CN111934730A - Symbol-level NOMA (non-synchronous access point) non-synchronous receiving method based on cross-slot message transfer algorithm - Google Patents

Symbol-level NOMA (non-synchronous access point) non-synchronous receiving method based on cross-slot message transfer algorithm Download PDF

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CN111934730A
CN111934730A CN202010780092.5A CN202010780092A CN111934730A CN 111934730 A CN111934730 A CN 111934730A CN 202010780092 A CN202010780092 A CN 202010780092A CN 111934730 A CN111934730 A CN 111934730A
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CN111934730B (en
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王培森
王爱华
王力男
叶能
李娜
杨松立
王丽冲
杨佳程
董俊伟
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Beijing Institute of Technology BIT
CETC 54 Research Institute
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • 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
    • H04B7/0413—MIMO systems
    • H04B7/0452—Multi-user MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • 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
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • 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
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/0848—Joint weighting
    • H04B7/0854—Joint weighting using error minimizing algorithms, e.g. minimum mean squared error [MMSE], "cross-correlation" or matrix inversion
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • 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
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/0848—Joint weighting
    • H04B7/0857—Joint weighting using maximum ratio combining techniques, e.g. signal-to- interference ratio [SIR], received signal strenght indication [RSS]

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Abstract

The invention discloses a symbol-level NOMA (non-asynchronous multiple access) receiving method based on a cross-slot message transfer algorithm, relates to a symbol-level non-orthogonal multiple access asynchronous multi-user detection method based on a factor graph, and belongs to the field of communication. The implementation method of the invention comprises the following steps: the time dimension is introduced into a traditional two-dimensional factor graph to form a time slot spanning message transmission method based on a three-dimensional factor graph model, the code elements of each user are estimated by spanning time slots on each frequency resource used for transmission by using the message transmission method, multi-user detection of an asynchronous LDS system is realized, the problem that the traditional symbol-level NOMA system can only carry out synchronous transmission is solved, symbol-level NOMA asynchronous reception is realized, the data transmission efficiency is improved, the capability range of the LDS system is expanded, and the availability of the LDS in massive Internet of things communication is enhanced.

Description

Symbol-level NOMA (non-synchronous access point) non-synchronous receiving method based on cross-slot message transfer algorithm
Technical Field
The invention relates to a Non-Orthogonal Multiple Access (NOMA) asynchronous multi-user detection method based on a factor graph, in particular to a multi-user detection method of an uplink asynchronous LDS system of an asynchronous transmission, an uplink Low-Density Signature (LDS) system and a message transfer algorithm, and belongs to the field of communication.
Technical Field
In recent years, the wireless communication system connection equipment has been increased explosively, and the problem of scarcity of frequency resources is gradually highlighted. In order to alleviate the problem of scarce wireless resources, the academic world proposes a non-orthogonal multiple access technology, which improves the utilization rate of frequency spectrum and gradually becomes a promising technology.
The non-orthogonal multiple access technology is a technology capable of performing multi-user transmission on the same wireless resource, and is an enabling technology with important potential for realizing throughput improvement under the scene of massive internet of things communication. In a massive internet of things communication scene, how to realize accurate receiving of massive data under the condition of asynchronous transmission is one of research focuses of multiple access technologies. Current non-orthogonal multiple access techniques can be divided into two categories: 1) bit-level NOMA, which is realized by using techniques such as bit expansion, bit interleaving and the like, and can adopt serial interference deletion at a receiving end to carry out multi-user detection; 2) the symbol-level NOMA is realized by using technologies such as sparse/dense expansion, sequence design and the like, and multi-user detection can be realized at a receiving end by adopting technologies such as message transmission, serial interference deletion and the like.
Most of the researches of the two types of NOMA are carried out under the assumption of synchronous transmission, which not only requires accurate synchronization among users, but also greatly influences the transmission efficiency of data. And the non-synchronous transmission can avoid strict synchronization among users, and can overcome the problems to a certain extent. At present, compared with the NOMA of bit level, the research of multi-user detection of NOMA of non-synchronous symbol level is not related, and needs to be studied deeply. LDS is used as a symbol-level NOMA, and a pre-designed codebook is utilized to map bit information of each user to a plurality of frequency resources in a sparse manner to realize overload, so that the spectrum efficiency is improved, and the system access quantity and the throughput are improved. In asynchronous transmission, data superimposed on the same frequency resource by each user in the LDS system are staggered in time, and a multi-user detection receiver under the assumption of synchronization cannot achieve correct reception.
Disclosure of Invention
In order to solve the multi-user detection problem of the symbol-level NOMA of the uplink LDS system in the asynchronous transmission scene, the invention discloses a symbol-level NOMA asynchronous receiving method based on a cross-slot message transfer algorithm, which aims to solve the technical problems that: the code element of each user is estimated by spanning the time slot on each frequency resource for transmission by using a message transmission method, so that the interference among multiple users caused by non-synchronization is eliminated, the multi-user detection of the LDS system under the non-synchronization is realized, and the transmission efficiency of the system is improved.
