CN109687932B - Message transmission-based multi-user non-orthogonal demodulation simplification method - Google Patents

Message transmission-based multi-user non-orthogonal demodulation simplification method Download PDF

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CN109687932B
CN109687932B CN201811597803.4A CN201811597803A CN109687932B CN 109687932 B CN109687932 B CN 109687932B CN 201811597803 A CN201811597803 A CN 201811597803A CN 109687932 B CN109687932 B CN 109687932B
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likelihood function
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CN109687932A (en
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倪祖耀
梁煜
林新聪
辛睿
刘秉坤
匡麟玲
姜春晓
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Tsinghua University
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Abstract

The invention discloses a message-passing-based multi-user non-orthogonal demodulation simplifying method, which comprises the following steps: step 1: storing prior information and initializing parameters; step 2: estimating a likelihood function of the observation node; and step 3: estimating a user node likelihood function; and 4, step 4: estimating posterior distribution of user nodes; and 5: judging whether the iteration is finished; and if the iteration is not finished, returning to the step 2, and if the iteration is finished, taking the average value of the posterior distribution of the obtained user symbols as the multi-user non-orthogonal demodulation information.

Description

Message transmission-based multi-user non-orthogonal demodulation simplification method
Technical Field
The invention relates to the technical field of wireless communication, in particular to a multi-user non-orthogonal demodulation simplification method based on message transmission.
Background
In the traditional communication, the orthogonal multiple access such as time division multiple access, frequency division multiple access, orthogonal frequency division multiple access and the like is a main way for distinguishing multiple users, in the orthogonal multiple access, the multiple users use orthogonal bases to carry out data transmission, interference does not exist among the users, but the number of the orthogonal bases is limited under the condition of a certain frequency band, and the frequency spectrum utilization rate is difficult to improve.
With the increasing traffic demands in modern communications, traditional orthogonal multiple access communications have been unable to meet the traffic demands. Non-orthogonal multiple access methods such as Code Division Multiple Access (CDMA) and Sparse Code Multiple Access (SCMA) can significantly improve the utilization efficiency of frequency bands and the capacity of a communication system. However, in the non-orthogonal multiple access, since signals of each user cannot be completely orthogonal, multiple access interference inevitably occurs, and in order to avoid the non-orthogonal multiple access interference, the problem of the non-orthogonal interference is usually solved by matrix inversion during demodulation, but the complexity caused by the problem is large, and the method is not suitable for a low-delay communication system. To avoid the constraint of non-orthogonal multiple access interference in real-time communication systems, a multi-user non-orthogonal demodulation simplification method can be applied to the above systems.
One class of commonly used algorithms in non-orthogonal demodulation is the least squares algorithm (LS) and the minimum mean square error algorithm (MMSE). However, such methods often require matrix inversion operations, and the computational complexity is proportional to the third power of the number of users. In recent years, a class of algorithms based on message passing is applied to different fields, iteration is carried out through information passing between a user node and an observation node, and the posterior probability of a symbol to be demodulated can be estimated through the characteristics of message passing. However, if a standard sum-product algorithm is adopted, the calculation complexity is also high, which is not favorable for engineering implementation, especially in a communication system with many users. The probability distribution is projected to the gaussian distribution based on the approximate message transmission method, so that the calculation complexity is greatly reduced, but the method is not beneficial to fixed-point hardware realization due to more required digital processing units.
It is therefore desirable to have a simplified message-passing based multi-user non-orthogonal demodulation method that solves the problems of the prior art.
Disclosure of Invention
The invention discloses a multi-user non-orthogonal demodulation simplifying method based on message transmission, which is an algorithm improvement based on an approximate message transmission Algorithm (AMP), and comprises the following steps:
1. initialization
Figure BDA0001921754070000021
2. Updating factor nodes:
Figure BDA0001921754070000022
Figure BDA0001921754070000023
3. variable node update
Figure BDA0001921754070000024
Figure BDA0001921754070000025
4. Posterior distribution update
Figure BDA0001921754070000026
Figure BDA0001921754070000027
Wherein,
Figure BDA0001921754070000028
the original message passing algorithm needs a plurality of matrix operations, and large-scale real-time calculation on line is difficult to carry out, and the multi-user non-orthogonal demodulation simplifying method based on message passing disclosed by the invention is a simplifying method based on the message passing algorithm.
