CN113078983B - LLR (LLR) calculation method based on double-Gaussian approximation - Google Patents
LLR (LLR) calculation method based on double-Gaussian approximation Download PDFInfo
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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,…,yN(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,…,λNAnd 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
Technical Field
The invention belongs to the field of channel decoding, relates to the LLR (Log-Likelihood Ratio) calculation problem in channel decoding under a multi-user interference scene, and particularly relates to an LLR calculation method based on double-Gaussian approximation.
Background
In recent years, wireless communication technology has been rapidly developed, and fifth generation mobile communication technology has also been put into use. Channel coding plays an important role in wireless communication systems as a key technology that can effectively improve channel reliability. Turbo codes and LDPC codes widely used in 3G and 4G systems and Polar codes introduced in 5G have performance close to the Shannon theoretical limit, and are largely attributed to the adoption of a soft information transfer decoding mode.
As shown in fig. 1, in the physical layer of mobile communication nowadays, information bits are channel-coded by an encoder and then transmitted after BPSK modulation, and a receiving end needs to demodulate a received signal and then input the demodulated signal to a decoder for channel decoding, thereby recovering the information bits. Because modern channel coding adopts a decoding mode of soft information transmission, channel output needs to be subjected to soft demodulation, LLR is output, and then the LLR is input into a decoder for decoding. The calculation of LLR has a direct impact on the accuracy and complexity of channel decoding.
To solve the calculation of LLR in different scenarios, many research results have been obtained, such as simplified LLR calculation in high-order modulation, LLR calculation in impulse interference scenarios such as PLC (Power Line Communication), and LLR calculation in scenarios such as wireless fading channel, MIMO (Multiple-Input Multiple-Output), NOMA (Non-orthogonal Multiple Access).
For the mobile communication at present, the multi-user interference scene also has important research significance.
Under the multi-user interference scene, the total noise includes interference and channel noise, which are in non-gaussian distribution, and it is usually difficult to obtain the probability density distribution, and to accurately write the probability density function of the total noise, channel measurement needs to be performed on all interference sources. With the great increase of mobile communication users and the isomerization of communication networks, the communication interference may be interference in different cells or interference between different systems, such as interference of different operators, interference of WiFi to a cellular network, and the like. Therefore, it is not easy to require the receiver to measure the channel gain of each interferer to the receiving end, and even the number of interferers is difficult to know.
For a multi-user interference scene, existing technologies such as multi-user joint detection and soft interference cancellation are all performed on the basis that a receiving end knows information of all interference sources. For the case that the interference source is unknown, methods such as adding a probability density estimator in a decoder have been studied, but the iterative computation of the probability density estimator also leads to great increase of complexity.
The LLR calculation problem under the multi-user interference scene is particularly important for the mobile communication, and the receiving end reasonably improves the LLR calculation accuracy of a single expected signal, namely the channel decoding performance can be improved with the minimum cost. It is inspired thereby that: information is extracted from the received signals, LLR calculation is reasonably optimized, and decoding performance under multi-user interference can be effectively improved.
Disclosure of Invention
In order to reasonably optimize LLR calculation and effectively improve channel decoding performance under multi-user interference with minimum cost, the invention provides an LLR calculation method based on double-Gaussian approximation.
In the LLR calculation method based on double-Gaussian approximation, 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 method specifically comprises the following 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,…,yNCalculating statistical average, which is equivalent to the statistical characteristic of the received signal, and further calculating the statistical characteristic of the total noise z;
the received signals of the receiving base station are:
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 ofkIs an interference signal sent by the kth interference user and meets the requirement
gkPath gain from the kth interfering user to the corresponding receiving end; k is the number of interfering users and w is gaussian noise.
