CN110868244B - Low-complexity communication signal detection method based on channel puncture - Google Patents

Low-complexity communication signal detection method based on channel puncture Download PDF

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CN110868244B
CN110868244B CN201911115281.4A CN201911115281A CN110868244B CN 110868244 B CN110868244 B CN 110868244B CN 201911115281 A CN201911115281 A CN 201911115281A CN 110868244 B CN110868244 B CN 110868244B
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CN110868244A (en
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蔡兴蔚
邱玲
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University of Science and Technology of China USTC
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
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    • H04B7/0452—Multi-user MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045—Arrangements at the receiver end
    • H04L1/0046—Code rate detection or code type detection
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
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Abstract

The invention discloses a low-complexity confidence coefficient transmission communication signal detection method based on channel puncture in a multi-user multi-input multi-output system, which is characterized in that a specific element in a converted channel matrix is cleared by utilizing the channel puncture so as to construct a loop-free factor graph; on the basis of the loop-free factor graph, a confidence coefficient updating formula of a confidence coefficient propagation algorithm is adjusted to calculate more accurate confidence coefficient; the method can be converged within a plurality of iteration times; the hierarchical detection structure design and the assistance of the maximum likelihood detector enable the method to solve the influence of distortion noise caused by channel puncture. Compared with the existing confidence propagation detector, the confidence coefficient calculated by adopting the method of the invention is more accurate, the correlation degree of the confidence coefficient is not increased due to iteration, so the convergence is quicker, the detection performance of the optimal detector can be achieved, and simultaneously, the complexity is greatly reduced compared with the existing detector based on the confidence propagation algorithm.

Description

Low-complexity communication signal detection method based on channel puncture
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a channel puncture-based low-complexity confidence coefficient propagation communication signal detection method suitable for a multi-user multi-input multi-output system.
Background
The international institute of electrical and electronics engineers communication report ("Design of adaptive constrained antenna multi-dimensional signal detection for high-order modulation." "IEEE Transactions on Communications, vol.67, No.3, pp.1986-2001,2018") states that a multiple-user multiple-input multiple-output system equipped with a large number of antennas in both transmission and reception is attracting attention as a potential technology for meeting the ever-increasing demand of wireless communication systems. In the uplink scenario, the transmitted signal is corrupted by interference and noise from different users, and therefore a detection algorithm is needed to recover the transmitted symbols. The International society of Electrical and electronics Engineers Communications research and review ("Fifty layers of MIMO detection: The road beyond dimensions-scales MIMOs," IEEE Communications Surveys & turbines, vol.17, No.4, pp.1941-1988,2015 ") states that even low complexity MIMO detection algorithms can impose excessive energy consumption burdens on base stations. Therefore, a detection algorithm with low complexity and high system performance is one of the requirements for practical mimo system applications. The Journal of the specific field of Communications of the institute of electrical and electronics engineers ("Graph-based detection algorithms for layerdspace-time architecture," IEEE Journal on Selected Areas in Communications, vol.26, No.2, pp.269-280,2008) utilizes a belief propagation algorithm to detect a mimo system, and may have a better detection effect in the case of fewer loops, but in a rich scattering wireless communication environment, detection based on belief propagation may have a serious convergence problem and performance degradation. The detection performance is improved by applying QR decomposition to a belief propagation algorithm in electronic newspaper (QR decomposition aid detection for MIMO systems, Electronics Letters, vol.51, No.11, pp.873-874,2015), but a loop existing in a factor graph still has a certain gap between the detection performance and an optimal detector. Meanwhile, the detection based on the confidence propagation algorithm shows more serious performance reduction under the condition that the ratio of the number of base station antennas to the total number of user number antennas is close to 1.
