MMF problem optimization method of received signal SINR of RIS-AFDM-NOMA system

Abstract

The invention discloses an MMF problem optimization method for a received signal SINR of an RIS-AFDM-NOMA system. The MMF problem optimization method comprises the following steps: constructing an uplink communication link of the RIS-AFDM-NOMA system; iDAFT is carried out on the DAFT domain signals of the K user terminals to generate transmission signals; the method comprises the following steps of: establishing a double-selectivity channel model, after a transmission signal passes through the channel, acquiring a total receiving signal by a receiving end, and performing DAFT conversion, matrix-vector form, sorting and SIC operation processing; and an MMF optimization problem of the UTk received signal SINR is constructed, and a power distribution coefficient, a precoding matrix and an RIS phase shift matrix are adjusted to carry out joint optimization solution. By the adoption of the method, on the basis of original signal enhancement and user rate improvement, parameter configuration during optimization of the multi-user SINR on the premise that fairness is met is obtained, and corresponding technical support is provided for AFDM communication in a 6G high mobility scene.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, and particularly relates to a max-min fairness (MMF) optimization method for receiving signal to interference plus noise ratio (SINR) of a reconfigurable intelligent surface (RIS)-affine frequency division multiplexing (AFDM)-non-orthogonal multiple access (NOMA) system. BACKGROUND

[0002] Wireless communication systems for 6G need to support reliable communication in high mobility scenarios such as space-air-ground integrated networks, high-speed trains, and Internet of Vehicles, while meeting the demands of ultra-low latency, ultra-high reliability, and large-scale connectivity.

[0003] Although the traditional orthogonal frequency division multiplexing (OFDM) technology performs excellently in non-time-varying or slow-time-varying fading channels, it faces major challenges in fast-time-varying environments with serious Doppler shift. Industry has developed new waveform schemes such as orthogonal chirp division multiplexing (OCDM), filter bank multicarrier (FBMC), and orthogonal time-frequency space (OTFS). In recent years, AFDM has been proven to be able to achieve full diversity performance in double-selective channels by virtue of the dynamic parameter adjustment characteristics of the discrete affine Fourier transform (DAFT), and has the potential for 6G communication applications. However, existing AFDM-related researches mostly focus on detection, estimation, coding, and peak-to-average ratio suppression, and lack resource optimization schemes from the perspective of constructing optimization objective functions and constraint conditions. The achievements in this field are still in the blank.

[0004] In addition, although NOMA and RIS have been widely applied in various wireless systems, existing researches mostly combine them separately with OFDM or OTFS, and only a few schemes combine OTFS with NOMA and RIS together. The deep integration of AFDM-NOMA and RIS, especially in dynamic high mobility scenarios, has not been fully explored. Summary of the Invention

[0005] The purpose of this invention is to provide an optimization method for the MMF problem of the received signal SINR in a RIS-AFDM-NOMA system. By establishing a corresponding optimization model and using a corresponding algorithm to optimize multiple parameter variables in the model one by one, the method can obtain the optimal parameter configuration for the SINR of the received signal of multiple users while satisfying fairness, based on the original signal enhancement and user rate improvement. This provides corresponding technical support for AFDM communication in 6G high mobility scenarios.

[0006] To achieve the above objectives, this invention provides a method for optimizing the MMF problem of the received signal SINR in a RIS-AFDM-NOMA system, comprising the following steps: S1. Construct a reconfigurable smart surface-simulated radio frequency multiplexing-non-orthogonal multiple access RIS-AFDM-NOMA uplink communication link; S2, for the first User terminals The discrete affine Fourier transform (DAFT) domain signal is subjected to inverse discrete affine Fourier transform (IDAFT) to generate the final transmission signal. S3. Based on the final transmitted signal from S2, establish a dual-selective channel model and obtain the signal from the user terminal at the transmitting end. The total received signal; S4. Perform Discrete Affine Fourier Transform (DAFT) on the total received signal and express it in matrix-vector form. Then sort the signals and perform Sequential Interference Cancellation (SIC). S5. Construct the maximum minimum fair MMF problem for the received signal interference-to-noise ratio (SINR), and perform joint optimization by adjusting the power allocation coefficient, precoding matrix, and RIS phase shift matrix variables.

