OTFS cross-domain iteration detection method and system based on penalty term sharing alternating direction multiplier method

Abstract

The invention discloses an OTFS cross-domain iteration detection method and system based on a penalty term sharing alternating direction multiplier method, mainly solving the problem of poor performance in a high-order modulation scene in the prior art, and the scheme comprises the following steps: a sending end sends a time domain signal; a receiving end receives the sent signal and constructs a penalty term sharing maximum likelihood detection problem and an augmented Lagrange function about the received signal; solving a penalty term sharing problem by utilizing an alternating direction multiplier method to obtain time domain posterior information, and calculating out-of-time domain information by utilizing the time domain posterior information; information outside a time domain is converted to a time delay-Doppler domain through cross-domain message transmission, and time delay-Doppler domain prior information is obtained; and time delay-Doppler out-of-domain information is calculated and fed back to the time domain module. And repeating the steps of the receiving end until the covariance of the symbol to be detected is smaller than a certain threshold value or reaches the set maximum iteration times, thereby obtaining a final judgment bit. According to the method, good detection performance can still be kept in a high-order modulation scene, and the method can be used for recovering a transmitting signal from an OTFS system receiving signal.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of communication, and further relates to a signal detection method and system, which can be used to recover a transmitted signal from an OTFS system received signal. BACKGROUND

[0002] At present, the orthogonal frequency division multiplexing (OFDM) modulation technology widely used in 4G, 5G and WIFI wireless networks is susceptible to the influence of the Doppler effect. The orthogonal time frequency space (OTFS) modulation has better performance than OFDM in high mobility wireless communication scenarios. OTFS is a two-dimensional modulation scheme that modulates in the delay-Doppler domain, and converts a double dispersion channel into a nearly non-fading channel in the delay-Doppler domain through a series of two-dimensional transformations. The two challenges faced by the OTFS system are: how to accurately estimate the channel state information (CSI) in the delay-Doppler domain, and another is that after obtaining the CSI, a low complexity and efficient algorithm is needed for received signal detection. Received signal detection is to detect the corresponding symbol consistent with the transmitted symbol from the received signal. If the detection algorithm of the OTFS system has high complexity, it will cause the detection of the received symbol to be slow and result in high latency, which is not conducive to the practicality of the actual system.

[0003] The patent document with the application number CN202010158335.1 discloses a "signal detection method and device for OTFS system". It first establishes a corresponding factor graph, and constructs a neural network according to the factor graph. The number of hidden layers of the neural network is the same as the number of iterations of message passing, and the hidden layer includes message calculation neurons and probability calculation neurons. The message calculation neurons correspond to the nodes and / or edges of the factor graph; the probability calculation neurons are used to calculate the probability of each modulation symbol in the transmitted signal obtained after the transmitted signal passes through the channel according to the signal detection performance parameters and the data output by the message calculation neurons. This method uses neural network training to obtain optimized signal detection performance parameters, thereby improving the signal detection performance. However, the disadvantage of this method is that since the detection method uses neural network for data detection, a large amount of training data is needed to support the system when the scene changes, and the performance of the detection method will deteriorate sharply. SUMMARY

[0004] The present application aims to overcome the shortcomings of the prior art and provides an OTFS cross-domain iterative detection method and system based on a penalty term shared alternating direction multiplier method to improve the detection performance.

[0005] To achieve the above-mentioned purpose, the technical solution of the present application includes:

[0006] 1. An OTFS cross-domain iterative detection method based on a penalized shared alternating direction multiplier method, comprising:

[0007] (1) A transmitting end generates a transmitting time-domain signal that goes through a wireless channel to a receiving end to obtain a time-domain received signal r;

[0008] (2) A penalized shared maximum likelihood detection problem and an augmented Lagrangian function about the received signal r are constructed;

[0009] (3) The penalized shared problem is solved by using an alternating direction multiplier method to obtain a time-domain mean vector of the time-domain received signal r and a posteriori covariance matrix

[0010] (4) A time-domain extrinsic mean vector and an extrinsic covariance matrix are calculated by using and

[0011] (5) The time-domain extrinsic mean vector and the extrinsic covariance matrix are cross-domain message passed to be transformed into a delay-Doppler domain priori mean vector and a priori covariance matrix

[0012] (6) A delay-Doppler domain extrinsic mean vector and an extrinsic covariance matrix are calculated by using the delay-Doppler domain priori mean vector and the priori covariance matrix

[0013] (7) Steps (3)-(6) are repeatedly executed until a to-be-detected symbol covariance is less than a set threshold or a set maximum number of iterations is reached to obtain a final decision bit.