The invention discloses a multi-user non-orthogonal demodulation simplifying method based on message transmission, which comprises the following steps:
step 1: storing prior information and initializing parameters; initializing the mean and variance of the likelihood function and the mean and variance of the posterior distribution of the user symbol, calculating and storing parameters of each iteration according to the noise and channel parameters of the communication system;
step 2: estimating a likelihood function of the observation node; inputting the mean value and the iteration times of the posterior distribution of the user symbol, and outputting the mean value as the likelihood function of the observation node;
and step 3: estimating a user node likelihood function; inputting the mean value and the iteration times of the observation node likelihood function in the step 2, and outputting the mean value of the user node likelihood function;
and 4, step 4: estimating posterior distribution of user nodes; inputting the mean value and the iteration times of the user node likelihood function in the step 3, and outputting the mean value of the posterior distribution of the user symbol;
and 5: judging whether the iteration is finished; if the iteration is not finished, returning to the step 2, and if the iteration is finished, taking the average value of the posterior distribution of the obtained user symbols as multi-user non-orthogonal demodulation information;
setting M as an observation node subscript, wherein M is 1,2, … M, and M is the total number of observation nodes; n is the number of existing users, N is 1,2, … N, and N is the total number of users; according to the characteristic of non-orthogonal demodulation, the number of observation nodes is equal to the number of user nodes; t is the iteration time, T is 1,2, … T, and T is the maximum iteration time; h is a channel parameter of the non-orthogonal multiple access, the main diagonal line of the channel parameter represents the receiving intensity of each user signal, and other elements represent the interference intensity of the non-orthogonal multiple access;
setting the symbol sent by the nth user as xn，xnTaking values in a discrete symbol set, wherein the received symbol of the mth observation node is ymThe two satisfy the relationship
Figure BDA0001921754070000031
Wherein wmIs a noise term; the mean value of the likelihood function of the observation node in the t-th iteration process is recorded as
Figure BDA0001921754070000032
The variance is recorded as
Figure BDA0001921754070000033
The mean value of the likelihood function of the user node is recorded as
Figure BDA0001921754070000034
The variance is recorded as
Figure BDA0001921754070000035
The mean value of the posterior distribution of the user nodes is recorded as
Figure BDA0001921754070000036
The variance is recorded as
Figure BDA0001921754070000037
Preferably, the step 1 specifically comprises the following steps:
initializing parameters; calculating and storing the related parameters of each iteration according to the noise and channel parameters of the communication system, and initializing the mean value of the likelihood function and the mean value of the posterior distribution of the user symbol
Step 1.1: the storing of the prior information, wherein the prior information comprises: each parameter related to the variance of the variable node, the variance of the observation node and the noise variance in each iteration;
step 1.2: initializing the parameters, wherein the parameters comprise: the iteration times, the mean value of posterior distribution during the first iteration and the mean value of the likelihood function of the observation node of the first iteration are set, and the initial value of the iteration is set
Figure BDA0001921754070000038
Preferably, said step 2 of estimating the observation node likelihood function f (z)i)＝p(zi| x), including projecting the observation node likelihood function to a gaussian distribution, and obtaining the variance of the observation node likelihood function through approximate derivation as:
Figure BDA0001921754070000041
the mean value of the likelihood function of the observation node is expressed as
Figure BDA0001921754070000042
where β is a gain factor less than 1.