[0007] Preferably, the uplink communication link in S1 is as follows: The transmitter is Each user terminal (UT) has a single antenna and a receiver is a single antenna access point (AP). Each RIS of the reflection unit acts as a relay for coordinated communication.

[0008] Preferably, S2 is as follows: S21, regarding the first User terminals DAFT domain signal It performs NOMA power allocation, precoding processing, and serial-to-parallel conversion to obtain the intermediate signal. ; S22, For intermediate signals Perform IDAFT to obtain the time-domain signal. ; S23, Regarding time-domain signals Add the chirped periodic prefix CPP, and after performing the parallel / serial conversion operation, obtain the first... User terminals The final transmitted signal .

[0009] Preferably, S3 is as follows: S31. Define a dual-selectivity channel in Point channel response The matrix form is ;in, Indicates the number of paths; , and They represent the first Channel gain coefficient, delay factor, and Doppler factor for each propagation path; Represents the delay matrix; Represents the Doppler frequency shift matrix; S32. Based on S31, the dual-selective channel, after removing the chirped periodic prefix (CPP) at the receiver, receives the signal from the transmitter... User terminals The signals can be divided into: (1) Direct Link The received signal is shown below: ; in, It is the symbol for the imaginary unit; Representing the User terminals ; It is the first of the transmitting end User terminals The final transmitted signal after P / S conversion, excluding CPP; Indicates the first One multipath propagation component; It is the total number of multipath propagation components; , and They are the first Channel gain coefficient, delay coefficient, and Doppler coefficient of each multipath propagation component; yes exist Additive white Gaussian noise (AWGN) generated at the point; (2) Reflection Link The received signal from RIS-AP is shown below: ; in, It is the first in RIS The phase coefficients on each reflecting unit, of which ; This represents the total number of reflection units in the RIS. It is the first in RIS-AP The first reflector unit The delay coefficient of each multipath propagation component; yes The total number of multipath propagation components in the middle; , and They are respectively The Middle The first reflector unit Channel gain coefficient, delay coefficient, and Doppler coefficient of each multipath propagation component; and They are and RIS-AP Additive white Gaussian noise (AWGN) generated at each moment; S33, Based on S32, the total received signal is As shown below: ; in, It is the sum of additive white Gaussian noise (AWGN) in the direct link and the reflected link.

[0010] Preferably, S4 is as follows: S41, Total Received Signal Perform a Discrete Affine Fourier Transform (DAFT) to obtain the DAFT domain signal; S42, Establish the first User terminals Matrix-vector form of the DAFT domain received signal ; S43. Matrix-vector form of the DAFT domain received signal in S42 ,right One from the transmitter user terminal UTs The signals are superimposed to obtain the total received signal. : ; in, It is the original signal vector in the DAFT domain; It is the power distribution factor; It is a precoding matrix; and They are Channel and The channel response matrix of the channel; Θ and They are The RIS phase shift matrix and RIS-AP channel response matrix formed by the reflection units; v is The sum of the time-domain signal vectors of each AWGN; S44, The total received signal in S43 ,Will The user terminals (UTs) are sorted in descending order according to channel conditions, and then the SIC operation is performed to decode the total received signal from the transmitting user terminals (UTs). ; S45. Define two performance metrics for UTS: (1) From the transmitting end The signal-to-interference-plus-noise ratio (SINR) of the received signal is: ;in, yes The variance of the additive white Gaussian noise (AWGN) term; , They represent The power allocation coefficients and precoding matrix, ; , They represent the first User terminals The corresponding direct channel matrix and reflection channel matrix; (2) Receiving end Total rate of UTs for: ;in, yes The rate.

[0011] Preferably, S5 is as follows: S51. Establish the maximum and minimum fair MMF multi-parameter joint optimization problem for the received signal interference-to-noise ratio (SINR): S52. Using the alternating optimization AO method, the MMF multi-parameter joint optimization problem of the received signal SINR is decomposed into two sub-problems and solved one by one. S521, By fixing the power distribution coefficient With precoding matrix By introducing auxiliary variables and eliminating non-affine variables using binomial inequalities, and then obtaining the values ​​one by one using the auxiliary angle formulas in trigonometric functions, we can find the values ​​one by one. The optimal phase angle of each reflection unit is determined, and the optimal phase shift matrix of RIS is obtained. The entire optimization process is based on the phase shift matrix optimization algorithm of TS. S522, by fixing the RIS optimal phase shift matrix in S521, by the binomial inequality, the basic inequality, the Schur complement theorem respectively remove the non-affine and coupling between variables; the whole optimization process is based on LI-based precoding matrix optimization algorithm to realize; S53, according to the TS-based and LI-based algorithms in S521 and S522, form a total joint optimization algorithm to solve the optimization problem of MMF of received signal SINR.