[0014] Further, the penalized shared maximum likelihood detection problem and the augmented Lagrangian function about the received signal r in step (2) are constructed, and the implementation includes the following:

[0015] 3a) The delay-Doppler domain transmitting symbol vector x is decomposed into a linear combination x of a plurality of low-order modulation signals x q .

[0016] 3b) A discrete constellation set is relaxed into a continuous constellation set

[0017] 3c) A conversion relationship between the time-domain transmitting signal s and the delay-Doppler domain transmitting symbol vector x is taken as a new constraint to construct the penalized shared maximum likelihood detection problem:

[0018] 3d) constructing an augmented Lagrangian function that solves the penalized shared maximum likelihood detection problem where u represents the dual variable and Q represents the total number of constellation points.

[0019] 2. An OTFS cross-domain iterative detection system based on a penalized shared alternating direction method of multipliers, comprising:

[0020] An OTFS transmitting module for generating an OTFS transmitting signal;

[0021] A simulation channel module for simulating an actual channel;

[0022] A time domain processing module for receiving a time domain transmitting signal that has passed through a channel and performing time domain processing on the received signal;

[0023] A first extrinsic information calculation module for calculating time domain extrinsic information;

[0024] A time delay-Doppler domain processing module for processing the time domain extrinsic information in a time delay-Doppler domain;

[0025] A second extrinsic information calculation module for calculating time delay-Doppler domain extrinsic information.

[0026] Compared with the prior art, the present application has the following advantages:

[0027] Firstly, the traditional cross-domain iterative detection algorithm will suffer from serious performance degradation in a high-order modulation scenario, which severely limits its application in actual communication systems. The present application decomposes a high-order signal into a sum of multiple low-order signals to ensure that a better local solution can be obtained in each iteration process, thereby improving the system performance.

[0028] Secondly, since the present application performs equalization in the time domain, it can avoid the problem of further increasing the system complexity caused by fractional Doppler dispersion. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 is a flowchart of the OTFS cross-domain iterative detection method of the present application based on a penalized shared alternating direction method of multipliers;

[0030] Figure 2 is a block diagram of the OTFS cross-domain iterative detection system of the present application based on a penalized shared alternating direction method of multipliers;

[0031] Figure 3 is a block diagram of the time domain processing module in the system of the present application;

[0032] Figure 4is a performance comparison chart when the modulation mode is 4QAM, respectively using the present application and the existing cross-domain iterative detection algorithm for detection;

[0033] Figure 5 is a performance comparison chart when the modulation mode is 64QAM, respectively using the present application and the existing cross-domain iterative detection algorithm for detection. DETAILED DESCRIPTION

[0034] In order for those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all. Based on the embodiments in the present application, other embodiments obtained by those skilled in the art without creative labor should be within the protection scope of the present application.

[0035] It should be noted that the step labels in the specification and claims of the present application are only for clearly describing the embodiments of the present application, for the convenience of understanding, and the order of the labels is not limited.

[0036] Embodiment one, OTFS cross-domain iterative detection method based on penalty term shared alternating direction multiplier method

[0037] Reference Figure 1 The implementation steps of the present example are as follows:

[0038] Step 1: The time domain signal sent by the sending end reaches the receiving end after passing through the wireless channel, and the time domain received signal r is obtained.

[0039] 1.1) The sending end randomly generates a bit stream b, and decomposes it into a plurality of sequences with a length of S {b n = [b n,1 ,b n,2 ,...,b n,S ]}. Then each sequence b n is mapped to a symbol sequence x through a symbol constellation set;

[0040] 1.2) The symbol sequence x is rearranged by column to a time delay-Doppler domain transmission symbol matrix X DD , where M and N are the number of subcarriers and the number of time slots of each OTFS frame, respectively;

[0041] 1.3) The time delay-Doppler domain transmission symbol matrix X DD is transformed into a time-frequency domain transmission symbol matrix

[0042]

[0043] where F M denotes the M-point DFT matrix, denotes the conjugate transpose matrix of the N-point DFT matrix;

[0044] 1.4) The rectangular pulse is taken as the shaping pulse at the transmitting end, and the time-frequency domain transmission symbol matrix X TF is transformed into the time domain transmitting signal matrix X T by the Heisenberg transformation:

[0045]

[0046] where I M denotes the unit matrix with dimension M;

[0047] 1.5) For the convenience of representation, the time domain transmitting signal matrix X T is rearranged by column to the time domain transmitting signal s, which is then sent into the wireless channel H T ;

[0048] 1.6) After the transmitting signal s goes through the wireless channel, the time domain receiving signal r is obtained:

[0049] r = H T s + n

[0050] where n denotes the time domain noise vector.