Disclosure of Invention
The invention aims to provide a confidence coefficient transmission communication signal detection method of a low-complexity multi-user multi-input multi-output system based on channel puncture under a multi-user multi-input multi-output system, so as to improve the convergence of a confidence coefficient transmission detection algorithm and the reduction of bit error rate performance brought by a factor graph loop in a rich scattering wireless communication environment, and reduce the calculation complexity of detection by eliminating the loop and adjusting a confidence coefficient updating formula.
The invention discloses a low-complexity confidence coefficient transmission communication signal detection method based on channel puncture under a multi-user multi-input multi-output system, which is characterized by comprising the following steps:
consider a multiple-user multiple-input multiple-output system, equipped with NrBase station service N of single receiving antennatSingle antenna user, consider NrAnd NtIn the case of equality, each user independently modulates a data sequence and then transmits it through the uplink; if the base station side has a channel matrix HcThe received signal at the base station side is represented as:
yc＝Hcxc+nc (1)
wherein HcRepresenting an independent identically distributed Rayleigh fading channel matrix whose elements obey a complex Gaussian distribution with mean 0 and variance 1, xcRepresenting transmitted signal vectorsThe elements of which are generated independently from a constellation diagram of modulation order Q, ncRepresenting element obedience CN (0, N)0) The noise vector of (2); for each received signal vector yc，xcThe detection process of (2) is as follows:
the first step is as follows: the channel model described by the formula (1) is subjected to real-value decomposition, and the decomposition rule is
Figure GDA0002997033270000021
Figure GDA0002997033270000022
After transformation, Nr×NtThe complex multi-user multiple-input multiple-output channel is equivalent to a real value of 2Nr×2NtMatrix of which
Figure GDA0002997033270000023
Respectively representing the real part and the imaginary part of the element in the square and the square;
the second step is that: performing channel puncturing on the channel matrix;
circularly shifting the real value matrix H by every two columns to obtain NrA channel matrix, for example the first channel matrix, is QR decomposed, H-QR, where Q is a 2N channel matrixr×2NrR is a 2N unitary matrixr×2NtThe upper triangular matrix of (a); contract qkThe k column vector, r, representing the matrix qmnAn element representing the mth row and nth column of the matrix R; according to the properties of the unitary matrix and the upper triangular matrix, the following parameters are obtained: q. q.smhn＝rmnAnd q isnhn＝rnnDefinition of
Figure GDA0002997033270000024
For m 2Nt-2，m＝2Nt-3 to m-1 and corresponding N-2Nr-1，n＝2Nr-2 to n ═ m +1, the following operations being repeated: q. q.sm＝qm-qnemn，rmn＝rmn-rnnemn，
Figure GDA0002997033270000025
Figure GDA0002997033270000026
Represents the m-th row 2N of the matrix RrElements of a column; by using
Figure GDA0002997033270000027
R after the operation is finished, and Q after the operation is finished is represented by W; at this time
Figure GDA0002997033270000028
Is a matrix with zero elements except the diagonal elements and the last column of elements which are not zero, and is expressed as:
Figure GDA0002997033270000031
other Nr-1 matrix is processed in parallel with the same processing method;
the third step: according to the matrix obtained in the second step
Figure GDA0002997033270000032
And W, combining the received signal vector y, and calculating the log-likelihood ratio of the transmitted symbol by using an improved confidence propagation method; and c, multiplying y by W obtained in the second step, and rewriting the received signal vector into:
Figure GDA0002997033270000033
vector of prior information from ith symbol node to jth factor node
Figure GDA0002997033270000034
And a posteriori information vector from the jth factor node to the ith symbol node
Figure GDA0002997033270000035
Are all initialized to 0, wherein skRepresenting a constellation diagramM represents the total number of symbols in the constellation;
during the course of the l-th iteration,
Figure GDA0002997033270000036
is represented as follows:
Figure GDA0002997033270000037
p(l)(xi＝sk) Represents the ith symbol node x in the ith iteration processiIs a symbol skIs x, andithe edge probability of (d) is expressed as:
Figure GDA0002997033270000038
on the other hand, during the first iteration,
Figure GDA0002997033270000039
the log likelihood ratio form of (a) is expressed as follows:
Figure GDA0002997033270000041
wherein
Figure GDA0002997033270000042
Is a signal vector consisting of two factor nodes corresponding to the jth factor node,
Figure GDA0002997033270000043