[0012] Preferably, S51 is specifically: First, according to the power allocation coefficient , the precoding matrix and the RIS optimal phase shift matrix Θ, the MMF joint optimization problem is established, as follows: ; ; ; ; ; Wherein, , and respectively represent the rate constraint, the power allocation coefficient constraint and the power constraint of the precoding matrix ; , and respectively represent the lower limit value of the rate, the upper limit value of the power allocation coefficient and the upper limit value of the precoding matrix power; Indicates the phase constraint of any one reflection unit in the phase shift matrix Θ of the RIS; Indicates the total channel response matrix of ; Indicates the total channel response matrix of ; Indicates the noise standard deviation of ; Then, introduce auxiliary variable , and set the auxiliary variable as the minimum value of the received signal SINR from the transmitting end user terminal UTs, therefore, P1 can be transformed into: ; ; .

[0013] Preferably, S521 is specifically: First, by fixing the power allocation coefficient and precoding matrix In S51 Transformed into the RIS optimal phase shift matrix Θ and auxiliary variables For the subproblems of the optimization object; Secondly, for Perform logarithmic elimination operation to obtain the result. Equivalent linear constraints; Then, for any phase shift parameter variable in the subproblem The phase shift parameter variables are obtained by using the binomial inequality and the auxiliary angle formula in trigonometric functions. The corresponding optimal phase shift parameters ; Finally, we obtain the result through iterative loops. The optimal phase shift parameters of each reflecting unit are determined, and the optimal phase shift matrix is ​​then output. .

[0014] Preferably, S522 is as follows: First, the optimal phase shift matrix obtained in step S521 is... The objective function in S521 is fixed as a constant. Convert to power allocation factor Precoding matrix And auxiliary variables are subproblems that are the objects of optimization; Secondly, for non-convex constraints First, eliminate the logarithm, then use Schuler's complement theorem to define the non-convex constraint. Inequalities containing non-affine terms are equivalently transformed into matrix inequalities that do not contain non-affine terms. Then, for and Approximate equivalent transformations are performed using binomial inequalities and basic inequalities respectively to eliminate... The sum of non-affine terms of the square of a single variable Bivariate coupled product terms; Finally, by performing alternating LI using a cyclic iterative LI precoding matrix optimization algorithm, the optimal power allocation coefficient is output. and optimal precoding vector .

[0015] Preferably, S53 is as follows: The first step is to input the initial parameters: channel matrix and auxiliary variables. ; The second step is to initialize the auxiliary variables. Channel matrix, power allocation coefficient and precoding matrix ; Third step, based on the given channel matrix, fixing the initialized power allocation coefficient and precoding matrix , calling TS algorithm to obtain the optimal phase shift matrix Fourth step, based on the given channel matrix, fixing the optimal phase shift matrix , calling LI algorithm to obtain the optimal power allocation coefficient and optimal precoding vector ; Fifth step, outputting the optimal power allocation coefficient , optimal precoding vector and optimal phase shift matrix , obtaining the optimization result of the maximum minimum fair (MMF) problem of signal to interference and noise ratio (SINR).

[0016] Therefore, the optimization method of the MMF problem of the received signal SINR of the RIS-AFDM-NOMA system in the above-mentioned DD environment is adopted, the AFDM can adapt to the time-frequency dual selection channel by adjusting the DAFT parameter, realize channel path separation, obtain complete time and frequency diversity gain, and has strong anti-interference ability; the NOMA has higher system capacity, better user fairness and lower time delay than the traditional orthogonal multiple access (OMA); by jointly optimizing the RIS phase, the power allocation coefficient and the precoding matrix, the parameter configuration of the optimalization of the SINR of the multi-user received signal under the premise of meeting the fairness can be obtained on the basis of the original signal enhancement and user rate improvement.