Preferably, the optimization of step 2 comprises: the mean solution of the likelihood function of the observation node is realized by the following method:
inputting the input into the mean value of the posterior distribution of the user nodes
Figure BDA0001921754070000043
The output channel parameter H, the output result is
Figure BDA0001921754070000044
Is an M-dimensional vector;
② the first lookup table with the input of
Figure BDA0001921754070000045
The output is the product of the current iteration gain and the input signal, the gain being based on
Figure BDA0001921754070000046
The calculation is obtained, and the calculation is simplified in a mode of pre-calculating, storing and on-line table look-up;
the first input is the output of the matrix multiplier, the second input is the output of the first lookup table, and the first input and the second input are subtracted to obtain the mean value of the likelihood function of the observation node
Figure BDA0001921754070000047
Preferably, said estimating of the likelihood function m (x) of the user node of step 3i)＝p(y|xi) The method comprises the following steps:
the calculation method of the user node likelihood function mean value is represented as follows:
Figure BDA0001921754070000048
the calculation method of the user node likelihood function variance is represented as follows:
Figure BDA0001921754070000049
preferably, the first optimization of step 3: the method for solving the mean value of the user node likelihood function comprises the following steps:
① second lookup table has ① input of
Figure BDA0001921754070000051
The output is the product of the current iteration gain and the input signal, the gain being based on
Figure BDA0001921754070000052
The calculation is obtained, and the calculation is simplified in a mode of pre-calculating, storing and on-line table look-up;
② matrix multiplier with first input being transpose H of channel parametersHThe second input is the output of the second lookup table, and the output result is
Figure BDA0001921754070000053
Is an N-dimensional vector;
thirdly, a third look-up table, wherein the input is the N-dimensional vector output by the matrix multiplier, and the output is the product of the current iteration gain and the input signal, and the gain is based on
Figure BDA0001921754070000054
The calculation is obtained, and the calculation is simplified in a mode of pre-calculating, storing and on-line table look-up;
an adder: the first input is the output of the third lookup table, and the second input is the mean of the posterior distribution of the user nodes
Figure BDA0001921754070000055
The output is the mean value of the likelihood function of the user node
Figure BDA0001921754070000056
Preferably, the second optimization of step 3:
mean square error
Figure BDA0001921754070000057
When not varying with m, the factors inside the symbol will be summed
Figure BDA0001921754070000058
And extracting to the outside, and simplifying the mean value calculation formula of the user node likelihood function into:
Figure BDA0001921754070000059
in this case, the second lookup table is omitted, the third lookup table is changed to a fourth lookup table, and the gain of the output of the fourth lookup table with respect to the input is adjusted to
Figure BDA00019217540700000510
Preferably, said estimating of the posterior distribution p (x) of the user nodes of step 4iY) includes:
signal amplitude of anPrior probability
Figure BDA00019217540700000511
According to the bayesian formula, the posterior distribution is equal to the product of the prior distribution and the likelihood function:
p(xi|y)∝p(xi)p(y|xi)
since the prior distribution is a discrete distribution, the posterior distribution can be expressed as:
Figure BDA0001921754070000061
wherein p isnIs + anThe probability of (a) of (b) being,
Figure BDA0001921754070000062
is-anThe probability of (d);
according to the mean and variance of the likelihood function of the observation node and the Gaussian projection of the likelihood function of the observation node in the step 2, the likelihood function is obtained as follows:
Figure BDA0001921754070000063
therefore, there are:
Figure BDA0001921754070000064
Figure BDA0001921754070000065
thus, the mean and variance of the posterior probability can be expressed as:
Figure BDA0001921754070000066
Figure BDA0001921754070000067
preferably, the first optimization of step 4: at a signal amplitude anWhen not fixed, two lookup tables are needed for the exponential operation, and one multiplier is needed for calculating the mean of the posterior distribution,
the fifth lookup table is entered as
Figure BDA0001921754070000068
Output is as
Figure BDA0001921754070000069
The sixth lookup table is entered as
Figure BDA00019217540700000610
Output is as
Figure BDA00019217540700000611
The multiplier inputs as the signal amplitude anDifference from outputs of the fifth and sixth lookup tables
Figure BDA00019217540700000612
The result is the mean of the posterior distribution of the user nodes
Figure BDA00019217540700000613
Preferably, the second optimization of step 4: at a signal amplitude anAt the time of fixing, a seventh look-up table is required,
the seventh lookup table has as inputs
Figure BDA0001921754070000071
The output is the mean value of the posterior distribution of the user nodes
Figure BDA0001921754070000072
The invention discloses a multi-user non-orthogonal demodulation simplifying method based on message transmission, which has the following three beneficial effects: (1) demodulation of non-orthogonal multiple access; (2) a statistical method based on probability distribution Gaussian projection; (3) the method has low operation complexity and is suitable for the realization based on a fixed-point field programmable logic array (FPGA) and a digital signal processing chip (DSP).