is provided with
Figure GDA0002997033270000044
A possible choice of symbols, xjOnly skAnd s0Two kinds of symbol selection are carried out,
Figure GDA0002997033270000045
is that
Figure GDA0002997033270000046
The jth column of non-zero elements of (a) of (b),
Figure GDA0002997033270000047
respectively represent matrices
Figure GDA0002997033270000048
J (th) row and 2N (th) column of (2)rAn element of a row;
for i is more than or equal to 1 and less than or equal to 2Nt-1 and j ═ i update the a priori information from the ith symbol node to the jth factor node, the update formula is as follows:
Figure GDA0002997033270000049
to 2NrThe update formula of each symbol node is as follows:
Figure GDA00029970332700000410
updating the information of each factor node and each symbol node by using the formula (5), the formula (6) and the formula (7) until the preset iteration number L; reserved 2Nt-2 and 2Nt-1 layer confidence vector values for transmitted information symbols; to the second step in total of NrRepeating all the steps in the third step by the channel matrixes, and combining the results to obtain confidence vectors of all the transmitted signal symbols;
the fourth step: checking the confidence coefficient vector of each transmitted signal symbol, presetting a selection threshold lambda of a confidence coefficient value, and selecting the symbol with the maximum confidence coefficient as an estimation for x of which the absolute value of the maximum value in the confidence coefficient vector is greater than lambda; for x with the absolute value of the maximum value in the confidence coefficient vector being smaller than lambda, setting the estimated symbol as blank; the blank symbol estimates are sent to an auxiliary maximum likelihood detector along with the determined symbols to obtain the final detection result of the transmitted vector x.
The channel puncture-based low-complexity confidence coefficient transmission communication signal detection method under the multi-user multi-input multi-output system has the advantages that the channel puncture is utilized to clear elements between the diagonal line and the last column of the channel matrix after QR decomposition, so that a complete loop-free factor graph structure is constructed; due to the information updating formula of the confidence coefficient propagation algorithm which is adjusted on the structure, compared with the existing communication signal detection method based on the confidence coefficient propagation algorithm, the method can calculate more accurate confidence coefficient information and can converge more quickly; meanwhile, the influence of distortion noise caused by channel puncture is eliminated by adopting a layered detection structure and an auxiliary maximum likelihood detector, the detection performance of the maximum likelihood detector can be achieved on the bit error rate performance, and the calculation complexity of the system is greatly reduced relative to the maximum likelihood detector.
Description of the drawings:
FIG. 1 is a diagram showing the bit error rate performance comparison between the method of the present invention and the existing multi-user MIMO system communication signal detection method under different signal-to-noise ratio (SNR) settings;
fig. 2 is a comparison diagram of the multiplication calculation numbers required by the method of the present invention and the conventional method for detecting the communication signals of the multi-user mimo system under different antenna number settings.
Detailed Description
The method for detecting a low-complexity belief propagation communication signal based on channel puncturing in a multi-user multiple-input multiple-output system according to the present invention is further described in detail and specifically illustrated in the following figures.
Example 1:
to facilitate understanding of the specific implementation of the method, a factor graph-based confidence propagation algorithm for the multi-antenna system is briefly introduced. Each symbol node corresponds to one element in the transmission information vector and independently stores the information of the symbol transmitted at the transmitting end; the factor nodes correspond to the received signals, in turn storing the signals observed at the receiver. The channel response is used to determine the coupling strength and the number of primary connections between the two nodes. The transmission signal detected at each factor node is delivered as a message (external information) to the corresponding symbol node; and adding external information at the symbol nodes for updating the prior information of each symbol node, and then sending the corresponding factor node to calculate the log-likelihood ratio of the posterior information. The process is repeated until convergence or set iteration times are reached, and finally judgment of the transmitted symbol is output.
