoders generate 3 bits of tail bits respectively, and the code rate is 1/3, then the length of the code word after encoding is N=3018 bits. After being modulated by BPSK and sent, the channel gain from the transmitter to the receiver is known and normalized to 1. The receiver receives signals y ₁ , y ₂ ,...,y _N , in which the number of interference sources and their channel gains are unknown; the specific process is:

Step 1: The receiver calculates the statistical average of the received signal

Step 2: The receiver performs a double-Gaussian approximation to the sum of noise and interference, and calculates the parameters of the double-Gaussian distribution:

计算LLR，得到λ₁,λ₂,…,λ_N；Step 3: Pass-through

Calculate LLR to get λ ₁ ,λ ₂ ,...,λ _N ;

Step 4: take λ ₁ , λ ₂ , . . . , λ _N as the input of the decoder, and perform decoding to obtain the transmitted signal.

Claims (3)

1. A LLR calculation method based on double Gaussian approximation is characterized in that under a multi-user interference scene, a received signal is simultaneously interfered by unknown interference sources with unknown quantity, and the sum of all interference signals and channel noise is total noise, and the LLR calculation method comprises the following specific steps:

step one, aiming at the complete code word with the length of N, utilizing a receiving base station to receive a signal y₁,y₂,…,y_NCalculating statistical average, which is equivalent to the statistical characteristic of the received signal, and further calculating the statistical characteristic of the total noise z;

step two, calculating the statistical characteristics of double-Gaussian distribution according to the probability density function of the double-Gaussian distribution;

first, the probability density function of the double Gaussian distribution is

Mu is the approximate absolute value of the interference signal, sigma²Is the variance of the approximated gaussian noise;

then, according to the target probability density p_BG(z) calculating 2 and 4 orders of moments in the statistical characteristics of the double Gaussian distribution;

the calculation result is as follows:

step three, calculating parameters mu and sigma in double-Gaussian distribution under the condition of ensuring that the total noise z is the same as the statistical characteristics of the double-Gaussian distribution²；

The statistical characteristics are the same as: first fourth moment of total noise z of received signal and target probability density p_BG(z) the first four moments are the same; due to the target probability density p_BG(z) the 1 and 3 orders of moment are zero, namely the 2 and 4 orders of moment are the same; namely, the following conditions are satisfied:

thereby calculating parameters mu and sigma of double Gaussian distribution²：

Respectively 2, 4 orders of moment in the statistical characteristics of the received signal, and the approximate calculation formula is:

step four, receiving end pair receiving signal y₁,y₂,…,y_NPerforming soft demodulation to obtain parameters μ and σ in double Gaussian distribution²Substituting LLR, calculating to obtain the corresponding result lambda of the received signal₁,λ₂,…,λ_NAnd input to a decoder for channel decoding to obtain the desired signal.

2. The method of claim 1, wherein each received signal of the receiving base station in the first step is:

wherein, g₀Is a target user U₀To the receiving base station B₀The path gain of (1); x is the number of₀Is a target user U₀The transmitted desired signal; x is the number of_kIs an interference signal sent by the kth interference user and meets the requirement

g_kPath gain from the kth interfering user to the corresponding receiving end; k is the number of interference users, and w is Gaussian noise;

the total noise is expressed as:

the calculation formula of the 2 and 4 orders of moments in the statistical characteristics of the total noise z is as follows:

3. the method of claim 1, wherein the step four, the phase of LLR calculation is based on a double gaussian approximationSight signal x₀With BPSK modulation, the LLR calculation formula based on the double gaussian approximation is:

pr {. | · } represents a conditional probability; wherein,

a correction term representing lambda.

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