The purpose of the invention is realized by the following technical scheme.
A symbol-level NOMA non-synchronous receiving method based on a cross-slot message transfer algorithm comprises the following steps:
the method comprises the following steps that firstly, a transmitting end carries out channel coding, modulation, LDS codebook mapping and shaping filtering on respective information bits of K users in sequence to obtain a waveform signal to be transmitted, and all the users adopt the waveform signal which is known by a receiver and is the same.
The sending end has K users to carry out LDS uplink transmission. For any user k, the information bits are in turnPerforms encoding and Mod modulation to generate a modulated signal b with length pk。
Mapping each Mod modulation symbol to an N-dimensional LDS complex codebook with the size of K to generate a complex LDS codeword ck. The code book has the real part and the imaginary part of each code element with mapping relation of 2ModPossible values are selected and positive and negative pairs appear.
Obtained by shaping filtering:
Figure BDA0002619894580000021
wherein the content of the first and second substances,
Figure BDA0002619894580000022
the i-th, i-1 … p symbols of user K, K-1 … K on frequency resource N, N-1 … N, and s (T) is a waveform signal with unit energy of a period T. And all users employ a waveform signal that is known and identical to the receiver.
And step two, the waveform signal generated by the transmitting end in the step one passes through a Rayleigh fading channel in an asynchronous mode, and the receiving end receives the waveform signal on each frequency resource respectively.
Considering the channel type as Rayleigh fading hkCN (0,1), K1 … K, and the channel coefficients are known to the receiver
Figure BDA0002619894580000025
And default frame synchronization has been achieved, considering only the case of symbol asynchronous transmission. Thus, with τkDenotes the transmission delay of user k, and 0 ═ τ1≤…≤τk< T. N (t) is a bilateral power spectral density of N0White Gaussian noise of/2. Receiving a signal y of a signal on a frequency resource nn(t) is expressed as:
Figure BDA0002619894580000023
wherein h isk,nRepresenting the channel coefficient h of user kkValue n on the nth frequency resourcen(t) denotes the truncation of n (t) on frequency resource n.
And step three, performing matched filtering and down sampling on the signals on the frequency resources output in the step two to obtain the symbol sequences received on the frequency resources.
Signal y on each frequency resourcen(T), N-1 … N is mapped to waveform s (T- (i-1) T- τk) And K is in the direction of 1 … K, namely, the two directions are convoluted and downsampled to obtain signals matched and filtered on each frequency resource by each user
Figure BDA0002619894580000024
Figure BDA0002619894580000031
Wherein the content of the first and second substances,
Figure BDA0002619894580000032
represents interference of other users to user k, and is
Figure BDA0002619894580000033
The interference of (2) is caused by the time slot and the adjacent time slot,
Figure BDA0002619894580000034
for the sum of the interference of the other users to user k and white Gaussian noise, hk,nRepresenting the channel coefficients of user k on frequency resource n,
Figure BDA0002619894580000035
and | hm,nL respectively represent the complex conjugate and the modulus of the channel coefficient of user m ≠ k on frequency resource n,
Figure BDA0002619894580000036
to represent
Figure BDA0002619894580000037
Corresponding white gaussian noise.
And step four, estimating the code element of each user by spanning the time slot on each frequency resource for the symbol sequence output by the step three by using a message transmission method so as to eliminate the interference among multiple users brought by non-synchronization.
Symbol sequence output by step three
Figure BDA0002619894580000038
Is composed of
Figure BDA0002619894580000039
And the rest of the users are superposed with the adjacent time slot symbols in the time slot, so that the factor graph utilized by the message transfer algorithm comprises a time dimension, and the algorithm is called a cross-time-slot message transfer algorithm in the following. In the factor graph, the transmitted symbols
Figure BDA00026198945800000310
As a node of the user,
Figure BDA00026198945800000311
as a sum node. And as is known from the formula (1),
Figure BDA00026198945800000312
and
Figure BDA00026198945800000313
Figure BDA00026198945800000314
and
Figure BDA00026198945800000315
there are "edges" in between.
The detection process of the cross-slot message passing algorithm is divided into two rounds. First round detection as estimation
Figure BDA00026198945800000316
The positive and negative characteristics of the composition; the second round being detected by the first round
Figure BDA00026198945800000317
Based on the positive and negative characteristics of
Figure BDA00026198945800000318
Magnitude of absolute value. After the two-wheel detection is finished, summarizing all frequency resources
Figure BDA00026198945800000319
Is calculated to obtain
Figure BDA00026198945800000320
An estimate of (d).