Next, how to construct a loop-free factor graph and adjust a belief propagation algorithm based on the loop-free factor graph to achieve performance improvement and complexity reduction of a multi-user multiple-input multiple-output system is specifically described. Consider a multiple user multiple input multiple output system; base station service N equipped with Nr receiving antennastFor a single antenna user, consider Nr and NtThe case of equality; each user independently modulates a data sequence and then transmits the data sequence through an uplink; if the base station side has a channel matrix HcThe received signal at the base station side is represented as:
yc＝Hcxc+nc (1)
wherein HcRepresenting an independent identically distributed Rayleigh fading channel matrix whose elements obey a complex Gaussian distribution with mean 0 and variance 1, xcRepresenting a transmitted signal vector whose elements are generated independently from a constellation diagram of modulation order Q, ncRepresenting element obedience CN (0, N)0) The noise vector of (2); for each received signal vector yc，xcThe detection process of (2) is as follows:
the first step is as follows: for the channel model real-valued decomposition described by the formula (1), the decomposition rule is
Figure GDA0002997033270000061
Figure GDA0002997033270000062
After transformation, Nt×NrThe complex multi-user multiple-input multiple-output channel is equivalent to a real value of 2Nt×2NrMatrix of which
Figure GDA0002997033270000063
Respectively representing the real part and the imaginary part of the element in the square and the square;
the second step is that: performing channel puncturing on the channel matrix;
step 2A: circularly shifting the real value matrix H by every two columns to obtain NrA channel matrix;
and 2B, substep: taking the first channel matrix as an example, QR decomposition is performed, H — QR, where Q is a 2N channel matrixr×2NrR is a 2N unitary matrixr×2NtThe upper triangular matrix of (a); contract qkThe k column vector, r, representing the matrix qmnAn element representing the mth row and nth column of the matrix R; according to the properties of the unitary matrix and the upper triangular matrix, the following parameters are obtained: q. q.smhn＝rmnAnd q isnhn＝rnn(ii) a Definition of
Figure GDA0002997033270000064
For m 2Nt-2，m＝2Nt-3 to m-1 and corresponding N-2Nr-1，n＝2Nr-2 to n ═ m +1, the following operations being repeated: q. q.sm＝qm-qnemn，rmn＝rmn-rnnemn，
Figure GDA0002997033270000065
Figure GDA0002997033270000066
Represents the m-th row 2N of the matrix RrElements of a column; by using
Figure GDA0002997033270000067
R after the operation is finished, and Q after the operation is finished is represented by W; at this time
Figure GDA0002997033270000068
Is a matrix with zero elements except the diagonal elements and the last column of elements which are not zero, and is expressed as:
Figure GDA0002997033270000069
other Nr-1 matrix is processed in parallel with the same processing method;
the third step: according to the matrix obtained in the second step
Figure GDA00029970332700000610
And W, combining the received signal vector y, and calculating the log-likelihood ratio of the transmitted symbol by using an improved confidence propagation algorithm;
and step 3A: and c, multiplying y by W obtained in the second step, and rewriting the received signal vector into:
Figure GDA0002997033270000071
and step 3B: vector of prior information from ith symbol node to jth factor node
Figure GDA0002997033270000072
Figure GDA0002997033270000073
And a posteriori information vector from the jth factor node to the ith symbol node
Figure GDA0002997033270000074
Are all initialized to 0, wherein skRepresenting the kth symbol in the constellation diagram, and M representing the total number of symbols in the constellation diagram;
during the course of the l-th iteration,
Figure GDA0002997033270000075
is represented as follows:
Figure GDA0002997033270000076
p(l)(xi＝sk) Indicating the ith symbol in the ith iteration processNumber node xiIs a symbol skIs x, andithe edge probability of (d) is expressed as:
Figure GDA0002997033270000077
on the other hand, during the first iteration,
Figure GDA0002997033270000078
the log likelihood ratio form of (a) is expressed as follows:
Figure GDA0002997033270000079
wherein
Figure GDA00029970332700000710