[0017] The technical solutions of the present application will be further described in detail below with the help of the accompanying drawings and embodiments. DETAILED DESCRIPTION

[0018] Figure 1 is the flow chart of the MMF problem optimization method of the received signal SINR of the RIS-AFDM-NOMA system of the present application; Figure 2 is the uplink architecture diagram of the RIS-assisted MU communication of the embodiment of the present application; Figure 3 is the configuration block diagram of the AFDM-NOMA system of the embodiment of the present application; Figure 4 is the change curve diagram of the SINR when the number of reflecting units in the RIS of the embodiment of the present application is different; Figure 5 is the change curve diagram of the BER with the SINR when the number of multipaths is different in the embodiment of the present application; Figure 6This is a graph showing the change in SINR when the number of UTS is different according to an embodiment of the present invention. Figure 7 This is an embodiment of the present invention. P max The SINR variation curves at different times; Detailed Implementation

[0019] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0020] like Figure 1 As shown, the method for optimizing the MMF problem of the received signal SINR of the RIS-AFDM-NOMA system of the present invention includes the following steps: S1. Construct a reconfigurable smart surface-simulated radio frequency multiplexing-non-orthogonal multiple access RIS-AFDM-NOMA uplink communication link; S2, for the first User terminals The discrete affine Fourier transform (DAFT) domain signal is subjected to inverse discrete affine Fourier transform (IDAFT) to generate the final transmission signal. S3. Based on the final transmitted signal of S2, establish a dual-selective channel model and obtain the total received signal from the user terminal UTs at the receiving end. S4. Perform Discrete Affine Fourier Transform (DAFT) on the total received signal and express it in matrix-vector form. Then sort the signals and perform Sequential Interference Cancellation (SIC). S5. Construct the maximum minimum fair MMF optimization problem for the received signal interference noise ratio (SINR), and jointly optimize and solve it by adjusting the power allocation coefficient, precoding matrix, and RIS phase shift matrix variables.

[0021] Example like Figure 1 As shown, the method for optimizing the MMF problem of the received signal SINR of the RIS-AFDM-NOMA system of the present invention includes the following steps: S1. Construct a reconfigurable smart surface-simulated RF multiplexing-nonorthogonal multiple access RIS-AFDM-NOMA uplink communication link.

[0022] S11, Uplink communication system, such as Figure 2 As shown, specifically: the transmitter is Each user terminal (UT) has a single antenna and a receiver is a single antenna access point (AP). A reconfigurable smart surface RIS with 10 reflective units acts as a relay for collaborative communication. These passive reflective units achieve optimal transmission links by flexibly adjusting the phase characteristics of their reflection coefficients.

[0023] S12, the first user terminal , and the AP is a system structure of AFDM-NOMA, as shown in Figure 3 .

[0024] S2, the discrete affine Fourier transform (DAFT) domain signal of the first user terminal , , an inverse discrete affine Fourier transform (IDAFT) operation is performed to generate a final transmission signal.

[0025] S21, the DAFT domain signal of , , NOMA power allocation, precoding processing and serial-to-parallel (S / P) conversion operations are performed to obtain an intermediate signal .

[0026] First, define is the DAFT domain symbol vector sent to the AP, where is the number of chirp subcarriers. N Second,

[0027] , NOMA power allocation, precoding processing and S / P conversion operations are performed to obtain an intermediate signal ; wherein ; and are the precoding matrix and power allocation coefficient of , respectively. S22, IDAFT is performed on

[0028] , to obtain a time domain signal .

[0029] Let be the th symbol in , after performing point IDAFT operation, the time domain signal at point is obtained; wherein ; is the chirp orthogonal basis function of IDAFT, ​are two chirp parameters in the inverse discrete Fourier transform (IDFT).

[0030] The time-domain signal may also be represented in a matrix-vector form as wherein, is a DAFT matrix; is an IDAFT matrix; , is a diagonal matrix; is an IDFT matrix.

[0031] S23, the generated is added with a chirp-periodic prefix (CPP), and a parallel to serial (P / S) conversion is performed to obtain a final transmission signal . .

[0032] First, the generated is added with a CPP to obtain ; wherein, denotes the time after adding the CPP, is the length of the CPP; when is an integer value and N is an even number, there is , and ; thus, may be represented as .

