Finite field multiple access system based on polarization adjustment, power distribution method and decoding method

Abstract

The invention discloses a finite field multiple access system based on polarization adjustment, a power distribution method and a decoding method, and belongs to the technical field of 6G communication. The invention aims to solve the problem of low-rate channel coding in a communication scene and the problem of obtaining coding gain by multi-user channel coding in a multi-user transmission scene in an uplink. According to the method, power distribution is carried out on an FFMA system in a diagonal form, a corresponding finite field multiple access system is formed, and in the power distribution process, the power is distributed to different symbols for modulating and sending useful information parts by utilizing elements or polarization coefficients in a polarization adjustment vector; aiming at the condition that power distribution is carried out by utilizing a polarization coefficient, decoding is carried out by adopting a binary minimum distance decoding algorithm, information bit parts are preliminarily screened in an information bit detection stage, all the information parts screened in the information bit detection stage are combined in a joint decoding stage, and decoding is carried out by combining a parity check part after code word reconstruction.

Description

Technical Field

[0001] The present invention belongs to the field of 6G communication technology and relates to a transmitter design for limited domain multiple access and a branch minimum distance decoding method. Background Art

[0002] In modern wireless communication systems, channel coding is a key component to ensure the reliability of data transmission. With the growth of the number of wireless network users and the demand for higher data rates, how to effectively manage multiple users sharing the same spectrum resources has become a research focus. Especially for uplink communications, since users in different locations need to send information to the base station through the same channel, it is particularly important to design an efficient coding scheme that can support multiple users at the same time. At the same time, when users communicate short data packets, the data transmission at this time relies on a low-rate codeword scheme, and the problem of low-rate coding must be solved to ensure reliability. The following are the specific challenges faced by low-rate coding (low-rate channel code) and multi-user channel coding (multiuser channel code) in multiple access scenarios.

[0003] First, low-rate coding: In coding theory, designing low-rate channel codewords is a very challenging problem. In some communication scenarios with short data packet transmission, each user transmits a short data packet, for example, K = 10 bits / user, and the total number of degrees of freedom (DoF) represented by N is usually large, for example, N = 10000, which means that the channel coding must be designed as R SU = K / N = 10 / 10000 = 0.001, where the subscript "SU" means single user. There is currently no definite method to design channel codewords for such a low rate, which makes this an unresolved problem in the field.

[0004] Second, multi-user channel coding: Currently, there are few schemes focusing on uplink multi-user channel coding, because different users are located in different locations and their information sequences are independent. This leads to a lack of cooperation between users, preventing them from obtaining coding gains, which is usually required for multi-user transmissions. Although there have been works on multiple access codes, these studies have mainly focused on multi-user detection rather than achieving coding gains through multi-user channel coding. Multi-user channel coding is a very attractive problem because it has the potential to provide coding gain and user separation at the same time. Obviously, the design of multi-user channel coding remains a challenging research problem.

[0005] Low-rate coding and multi-user channel coding play a vital role in modern wireless communication systems. Low-rate coding improves the reliability of short data packet transmission by adding redundant information, ensuring accurate data reception in noisy and interfering environments, which is particularly important for applications such as IoT devices and emergency messaging. Multi-user channel coding significantly improves system performance and reliability when multiple users share the same channel by providing additional coding gain and effective user signal separation, supporting large-scale connections and reducing mutual interference. These two technologies not only solve key problems in current communications, but also lay the foundation for the development of future wireless communication technologies, promoting the improvement of spectrum efficiency and the realization of emerging applications. Summary of the invention

[0006] The present invention aims to solve the problem of low-rate channel coding in communication scenarios and the problem of obtaining coding gain by multi-user channel coding in multi-user transmission scenarios in uplinks.

[0007] A power allocation method for a finite field multiple access system based on polarization adjustment, which performs power allocation based on a DF-FFMA system;

[0008] The DF-FFMA system refers to the diagonal FFMA system, that is, the codeword matrix V D Contains information array U used to carry user information D and parity check array E D , and the vector b corresponding to the user bit sequence j Located in the information array U D The FFMA system on the main diagonal line of , the FFMA system is a finite field multiple access system;

[0009] For the codeword matrix V D The diagonal codeword v in j,D =(u j,D ,v j,D,red ), the information sequence u of the jth user j,D =(0,...,0,b j ,0,...,0), where the jth user corresponds to b j The 1×K bit sequence is located at u j,D The jth item of , and all other items are 0;

[0010] DF-FFMA only modulates and sends the useful information part during modulation. j,D,S , v j,D,S Indicates v j,D The useful information part in v j,D,S =(b j ,v j,D,red ), v j,D,S The subscript “S” indicates shortening;

[0011] DF-FFMA distributes power in one of the following two ways:

[0012] Method 1: v j,D,S =(b j ,v j,D,red ) has a parity check block length of R, v j,D,S The codeword length is K+R, and the power is allocated to v j,D,S The total transmission power of each user is NP avg ; The polarization adjustment vector is Among them, μ pav The subscript "pav" represents the polarization adjustment vector, is an element in the polarization adjustment vector, 0≤n S <K+R, v j,D,S The power of each symbol is determined by:

[0013]

[0014] Among them, P avg represents the average transmit power of each symbol;

[0015] Method 2: v j,D,S =(b j ,v j,D,red ) has a parity check block length of R, v j,D,S The codeword length is K+R, and the power is allocated to v j,D,S The total transmission power of each user is NP avg ; For v j,D,S The information part and parity part of the symbol are allocated with a power of μ1P. avg , and the power allocated to the parity part of each symbol is μ2P avg , μ1 and μ2 are polarization coefficients; the power distribution condition is

[0016] C1:N·P avg =K·(μ1P avg )+R·(μ2P avg )

[0017] C2:

[0018] in, is the polarization scaling factor, and the subscript “pas” indicates polarization adjustment;

[0019] The power distribution mode is determined according to the power distribution conditions C1 and C2 to realize the power distribution.

[0020] Furthermore, the maximum power allocated to the information part of each symbol in mode 2 is mP avg .

[0021] A limited field multiple access system based on polarization regulation, wherein the system is a regular PA-DF-FFMA, i.e., a polarization regulated DF-FFMA capable of implementing regular power allocation;

[0022] The DF-FFMA system refers to the diagonal FFMA system, that is, the codeword matrix V D Contains information array U used to carry user information D and parity check array E D , and the vector b corresponding to the user bit sequence j Located in the information array U D The FFMA system on the main diagonal line of , the FFMA system is a finite field multiple access system;

[0023] For the codeword matrix V D The diagonal codeword v in j,D =(u j,D ,v j,D,red ), the information sequence u of the jth user j,D =(0,...,0,b j ,0,...,0), where the jth user corresponds to b j The 1×K bit sequence is located at u j,D The jth item of , and all other items are 0;

[0024] DF-FFMA only modulates and sends the useful information part during modulation. j,D,S , v j,D,S Indicates v j,D The useful information part in v j,D,S =(b j ,v j,D,red ), v j,D,S The subscript “S” indicates shortening;

[0025] The polarization-adjustable DF-FFMA that can achieve regular power distribution performs power distribution in the following manner:

[0026] v j,D,S =(b j ,v j,D,red ) has a parity check block length of R = N-mK, v j,D,S The codeword length is K+R, and the power is allocated to v j,D,S The total transmission power of each user is NP avg ; The polarization adjustment vector is Among them, μ pavThe subscript "pav" represents the polarization adjustment vector, is an element in the polarization adjustment vector, 0≤n S <K+R, v j,D,S The power of each symbol is determined by:

[0027]

[0028] Among them, P avg Represents the average transmit power of each symbol.