[0051] Step 2: Construct the penalty term shared maximum likelihood detection problem and the augmented Lagrange function in the time domain with respect to the receiving signal r.

[0052] 2.1) The time delay-Doppler domain transmitting symbol vector x is decomposed into a linear combination of multiple low-order modulation signals x q :

[0053]

[0054] where Q denotes the total number of constellation points, thereby avoiding misjudgment caused by too close distance of high-order modulation constellation points;

[0055] 2.2) The discrete constellation set is relaxed to the continuous constellation set

[0056] According to the alternating direction multiplier method, in order to make the approximate solution obtained by the algorithm closer to the optimal solution of the ML detection problem, the discrete set needs to be relaxed and expanded to the feasible region of the approximate solution update, so that it is updated in the continuous solution space:

[0057]

[0058] where x q , x qR and xqI denote the value, real part and imaginary part of the qth low-order modulation constellation point, respectively;

[0059] 2.3) The conversion relationship between the time-domain transmitted signal s and the time-delay-Doppler domain transmitted symbol vector x is taken as a new constraint:

[0060]

[0061] wherein, denote the conjugate transpose matrix of the N-point DFT matrix, I M denote the unit matrix with dimension M;

[0062] 2.4) To ensure the convergence of the real part and the imaginary part of the decomposed low-order signal, a penalty term is added to the objective function:

[0063]

[0064] wherein, Q denotes the total number of constellation points, s denotes the time-domain transmitted signal, and q denote the penalty coefficient corresponding to the qth cost function, denote the local cost function of the qth low-order symbol vector, denote the shared objective function, and MN denotes the number of time-domain OTFS transmitted symbols, denote the Kronecker product operation, I MN denote the unit matrix with dimension MN, denote the conjugate transpose matrix of the N-point DFT matrix, H T denote the time-domain wireless channel;

[0065] 2.5) An augmented Lagrangian function is constructed to solve the penalty term shared maximum likelihood detection problem

[0066]

[0067] wherein, u denotes the dual variable, and

[0068] Step 3: The alternating direction multiplier method is used to solve the penalty term shared problem, and the time-domain mean vector of the time-domain received signal r is obtained and the posterior covariance matrix

[0069] The alternating direction multiplier method is an iterative algorithm combining the advantages of dual decomposition method and augmented Lagrange multiplier method, mainly used for solving convex optimization problems with separable structure. The core idea is to decompose the original problem into multiple sub-problems which are easy to solve, and gradually approach the optimal solution by alternately updating the variables and Lagrange multipliers. In the present application, the alternating direction multiplier method is selected but not limited to solving multiple low-order signal sub-problems obtained by high-order signal decomposition. The implementation includes:

[0070] 3.1) Iteratively solving the time domain mean vector by alternating direction multiplier method

[0071] 3.1.1) Solving the qth low-order modulation constellation point in the continuous solution space :

[0072] When the penalty coefficient α q satisfies 4 q-1 ρ-α q > 0, set the first derivative of the objective function with respect to the low-order modulation signal x q to 0 to obtain the optimal solution of the low-order modulation constellation point , which is expressed as:

[0073]

[0074] Where t represents the number of current iterations, ρ > 0 represents the augmented Lagrange multiplier parameter, u t-1 represents the dual variable, I M represents the unit matrix with dimension M, represents the conjugate transpose matrix of the N-point DFT matrix, represents the value of the ith low-order modulation constellation point in the continuous solution space in the t-1th iteration, m t-1 represents the mean vector in the t-1th iteration, represents the projection function, and its specific expression is:

[0075]

[0076] 3.1.2) Solving the value of the dual variable u t :

[0077] When ρ > 0, set the first derivative of the objective function with respect to the time domain transmit signal s to 0 to obtain the optimal solution of the dual variable u t , which is expressed as:

[0078]