Is a signal vector consisting of two factor nodes corresponding to the jth factor node,
Figure GDA00029970332700000711
is provided with
Figure GDA00029970332700000712
A possible choice of symbols, xjOnly skAnd s0Two kinds of symbol selection are carried out,
Figure GDA00029970332700000713
is that
Figure GDA00029970332700000714
The jth column of non-zero elements of (a) of (b),
Figure GDA00029970332700000715
respectively represent matrices
Figure GDA00029970332700000716
J (th) row and 2N (th) column of (2)rAn element of a row;
for i is more than or equal to 1 and less than or equal to 2Nt-1 and j ═ i update the a priori information from the ith symbol node to the jth factor node, the update formula is as follows:
Figure GDA0002997033270000081
to 2NrThe update formula of each symbol node is as follows:
Figure GDA0002997033270000082
and a 3C substep: updating the information of each factor node and each symbol node by using the formula (5), the formula (6) and the formula (7) until the preset iteration number L; reserved 2Nt-2 and 2Nt-1 layer confidence vector values for transmitted information symbols;
a 3D substep: to the second step in total of NrCarrying out 3A-3C steps on each channel matrix, and combining results to obtain confidence vectors of all transmitted signal symbols;
the fourth step: checking the confidence coefficient vector of each transmitted signal symbol, presetting a selection threshold lambda of a confidence coefficient value, and selecting the symbol with the maximum confidence coefficient as an estimation for x of which the absolute value of the maximum value in the confidence coefficient vector is greater than lambda; for x with the absolute value of the maximum value in the confidence coefficient vector being smaller than lambda, setting the estimated symbol as blank; the blank symbol estimates are sent to an auxiliary maximum likelihood detector along with the determined symbols to obtain the final detection result of the transmitted vector x.
In the following, simulation is utilized to compare the low-complexity belief propagation communication signal detection method based on channel puncture in the multi-user multi-input multi-output system of the invention with the existing maximum likelihood detector, standard belief propagation detector and belief propagation detector based on QR decomposition. The indexes compared include: bit error rate of the system and the number of multiplications required for detection.
The simulation of the low-complexity confidence propagation communication signal detection method based on channel puncture in the multi-user multi-input multi-output system of the embodiment is specifically set as follows:
for bit error rate simulation, the number of base station antennas is 8, and the number of single antenna users served is 8. User data is modulated by QPSK, and the transmitted power is normalized. The channel is a Rayleigh fading channel, the noise is 0 in mean and the variance is N0White gaussian noise. The signal-to-noise ratio is simulated every 2 dB from 0 to 10, the number of data frames sent by each user in each simulation is 1250000, and the final bit error rate result is the average value of all frame results.
For the numerical calculation of the calculation complexity, according to the derived multiplication calculation number expressions required by different detection methods, the numerical calculation is carried out on every 2 of the antenna numbers from 4 to 16, and the multiplication calculation number expressions of the different methods are as follows:
Figure GDA0002997033270000083
Figure GDA0002997033270000091
the specific setting of the relevant formula parameters in the channel puncture-based low-complexity confidence propagation communication signal detection method in the multi-user multiple-input multiple-output system of the present invention used in this embodiment is as follows: under QPSK modulation, Q in the table above is 2; a priori information alphai,jAnd posterior information betaj,iAll the initial values of (a) are set to 0; the selection threshold lambda of the confidence coefficient value is 1; the number of iterations of the standard belief propagation algorithm is set to 20, the number of iterations of the QR decomposition-based belief propagation algorithm is set to 10, and the number of iterations of the channel puncture-based low-complexity belief propagation method is set to 3.