[0029] A limited field multiple access system based on polarization regulation, wherein the system is an irregular PA-DF-FFMA, that is, a polarization regulation DF-FFMA capable of realizing irregular power distribution;

[0030] The DF-FFMA system refers to the diagonal FFMA system, that is, the codeword matrix V D Contains information array U used to carry user information D and parity check array E D , and the vector b corresponding to the user bit sequence j Located in the information array U D The FFMA system on the main diagonal line of , the FFMA system is a finite field multiple access system;

[0031] For the codeword matrix V D The diagonal codeword v in j,D =(u j,D ,v j,D,red ), the information sequence u of the jth user j,D =(0,...,0,b j ,0,...,0), where the jth user corresponds to b j The 1×K bit sequence is located at u j,D The jth item of , and all other items are 0;

[0032] DF-FFMA only modulates and sends the useful information part during modulation. j,D,S , v j,D,S Indicates v j,D The useful information part in v j,D,S =(b j ,v j,D,red ), vj, D,S The subscript “S” indicates shortening;

[0033] Polarization-adjustable DF-FFMA that can achieve irregular power distribution distributes power in the following way:

[0034] v j,D,S =(b j,v j,D,red ) has a parity check block length of R = N-mK, v j,D,S The codeword length is K+R, and the power is allocated to v j,D,S The total transmission power of each user is NP avg ; For v j,D,S The information part and parity part of the symbol are allocated with a power of μ1P. avg , and the power allocated to the parity part of each symbol is μ2P avg , μ1 and μ2 are polarization coefficients; the power distribution condition is

[0035] C1:N·P avg =K·(μ1P avg )+R·(μ2P avg )

[0036] C2:

[0037] in, is the polarization scaling factor, and the subscript “pas” indicates polarization adjustment;

[0038] The power distribution mode is determined according to the power distribution conditions C1 and C2 to realize the power distribution.

[0039] Furthermore, the maximum power allocated to the information part of each symbol is mP avg .

[0040] A decoding method for a limited domain multiple access system based on polarization adjustment, the method being a decoding method for the limited domain multiple access system based on polarization adjustment, comprising the following steps:

[0041] The received signal sequence Divided into information part and parity check part, that is, y = (y inf ,y red ), where y inf =(y[0],y[1],...,y[j],...,y[J]) represents the information part, including J data blocks. For the jth data block, y[j] = (y j·K ,y j·K+1 ,...,y j·K+k ,...,y j·K+K-1 ), where the block length of each block is K;

[0042] (1) Information bit detection stage:

[0043] First, the information is divided into blocks for detection, based on the decision threshold δ th For infPreliminary judgment:

[0044] For the j-th information sub-block y[j], the decision process is as follows:

[0045]

[0046] in, represents the kth bit in the jth information sub-block estimated from the received signal; is the log-likelihood value calculated based on the received signal;

[0047] After this decision process, the number of unknown information bits in the sub-block is D j，k (0) and D j，k (1) respectively represent the estimated received signal and Distance to receiving signal:

[0048]

[0049] All estimated signals of the sub-block Combined together, the estimated sequence corresponding to the user get Distance D from receiving signal inf,j,d ;right Distance Arrange in ascending order, select the first I1 distance values ​​to form the distance set of the information segment, and record it as in 1≤i≤I1,1≤j≤J,

[0050] For each distance value Through the decimal to binary conversion function F D2B The distance value corresponding to d i Transformed into an estimated binary vector Υ inf,j Each element in corresponds to a unique vector; for each information sub-block, a binary vector set is obtained. Right now

[0051] (2) Joint decoding stage:

[0052] After the information bit detection stage, J binary sets are obtained, namely {Ω1,Ω2,...,Ω j ,...,Ω J}, the sub-blocks and the corresponding binary sets are combined in turn. The combination process is to first take an element combination from Ω1 and Ω2 respectively, concatenate the sequences corresponding to the two elements, and superimpose the corresponding distance values. When Ω1 and Ω2 are combined, M1×M2 element combinations can be generated. Assuming that after each combination is completed, the first I2 elements are selected according to the distance value as the candidate set for the next combination. After J sub-blocks are combined, I2 candidate information sequence sets are obtained, which can be expressed as is the candidate estimated information sequence obtained by combining J sub-blocks, with a length of JK. Each candidate information sequence in the set corresponds to the calculated distance value, so the corresponding distance sorted list is

[0053] For the i-th candidate estimated information sequence It consists of J binary sequences of length K, represented as Using channel coding C gc The generating matrix G of the system form gc，sym According to the DF-FFMA coding method, the transmission codeword is reconstructed for each sub-block, and the parity check block obtained is v i,j,red , the parity check block passes through the transformation function F from the finite field to the complex field F2C Modulation signal x i,j,red , get the modulated signal of J check bits: x i,0,red ,x i,1,red ,...,x i,j,red ,...,x i,J-1,red , and then sum the modulated signals to get r red,i ;

[0054] Calculate the parity part y red With r red,i Distance:

[0055]

[0056] Among them, 0≤i<I2, the alternative information sequence The corresponding total distance is In ascending order Sort by The minimum distance of the binary sequence is given by:

[0057]

[0058] What you get That is the multi-user information sequence obtained by decoding.

[0059] Furthermore, the log-likelihood value calculated based on the received signal as follows:

[0060]

[0061] Among them, σ 2 is the estimated noise variance, and is the posterior probability calculated based on the received signal.

[0062] Furthermore, the estimated binary vector

[0063] Furthermore, the The corresponding parity part y red With r red,i Distance

[0064] Furthermore, the Distance D from receiving signal inf,j,d as follows:

[0065]

[0066] Where d represents The decimal number is The subscript "B2D" indicates binary to decimal conversion.

[0067] The present invention has the following beneficial effects:

[0068] The present invention is a polarization adjusted finite field multiple access scheme designed for multi-user transmission, and a corresponding bifurcated minimum distance (BMD) decoding method approaching the maximum a posteriori probability; at the same time, the scheme overcomes the difficulty of low-rate channel coding and solves the problem of obtaining coding gain for multi-user channel coding in the uplink. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 This is the structural block diagram of the FFMA uplink system in GMAC.

[0070] Figure 2 Schematic diagram of the BMD algorithm.

[0071] Figure 3 BER performance of the low-rate channel code constructed based on PA-DF-FFMA.

[0072] Figure 4 BER performance of the low-rate channel code constructed based on PA-DF-FFMA.