Drawings
FIG. 1 is a block diagram of an FPGA implementation of a message-passing based multi-user non-orthogonal demodulation reduction method.
Fig. 2 is a block diagram of an implementation of the user node likelihood function calculation according to the present invention.
Fig. 3 is a simplified block diagram of the user node likelihood function calculation of the present invention.
Fig. 4 is a block diagram of an implementation of the posterior distribution computation of the user node according to the present invention.
Fig. 5 is a simplified block diagram of a posterior distribution computation of a user node in accordance with the present invention.
Figure 6 is a DSP flow diagram of a simplified message-passing based multi-user non-orthogonal demodulation method of the present invention.
Fig. 7 is a performance curve of the method of the present invention in the case of 10-user cdma.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, but not all embodiments of the invention. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1-6, N spread spectrum signals at the same frequency point are used as non-orthogonal signals to be demodulated, and an observation signal y is an N-dimensional vector and represents a despreading result of each received signal on a spread spectrum code of each user. User node x is also an N-dimensional vector representing one symbol transmitted by each user. Satisfaction between observed signal and user transmitted signal
y＝Hx+w
Where H represents the channel parameters for spread spectrum multiple access, and each element represents the channel gain from one user node to one observation node
Figure BDA0001921754070000081
Wherein h isijI-j represents the despread amplitude of each user, hijAnd i ≠ j represents the interference strength of the user i to the user j.
According to the method provided by the invention, the initial value of iteration is set to
Figure BDA0001921754070000082
The variance in the look-up table at each iteration needs to be calculated and stored. The data to be stored includes:
the first lookup table, the output is input and
Figure BDA0001921754070000083
the product of (a);
a second lookup table, the output being input and
Figure BDA0001921754070000084
the product of (a);
a third look-up table with inputs and outputs
Figure BDA0001921754070000085
The product of (a);
the fourth and fifth lookup tables have output and input relationships of
Figure BDA0001921754070000086
According to the above setting, the algorithm of the present invention comprises the steps of:
and step 1) initializing the iteration initial value according to the setting, and performing offline calculation and storage on the related parameter lookup table.
Step 2) inputting the input posterior distribution mean value into a matrix multiplier, and simultaneously inputting the received signal ymZ from last iterationm t-1Subtracted and the result is input to a look-up table. Subtracting the output of the matrix multiplier and the output of the lookup table to obtain the observation node likelihood function mean value Z of a new iterationm t。
Step 3) subtracting the mean value of the likelihood function of the receiving signal and the observation node
Figure BDA0001921754070000087
Input to the second look-up table. The output of the lookup table is
Figure BDA0001921754070000088
Multiplying the output by the transpose of the channel matrix to obtain a calculation result, inputting the calculation result into a third lookup table, and adding the obtained output and the posterior distribution mean of the last iteration to obtain the mean of the user node likelihood function of the current iteration
Figure BDA0001921754070000098
Step 4) according to
Figure BDA0001921754070000099
And the amplitude a of the transmitted signalnThe results are input to two look-up tables, which are used to calculate the exponential operation. The fourth lookup table is entered as
Figure BDA0001921754070000091
Output is as
Figure BDA0001921754070000092
The fifth lookup table is entered as
Figure BDA0001921754070000093
Output is as
Figure BDA0001921754070000094
Signal amplitude anAnd the difference between the outputs of the fourth lookup table and the fifth lookup table
Figure BDA0001921754070000095
Multiplication, the result being the mean of the posterior distribution of the user nodes
Figure BDA0001921754070000096
And 5) judging whether the iteration times reach the maximum, if not, returning to the step 2, otherwise, terminating the iteration. Will be provided with
Figure BDA0001921754070000097
Output as demodulated soft information.