FIG. 1 shows the comparison result of bit error rate performance between the method of the present invention and the existing detection method under different SNR, in which the uppermost dotted line A1 represents the standard belief propagation detector, the lowermost dotted line A2 represents the maximum likelihood detector, and the middle dotted line A3 represents the QR-based scoreThe solution belief propagation detector, solid line a4, represents the inventive method. As can be seen from the attached FIG. 1, the bit error rate of the multi-user multiple-input multiple-output system adopting the method of the present invention is lower than that of the standard belief propagation detector and the belief propagation detector based on QR decomposition under the condition that the signal-to-noise ratio is greater than 5, and is the same as that of the optimal detector maximum likelihood detector under the condition that the signal-to-noise ratio is greater than 8. At the same bit error rate level 10-4In this case, the method of the present invention has a gain of about 1.5 db over the confidence propagation detector based on QR decomposition. Therefore, the method achieves better bit error rate performance.
Fig. 2 compares the number of multiplications required by the method of the present invention with the existing method for different numbers of antennas. Wherein the uppermost and lower dashed line B1 represents a standard belief propagation detector, the lowermost dashed line B3 represents a maximum likelihood detector, the middle dashed line B3 represents a belief propagation detector based on QR decomposition, and the solid line B4 represents the inventive method. As can be seen from fig. 2, under the same number of antennas, the number of multiplications required for the detection of the mimo system using the method of the present invention is the least, and under the condition of 8 antennas, the number of multiplications required by the method is only 35.5% of that required by the maximum likelihood detector. Thus, the method has low computational complexity.
Through the above embodiments, it is proved that compared with the existing belief propagation detector, the improved belief propagation communication signal detection method of the present invention can ensure fast convergence of the algorithm and reduce the computational complexity required for detection because a complete loop-free factor graph structure is constructed by using channel puncturing and the information updating formula of the belief propagation detector is more accurate. Meanwhile, the layered detection structure and the auxiliary maximum likelihood detector adopted by the invention eliminate the influence of distortion noise caused by channel puncture, so that the detection performance of the detector can reach the level of the optimal detector.

Claims (1)

1. A low-complexity confidence coefficient transmission communication signal detection method based on channel puncture under a multi-user multi-input multi-output system is characterized in that:
consider a multiple user multiple input multiple output system; is equipped with NrBase station service N of single receiving antennatSingle antenna user, consider NrAnd NtIn the case of equality, each user independently modulates a data sequence and then transmits it through the uplink; if the base station side has a channel matrix HcThe received signal at the base station side is represented as:
yc＝Hcxc+nc (1)
wherein HcRepresenting an independent identically distributed Rayleigh fading channel matrix whose elements obey a complex Gaussian distribution with mean 0 and variance 1, xcRepresenting a transmitted signal vector whose elements are generated independently from a constellation diagram of modulation order Q, ncRepresenting element obedience CN (0, N)0) The noise vector of (2); for each received signal vector yc，xcThe detection process of (2) is as follows:
the first step is as follows: the channel model described by the formula (1) is subjected to real-value decomposition, and the decomposition rule is
Figure FDA0002997033260000011
Figure FDA0002997033260000012
After transformation, Nr×NtThe complex multi-user multiple-input multiple-output channel is equivalent to a real value of 2Nr×2NtMatrix of which
Figure FDA0002997033260000013
Respectively representing the real part and the imaginary part of the element in the square and the square;
the second step is that: performing channel puncturing on the channel matrix;