Considering LDS as a complex codebook, the detection of which by the receiving end will be divided into a real part and an imaginary part. According to the theorem of central limit,
Figure BDA00026198945800000321
real part of
Figure BDA00026198945800000322
And imaginary part
Figure BDA00026198945800000323
Are respectively expressed as a conditional probability density function:
Figure BDA00026198945800000324
Figure BDA0002619894580000041
wherein the content of the first and second substances,
Figure BDA0002619894580000042
r (-) and I (-) denote the real and imaginary parts of the complex variable, respectively,
Figure BDA0002619894580000043
and
Figure BDA0002619894580000044
respectively represent
Figure BDA0002619894580000045
The real and imaginary parts, E, of the symbols possibly being selected on the codebookR[·]And EI[·]Means, V, representing the real and imaginary parts of a complex random variableR[·]And VI[·]The variances of the real and imaginary parts of the complex random variable are represented, respectively. Considering that the size of the code element in the LDS codebook is symmetrical about the origin, the first round of detection is selected
Figure BDA0002619894580000046
In the second round of the test,
Figure BDA0002619894580000047
is ci k,nOne group of the selectable symbols and the first round of detection
Figure BDA0002619894580000048
And the real part of the code element with consistent positive and negative.
Figure BDA0002619894580000049
Is that
Figure BDA00026198945800000410
One group of the selectable symbols and the first round of detection
Figure BDA00026198945800000411
And symbol imaginary parts with consistent positive and negative polarities.
From the equations (3.1) and (3.2),
Figure BDA00026198945800000412
the log-likelihood ratios of the real and imaginary parts are expressed as
Figure BDA00026198945800000413
Figure BDA00026198945800000414
Is a message transmitted by the node to the user node. Wherein the first round of detection takes R (x)1)＝I(x1)＝+1,R(x2)＝I(x2) -1; in the second round of detection, take
Figure BDA00026198945800000415
Wherein
Figure BDA00026198945800000416
Is that
Figure BDA00026198945800000417
The real part of the optional code element in the codebook is obtained by the first detection
Figure BDA00026198945800000418
The absolute value is larger with the same positive and negative; while
Figure BDA00026198945800000419
Is also that
Figure BDA00026198945800000420
The real part of the optional symbol in the codebook, but is not equal to
Figure BDA00026198945800000421
Different from the first round of detection
Figure BDA00026198945800000422
The absolute value of the positive and negative is small. Similarly, take
Figure BDA00026198945800000423
Wherein
Figure BDA00026198945800000424
Is that
Figure BDA00026198945800000425
The imaginary part of the optional code element in the code book is obtained by satisfying the first detection
Figure BDA00026198945800000426
A value having a large absolute value of positive and negative; while
Figure BDA00026198945800000427
Is also that
Figure BDA00026198945800000428
Imaginary part of optional symbol in codebook, but not
Figure BDA00026198945800000429
Different and satisfy the first round of detection
Figure BDA00026198945800000430
The absolute value of the positive and negative is small.
The message transmitted by the user node to the sum node is the user node
Figure BDA00026198945800000431
Received (a)
Figure BDA00026198945800000432
And
Figure BDA00026198945800000433
and only the message needs to be forwarded to each of its edges.
After the two-wheel detection is finished, the detection is combined with the first wheel detection
Figure BDA0002619894580000051
And
Figure BDA0002619894580000052
positive and negative characteristics of and obtained by the second round of detection
Figure BDA0002619894580000053
And
Figure BDA0002619894580000054
magnitude of absolute valueTo obtain a pair
Figure BDA0002619894580000055
An estimate of the exact likelihood.
Subsequently exporting on each resource
Figure BDA0002619894580000056
By the probability of occurrence of each codeword
Figure BDA0002619894580000057
And the output result of the step four is used for next decoding of the mapping.
And step five, utilizing the probability of each code word of the user output in the step four and combining the LDS codebook mapping relation to solve the LDS codebook mapping to obtain an estimated value of the modulation signal.
According to the occurrence probability of each code word output in the step four
Figure BDA0002619894580000058
Combining the mapping relation of LDS codebook of each user to obtain modulation symbol
Figure BDA0002619894580000059
And step six, demodulating and de-channel coding the modulation symbols obtained in the step five in sequence to obtain an estimated value of information bits, and completing the multi-user detection of the asynchronous uplink LDS system.
For step five modulation symbols
Figure BDA00026198945800000510
Demodulating and decoding the channel to obtain the estimated value of the information bit
Figure BDA00026198945800000511
Namely, multi-user detection of the LDS system under non-synchronization is realized.
Has the advantages that:
the invention discloses a symbol-level NOMA asynchronous receiving method based on a cross-time-slot message transfer algorithm, which introduces time dimension into a traditional two-dimensional factor graph to form the cross-time-slot message transfer method based on a three-dimensional factor graph model, estimates a code element of each user by utilizing the message transfer method to cross time slots on each frequency resource used for transmission, realizes multi-user detection of an asynchronous LDS system, solves the problem that the traditional symbol-level NOMA system can only synchronously transmit, realizes symbol-level NOMA asynchronous receiving, improves data transmission efficiency, expands the capacity range of the LDS system, and enhances the availability of the LDS in massive Internet of things communication.