[0079] Wherein, denotes the value of the q-th low order modulation constellation point in the successive solution space in the t-th iteration, m t is initialized to the outer mean of the delay-Doppler domain module output by the delay-Doppler domain module

[0080] 3.1.3) Solving the mean vector m t

[0081]

[0082] where r denotes the received signal, H T denotes the time domain wireless channel, denotes the conjugate transpose matrix of the time domain wireless channel, u t-1 denotes the value of the dual variable in the t-1-th iteration;

[0083] 3.1.4) Repeating steps 3.1.1) - 3.1.3) until the variable residual is smaller than a set threshold or the maximum number of iterations is reached, the iteration is ended, and the mean vector m t is output by the time domain module as the time domain posterior mean vector

[0084] 3.2) Solving the posterior covariance

[0085]

[0086] where denotes the time domain prior covariance matrix, which is initialized to the outer covariance matrix H T denotes the time domain wireless channel, denotes the conjugate transpose matrix of the time domain wireless channel H T , and N0denotes the noise power.

[0087] Step 4: Using and to calculate the time domain outer mean vector and the outer covariance matrix and obtain the delay-Doppler domain prior mean vector and the prior covariance matrix

[0088] 4.1) Calculating the outer mean and the outer covariance

[0089]

[0090] where ​denotes the posterior mean, and denote the prior mean vector and the prior covariance matrix transferred by the delay-Doppler domain module, respectively;

[0091] 4.2) Transform the delay-Doppler domain prior information and to the time-domain prior information by cross-domain message passing:

[0092]

[0093] where, denotes the delay-Doppler domain prior mean, denotes the delay-Doppler domain prior covariance, F N denotes the N-point DFT matrix, I M denotes the identity matrix with dimension M.

[0094] Step 5: Calculate the delay-Doppler domain extrinsic mean vector and the extrinsic covariance matrix using the delay-Doppler domain prior mean vector and the prior covariance matrix

[0095] 5.1) Calculate the posterior mean and the posterior covariance

[0096]

[0097] where, 1≤k≤MN,

[0098] denotes the i-th element in the constellation mapping set , 1≤i≤Q, Q denotes the number of elements in the constellation mapping set, denotes the probability of the transmitted symbol given the known time-domain extrinsic mean vector

[0099] 5.2) Rearrange the posterior mean and the posterior covariance of each estimated symbol to obtain the delay-Doppler domain posterior mean vector and the posterior covariance matrix

[0100]

[0101] where, diag[·] denotes the diagonal matrix conversion;

[0102] 5.3) Calculate the posterior mean vector and the covariance matrix of the time-domain transmitted symbol s​

[0103]

[0104] where F N denotes the N-point DFT matrix, denotes the conjugate transpose matrix of the N-point DFT matrix, I M denotes the identity matrix of dimension M;

[0105] 5.4) Calculate the outer mean of the delay-Doppler domain module and the outer covariance

[0106]

[0107] where, denotes the outer mean of the time domain module.

[0108] Step 6: Repeat steps (3)-(5) until the covariance of the symbol to be detected is less than the set threshold or the maximum number of iterations is reached, and the final detection signal is obtained.

[0109] Example two, OTFS cross-domain iterative detection system based on penalty term shared alternating direction multiplier method

[0110] Referring to Figure 2 and Figure 3 , the present example comprises: an OTFS transmission module 1, a simulation channel module 2, a time domain processing module 3, a first outer information calculation module 4, a delay-Doppler domain processing module 5, and a second outer information calculation module 6, wherein the time domain processing module 3 comprises: a low-order signal decomposition sub-module 31, an augmented Lagrangian function construction sub-module 32, a time domain posteriori information calculation sub-module 33, a time domain outer information calculation sub-module 34, and a cross-domain message passing sub-module 35. The working principle of the whole system is as follows:

[0111] The OTFS transmission module 1 is used to generate an OTFS sending signal and transmit the time domain sending signal to the simulation channel module 2;

[0112] The simulation channel module 2 is used to simulate the actual channel and transmit the time domain sending signal after the channel to the time domain processing module 3;