[0073] Figure 5BER performance of PA-DF-FFMA and IDMA systems in GMAC.

[0074] Figure 6 BER performance of PA-DF-FFMA and IDMA systems in GMAC. DETAILED DESCRIPTION

[0075] The present invention is widely applicable to multiple application fields such as Internet of Things (IoT), ultra-large-scale machine type communication (uMTC), enhanced mobile broadband (eMBB), ultra-reliable low latency communication (URLLC), vehicle-to-everything (V2X), etc. By optimizing the multiple access mechanism and decoding method, the present invention can significantly improve the access efficiency and data transmission reliability of the system, and meet the diverse and high-demand communication application needs in the future.

[0076] The present invention is based on a diagonal form finite-field multiple access (DF-FFMA) scheme and provides a corresponding polarization-adjusted finite-field multiple access scheme (PA-DF-FFMA), which improves power utilization efficiency, has better bit error rate (BER) performance under low-speed channel coding, and can obtain coding gain in a multi-user transmission scenario.

[0077] The PA-DF-FFMA scheme utilizes the resources of the entire channel in a polarized manner, making full use of the degree of freedom (DoF) of the entire channel. In a multi-user scenario, the scheme can coordinate the power allocation and channel coding in multi-user transmission to ensure efficient use of channel resources. In the single-user case, it essentially becomes a low-rate channel codeword. When LDPC coding is used as a multi-user transmission codeword, the polarization method can convert the LDPC code designed for high data rates into an LDPC code suitable for lower data rates. Through experimental comparison, the scheme still maintains good BER performance at low rates, which is an important breakthrough in the challenge of low-rate coding.

[0078] In addition, the scheme allows the receiver to perform channel decoding before multi-user separation, so that the system can obtain coding gain from multiple concurrent user transmissions at the same time. By comparing the PA-DF-FFMA scheme with the classic IDMA scheme, it is found that the PA-DF-FFMA scheme can obtain coding gain and maintain good reliability even when the number of users is large. Specific implementation method one:

[0080] This embodiment is a limited domain multiple access system based on polarization adjustment and a power allocation method thereof.

[0081] For the limited field multiple access scheme for uplink multi-user transmission, when LDPC coding is used as the transmission codeword, the receiving end cannot reflect the performance by using MSA as the iterative decoding algorithm. This is because the decoding performance of MSA is difficult to reach the optimal level under low-rate conditions and cannot fully reflect the potential advantages of the system.

[0082] Based on the existing FFMA scheme, the present invention introduces a polarization-adjusted transmission mode, which can optimize the allocation of channel resources in the modulation and transmission stage, and use a binary minimum distance decoding algorithm at the receiving end to maximize the performance of the PA-DF-FFMA system.

[0083] The concept of EP code encoding:

[0084] The encoding of EP code is based on the binary to finite field GF(q) transformation function (denoted as F B2q ) is implemented. Let the information sequence sent by the jth user be b j =(b j,0 ,b j,1 ,...,b j,k ,...,b j,K-1 ), where K is a positive integer representing the number of messages sent by the user, 1≤j≤J,0≤k<K. The EP encoder converts each bit sequence b j Transformation function F from binary to finite field GF(q) B2q Uniquely maps to the element sequence u j =(u j,0 ,u j,1 ,...,u j,k ,...,u j,K-1 ), i.e. u j,k =F B2q (b j,k ); Similarly, the decoding of EP code can be done through a finite field to binary conversion function F q2B To achieve this, b j,k =F q2B (u j,k ).

[0085] Assume that each user is assigned an EP. For example, the jth EP is Assigned to the jth user, 1≤j≤J, l j，0 and l j,1 The subscript "j" represents the jth EP, and the subscripts "0" and "1" represent the input information bits (0)2 and (1)2. j The kth component u j,k It is expressed as:

[0086]

[0087] Among them, b j,k ⊙C j Defined as a switch function, if the input information is b j,k =(0)2, then the transformed element components are Otherwise Assume that the bit block composed of the kth component of the J user input bit information is b[k]=(b 1,k ,b 2,k ,...,b J,k ), 0≤k<K, then its corresponding EP codeword (u 1,k ,u 2,k ,...,u J,k ) is the output element block component corresponding to the k-th bit of J users, expressed as u[k]=(u 1,k ,u 2,k ,...,u J,k ).

[0088] The concept of AIEP code over finite field:

[0089] For a binary source transmission system, the information sent has only two cases: (0)2 and (1)2. To represent a set of element pairs, where 0≤l j,0 ,l j,1 ≤p m -2 and l j,0 and l j,1 The subscript j in indicates that the element pair is the jth element pair, and the 0 and 1 therein indicate whether the information to be transmitted is (0)2 or (1)2. In the following, Cj and Ψ are used to represent EP and EP code, respectively.

[0090] The p-1 non-zero elements of GF(p) are denoted as GF(p)\{0}, which is divided into (p-1) / 2 mutually disjoint EPs. Each EP consists of a non-zero element j in GF(p)\{0} and its additive inverse pj. Such an element pair (j, pj) is called an additive inverse EP (AIEP). The set of AIEPs that GF(p)\{0} is divided into is denoted as This partition is called AIEP partition. When p = 2, there is only one EP in GF(2) = {0,1}, namely C B ={0,1}, the subscript “B” indicates the binary or p=2 case.

[0091] set up for where J is a positive integer not greater than (p-1) / 2, i.e., 1≤J≤(p-1) / 2. The superscript “s” indicates a single symbol. For 1≤j≤J, let the AIEP be (j,pj), i.e. definition Reverse order AIEP (R-AIEP) for

[0092] This AIEP The partition that constitutes a 2J-element subset in GF(p)\{0} is Subdividing into J R-AIEP Composition s The reverse order set of or

[0093] Let (u1,u2,...,u j ,...,u J ) is a J-tuple defined on GF(p), where the jth component u j From and 1≤j≤J, the J-tuple is Ψ s Cartesian product of AIEPs in An element in j ,...,u J ) is regarded as A J user AIEP codeword in It constitutes the J-user AIEP codeword defined in GF(p) and has 2 J A code word.

[0094] The J-tuple (u1,u2,...,u j ,...,u J ) and then calculate modulo p, expressed as This calculation method is called (u1,u2,...,u j ,...,u J ) is a finite field sum pattern (FFSP). Assume (u1,u2,...,u J ) and (u1',u'2,...,u' J ) is s For any two J-tuples, if Then the FFSP result ω is mapped one-to-one with the corresponding J-tuple. If J tuples can be uniquely recovered from ω, then we call Ψ s With unique sum-pattern mapping (USPM) structural characteristics. (u1,u2,...,u J ) as a J user codeword, then It is called the J-user uniquely decodable AIEP code (UD-AIEP) on GF(p).