Drawings
FIG. 1 is a diagram of a transmitter system model for an unsynchronized LDS system;
FIG. 2 is a diagram of an interference model for an LDS transmission system with symbol asynchronism;
FIG. 3 is a system model of an unsynchronized multi-user receiver;
FIG. 4 is a factor graph model of a cross-slot messaging algorithm;
fig. 5 is a flow chart of a symbol-level NOMA asynchronous receiving method based on a cross-slot message transfer algorithm disclosed by the invention.
Detailed description of the invention
In order to make those skilled in the art understand the implementation idea of the present invention more deeply, the technical solution in the embodiment of the present invention will be described carefully and clearly with reference to the drawings in the embodiment of the present invention. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without any creative efforts shall fall within the protection scope of the present invention.
The following describes specific steps of the embodiment of the present invention with reference to specific scenarios:
the symbol-level NOMA asynchronous receiving method based on the cross-slot message transfer algorithm disclosed by the embodiment specifically comprises the following implementation steps:
the method comprises the following steps that firstly, a transmitting end carries out channel coding, modulation, LDS codebook mapping and shaping filtering on respective information bits of K users in sequence to obtain a waveform signal to be transmitted, and all the users adopt the waveform signal which is known by a receiver and is the same.
As shown in fig. 1, the LDS uplink transmission is performed asynchronously by K ═ 6 users. Information bits of an arbitrary user k are sequentially encoded and Mod-2-order QPSK modulated, and a modulated signal having a length p is generated:
Figure BDA0002619894580000061
where the subscript k represents user k.
Every Mod 2 modulation symbols are mapped to N4-dimensional LDS complex codebook with size K6 [ [ (c)1)T,…,(cK)T]TGenerating a complex LDS code word:
ck＝[ck,1,...,ck,N]T
wherein [. ]]TRepresenting the transpose of a matrix or vector, N can be considered as a spreading factor. The code book has the real part and the imaginary part of each code element with mapping relation of 2ModPossible values are obtained, and the optional code elements are symmetrical about the origin and appear in pairs of positive and negative.
Figure BDA0002619894580000062
And (3) performing forming filtering by using a root raised cosine s (t) sampled for 7 times in a period to obtain:
Figure BDA0002619894580000063
wherein the content of the first and second substances,
Figure BDA0002619894580000064
representing a user
Figure BDA0002619894580000065
On spread spectrum resources
Figure BDA0002619894580000066
The i-th symbol above is 1 … p symbols, s (T) has a period T and has unit energy, and the receiver knows the waveform information of s (T).
And step two, the waveform signal generated by the transmitting end in the step one passes through a Rayleigh fading channel in an asynchronous mode, and the receiving end receives the waveform signal on each frequency resource respectively.
Considering the channel type as Rayleigh fading hkCN (0,1), K1 … K, and the channel coefficients are known to the receiver
Figure BDA0002619894580000067
And default frame synchronization has been achieved, considering only the case of symbol asynchronous transmission. Thus, with τkDenotes the transmission delay of user k, and 0 ═ τ1≤…≤τk< T. N (t) is a bilateral power spectral density of N0White Gaussian noise of/2. Receiving a signal y of a signal on a frequency resource nn(t) is expressed as:
Figure BDA0002619894580000071
wherein h isk,nRepresenting the channel coefficient h of user kkValue n on the nth frequency resourcen(t) denotes the truncation of n (t) on frequency resource n.
And step three, performing matched filtering and down sampling on the signals on the frequency resources output in the step two to obtain the symbol sequences received on the frequency resources.
Signal y on each frequency resourcen(T), n-1 … 4 is mapped to waveform s (T- (i-1) T- τk) And k is in the direction of 1 … 6, i.e. the two directions are convoluted and down-sampled to obtain signals matched and filtered by each user on each frequency resource
Figure BDA0002619894580000072
Figure BDA0002619894580000073
Wherein, among others,
Figure BDA0002619894580000074
represents interference of other users to user k, and is
Figure BDA0002619894580000075
The interference of (2) is caused by the time slot and the adjacent time slot,
Figure BDA0002619894580000076
for the sum of the interference of the other users to user k and white Gaussian noise, hk,nRepresenting the channel coefficients of user k on frequency resource n,
Figure BDA0002619894580000077
and | hm,nL respectively represent the complex conjugate and the modulus of the channel coefficient of user m ≠ k on frequency resource n,
Figure BDA0002619894580000078
to represent
Figure BDA0002619894580000079
Corresponding white gaussian noise. ,
Figure BDA00026198945800000710
representing the autocorrelation coefficients.
And step four, estimating the code element of each user by spanning the time slot on each frequency resource for the symbol sequence output by the step three by using a message transmission method so as to eliminate the interference among multiple users brought by non-synchronization.