[0033] Second, after the P / S conversion is completed, the UT k may represent the final transmission signal vector to the AP as .

[0034] S3, based on the in S2, a double-selective channel model is established, and a total received signal from the transmitting end UTs is obtained at the receiving end.

[0035] S31, the channel impulse response of the double-selective channel at may be represented as , P denotes the number of paths; , , respectively denote the channel gain coefficient, the delay coefficient, and the Doppler coefficient of the th propagation path; in addition, the The normalized delay offset and Doppler frequency offset of each propagation path are expressed as follows: and , It is the sampling period; It is a linear frequency modulation interval; is a positive integer; , and These are the integer and fractional normalized Doppler shifts, respectively.

[0036] Furthermore, the matrix form H of the channel impulse response of a dual-selective channel can be expressed as: ;in, and They represent the first The normalized delay offset and Doppler frequency shift of each propagation path; the delay matrix and Doppler frequency shift matrix can be expressed as follows: and .

[0037] according to Figure 1 It can be seen that the uplink communication system consists of both a reflection link and a direct link, where the direct link is... The channel, while the reflection link is... The cascaded channel with RIS-AP, considering that in practice the positions of RIS and AP usually remain fixed, Each UT is almost always in a state of movement, even high-speed movement.

[0038] exist The channel response at time t is ; in, It is the symbol for the imaginary unit; Indicates the first One multipath propagation component; It is the total number of multipath propagation components; , and They are the first Channel gain coefficient, delay coefficient, and Doppler coefficient of each multipath propagation component; Indicates delay The unit impulse response at time step.

[0039] exist The channel response at time t is ;in, Indicates the first One multipath propagation component; It is the total number of multipath propagation components; , and They are the first Channel gain coefficient, delay coefficient, and Doppler coefficient of each multipath propagation component; Indicates delay The unit impulse response at time step.

[0040] RIS-AP in The channel response at time t is ;in Indicates delay The unit impulse response at time step.

[0041] S32, a dual-selective channel based on S31, allows the received signal after CPP removal at the receiver to be divided into direct link signal and reflected link signal. Wherein: Direct link signal ;in, It is the symbol for the imaginary unit; Representing the User terminals ; It is the transmitting end The final transmitted signal after P / C conversion, excluding CPP; Indicates the first One multipath propagation component; It is the total number of multipath propagation components; , and They are the first Channel gain coefficient, delay coefficient, and Doppler coefficient of each multipath propagation component; yes exist Additive white Gaussian noise (AWGN) generated at the point.

[0042] Reflection link signal ; in, It is the first in RIS The phase coefficients on each reflecting unit, of which ; This represents the total number of reflection units in the RIS. It is the first in RIS-AP The first reflector unit The delay coefficient of each multipath propagation component; yes The total number of multipath propagation components in the middle; , and They are respectively The Middle the channel gain coefficient, delay coefficient and Doppler coefficient of the th multipath propagation component on the th and are respectively and the AWGN generated by the RIS-AP at .

[0043] S33, the total received signal can be expressed as: ; where, is the sum of the AWGN in the direct link and the reflected link.

[0044] S4, for , DAFT is performed and expressed in the form of matrix-vector, and after sorting, the operation of successive interference cancellation (SIC) is performed, which is specifically as follows: S41, for , DAFT is performed to obtain the DAFT domain signal ; where, represents DAFT at the point.

[0045] S42, the is expressed in the form of matrix ; where, is an identity matrix; is the AWGN vector in the time domain; represents the direct channel matrix, and are the normalized delay offset and Doppler frequency offset of the th propagation path respectively; the reflected channel matrix can be expressed as , is the Kronecker product; is the RIS phase shift matrix, , , , represents the phase shift coefficient of the th m reflection unit; is expressed as the channel matrix of the th m reflection unit, , ; is expressed as the RIS-AP channel matrix of the th reflection unit, m .

[0046] Therefore,​ denote the RIS phase shift matrix after coupling with and denote the channel matrix of the M

[0047] S43, superimpose the received signals from the transmitting UTs to obtain the total received signal ; where ; ; is the power allocation factor; is the precoding matrix; and are the channel response matrices of the ; v is the sum of the AWGN time-domain signal vectors.

[0048] S44, sort the UTs in S43 and perform SIC operation to obtain the total received signal after decoding.