[0095] The concept of orthogonal uniquely decipherable AIEP code:

[0096] Assume that α is GF(p m ) is the original element, then Can express GF(p m ), GF(p m ) on each element α j can be expressed as α 0 =1,...,α m-1 A linear combination of:

[0097] α j =a j,0 +a j,1 α+a j,2 α 2 +...+a j,m-1 α m-1 ,

[0098] Where j = -1, 0, ..., p m -2 and coefficient a j,0 ,a j,1 ,...,a j,m-1 is an element on GF(p). From the above formula, we can see that α j It can be obtained by the vector (a) of length m on GF(p) j,0 ,a j,1 ,...,a j,m-1 ) only indicates.

[0099] Finite field GF(p m ) can form an m-dimensional vector space V on GF(p) p (m), V p Each vector in (m) is an m-tuple on GF(p). For 1≤j<m, we know that α i =(0,0,...,1,0,...,0) is a tuple of length m, which has a value of 1 only in the i-th position and 0 in the other positions, so it can be called A tuple of length m α 0 ,α 1 ,α 2 ,...,α m-1 Constitutes V p (m) is an orthogonal basis.

[0100] Given two elements and Their sum can be expressed as:

[0101]

[0102] The tuple representation of the above results is For 1≤j<m, if is an additive inverse pair or a pair of zero pairs (0,0) on GF(p), then Right now and are each other's additive inverse, Constitutes GF(p m )’s AIEP.

[0103] if is an AIEP on GF(p), then is GF(p m ) on AIEP, use represents the set of L AIEPs on GF(p), where 1≤l≤L, for 1≤i<m:

[0104]

[0105] Ψ o,i is GF(p m ) with the USPM structure characteristics, the subscript "o" means orthogonal, so the Cartesian product The L AIEPs in Ψ o,i A L user UD-AIEP codeword is formed in GF(p m ) is defined above, including 2 L codewords, each codeword is represented by GF(p m 2 of ) L When i=0,1,...,m-1, we can form m L user UD-AIEP codewords, which are Ψ o,0 ,Ψ o,1 ,...,Ψ o,m-1 , these codewords are mutually exclusive, i.e. k≠i, 0≤k, i<m.

[0106] Ψ o,i Each codeword in is composed of L m-tuples defined on GF(p), and each m-tuple has only one non-zero element from GF(p) at the corresponding position. In GF(p m ) constitutes an orthogonal UD-AIEP code with Lm users, which is obtained by concatenating these m L-user UD-AIEP codes Ψ o,0 ,Ψ o,1 ,...,Ψ o,m-1 formed.

[0107] Now, consider the orthogonal UD-AIEP code Ψ o A special case of GF(2 m ), which has only one basis EP, defined as C B =(0,1), not AIEP, so Ψ o is GF(2 m ) of the orthogonal UD-EP code, let Ψ o,B is defined in GF(2 m ) on orthogonal UD-EP codes.

[0108] This embodiment is based on the expansion domain GF(2) m ) based on the orthogonal unique decodable o,B Taking the diagonal form and the corresponding polarization form of the uplink FFMA system in the Gaussian multiple-access channel (GMAC) as an example, the corresponding multi-user decoding algorithm is given. This implementation method can also be directly extended when using the orthogonal UD-AIEP code on GF(q). q can be a prime number or a power of a prime number. However, the polarization adjustment method will become complicated in the case of multi-base, and the BMD decoding algorithm will also become more complicated. Of course, this implementation method is also applicable to fading channels.

[0109] FFMA system suitable for uplink multi-user communication scenarios:

[0110] The FFMA system in the uplink of GMAC is based on the extended area GF(2) m ) based on the orthogonal UD-EP code in 1≤j≤J,C B=(0,1) is the only EP code on GF(2). The parameter m represents the number of time slots in the finite field, which can be regarded as virtual resource blocks (VRBs). Therefore, the number of users J that the system can accommodate can be equal to or less than m. The FFMA uplink system structure diagram is as follows: Figure 1 As shown, F B2q and F q2B Represents binary to finite field GF(q) and finite field GF(q) to binary transformation; F q2Q and F Q2q It is the transformation from finite field GF(q) to finite field GF(Q) and vice versa; F F2C and F C2F It represents the transformation from finite field to complex field and from complex field to finite field. The transmitter first performs EP coding and channel coding on the information sequence sent by the user, then modulates the coded sequence, and finally sends the modulated sequence to the GMAC channel.

[0111] 1. Diagonal FFMA system:

[0112] The bit sequence output by the jth user is represented as b j =(b j,0 ,b j,1 ,...,b j,k ,...,b j,K-1 ), the transmitter sends the bit sequence b j uniquely maps to the element sequence u j =(u j,0 ,u j,1 ,...,u j,k ,...,u j,K-1 ), which is determined by the EP code For 0≤k<K, u j The kth component u j,k It is represented by its corresponding m-tuple on GF(2), that is, u j,k =(u j,k,0 ,u j,k,1 ,...,u j,k,i ,...,u j,k,m-1 ), where 0≤i<m. Then u j,k The m-tuple representation of

[0113]

[0114] u j,k The i-th position of

[0115]

[0116] u j,k is an m-length sparse vector with only one element.

[0117] Next, the sequence u obtained by EP encoding j It will pass through a (N,mK) linear block code, where N is the length of the block code and mK is the information bit length, and perform global channel coding to obtain the transmitted codeword v j ,Right now

[0118] v j =u j G gc =(v j,0 ,v j,1 ,...,v j,n ,...,v j,N-1 ),

[0119] G gc is the generator matrix of global channel coding, with dimension mK×N, where v j,n ∈GF(2), 0≤n<N. The whole coding can be regarded as a two-stage cascade coding, where EP coding is used as inner coding and channel coding C gc As an external code, this code is called Ψ o,B / C gc coding.

[0120] Each codeword v is encoded j The signal mapped to the complex domain after BPSK modulation That is x j =(x j,0 ,x j,1 ,...,x j,n ,...,x j,N-1 ), for 0≤n<N, x j The jth element x j,n It is expressed as:

[0121] x j,n =F F2C (v j,n )=2v j,n -1,

[0122] Among them, x j,n ∈{-1,+1}, this kind of j Map to x j The method is called the transformation from finite field to complex field, denoted as F F2C , then x j Sent to GMAC.

[0123] Received signal at the receiving end is the sum of the signals of J users and the noise signal, expressed as:

[0124]

[0125] in, is a distribution of The AWGN vector of y is called the complex domain sum pattern (CFSP) signal sequence.

[0126]

[0127] In general, the generator matrix can be of the systematic form G gc,sym and non-systematic form G gc,nonsym , two forms of G gc can be used in the FFMA system, however, the system form of G gc,sym This can provide greater flexibility in designing FFMA systems.