Considering the symbol asynchrony between users, as shown in fig. 2, the output after matched filtering and down sampling is the superposition of the symbol sequence and the symbols of the other users in the current time slot and the adjacent time slot. Therefore, we introduce the time dimension into the traditional two-dimensional factor graph to characterize the message passing process, and form the cross-slot message passing algorithm on the basis of the time dimension. The symbols transmitted in the factor graph are shown in FIG. 3
Figure BDA0002619894580000081
As a node of the user,
Figure BDA0002619894580000082
as a sum node. As can be seen from the equation (5),
Figure BDA0002619894580000083
is that
Figure BDA0002619894580000084
Figure BDA0002619894580000085
And
Figure BDA0002619894580000086
thus, a node
Figure BDA0002619894580000087
The user nodes are connected by 'edges', and the rest nodes are similar.
The detection process of the cross-slot message passing algorithm is divided into two rounds. Each round of detection will be performed niI is 1,2 iterations. First round detection as estimation
Figure BDA0002619894580000088
Positive and negative characteristics of (1), output characterization after iteration is over
Figure BDA0002619894580000089
Maximum likelihood ratio of positive and negative characteristics for next detection; the second round being detected by the first round
Figure BDA00026198945800000810
Based on the positive and negative characteristics of
Figure BDA00026198945800000811
Magnitude of absolute value, end of iteration output
Figure BDA00026198945800000812
And (4) accurate detection results. To obtain finally
Figure BDA00026198945800000813
The probability of occurrence of the codeword is obtained. In each round of detection, the message is repeatedly iterated on the 'edge' of the factor graph, each iteration and the node and the user node are processed once until the maximum iteration times is reached, and an estimation result is output.
Considering LDS as a complex codebook, the detection of which by the receiving end will be divided into a real part and an imaginary part. According to the central limit theorem, in equation (6)
Figure BDA00026198945800000814
Can be approximated as a gaussian variable, then
Figure BDA00026198945800000815
Real part of
Figure BDA00026198945800000816
And imaginary part
Figure BDA00026198945800000817
Are respectively expressed as a conditional probability density function: :
Figure BDA00026198945800000818
Figure BDA00026198945800000819
wherein the content of the first and second substances,
Figure BDA00026198945800000820
r (-) and I (-) denote the real and imaginary parts of the complex variable, respectively,
Figure BDA00026198945800000821
and
Figure BDA00026198945800000822
respectively represent
Figure BDA00026198945800000823
The real and imaginary parts, E, of the symbols possibly being selected on the codebookR[·]And EI[·]Means, V, representing the real and imaginary parts of a complex random variableR[·]And VI[·]The variances of the real and imaginary parts of the complex random variable are represented, respectively. Considering that the symbol size in the LDS codebook is symmetric about the origin, for simplicity, the first round of detection is selected
Figure BDA00026198945800000824
In the second round of the test,
Figure BDA00026198945800000825
is that
Figure BDA00026198945800000826
One group of the selectable symbols and the first round of detection
Figure BDA00026198945800000827
And the real part of the code element with consistent positive and negative.
Figure BDA0002619894580000091
Is that
Figure BDA0002619894580000092
One group of the selectable symbols and the first round of detection
Figure BDA0002619894580000093
And symbol imaginary parts with consistent positive and negative polarities.
From the equations (7.1) and (7.2),
Figure BDA0002619894580000094
the log-likelihood ratios of the real and imaginary parts are expressed as
Figure BDA0002619894580000095
Figure BDA0002619894580000096
Is a message transmitted by the node to the user node. Wherein the first round of detection takes R (x)1)＝I(x1)＝+1,R(x2)＝I(x2) -1; in the second round of detection, take
Figure BDA0002619894580000097
Wherein
Figure BDA0002619894580000098
Is that
Figure BDA0002619894580000099
The real part of the optional code element in the codebook is obtained by the first detection
Figure BDA00026198945800000910
The absolute value is larger with the same positive and negative; while
Figure BDA00026198945800000911
Is also that
Figure BDA00026198945800000912
The real part of the optional symbol in the codebook, but is not equal to
Figure BDA00026198945800000913
Different from the first round of detection
Figure BDA00026198945800000914
The absolute value of the positive and negative is small. Similarly, take
Figure BDA00026198945800000915
Wherein
Figure BDA00026198945800000916
Is that
Figure BDA00026198945800000917
The imaginary part of the optional code element in the code book is obtained by satisfying the first detection
Figure BDA00026198945800000918
A value having a large absolute value of positive and negative; while
Figure BDA00026198945800000919
Is also that
Figure BDA00026198945800000920
Imaginary part of optional symbol in codebook, but not
Figure BDA00026198945800000921
Different and satisfy the first round of detection
Figure BDA00026198945800000922
The absolute value of the positive and negative is small. In addition, the first and second substrates are,
Figure BDA00026198945800000923
and
Figure BDA00026198945800000924
calculated using the following formula:
Figure BDA00026198945800000925
Figure BDA0002619894580000101
Figure BDA0002619894580000102
Figure BDA0002619894580000103
wherein the content of the first and second substances,
Figure BDA0002619894580000104
Figure BDA0002619894580000105
and
Figure BDA0002619894580000106
to represent
Figure BDA0002619894580000107
The mean and the variance of the imaginary part,
Figure BDA0002619894580000108
Figure BDA0002619894580000109
and
Figure BDA00026198945800001010
the mean and variance of (c) may be calculated based on messages input by the user node, as follows:
Figure BDA00026198945800001011
Figure BDA00026198945800001012
wherein R (x)1),R(x2),I(x1),I(x2) The meaning is the same as that expressed by the formula (8). Notably, due to the first iteration R (x)1)＝I(x1)＝+1,R(x2)＝I(x2) Equation (11) is reduced to-1, the following equation:
Figure BDA0002619894580000111
Figure BDA0002619894580000112
in addition, at the first iteration,
Figure BDA0002619894580000113
and
Figure BDA0002619894580000114
should be initialized to zero.