The performance curve of the demodulation of the spread spectrum communication of 10 users through the above steps is shown in fig. 7
Finally, it should be pointed out that: the above examples are only for illustrating the technical solutions of the present invention, and are not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (7)

1. A message-passing-based multi-user non-orthogonal demodulation simplification method is characterized by comprising the following steps:
step 1: storing prior information and initializing parameters; initializing the mean and variance of the likelihood function and the mean and variance of the posterior distribution of the user symbol, calculating and storing parameters of each iteration according to the noise and channel parameters of the communication system;
step 2: estimating a likelihood function of the observation node; inputting the mean value and the iteration times of the posterior distribution of the user symbol, and outputting the mean value as the likelihood function of the observation node;
said step 2 estimating the likelihood function f (z) of the observation nodei)＝p(zi| x), including projecting the observation node likelihood function to a gaussian distribution, and obtaining the variance of the observation node likelihood function through approximate derivation as:
Figure FDA0002315980510000011
the mean value of the likelihood function of the observation node is expressed as
Figure FDA0002315980510000012
wherein β is a gain factor less than 1;
and step 3: estimating a user node likelihood function; inputting the mean value and the iteration times of the observation node likelihood function in the step 2, and outputting the mean value of the user node likelihood function;
the likelihood function m (x) of the user node is estimated in the step 3i)＝p(y|xi) The method comprises the following steps:
the calculation method of the user node likelihood function mean value is represented as follows:
Figure FDA0002315980510000013
the calculation method of the user node likelihood function variance is represented as follows:
Figure FDA0002315980510000014
and 4, step 4: estimating posterior distribution of user nodes; inputting the mean value and the iteration times of the user node likelihood function in the step 3, and outputting the mean value of the posterior distribution of the user symbol;
said step 4 of estimating the posterior distribution p (x) of the user nodesiY) includes:
signal amplitude of anPrior probability
Figure FDA0002315980510000021
According to the bayesian formula, the posterior distribution is equal to the product of the prior distribution and the likelihood function:
p(xi|y)∝p(xi)p(y|xi)
since the prior distribution is a discrete distribution, the posterior distribution can be expressed as:
Figure FDA0002315980510000022
wherein p isnIs + anThe probability of (a) of (b) being,
Figure FDA0002315980510000023
is-anThe probability of (d);
according to the mean and variance of the likelihood function of the observation node and the Gaussian projection of the likelihood function of the observation node in the step 2, the likelihood function is obtained as follows:
Figure FDA0002315980510000024
therefore, there are:
Figure FDA0002315980510000025
Figure FDA0002315980510000026
thus, the mean and variance of the posterior probability can be expressed as:
Figure FDA0002315980510000027
Figure FDA0002315980510000028
wherein,
Figure FDA0002315980510000029
is the variance of the user node likelihood function;
and 5: judging whether the iteration is finished; if the iteration is not finished, returning to the step 2, and if the iteration is finished, taking the average value of the posterior distribution of the obtained user symbols as multi-user non-orthogonal demodulation information;
setting M as an observation node subscript, wherein M is 1,2, … M, and M is the total number of observation nodes; n is the number of existing users, N is 1,2, … N, and N is the total number of users; according to the characteristic of non-orthogonal demodulation, the number of observation nodes is equal to the number of user nodes; t is the iteration time, T is 1,2, … T, and T is the maximum iteration time; h is a channel parameter of the non-orthogonal multiple access, the main diagonal line of the channel parameter represents the receiving intensity of each user signal, and other elements represent the interference intensity of the non-orthogonal multiple access;
setting the symbol sent by the nth user as xn，xnTaking values in a discrete symbol set, wherein the received symbol of the mth observation node is ymThe two satisfy the relationship
Figure FDA0002315980510000031
Wherein wmIs a noise term; the mean value of the likelihood function of the observation node in the t-th iteration process is recorded as
Figure FDA0002315980510000032
The variance is recorded as
Figure FDA0002315980510000033
The mean value of the likelihood function of the user node is recorded as
Figure FDA0002315980510000034
The variance is recorded as
Figure FDA0002315980510000035
The mean value of the posterior distribution of the user nodes is recorded as
Figure FDA0002315980510000036
The variance is recorded as
Figure FDA0002315980510000037
2. The message-passing based multi-user non-orthogonal demodulation simplification method of claim 1, characterized in that: the step 1 specifically comprises the following steps:
initializing parameters; calculating and storing relevant parameters of each iteration according to the noise and channel parameters of the communication system, and initializing the mean value of the likelihood function and the mean value of the posterior distribution of the user symbols;
step 1.1: the storing of the prior information, wherein the prior information comprises: each parameter related to the variance of the variable node, the variance of the observation node and the noise variance in each iteration;
step 1.2: initializing the parameters, wherein the parameters comprise: the iteration times, the mean value of posterior distribution during the first iteration and the mean value of the likelihood function of the observation node of the first iteration are set, and the initial value of the iteration is set
Figure FDA0002315980510000038
3. The message-passing based multi-user non-orthogonal demodulation simplification method of claim 1, characterized in that: the optimization of the step 2 comprises the following steps: the mean solution of the likelihood function of the observation node is realized by the following method:
inputting the input into the mean value of the posterior distribution of the user nodes
Figure FDA0002315980510000039
The input and outputChannel parameter H, output result is
Figure FDA00023159805100000310
Is an M-dimensional vector;
② the first lookup table with the input of
Figure FDA00023159805100000311
The output is the product of the current iteration gain and the input signal, the gain being based on
Figure FDA00023159805100000312
The calculation is obtained, and the calculation is simplified in a mode of pre-calculating, storing and on-line table look-up;
the first input is the output of the matrix multiplier, the second input is the output of the first lookup table, and the first input and the second input are subtracted to obtain the mean value of the likelihood function of the observation node
Figure FDA00023159805100000313
4. The message-passing based multi-user non-orthogonal demodulation simplification method of claim 1, characterized in that: the first optimization of the step 3: the method for solving the mean value of the user node likelihood function comprises the following steps:
① second lookup table has ① input of
Figure FDA0002315980510000041
The output is the product of the current iteration gain and the input signal, the gain being based on
Figure FDA0002315980510000042
The calculation is obtained, and the calculation is simplified in a mode of pre-calculating, storing and on-line table look-up;
② matrix multiplier with first input being transpose H of channel parametersHThe second input is the output of the second lookup table, and the output result is
Figure FDA0002315980510000043
Is an N-dimensional vector;
thirdly, a third look-up table, wherein the input is the N-dimensional vector output by the matrix multiplier, and the output is the product of the current iteration gain and the input signal, and the gain is based on
Figure FDA0002315980510000044
The calculation is obtained, and the calculation is simplified in a mode of pre-calculating, storing and on-line table look-up;
an adder: the first input is the output of the third lookup table, and the second input is the mean of the posterior distribution of the user nodes
Figure FDA0002315980510000045
The output is the mean value of the likelihood function of the user node
Figure FDA0002315980510000046
5. The message-passing based multi-user non-orthogonal demodulation simplification method of claim 1, characterized in that: second optimization of the step 3:
mean square error
Figure FDA0002315980510000047
When not varying with m, the factors inside the symbol will be summed
Figure FDA0002315980510000048
And extracting to the outside, and simplifying the mean value calculation formula of the user node likelihood function into:
Figure FDA0002315980510000049
in this case, the second lookup table is omitted, the third lookup table is changed to a fourth lookup table, and the gain of the output of the fourth lookup table with respect to the input is adjusted to
Figure FDA00023159805100000410
6. The message-passing based multi-user non-orthogonal demodulation simplification method of claim 1, characterized in that: the first optimization of the step 4: at a signal amplitude anWhen not fixed, two lookup tables are needed for the exponential operation, and one multiplier is needed for calculating the mean of the posterior distribution,
the fifth lookup table is entered as
Figure FDA00023159805100000411
Output is as
Figure FDA00023159805100000412
The sixth lookup table is entered as
Figure FDA0002315980510000051
Output is as
Figure FDA0002315980510000052
The multiplier inputs as the signal amplitude anDifference from outputs of the fifth and sixth lookup tables
Figure FDA0002315980510000053
The result is the mean of the posterior distribution of the user nodes
Figure FDA0002315980510000054
Wherein,
Figure FDA0002315980510000055
meaning the variance of the user node likelihood function.
7. The messaging-based multi-use of claim 1The user non-orthogonal demodulation simplification method is characterized in that: second optimization of the step 4: at a signal amplitude anWhen fixed, a seventh lookup table is required, the input of which is
Figure FDA0002315980510000056
The output is the mean value of the posterior distribution of the user nodes
Figure FDA0002315980510000057
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