[0128] Assume that the generator matrix of dimension mK×N defined on GF(2) is in systematic form, m is the maximum number of users, K is the number of user information bits, and N is the codeword length. In this case, the encoded codeword v j =(v j,0 ,v j,1 ,...,v j,n ,...,v j,N-1 ) has the following forms:

[0129] v j =u j ·G gc,sym =(u j ,v j,red )=(u j,0 ,u j,1 ,...,u j,K-1 ,v j,red ),

[0130] Among them, u j，k is a sparse vector, v j，red The redundancy added is the check block. The subscript "red" means redundancy. In the system form, the codewords of m users can be represented by an m×N codeword matrix V = [v1,v2,...,v j ,...,v m ] T To represent, 1≤j≤J, J=m, the codeword matrix V can be divided into two parts, the information part U and the check part E, as shown in the following formula:

[0131]

[0132] The information part U is a 1×K array, that is, U=[U0,U1,...,U k,...,U K-1 ], where U k is an m×m matrix. When J=m, the J information bits b of J users are 1,k ,b 2,k ,...,b J,k Located in U k On the main diagonal of 1,k ,b 2,k ,...,b J,k Still in U k On the main diagonal, and U k The remaining rows or columns are all 0. The parity check part E of V is a J×(N-mK) matrix consisting of all parity check bits formed based on the generator matrix.

[0133] In a multi-user transmission scenario, m may be very large. In this case, V is a sparse matrix. For the 1×K information array U of V, each item U k is an m×m matrix with m information bits b 1,k ,b 2,k ,...,b j,k ,...,b m,k Located in U k On the main diagonal of , all off-diagonal elements are 0, where 1≤j≤J<m, 1≤k<K. After permuting and rearranging the columns of U, we can get an m×m array U D , where b1, b2, ..., b j ,...,b m Located in U D All other entries on the main diagonal of are 0, as shown below:

[0134]

[0135] Among them, b1, b2, ..., b j ,...,b m is a 1×K vector, the subscript “D” means diagonal, let u j,D represents the information sequence of the jth user, with a length of 1×mK, u j,D =(0,...,0,b j ,0,...,0), where the jth user b j The 1×K bit sequence is located at u j,D The jth item of , and the other items are all 0.

[0136] Then the matrix G is generated by the system form gc,sym To u j,D Encode and get u j,D The code word vj,D =(u j,D ,v j,D,red ), where v j,D,red Yes j,D The parity check block is a (N-mK) tuple, and the user codewords together form a diagonal codeword matrix V D :

[0137]

[0138] V D The m×m information array U D and the m×1 parity check array E D Composition, E D =[v 1,D,red ,v 2,D,red ,…,v m,D,red ].

[0139] From the codeword v j,D It can be found that the useful vector is b j and v j,D,red Only located in u j,D The jth term and the parity term v j,D,red At , all other terms are 0. Therefore, for the diagonal codeword v j,D , we can only modulate and send the useful information part, namely v j,D,S =(b j ,v j,D,red ), the subscript "S" indicates shortened. This is a shortened block length structure, which can save transmission power, which is also desirable for short data packet transmission, based on the shortened v j,D The FFMA system is called a diagonal form FFMA system (DF-FFMA).

[0140] Note that the permutation and rearrangement operations do not affect the properties of the FFMA system. For the DF-FFMA system, the bit sequences of J users are transmitted in an orthogonal mode and J parity check sequences are appended, which greatly saves the transmission power.

[0141] 2. Polarization-adjusted DF-FFMA system:

[0142] Users in the DF-FFMA system have the characteristics of shortened block length and reduced power consumption, allowing P avg represents the average transmit power of each symbol, for (N,mK) channel code C gc , the code length is N, the information bit length is mK, the check bit length is R = N-mK, and the total transmission power of each user is NP avg ; The DF-FFMA system only uses (K+R)P to save transmission power. avgIf the performance of the entire system is to be fully utilized, the remaining (m-1)K·P avg Utilization of power.

[0143] PA-DF-FFMA redistributes unused power based on DF-FFMA, optimizes power allocation, and adjusts channel capacity according to the allocated power, thus forming a polarization form. Please note that when LDPC code is used as the channel code, when there is only one user, that is, J=1, PA-DF-FFMA actually becomes a polarization-adjusted LDPC (PA-LDPC) code. PA-DF-FFMA has two polarization adjustment modes: regular and irregular.

[0144] The regular and irregular PA-DF-FFMA power allocation methods are as follows:

[0145] (1) Irregular PA-DF-FFMA:

[0146] Further analysis of the shortened codeword v j,D,S =(b j ,v j,D,red ), since the parity block length is R, v j,D,S The codeword length is K+R, or equivalently, the number of symbols is K+R. In the irregular PA-DF-FFMA scheme, different powers are allocated to v j,D,S The polarization-adjusted vector (PAV) is defined as Where 0≤n S <K+R, the subscript “pav” represents the polarization adjustment vector, at this time v j,D,S The power of each symbol of is given by:

[0147]

[0148] in, This ensures that the total transmission power of PA-DF-FFMA is still NP avg .

[0149] Obviously, irregular PA-DF-FFMA provides significant flexibility, as the power of each bit can be customized; however, this flexibility brings design complexity due to the large number of parameters involved. The following mainly describes the regular PA-DF-FFMA system, which is easier to implement than the irregular version.

[0150] (2) Regular PA-DF-FFMA:

[0151] Examining the structure of DF-FFMA, we can see two different parts: the information part and the parity part (or block). Assume that the power allocated to the information part of each symbol is μ1P avg , and the power allocated to the parity part of each symbol is μ2P avg Then, the condition for power allocation (or polarization adjustment) is

[0152] C1:N·P avg =K·(μ1P avg )+R·(μ2P avg ),

[0153] C2:

[0154] in, Defined as the polarization scaling factor, the subscript "pas" means polarization adjustment. The C1 condition ensures that the total transmitted power remains constant; the C2 condition specifies that the information part receives more power than the parity part. Ideally, the goal is to maximize the reliability of the information part by allocating as much power as possible to it. In addition, considering that the unused power is (m-1)K·P avg , the maximum power that can be allocated to the information part of each symbol is mP avg , which is equivalent to repeating the information part of each symbol m times. The above power allocation conditions can determine the power allocation method of PA-DF-FFMA. Specific implementation method 2:

[0156] This embodiment is a decoding method for a limited field multiple access system (power allocation) based on polarization adjustment. This embodiment performs decoding through a binary minimum distance decoding algorithm.

[0157] Gradually increasing the power of the information part, its reliability will also gradually increase, that is, it has a high degree of reliability. Based on this characteristic, the present invention proposes a bifurcated minimum distance (BMD) decoding algorithm for PA-DF-FFMA. The algorithm is divided into two different stages, namely, the detection part of the information bit and the joint decoding of the information bit and the check bit:

[0158] (1) Information bit detection stage: This stage focuses on the preliminary screening of the information bit part. This process identifies a narrow detection range, thereby reducing the complexity of subsequent joint decoding;

[0159] (2) Joint decoding stage: This stage focuses on combining the information parts screened in the information bit detection stage, reconstructing the codeword and decoding the parity check part. The purpose of this stage is to combine the information bit and check bit parts to find the best solution that is closest to the multi-user information sequence;

[0160] The BMD algorithm proposed in the present invention aims to gradually improve efficiency and accuracy, and it is similar to maximum a posteriori (MAP) detection. The process of the BMD algorithm is as follows Figure 2 As shown, the processing process is as follows:

[0161] Considering the DF-FFMA structure, the received signal sequence It can be divided into the information part and the parity part, that is, y = (y inf ,y red ), y inf =(y[0],y[1],...,y[j],...,y[J]) represents the information part, including J data blocks. For the jth data block, y[j] = (y j·K ,y j·K+1 ,...,y j·K+k ,...,y j·K+K-1 ), the block length of each block is K.