The message transmitted by the user node to the sum node is the user node
Figure BDA0002619894580000115
Received (a)
Figure BDA0002619894580000116
And
Figure BDA0002619894580000117
and only this message needs to be forwarded to each of its edges for the next round of processing by the sum node.
After the two-wheel detection is finished, the first wheel is detected
Figure BDA0002619894580000118
And
Figure BDA0002619894580000119
are respectively characterized
Figure BDA00026198945800001110
And
Figure BDA00026198945800001111
maximum likelihood function of positive and negative characteristics, and second detection
Figure BDA00026198945800001112
And
Figure BDA00026198945800001113
are respectively characterized
Figure BDA00026198945800001114
And
Figure BDA00026198945800001115
maximum likelihood function of absolute value magnitude.
The first round of detection is
Figure BDA00026198945800001116
And
Figure BDA00026198945800001117
according to the basic formula of the maximum likelihood function shown in formula (8), the following is calculated:
Figure BDA00026198945800001118
Figure BDA00026198945800001119
wherein the content of the first and second substances,
Figure BDA00026198945800001120
and
Figure BDA00026198945800001121
respectively represent
Figure BDA00026198945800001122
The probability of being a positive number and a negative number,
Figure BDA00026198945800001123
and
Figure BDA00026198945800001124
respectively represent
Figure BDA00026198945800001125
The probability of a positive number and a negative number.
The second round of detection is
Figure BDA00026198945800001126
And
Figure BDA00026198945800001127
to obtain
Figure BDA00026198945800001128
Probability of larger and smaller absolute values
Figure BDA0002619894580000121
And
Figure BDA0002619894580000122
see formula (13.1).
Figure BDA0002619894580000123
And
Figure BDA0002619894580000124
the algorithm is the same, see equation (13.2).
Figure BDA0002619894580000125
Figure BDA0002619894580000126
At this time, the process of the present invention,
Figure BDA0002619894580000127
and
Figure BDA0002619894580000128
the probability of possible values of (a) can be expressed as:
Figure BDA0002619894580000129
Figure BDA00026198945800001210
Figure BDA00026198945800001211
Figure BDA00026198945800001212
wherein, the formulas (15.1) and (15.2) respectively represent
Figure BDA00026198945800001213
In the case of positive and negative values, the equations (16.1) and (16.2) represent the values, respectively
Figure BDA00026198945800001214
Both positive and negative.
Will be provided with
Figure BDA00026198945800001215
And
Figure BDA00026198945800001216
multiply by each other and get
Figure BDA00026198945800001217
Normalizing a group of results corresponding to possible values in the corresponding codebook to obtain a normalized result
Figure BDA0002619894580000131
Probability of possible values
Figure BDA0002619894580000132
To represent
Figure BDA0002619894580000133
Soft information of the estimated value of (a).
Therefore, the temperature of the molten metal is controlled,
Figure BDA0002619894580000134
can be expressed as:
Figure BDA0002619894580000135
is composed of
Figure BDA0002619894580000136
The corresponding serial numbers are multiplied.
Figure BDA0002619894580000137
Characterization pair
Figure BDA0002619894580000138
The estimation result of (2).
And step five, utilizing the probability of each code word of the user output in the step four and combining the LDS codebook mapping relation to solve the LDS codebook mapping to obtain an estimated value of the modulation signal.
According to the code word c output by the step four for each userkIs estimated by
Figure BDA0002619894580000139
Firstly, the LDS codebook is demapped, and
Figure BDA00026198945800001310
as a pair with a set of LDS code words corresponding to the maximum value of
Figure BDA00026198945800001311
Is estimated value of
Figure BDA00026198945800001312
By
Figure BDA00026198945800001313
The estimated value of the modulation symbol of the user k can be obtained
Figure BDA00026198945800001314
And step six, demodulating and de-channel coding the modulation symbols obtained in the step five in sequence to obtain an estimated value of information bits, and completing the multi-user detection of the asynchronous uplink LDS system.
For step five modulation symbols
Figure BDA00026198945800001315
Demodulating and decoding the channel to obtain the estimated value of the information bit
Figure BDA00026198945800001316
Namely, multi-user detection of the LDS system under non-synchronization is realized.