The total noise is expressed as:
2, 4 order moments in statistical characteristics of received signals
The approximate calculation formula is:
then, the calculation formula of the 2 and 4 moments in the statistical characteristics of the total noise z is as follows:
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 pBG(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 distribution;
the statistical characteristics are the same as: first fourth moment of total noise z of received signal and target probability density pBG(z) the first four moments are the same; due to the target probability density pBGThe 1 st and 3 rd moments of (z) are zero, i.e., the 2 nd and 4 th moments of both are the same. Namely, the following conditions are satisfied:
the parameters μ and σ of the double gaussian distribution are thus calculated:
step four, receiving end pair receiving signal y1,y2,…,yNPerforming soft demodulation, substituting parameters mu and sigma in double Gaussian distribution into LLR, and calculating to obtain a result lambda corresponding to the received signal1,λ2,…,λNAnd input to a decoder for channel decoding,the desired signal is obtained.
Desired 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.
The invention has the advantages that:
1) compared with traditional multi-user joint detection and interference cancellation, the LLR calculation method based on double-Gaussian approximation does not need to know channel gain of interference sources, quantity of the interference sources or even interference signals xkK is a constellation of 1,2, …, and the distribution parameters can be estimated by statistical observation of the received signal.
2) Compared with LLR calculation based on Gaussian approximation, double-Gaussian distribution is more matched with the true probability density of noise and interference, the added correction terms enable LLR to be more accurate, and then the decoding iteration times can be reduced, so that the double-Gaussian approximation is superior to common Gaussian approximation in the aspects of bit error rate and decoding complexity.
Drawings
FIG. 1 is a flow chart of soft information LLR calculation in the prior art according to the present invention;
FIG. 2 is a flow chart of an LLR calculation method based on double Gaussian approximation according to the present invention;
fig. 3 is a schematic view of communication scenarios in which an interfering user and a target user constructed by the present invention respectively correspond to respective base stations;
FIG. 4 is a schematic diagram of a double Gaussian distribution probability density curve according to the present invention.
Detailed Description
To further illustrate the method of practicing the present invention, an exemplary embodiment is given below. This example is merely intended to illustrate the principle of the invention and does not represent any limitation of the invention.
Aiming at the situation that a receiving signal of a receiving end contains interference from unknown interference sources with unknown quantity under a multi-user interference scene, the bit error rate and complexity of channel decoding can be effectively reduced by the LLR calculation method based on double-Gaussian approximation provided by the invention; the LLR calculation is applicable to all channel decoding requiring soft information, and the invention is not limited to the specific coding and decoding method used.
As shown in fig. 2, the specific steps are as follows:
step one, constructing communication scenes of K interference users and a target user which respectively correspond to respective base stations;
as shown in FIG. 3, target user U0Corresponding base station B0Interfering with user U1And U2Respectively corresponding to respective base station B1And B2(ii) a And unknown interference sources, e.g. interfering access point B in WiFi networks3And terminal U3(ii) a The unknown interference source means that the receiving end does not need to perform channel measurement on the interference source, and the LLR can be obtained by calculation processing on the received signal.
Step two, the target user and all the interference users respectively send signals to the corresponding base stations;
target user U0To the base station B where it is located through wireless0Sending an uplink signal; at the same time, interfering user U1And U2To base station B respectively1And B2Transmitting signals, access point B in WiFi network3To terminal U3Sending signals, wherein all K interference users send signals simultaneously, and all wireless links can share the same frequency band;
the receiving end and the interference source refer to equipment capable of performing wireless transmission, and the scene is also applicable to downlink communication: base station B0Wireless to its target user U0Sending a downlink signal; base station B1And B2Respectively to interfering users U1And U2Transmit downlink signals, etc.
Step three, eyesStandard user U0Receiving base station B0Receiving an expected signal sent by a target user, wherein the signal is simultaneously interfered by signals of K interference users, and the sum of all interference signals and channel noise is called total noise;
the receiving signal of the receiving end contains an expected signal, unknown interference and channel noise; receiving base station B0The received signals of (a) are:
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 ofkIs an interference signal sent by the kth interference user and satisfies the energy
gkPath gain from the kth interfering user to the corresponding receiving end; w is gaussian noise.