[0162] For the first stage of the BMD algorithm, the information bit part is detected in blocks. The input signal is the information part. Since it is in diagonal form, the jth received data block can be expressed as

[0163] y[j]=μ1·F F2C (b j )+z[j]=(2μ1·b j -1)+z[j],

[0164] in, is a distribution of Obviously, the polarization adjustment process enhances the Euclidean distance between information bits (0)2 and (1)2, thereby improving reliability.

[0165] In order to reduce the detection complexity, a decision threshold δ is given th For inf A preliminary judgment is made, and the first stage detection process is introduced by taking the jth information sub-block y[j] as an example. Since the information bits after polarization adjustment have improved reliability, the judgment process will not cause too much loss to the final decoding result. The judgment process is as follows:

[0166]

[0167] in, represents the kth bit in the jth information sub-block (the transmitted information sequence of the jth user) estimated from the received signal; σ 2 is the estimated noise variance, is the log-likelihood ratio (LLR) calculated based on the received signal. and is the posterior probability calculated based on the received signal;

[0168] After this decision process, the number of unknown information bits in the sub-block is D j，k (0) and D j，k (1) respectively represent the estimated received signal and The distance to the received signal can be calculated according to the following formula:

[0169]

[0170] For DF-FFMA, all estimated signals in this sub-block Combined together, the estimated sequence corresponding to the user From the collection After the judgment process, the elements of the set are divided into 2 K Reduce to Improved detection efficiency, therefore, The distance to the received signal is calculated as:

[0171]

[0172] Where d represents The decimal number is The subscript "B2D" indicates binary to decimal conversion.

[0173] right Distance Arrange in ascending order, select the first I1 distance values ​​to form the distance set of the information segment, and record it as in 1≤i≤I1,1≤j≤J,

[0174] For each distance value Through the transformation function F D2B The distance value corresponding to d i Transformed into an estimated binary vector Get the corresponding possible information sequence, where F D2B is the decimal to binary conversion function, that is

[0175]

[0176] Υ inf,j Each element in corresponds to a unique vector. Therefore, for each information sub-block, we can get a binary vector set Right now Then the set of each information sub-block Y inf,j and Ω j Used as input to the second stage of the BMD algorithm, they aid in the subsequent decoding process.

[0177] In the second stage of the BMD algorithm, it is necessary to first combine multiple information sub-blocks and then reconstruct the codeword to use the parity check part for decoding. To illustrate this, it is necessary to consider the set Ω of each information sub-block j As mentioned above, y inf It is divided into J sub-blocks, and after the first stage, J binary sets are obtained, namely {Ω1,Ω2,...,Ω j ,...,Ω J}, first of all, the sub-block sets are combined in turn. The combination process includes the concatenation of candidate sequences and the combination of distance values. For example, when the first sub-block Ω1 and the second sub-block Ω2 are combined, it is assumed that the two sub-blocks have M1 and M2 elements respectively. Each element carries two pieces of information. One is the possible estimated sequence corresponding to the element, and the other is the distance value between the estimated sequence and the received signal after modulation. When sub-blocks Ω1 and Ω2 are combined, M1×M2 element combinations can be generated, and the process completes two parts of work, namely the concatenation of the sequences corresponding to the elements and the superposition of the distance values. Assuming that after each combination is completed, the first I2 are selected according to the distance value as the candidate set for the next combination. After J sub-blocks are combined, I2 candidate information sequence sets are obtained, which can be expressed as is the candidate estimated information sequence obtained by combining J sub-blocks, with a length of JK. Each candidate information sequence in the set corresponds to the calculated distance value, so the corresponding distance sorted list is

[0178] Take the i-th candidate estimated information sequence For example, it consists of J binary sequences of length K, expressed as Using channel coding C gc The generating matrix G of the system form gc，sym According to the DF-FFMA coding method, the transmission codeword is reconstructed for each sub-block. At this time, the parity check block obtained is v i,j,red , the parity check block passes through the transformation function F from the finite field to the complex field F2C Modulation signal x i,j,red Therefore, the modulation signal of J check bits can be obtained: i,0,red ,x i,1,red ,...,xi,j,red ,...,x i,J-1,red , and then sum these modulated signals:

[0179]

[0180] r red,i Represents the sum of the parity bits of the reconstructed transmitted signal, which is used to calculate the distance of the parity bit part. Given the input parity part y red , which is related to r red,i The distance is:

[0181]

[0182] Among them, 0≤i<I2, the alternative information sequence The corresponding total distance is In ascending order Sort by The minimum distance of the binary sequence is given by:

[0183]

[0184] therefore, is the decoded multi-user information sequence.

[0185] The error performance and complexity of the BMD algorithm proposed in this invention are mainly affected by the threshold δ th and the effect of cutoff lengths I1 and I2, increasing δ th , I1, and I2 generally improve error performance but also increase complexity. th It is crucial to choose appropriate values ​​of I1 and I2 to balance error performance and complexity. The above BMD algorithm is based on the fact that it can be used directly when the number of user information K is small. For larger K, the BMD algorithm can be used directly only by performing block processing. Similarly, it is also applicable to non-binary cases, but at the cost of high complexity.

[0186] Example: PA-DF-FFMA Uplink System

[0187] Only channel codes with a rate greater than or equal to 0.5 are considered. This is because the BMD algorithm relies heavily on the reliability of the information part. Therefore, the analysis is restricted to channels that satisfy R c The following uses two different code rate QC-LDPC codes (6000, 3000) and (10000, 8400) as channel coding for PA-DF-FFMA system as examples to analyze the BER performance of low rate channel codes based on PA-DF-FFMA and compare the performance of IDMA system and FFMA system.

[0188] (1) BER performance of low-rate channel codes based on PA-DF-FFMA

[0189] When J = 1, the BER performance of the PA-DF-FFMA system is mainly determined by the (N, mK) channel code C gc Consider two cases: In the first case, the channel code C gc is binary (6000,3000) LDPC code C gc,b1 , the rate is 0.5; in the second case, the channel code C gc is binary (10000,8400) LDPC code C gc,b2 , with a rate of 0.84.

[0190] In the above two cases, the PA-DF-FFMA system proposed in the present invention is regarded as a low-rate LDPC code. In this case, due to the small number of information bits (e.g., K = 1, 2, 3, 10, 100) and the large block length (e.g., N = 10000), the PA-DF-FFMA system with J = 1 basically becomes a low-rate channel code (e.g., R = 1 / 10000, 2 / 10000, 3 / 10000, 1 / 1000, 1 / 100), and the BER performance of the PA-DF-FFMA system in the above two cases is shown in FIG. Figure 3-Figure 4 .