The above detailed description is intended to illustrate the object and technical solution of the present invention, and it should be understood that the above detailed description is only an example of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (7)

1. A symbol-level NOMA non-synchronous receiving method based on a cross-time slot message transfer algorithm is characterized in that: comprises the following steps of (a) carrying out,
the method comprises the steps that firstly, a transmitting end carries out channel coding, modulation, LDS codebook mapping and forming filtering on respective information bits of K users in sequence to obtain a waveform signal to be transmitted, and all the users adopt the same waveform signal known by a receiver;
step two, the waveform signal generated by the transmitting end in the step one passes through a Rayleigh fading channel in an asynchronous mode, and the receiving end receives the waveform signal on each frequency resource respectively;
step three, performing matched filtering and down-sampling on the signals on the frequency resources output in the step two to obtain symbol sequences received on the frequency resources;
step four, estimating the symbol sequence output in the step three by spanning the time slot on each frequency resource by using a message transmission method so as to eliminate the interference among multiple users brought by non-synchronization;
step five, utilizing the probability of each code word of the user output in the step four and combining the LDS codebook mapping relation to solve the LDS codebook mapping to obtain an estimated value of the modulation signal;
and step six, demodulating and de-channel coding the modulation symbols obtained in the step five in sequence to obtain an estimated value of information bits, and completing the multi-user detection of the asynchronous uplink LDS system.
2. The symbol-level NOMA asynchronous reception method based on a cross-slot message passing algorithm according to claim 1, characterized in that: the first implementation method comprises the following steps of,
a sending end has K users to carry out LDS uplink transmission; sequentially coding and Mod-order modulating the information bits of any user k to generate a modulation signal b with the length pk；
Mapping each Mod modulation symbol to an N-dimensional LDS complex codebook with the size of K to generate a complex LDS codeword ck(ii) a The code book has the real part and the imaginary part of each code element with mapping relation of 2ModPossible values are selected, and positive and negative pairs appear;
obtained by shaping filtering:
Figure FDA0002619894570000011
wherein the content of the first and second substances,
Figure FDA0002619894570000012
a waveform signal representing the i-th, i-1 … p symbols of user K, K-1 … K on frequency resource N, N-1 … N, and s (T) representing unit energy with a period T; and all users employ a waveform signal that is known and identical to the receiver.
3. The symbol-level NOMA asynchronous reception method based on a cross-slot message passing algorithm according to claim 2, characterized in that: the second step is realized by the method that,
considering the channel type as Rayleigh fading hkCN (0,1), K1 … K, and the channel coefficient h is known to the receiverk,
Figure FDA0002619894570000013
And default frame synchronization has been achieved, considering only the case of symbol asynchronous transmission; thus, with τkDenotes the transmission delay of user k, and 0 ═ τ1≤…≤τk< T; n (t) is a bilateral power spectral density of N0White Gaussian noise of/2; receiving a signal y of a signal on a frequency resource nn(t) is expressed as:
Figure FDA0002619894570000021
wherein h isk,nRepresenting the channel coefficient h of user kkValue n on the nth frequency resourcen(t) denotes the truncation of n (t) on frequency resource n.
4. A symbol-level NOMA asynchronous reception method based on a cross-slot message passing algorithm according to claim 3, characterized in that: the third step is to realize the method as follows,
signal y on each frequency resourcen(T), N-1 … N is mapped to waveform s (T- (i-1) T- τk) And K is in the direction of 1 … K, namely, the two directions are convoluted and downsampled to obtain signals matched and filtered on each frequency resource by each user
Figure FDA0002619894570000022
Figure FDA0002619894570000023
Wherein the content of the first and second substances,
Figure FDA0002619894570000024
represents interference of other users to user k, and is
Figure FDA0002619894570000025
Is interfered byA slot is brought into a neighboring one of the time slots,
Figure FDA0002619894570000026
for the sum of the interference of the other users to user k and white Gaussian noise, hk,nRepresenting the channel coefficients of user k on frequency resource n,
Figure FDA0002619894570000027
and | hm,nL respectively represent the complex conjugate and the modulus of the channel coefficient of user m ≠ k on frequency resource n,
Figure FDA0002619894570000028
to represent
Figure FDA0002619894570000029
Corresponding white gaussian noise.