The total noise is expressed as:
in this embodiment, the receiving end can detect the path gain g0For simplicity, will g0Normalized to 1 while not assuming gkK is known at 1,2, …, K is not assumed to be known, or even x is not assumed to be knownkThe constellation of k 1,2, … is known.
Step four, receiving the base station B in the same way0Receiving a complete codeword of length N and storing a corresponding received signal y1,y2,…,yN；
Step five, receiving the signal y1,y2,…,yNCalculating statistical average, which is equivalent to the statistical characteristic of the received signal, and further calculating the statistical characteristic of the total noise z;
first, the 2, 4 order moments in the statistical characteristics of the received signal
The approximate calculation formula is:
then, the calculation formula of the 2 and 4 moments in the statistical characteristics of the total noise z is as follows:
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
This double gaussian distribution can be understood as the distribution of the random variable Z ═ X + Y, i.e. the distribution of the sum of two random variables, where X equals ± μ; y is mean zero and variance σ2(ii) a gaussian random variable;
in the present invention, μ is the approximate absolute value of the interference signal, σ2Is the variance of the approximated gaussian noise.
The probability density curve of the double-Gaussian distribution adopted in the present embodiment is shown in FIG. 4.
Then, according to the target probability density pBG(z) calculating 2 and 4 orders of moments in the statistical characteristics of the double Gaussian distribution;
the calculation result is as follows:
seventhly, 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 distribution;
the statistical characteristics are the same as: first fourth moment of total noise z of received signal and target probability density pBG(z) the first four moments are the same; the traditional Gaussian approximation is analogized, wherein the traditional Gaussian approximation is that the variance of the total noise is the same as that of Gaussian distribution, namely the 1 st moment is zero and the 2 nd moment is the same, because the Gaussian approximation only needs to calculate one parameter and can be determined by the 2 nd moment; in the present application, the double-Gaussian approximation requires two parameters, and therefore the first four moments are the same, due to the target probability density pBGThe 1 st and 3 rd moments of (z) are zero, i.e., the 2 nd and 4 th moments of both are the same. Namely, the following conditions are satisfied:
the parameters μ and σ of the double gaussian distribution are thus calculated:
step eight, receiving end pair receiving signal y1,y2,…,yNPerforming soft demodulation, substituting parameters mu and sigma in double Gaussian distribution into LLR, and calculating to obtain a result lambda corresponding to the received signal1,λ2,…,λN。
Desired 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 λ; by the aid of the LLR calculation formula containing the correction term, LLR calculation is more accurate, and the LLR calculation formula is embodied in lower error rate and lower decoding complexity in channel decoding.
Step nine, calculating the result lambda of LLR1,λ2,…,λNThe input decoder performs channel decoding to obtain the desired signal.
Example (b):
assuming that the transmitting end uses Turbo code coding, the length of the information bit is 1000 bits, the two sub-encoders respectively generate 3-bit tail bits, and the code rate is 1/3, the length of the code word after coding is N3018 bits. After BPSK modulation, the channel gain from the transmitting end to the receiving end is known and normalized to 1. The receiving end receives the signal y1,y2,…,yNWherein the number of interferers and their channel gains are unknown; the specific process is as follows:
step 1: the receiving end calculates the statistical average of the received signal
Step 2: the receiving end carries out double-Gaussian approximation on the sum of the noise and the interference, and calculates double-Gaussian distribution parameters:
and step 3: passing through type
Calculating LLR to obtain lambda1,λ2,…,λN；
And 4, step 4: will be lambda1,λ2,…,λNThe transmission signal is obtained by decoding the signal as an input to a decoder.
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,…,yNCalculating 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 pBG(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 pBG(z) the first four moments are the same; due to the target probability density pBG(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：
step four, receiving end pair receiving signal y1,y2,…,yNPerforming 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,…,λNAnd 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 ofkIs an interference signal sent by the kth interference user and meets the requirement
gkPath 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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