[0113] The time domain processing module 3 is configured to receive a time domain signal transmitted through a channel and perform time domain processing on the received signal. The low-order signal decomposition submodule 31 is configured to decompose a high-order signal into a low-order signal and transmit the decomposed low-order signal to the augmented Lagrange function construction submodule 32. The augmented Lagrange function construction submodule 32 is configured to construct an augmented Lagrange function and transmit the augmented Lagrange function to the time domain posterior information calculation submodule 33. The time domain posterior information calculation submodule 33 is configured to calculate a time domain posterior mean vector and a time domain posterior covariance matrix and transmit the results to the time domain extrinsic information calculation submodule 34. The time domain extrinsic information calculation submodule 34 is configured to calculate a time domain extrinsic mean vector and a time domain extrinsic covariance matrix and transmit the results to the cross-domain message passing submodule 35. The cross-domain message passing submodule 35 is configured to convert the time domain extrinsic mean vector and the extrinsic covariance matrix into a delay-Doppler domain prior mean vector and a covariance matrix and transmit them to the first extrinsic information calculation module 4.

[0114] The first extrinsic information calculation module 4 is configured to calculate time domain extrinsic information and transmit it to the delay-Doppler domain processing module 5.

[0115] The delay-Doppler domain processing module 5 is configured to process the time domain extrinsic information in the delay-Doppler domain and transmit the processing results to the second extrinsic information calculation module 6.

[0116] The second extrinsic information calculation module 6 is configured to calculate delay-Doppler domain extrinsic information and transmit it to the time domain processing module 3 for the next round of iteration.

[0117] It should be noted that the above-mentioned functional modules can be realized by software, hardware, firmware, or any combination thereof, in whole or in part. When realized by software, the program instruction product can be realized in whole or in part. The program instruction product includes one or a group of program instructions. When loaded and executed on a computer, the program instructions produce the above-mentioned flow or function in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The program instructions can be stored in a computer readable and writable storage medium or transmitted from one computer readable and writable storage medium to another.

[0118] The direct coupling or communication connections between the modules shown or discussed in this embodiment can be achieved through indirect coupling or communication connections via interfaces, devices, or modules. The various functional modules and sub-modules in this embodiment can dynamically reside within a single processing unit, or each module can exist physically independently, or two or more modules can dynamically reside within a single processing unit. When these dynamic components are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable and writable storage medium. This storage medium can be a memory, disk, or optical disc, etc.

[0119] The effects of the present invention will be further explained below with reference to simulation experiments.

[0120] 1. Simulation conditions:

[0121] The hardware platform for the simulation experiment of this invention is: an Intel(R) Xeon(R) Gold 5218 CPU with a main frequency of 2.3GHz and 128GB of memory. The software platform is: Windows 10 operating system and Matlab R2022b simulation software.

[0122] The OTFS system used in the simulation experiment of this invention has a total number of subcarriers M equal to 128, a number of time slots N equal to 32, a complex Gaussian channel type, a channel path number of 4, a maximum channel delay tap of 8, a maximum Doppler tap of 8, and uses 4QAM and 64QAM modulation schemes respectively, and assumes that the channel state information is completely known at the receiving end.

[0123] 2. Simulation Content

[0124] Simulation 1: Under the above conditions, the present invention and existing cross-domain iterative detection methods were used to detect a 4QAM modulation signal, respectively, and the relationship between signal-to-noise ratio and bit error rate was obtained, as follows: Figure 4 As shown. Wherein:

[0125] Curve 1 shows the relationship between the bit error rate and signal-to-noise ratio of the detection algorithm proposed in this invention.

[0126] Curve 2 shows the relationship between the bit error rate and signal-to-noise ratio of the traditional cross-domain iterative detection algorithm.

[0127] from Figure 4 As can be seen, under low signal-to-noise ratio conditions, the performance of the present invention is close to that of the traditional cross-domain iterative detection method, but under high signal-to-noise ratio scenarios, the performance of the present invention is superior to that of the traditional cross-domain iterative detection method.

[0128] Simulation 2: Under the above conditions, the present invention and existing cross-domain iterative detection methods were used to detect a 64QAM modulation signal, respectively, and the relationship between signal-to-noise ratio and bit error rate was obtained, as follows: Figure 5 As shown. Wherein:

[0129] Curve 1 is the relationship between the bit error rate and the signal-to-noise ratio of a traditional cross-domain iterative detection algorithm,

[0130] Curve 2 is the relationship between the bit error rate and the signal-to-noise ratio of the detection algorithm provided by the present application,

[0131] It can be seen from Figure 5 In the higher-order modulation scenario such as 64QAM, the present application has better performance, which is mainly because the present application fully utilizes the decomposition characteristics of high-order signals, decomposes the high-order signals into a linear combination of multiple binary variables to simplify the processing, and at the same time, the present application relaxes the discrete set of the high-order modulation constellation to a continuous domain constraint, expands the space of variable updating, and thus approximates the maximum likelihood detection performance.