[0191] Figure 3 The BER performance of the low-rate channel code constructed based on PA-DF-FFMA (C gc,b1 , Rc=0.5), set J=1 and K=1,2,3,10,100bits / user for comparison. Figure 3 As shown in Figure 2, as the number of information bits K increases, R c = 0.5, the BER performance of the PA-DF-FFMA system improves when K = 1 to K = 10, and then starts to degrade when K = 10 to K = 100, that is, a local extremum appears in the range of K = 10 to K = 100. However, the exact value of K at which this extremum is reached is unknown, as all results are based on computer simulations; however, it is known that the typical traffic of a single user is about K = 10 to K = 100. Therefore, it can be concluded that K = 10 achieves better BER performance compared to K = 100. Specifically, when K = 10, R c = 0.5, the BER of the PA-DF-FFMA system shows a gain of about 3.2 dB. gc,b1 There is still a gap of about 4.4dB in performance.

[0192] Figure 4The BER performance of the low-rate channel code constructed based on PA-DF-FFMA (C gc,b2 , Rc=0.584), set J=1 and K=1, 2, 3, 10, 100 bits / user for comparison. Figure 4 As shown, with R c = 0.5, the BER of PA-DF-FFMA is the opposite, and the channel coding is C gc,b2 (R c =0.84) the BER performance of the PA-DF-FFMA system improves monotonically with the increase of K. Compared with the uncoded case, R c = 0.84, the BER of the PA-DF-FFMA system shows a gain of about 3.2 dB. gc,b2 There is still a gap of about 3.2dB in performance.

[0193] (2) Comparison between FFMA and IDMA systems

[0194] LDPC coding based on two different rates gc,b1 and C gc,b2 The BER performance of the PA-DF-FFMA proposed in the present invention is compared with that of the IDMA system, and the relevant performance simulation is shown in Figure 5-Figure 6 .

[0195] K = 10, the number of users is J = 1, 4, 10, 100, and the polarization scaling factor is μ pas =300. For fair comparison, the total resource utilization of the IDMA system is also N=6000. The transmitter of the IDMA system consists of a convolutional code, a repetition code, and an interleaver. After K=10 information bits are encoded by a 1 / 2 rate convolutional code, the length of the generated codeword is 20. The number of repetitions of the repetition code is SF=300, that is, each symbol of the codeword is repeated 300 times. Therefore, the frame length of each user is still N=6000, and the receiver uses Turbo iteration to recover the transmitted symbol sequence.

[0196] Figure 5 For the BER performance of PA-DF-FFMA and IDMA systems in GMAC (Rc=0.5), set K=10 bits / user and J=1, 4, 10, 100 for comparison. Figure 5 As shown in the figure, when J = 1, 4, 10, the PA-DF-FFMA system proposed in the present invention is better than the IDMA system. pas=300, the capability of the PA-DF-FFMA system is comparable to the repetition code used in the IDMA system. Therefore, the difference in BER is mainly attributed to the length of the channel codeword. In order to keep the same frame length for the FFMA and IDMA systems (e.g., N=6000), the parity block length in the IDMA system is 10, because channel coding must be performed before the multiplexing of complex domain resources. In contrast, the proposed PA-DF-FFMA system performs channel coding after the multiplexing of finite domain resources, enabling it to use a parity block length of 3000. According to Shannon's theory, longer channel coding can provide better coding gain; therefore, the BER performance of the PA-DF-FFMA system proposed in the present invention is worse than that of the IDMA system. However, when the number of users is J=100, the error performance of the PA-DF-FFMA system is not as good as that of the IDMA system.

[0197] Similarly, the channel code C gc,b2 (R c =0.84) for error control and the IDMA system with total resource occupancy of N = 10000. This comparison is fair. At this time, the IDMA system has SF = 840, K = 10 information bits, and generates a codeword sequence through a convolutional code at a rate of 0.84. The codeword length is 12. Since such a short channel codeword cannot provide effective error correction, R c = 0.84, the BER performance of the IDMA system is the same as that of the uncoded BPSK. Figure 6 . Figure 6 For the BER performance of PA-DF-FFMA and IDMA systems in GMAC (Rc=0.5 and 0.84), K=10 bits / user and J=100 are set for comparison; Figure 6 It can be observed that, compared with the IDMA system (or the uncoded case), R c = 0.84 provides a coding gain of about 2.1 dB. This finding shows that even when the number of users is large, the PA-DF-FFMA system proposed in the present invention can still achieve coding gain and maintain good transmission reliability, thus proving the effectiveness of the proposed FFMA system.

[0198] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A power allocation method for a limited domain multiple access system based on polarization adjustment, characterized in that: Power allocation based on DF-FFMA system; The DF-FFMA system refers to the diagonal FFMA system, that is, the codeword matrix V D Contains information array U used to carry user information D and parity check array E D , and the vector b corresponding to the user bit sequence j Located in the information array U D The FFMA system on the main diagonal line of , the FFMA system is a finite field multiple access system; For the codeword matrix V D The diagonal codeword v in j,D =(u j,D ,v j,D,red ), the information sequence u of the jth user j,D =(0,...,0,b j ,0,...,0), where the jth user corresponds to b j The 1×K bit sequence is located at u j,D The jth item of , and all other items are 0; DF-FFMA only modulates and sends the useful information part during modulation. j,D,S , v j,D,S Indicates v j,D The useful information part in v j,D,S =(b j ,v j,D,red ), v j,D,S The subscript "S" indicates shortening; DF-FFMA distributes power in one of the following two ways: Method 1: v j,D,S =(b j ,v j,D,red ) has a parity check block length of R, v j,D,S The codeword length is K+R, and the power is allocated to v j,D,S The total transmission power of each user is NP avg ; The polarization adjustment vector is Among them, μ pav The subscript "pav" represents the polarization adjustment vector, is an element in the polarization adjustment vector, 0≤n S <K+R, v j,D,S The power of each symbol is determined by: Among them, P avg represents the average transmit power of each symbol; Method 2: v j,D,S =(b j ,v j,D,red ) has a parity check block length of R, v j,D,S The codeword length is K+R, and the power is allocated to v j,D,S The total transmission power of each user is NP avg ; For v j,D,S The information part and parity part of the symbol are allocated with a power of μ1P. avg , and the power allocated to the parity part of each symbol is μ2P avg , μ1 and μ2 are polarization coefficients; the power distribution condition is C1:N·P avg =K·(μ1P avg )+R·(μ2P avg ) C2: in, is the polarization scaling factor, and the subscript "pas" indicates polarization adjustment; The power distribution mode is determined according to the power distribution conditions C1 and C2 to realize the power distribution.

2. The power allocation method for a limited domain multiple access system based on polarization adjustment according to claim 1, characterized in that: The maximum power allocated to the information part of each symbol in mode 2 is mP avg .