circularly shifting the real value matrix H by every two columns to obtain NrA channel matrix; taking the first channel matrix as an example, QR decomposition is performed, H — QR, where Q is a 2N channel matrixr×2NrR is a 2N unitary matrixr×2NtThe upper triangular matrix of (a); contract qkThe k column vector, r, representing the matrix qmnAn element representing the mth row and nth column of the matrix R; according to the properties of the unitary matrix and the upper triangular matrix, the following are obtained: q. q.smhn＝rmnAnd q isnhn＝rnn(ii) a Definition of
Figure FDA0002997033260000014
For m 2Nt-2，m＝2Nt-3 to m-1 and corresponding N-2Nr-1，n＝2Nr-2 to n ═ m +1, the following operations being repeated: q. q.sm＝qm-qnemn，rmn＝rmn-rnnemn，
Figure FDA0002997033260000015
Figure FDA0002997033260000016
Represents the m-th row 2N of the matrix RrElements of a column; by using
Figure FDA0002997033260000017
R after the operation is finished, and Q after the operation is finished is represented by W; at this time
Figure FDA0002997033260000021
Is a matrix with zero elements except the diagonal elements and the last column of elements which are not zero, and is expressed as:
Figure FDA0002997033260000022
other Nr-1 matrix is processed in parallel with the same processing method;
the third step: according to the matrix obtained in the second step
Figure FDA0002997033260000023
And W, combining the received signal vector y, and calculating the log-likelihood ratio of the transmitted symbol by using an improved confidence propagation algorithm; and c, multiplying y by W obtained in the second step, and rewriting the received signal vector into:
Figure FDA0002997033260000024
vector of prior information from ith symbol node to jth factor node
Figure FDA0002997033260000025
And a posteriori information vector from the jth factor node to the ith symbol node
Figure FDA0002997033260000026
Are all initialized to 0, wherein skRepresenting the kth symbol in the constellation diagram, and M representing the total number of symbols in the constellation diagram;
during the course of the l-th iteration,
Figure FDA0002997033260000027
is represented as follows:
Figure FDA0002997033260000028
p(l)(xi＝sk) Represents the ith symbol node x in the ith iteration processiIs a symbol skIs x, andithe edge probability of (d) is expressed as:
Figure FDA0002997033260000029
on the other hand, during the first iteration,
Figure FDA00029970332600000210
the log likelihood ratio form of (a) is expressed as follows:
Figure FDA0002997033260000031
wherein
Figure FDA0002997033260000032
Is a signal vector consisting of two factor nodes corresponding to the jth factor node,
Figure FDA0002997033260000033
is provided with
Figure FDA0002997033260000034
A possible choice of symbols, xjOnly skAnd s0Two kinds of symbol selection are carried out,
Figure FDA0002997033260000035
is that
Figure FDA0002997033260000036
The jth column of non-zero elements of (a) of (b),
Figure FDA0002997033260000037
respectively represent matrices
Figure FDA0002997033260000038
J (th) row and 2N (th) column of (2)rAn element of a row;
for i is more than or equal to 1 and less than or equal to 2Nt-1 and j ═ i update the a priori information from the ith symbol node to the jth factor node, the update formula is as follows:
Figure FDA0002997033260000039
to 2NrThe update formula of each symbol node is as follows:
Figure FDA00029970332600000310
updating the information of each factor node and each symbol node by using the formula (5), the formula (6) and the formula (7) until the preset iteration number L; reserved 2Nt-2 and 2Nt-1 layer confidence vector values for transmitted information symbols; to the second step in total of NrRepeating all the steps in the third step by the channel matrixes, and combining the results to obtain confidence vectors of all the transmitted signal symbols;
the fourth step: checking the confidence coefficient vector of each transmitted signal symbol, presetting a selection threshold lambda of a confidence coefficient value, and selecting the symbol with the maximum confidence coefficient as an estimation for x of which the absolute value of the maximum value in the confidence coefficient vector is greater than lambda; for x with the absolute value of the maximum value in the confidence coefficient vector being smaller than lambda, setting the estimated symbol as blank; the blank symbol estimates are sent to an auxiliary maximum likelihood detector along with the determined symbols to obtain the final detection result of the transmitted vector x.
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