5. The symbol-level NOMA non-synchronous reception method based on a cross-slot message-passing algorithm in accordance with claim 4, characterized in that: the implementation method of the fourth step is that,
symbol sequence output by step three
Figure FDA00026198945700000210
Is composed of
Figure FDA00026198945700000211
And the superposition of other users on the code elements of the time slot and the adjacent time slot, so that the factor graph utilized by the message transmission algorithm contains a time dimension, and the algorithm is called a cross-time-slot message transmission algorithm in the following; in the factor graph, the transmitted symbols
Figure FDA00026198945700000212
As a node of the user,
Figure FDA00026198945700000213
as a sum node; and as is known from the formula (1),
Figure FDA00026198945700000214
and
Figure FDA00026198945700000215
Figure FDA00026198945700000216
and
Figure FDA00026198945700000217
there is an "edge" between;
the detection process of the cross-time slot message transmission algorithm is divided into two rounds; first round detection as estimation
Figure FDA00026198945700000218
The positive and negative characteristics of the composition; the second round being detected by the first round
Figure FDA00026198945700000219
Based on the positive and negative characteristics of
Figure FDA00026198945700000220
The magnitude of the absolute value; after the two-wheel detection is finished, summarizing all frequency resources
Figure FDA00026198945700000221
Is calculated to obtain
Figure FDA00026198945700000222
An estimated value of (d);
the LDS is considered as a complex codebook, and the detection of the LDS by a receiving end is divided into a real part and an imaginary part; according to the theorem of central limit,
Figure FDA0002619894570000031
real part of
Figure FDA0002619894570000032
And imaginary part
Figure FDA0002619894570000033
Are respectively expressed as a conditional probability density function:
Figure FDA0002619894570000034
Figure FDA0002619894570000035
wherein the content of the first and second substances,
Figure FDA0002619894570000036
r (-) and I (-) denote the real and imaginary parts of the complex variable, respectively,
Figure FDA0002619894570000037
and
Figure FDA0002619894570000038
respectively represent
Figure FDA0002619894570000039
The real and imaginary parts, E, of the symbols possibly being selected on the codebookR[·]And EI[·]Means, V, representing the real and imaginary parts of a complex random variableR[·]And VI[·]Respectively representing the variances of the real part and the imaginary part of the complex random variable; considering that the size of the code element in the LDS codebook is symmetrical about the origin, the first round of detection is selected
Figure FDA00026198945700000310
In the second round of the test,
Figure FDA00026198945700000311
is that
Figure FDA00026198945700000312
One group of the selectable symbols and the first round of detection
Figure FDA00026198945700000313
A code element real part with consistent positive and negative characters;
Figure FDA00026198945700000314
is that
Figure FDA00026198945700000315
One group of the selectable symbols and the first round of detection
Figure FDA00026198945700000316
A symbol imaginary part with consistent positive and negative;
from the equations (3.1) and (3.2),
Figure FDA00026198945700000317
the log-likelihood ratios of the real and imaginary parts are expressed as
Figure FDA00026198945700000318
Figure FDA00026198945700000319
Is a message transmitted by the node to the user node; wherein the first round of detection takes R (x)1)＝I(x1)＝+1,R(x2)＝I(x2) -1; in the second round of detection, take
Figure FDA00026198945700000320
Wherein
Figure FDA00026198945700000321
Is that
Figure FDA00026198945700000322
The real part of the optional code element in the codebook is obtained by the first detection
Figure FDA00026198945700000323
The absolute value is larger with the same positive and negative; while
Figure FDA00026198945700000324
Is also that
Figure FDA00026198945700000325
The real part of the optional symbol in the codebook, but is not equal to
Figure FDA0002619894570000041
Different from the first round of detection
Figure FDA0002619894570000042
A smaller absolute value of positive and negative; similarly, take
Figure FDA0002619894570000043
Wherein
Figure FDA0002619894570000044
Is that
Figure FDA0002619894570000045
The imaginary part of the optional code element in the code book is obtained by satisfying the first detection
Figure FDA0002619894570000046
A value having a large absolute value of positive and negative; while
Figure FDA0002619894570000047
Is also that
Figure FDA0002619894570000048
Optional codes in a codebookImaginary part of the element, but not
Figure FDA0002619894570000049
Different and satisfy the first round of detection
Figure FDA00026198945700000410
A smaller absolute value of positive and negative;
the message transmitted by the user node to the sum node is the user node
Figure FDA00026198945700000411
Received (a)
Figure FDA00026198945700000412
And
Figure FDA00026198945700000413
and only the message needs to be forwarded to each of its edges;
after the two-wheel detection is finished, the detection is combined with the first wheel detection
Figure FDA00026198945700000414
And
Figure FDA00026198945700000415
positive and negative characteristics of and obtained by the second round of detection
Figure FDA00026198945700000416
And
Figure FDA00026198945700000417
the magnitude of the absolute value, get pair
Figure FDA00026198945700000418
An estimate of the exact likelihood;
subsequently exporting on each resource
Figure FDA00026198945700000419
By the probability of occurrence of each codeword
Figure FDA00026198945700000420
And the output result of the step four is used for next decoding of the mapping.
6. The symbol-level NOMA asynchronous reception method based on a cross-slot message passing algorithm according to claim 5, characterized in that: the fifth step is to realize that the method is that,
according to the occurrence probability of each code word output in the step four
Figure FDA00026198945700000421
Combining the mapping relation of LDS codebook of each user to obtain modulation symbol
Figure FDA00026198945700000422
7. The symbol-level NOMA asynchronous reception method based on a cross-slot message passing algorithm according to claim 6, characterized in that: the sixth realization method comprises the following steps of,
for step five modulation symbols
Figure FDA00026198945700000423
Demodulating and decoding the channel to obtain the estimated value of the information bit
Figure FDA00026198945700000424
Namely, multi-user detection of the LDS system under non-synchronization is realized.
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