3. A limited domain multiple access system based on polarization adjustment, characterized in that: The system is a regular PA-DF-FFMA, i.e. a polarization-regulated DF-FFMA capable of achieving regular power distribution; The DF-FFMA system refers to the diagonal FFMA system, that is, the codeword matrix V D Contains information array U used to carry user information D and parity check array E D , and the vector b corresponding to the user bit sequence j Located in the information array U D The FFMA system on the main diagonal line of , the FFMA system is a finite field multiple access system; For the codeword matrix V D The diagonal codeword v in j,D =(u j,D ,v j,D,red ), the information sequence u of the jth user j,D =(0,...,0,b j ,0,...,0), where the jth user corresponds to b j The 1×K bit sequence is located at u j,D The jth item of , and all other items are 0; DF-FFMA only modulates and sends the useful information part during modulation. j,D,S , v j,D,S Indicates v j,D The useful information part in v j,D,S =(b j ,v j,D,red ), v j,D,S The subscript "S" indicates shortening; The polarization-adjustable DF-FFMA that can achieve regular power distribution performs power distribution in the following manner: v j,D,S =(b j ,v j,D,red ) has a parity check block length of R = N-mK, v j,D,S The codeword length is K+R, and the power is allocated to v j,D,S The total transmission power of each user is NP avg ; The polarization adjustment vector is Among them, μ pav The subscript "pav" represents the polarization adjustment vector, is an element in the polarization adjustment vector, 0≤n S <K+R, v j,D,S The power of each symbol is determined by: Among them, P avg Represents the average transmit power of each symbol.

4. A limited domain multiple access system based on polarization adjustment, characterized in that: The system is an irregular PA-DF-FFMA, i.e., a polarization-regulated DF-FFMA capable of achieving irregular power distribution; The DF-FFMA system refers to the diagonal FFMA system, that is, the codeword matrix V D Contains information array U used to carry user information D and parity check array E D , and the vector b corresponding to the user bit sequence j Located in the information array U D The FFMA system on the main diagonal line of , the FFMA system is a finite field multiple access system; For the codeword matrix V D The diagonal codeword v in j,D =(u j,D ,v j,D,red ), the information sequence u of the jth user j,D =(0,...,0,b j ,0,...,0), where the jth user corresponds to b j The 1×K bit sequence is located at u j,D The jth item of , and all other items are 0; DF-FFMA only modulates and sends the useful information part during modulation. j,D,S , v j,D,S Indicates v j,D The useful information part in v j,D,S =(b j ,v j,D,red ), v j,D,S The subscript "S" indicates shortening; Polarization-adjustable DF-FFMA that can achieve irregular power distribution distributes power in the following way: v j,D,S =(b j ,v j,D,red ) has a parity check block length of R = N-mK, v j,D,S The codeword length is K+R, and the power is allocated to v j,D,S The total transmission power of each user is NP avg ; For v j,D,S The information part and parity part of the symbol are allocated with a power of μ1P. avg , and the power allocated to the parity part of each symbol is μ2P avg , μ1 and μ2 are polarization coefficients; the power distribution condition is C1:N·P avg =K·(μ1P avg )+R·(μ2P avg ) C2: in, is the polarization scaling factor, and the subscript "pas" indicates polarization adjustment; The power distribution mode is determined according to the power distribution conditions C1 and C2 to realize the power distribution.

5. The polarization-adjusted limited domain multiple access system according to claim 4, characterized in that: The maximum power allocated to the information part of each symbol is mP avg .

6. A decoding method for a limited field multiple access system based on polarization adjustment, characterized in that: The method is a decoding method for the polarization-adjusted limited domain multiple access system according to claim 4 or 5, comprising the following steps: The received signal sequence Divided into information part and parity check part, that is, y = (y inf ,y red ), where y inf =(y[0],y[1],...,y[j],...,y[J]) represents the information part, including J data blocks. For the jth data block, y[j] = (y j·K ,y j·K+1 ,...,y j·K+k ,...,y j·K+K-1 ), where the block length of each block is K; (1) Information bit detection stage: First, the information is divided into blocks for detection, based on the decision threshold δ th For inf Preliminary judgment: For the j-th information sub-block y[j], the decision process is as follows: in, represents the kth bit in the jth information sub-block estimated from the received signal; is the log-likelihood value calculated based on the received signal; After this decision process, the number of unknown information bits in the sub-block is D j，k (0) and D j，k (1) respectively represent the estimated received signal and Distance to receiving signal: All estimated signals of the sub-block Combined together, the estimated sequence corresponding to the user get Distance D from receiving signal inf,j,d ;right Distance Arrange in ascending order, select the first I1 distance values ​​to form the distance set of the information segment, and record it as in 1≤i≤I1,1≤j≤J, For each distance value Through the decimal to binary conversion function F D2B The distance value corresponding to d i Transformed into an estimated binary vector Υ inf,j Each element in corresponds to a unique vector; for each information sub-block, a binary vector set is obtained. Right now (2) Joint decoding stage: After the information bit detection stage, J binary sets are obtained, namely {Ω1,Ω2,...,Ω j ,...,Ω J }, the sub-blocks and the corresponding binary sets are combined in turn. The combination process is to first take an element combination from Ω1 and Ω2 respectively, concatenate the sequences corresponding to the two elements, and superimpose the corresponding distance values. When Ω1 and Ω2 are combined, M1×M2 element combinations can be generated. Assuming that after each combination is completed, the first I2 elements are selected according to the distance value as the candidate set for the next combination. After J sub-blocks are combined, I2 candidate information sequence sets are obtained, which can be expressed as is the candidate estimated information sequence obtained by combining J sub-blocks, with a length of JK. Each candidate information sequence in the set corresponds to the calculated distance value, so the corresponding distance sorted list is For the i-th candidate estimated information sequence It consists of J binary sequences of length K, represented as Using channel coding C gc The generating matrix G of the system form gc，sym According to the DF-FFMA coding method, the transmission codeword is reconstructed for each sub-block, and the parity check block obtained is v i,j,red , the parity check block passes through the transformation function F from the finite field to the complex field F2C Modulation signal x i,j,red , get the modulation signal of J check bits: x i,0,red ,x i,1,red ,...,x i,j,red ,...,x i,J-1,red , and then sum the modulated signals to get r red,i ; Calculate the parity part y red With r red,i Distance: Among them, 0≤i<I2, the alternative information sequence The corresponding total distance is In ascending order Sort by The minimum distance of the binary sequence is given by: What you get That is the multi-user information sequence obtained by decoding.

7. The decoding method of a limited domain multiple access system based on polarization adjustment according to claim 6, characterized in that: Log-likelihood value calculated from the received signal as follows: Among them, σ 2 is the estimated noise variance, and is the posterior probability calculated based on the received signal.

8. The decoding method of a limited domain multiple access system based on polarization adjustment according to claim 6, characterized in that: Estimated binary vector 9. The decoding method of a limited domain multiple access system based on polarization adjustment according to claim 6, characterized in that: Said , the corresponding parity part y red With r red,i Distance 10. A decoding method for a limited field multiple access system based on polarization adjustment according to any one of claims 6 to 9, characterized in that: Said Distance D from receiving signal inf,j,d as follows: Where d represents The decimal number is The subscript "B2D" indicates binary to decimal conversion.

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