Claims

1. An OTFS cross-domain iterative detection method based on a penalty term shared alternating direction multiplier method, characterized in that, Comprise: (1) the sending end generates a sending time domain signal through a wireless channel to reach the receiving end, and obtains a time domain receiving signal r; (2) a penalty term shared maximum likelihood detection problem and an augmented Lagrangian function about the receiving signal r are constructed; (3) The time-domain mean vector of the time-domain received signal r is obtained by solving the penalized item sharing problem using the alternating direction multiplier method and the posterior covariance matrix (4) using and computing the time-domain outer mean vector and the outer covariance matrix (5) the time-domain outer mean vector and outer covariance matrix perform cross-domain message passing, transforming it into a time-delay-Doppler domain prior mean vector and prior covariance matrix (6) Utilizing a time-delay-Doppler domain prior mean vector and a prior covariance matrix to compute a time-delay-Doppler domain out-of-mean vector and an out-of-covariance matrix (7) steps (3)-(6) are repeatedly executed until the covariance of the symbol to be detected is less than a set threshold or a set maximum iteration number is reached, and a final decision bit is obtained.

2. The method of claim 1, wherein, The time domain transmitting symbol generated by the sending end in step (1) reaches the receiving end through a wireless channel, and a time domain receiving signal r is obtained, and the implementation comprises: performing high order constellation mapping on the randomly generated bit stream to obtain a delay-Doppler domain transmit symbol vector x, and rearranging x into a delay-Doppler domain transmit symbol matrix X DD ; a symbol matrix X is transmitted in the delay-Doppler domain DD respectively, and then vectorized to obtain a time-domain transmitted signal s, which goes through a time-domain wireless channel H T After that, the OTFS receiving end obtains a time-domain received signal r: r = H T s + n, Wherein, n represents a time domain noise vector.

3. The method of claim 1, wherein, In step (2), the penalty term shared maximum likelihood detection problem and the augmented Lagrangian function about the receiving signal r are constructed, and the implementation comprises: 2a) decomposing the time-delay-Doppler domain transmitted symbol vector x into a linear combination of a plurality of low order modulation signals x q : Wherein, q=1,…Q, Q represents the total number of constellation points; 2b) relaxing the set of discrete constellations into a set of continuous constellations where x q , x qR and x qI represent the value, real part and imaginary part of each low-order modulation constellation point, respectively. 2c) the conversion relationship between the time domain transmitting signal s and the time delay-doppler domain transmitting symbol vector x is taken as a new constraint: where s represents a time-domain transmission signal, denotes a conjugate transpose matrix of an N-point DFT matrix, I M denotes a unit matrix of dimension M; 2d) a penalty term shared maximum likelihood detection problem is constructed: wherein Q represents the total number of constellation points, s represents a time-domain transmitted signal, a q represents a penalty coefficient corresponding to the qth cost function, MN represents a time-domain OTFS sending symbol number, represents a Kronecker product operation, I M represents a unit matrix with a dimension of M, represents a conjugate transpose matrix of an N-point DFT matrix, H T represents a time-domain wireless channel; 2e) Constructing an augmented Lagrangian function that solves the maximum likelihood detection problem shared by the penalty terms, according to the maximum likelihood detection problem Wherein, u represents a dual variable, and ρ>0 represents an augmented Lagrangian multiplier parameter.

4. The method of claim 1, wherein, The time-domain penalized item sharing problem in step (3) is solved by using the alternating direction multiplier method to obtain a time-domain posterior mean vector of the time-domain received signal r and a posterior covariance matrix The implementation comprises: 3a) Iterative solution of the time domain mean vector by the alternating direction multiplier method 3a1 ) Solving for the value of the qth low order modulation constellation point within the continuous solution space of the qth low order modulation constellation point within the continuous solution space where t denotes the number of current iteration, p > 0 denotes the augmented Lagrangian multiplier parameter, u t-1 denotes the dual variable, I M denotes the identity matrix of dimension M, denotes the conjugate transpose matrix of N-point DFT matrix, denotes the value of the i-th low-order modulation constellation point in the successive solution space in the t-1th iteration, m t-1 denotes the mean vector of the t-1th iteration; 3a2) Solving for the dual variable u t the value of: wherein, denotes the value of the qth low order modulation constellation point in the successive solution space in the tth iteration, m t the initial value of is set to the outer mean of the delay-Doppler domain module output by the delay-Doppler domain module 3a3) Solving the mean vector m t of values: where r denotes a received signal, H T denotes a time-domain wireless channel, denotes a conjugate transpose matrix of the time-domain wireless channel, u t-1 denotes a value of a dual variable in the t-1th iteration; 3a4) repeat steps 3a1) - 3a4) until the variable residual is less than a set threshold or the maximum number of iterations is reached, output the mean vector m t time domain posterior mean vector output by the time domain module 3b) solving the time-domain posterior covariance matrix wherein denotes the time-domain prior covariance matrix, which is initialized as the outer covariance matrix output by the delay-Doppler domain module H T denotes the time-domain wireless channel, denotes the conjugate transpose matrix of the domain wireless channel H T and N0denotes the noise power.

5. The method of claim 1, wherein, In step (4) the following is used and The time-domain outer mean vector is calculated and the outer covariance matrix The formula is as follows: where, denotes the posterior mean, and denote the prior mean vector and the prior covariance matrix, respectively, transferred by the delay-Doppler domain module.

6. The method of claim 1, wherein, The time-domain outer mean vector in step (5) and outer covariance matrix is transformed into a time-delay-Doppler domain prior mean vector and prior covariance matrix where F N denotes an N-point DFT matrix, I M denotes an M-dimensional identity matrix, and denote the a priori mean vector and a priori covariance matrix, respectively, transferred by the time-delay-Doppler domain module.

7. The method of claim 1, wherein, utilizing a time-delay-Doppler domain prior mean vector in step (6) and a prior covariance matrix calculating a time-delay-Doppler domain out-mean vector and an out-covariance matrix The implementation includes: 6a) Calculate the posterior mean of each estimated symbol and the posterior covariance where 1 < k < MN, represents the i-th element in the constellation mapping set, 1≤i≤Q, Q represents the number of elements in the constellation mapping set, represents the i-th element in the constellation mapping set, 1≤i≤Q, Q represents the number of elements in the constellation mapping set, represents the i-th element in the constellation mapping set, 1≤i≤Q, Q represents the number of elements in the constellation mapping set, represents the i-th element in the constellation mapping set, 1≤i≤Q, Q represents the number of elements in the constellation mapping set, represents the i-th element 6b) Rearranging the post-processed mean values of each estimated symbol and the post-processed covariance matrix to obtain a rearranged time-delay-Doppler domain post-processed mean vector and a post-processed covariance matrix Wherein, diag[·] represents a diagonal matrix conversion; 6c) calculating a posterior mean vector of time domain transmit symbols s and covariance matrix where F N denotes an N-point DFT matrix, denotes the conjugate transpose matrix of the N-point DFT matrix, I M denotes the identity matrix of dimension M; 6d) The result from 6c) and the time-domain outer mean vector and the delay-Doppler domain prior covariance matrix Computing the outer mean of the delay-Doppler domain module and the outer covariance 8. An OTFS cross-domain iterative detection system based on a penalized share alternating direction multiplier method, characterized in that, Comprise: OTFS transmitting module: used for generating an OTFS sending signal; Simulation channel module: used for simulating an actual channel; Time domain processing module: used for receiving a time domain transmitting signal through a channel, and performing time domain processing on the receiving signal; First extrinsic information calculation module: used for calculating time domain extrinsic information; Time delay-doppler domain processing module: used for processing the time domain extrinsic information in a time delay-doppler domain; Second extrinsic information calculation module: used for calculating time delay-doppler domain extrinsic information.

9. The system of claim 9, wherein, The time domain processing module comprises: Low-order signal decomposition submodule: used for decomposing a high-order signal into a low-order signal; Augmented Lagrangian function construction submodule: used for constructing an augmented Lagrangian function; Time domain posterior information calculation submodule: used for calculating a time domain posterior mean vector and a time domain posterior covariance matrix; Time domain extrinsic information calculation submodule: used for calculating a time domain extrinsic mean vector and a time domain extrinsic covariance matrix; Cross-domain message passing submodule: used for converting the time domain extrinsic mean vector and the extrinsic covariance matrix into a time delay-doppler domain prior mean vector and a covariance matrix.

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