[0049] First, sort the UTs in descending order according to the channel conditions (assuming that UT1 is the best and UT4 is the worst), i.e. .

[0050] Second, according to the mechanism of SIC, the received signal of UT4 can be expressed as ; where is the noise term after SCI.

[0051] S45, define two performance indicators of the user terminal UTs.

[0052] (1) The received signal-to-interference-and-noise ratio (SINR) from the transmitting end: ; where is the variance of the AWGN term in ; , are the power allocation factor and the precoding matrix of , respectively; ;​​​​​​​​​​​​​​​ and They represent the first User terminals The corresponding direct channel matrix and reflection channel matrix.

[0053] (2) Receiving end Total rate of UTs : ;in, yes The rate.

[0054] S5. Construct and solve the MMF multi-parameter joint optimization problem for the SINR of the received signal in the RIS-AFDM-NOMA system.

[0055] S51. Establish the MMF multi-parameter joint optimization problem for the SINR of the received signal.

[0056] First, based on the power allocation factor Precoding matrix Together with the optimal phase shift matrix Θ of RIS, we establish the MMF joint optimization problem as follows: ; ; ; ; ; in, , and They represent Rate constraints, power allocation coefficient constraints, and power constraints of the precoding matrix; , and These represent the lower limit of the rate, the upper limit of the power allocation coefficient, and the upper limit of the precoding matrix power, respectively. Represents any reflection unit in the phase shift matrix Θ of the RIS. Phase constraint; express The total channel response matrix; express The total channel response matrix; express The noise standard deviation.

[0057] Analysis shows that P1 is a non-convex optimization problem, mainly because: (1) the objective function is an MMF problem; (2) the objective function and Optimization variables exist in all of them. , and the depth coupling between Θ and ; (3) The variable expression in (4) is non-affine; (4) There exists a unit modulus constraint in (4).

[0058] Based on this, introduce auxiliary variable and set it to be the minimum value of the received signal SINR from the transmitting end UTs, and set it to be Therefore, P1 can be transformed into: ; ; .

[0059] S52, the method of alternating optimization (alternating optimization, AO) is used to decompose the MMF multi-parameter variable joint optimization problem of the received signal SINR into two sub-problems and solve them one by one.

[0060] S521, by fixing and , introduce auxiliary variable and remove non-affine variables through the binomial inequality, and through the auxiliary angle formula in the trigonometric function, the optimal phase angle of each of the reflection units is obtained one by one, and the optimal phase shift matrix of the RIS is obtained; the whole optimization process is based on the phase shift matrix optimization algorithm of the TS.

[0061] First, by fixing and , transform in S51 into Θ and as the optimization object of the sub-problem: ; .

[0062] Second, eliminate the logarithmic operation on , assuming , then .

[0063] Then, expand the term in the channel term of the phase shift, and get ; therefore, can be represented as . Similarly, can also be represented as .

[0064] Thus, the sub-problem is transformed into: .

[0065] Subsequently, the decomposition and triangular transformation are performed on as follows: ; where and are two coefficients; , are the first and the second row in and and denote the real and imaginary part operations, respectively; according to the auxiliary angle formula adopted at , where satisfies: , reaches the maximum value, therefore, the optimal solution of is . .

[0066] Finally, the optimal phase shift matrix is output by Algorithm 1, TS-based phase shift matrix optimization algorithm.

[0067] Algorithm 1: TS-based phase shift matrix optimization algorithm: 1. Input: channel matrix , fixed variables and , auxiliary variables , and the number of iterations .

[0068] 2. Stage 1: Initialization.

[0069] 3. Obtain the initial by the corresponding initialization method. .

[0070] 4. For a given , , , and , calculate the matrix obtained by the power allocation coefficient, the channel and the precoding effect, and the auxiliary matrix .

[0071] 5. Stage 2: Calculation.

[0072] 6. Regarding arrive Execute the loop.

[0073] 7. For a given , and The optimal value is obtained by expanding the complex number modulus square, summing the real and imaginary parts separately, transforming the auxiliary angle formula, and analyzing the maximum value of the cosine function. .

[0074] 8. Update and optimize variables.

[0075] 9. .

[0076] 10. End the loop.

[0077] 11. Phase 3: Termination of inspection.

[0078] 12. If ,but, 13. Exit the loop and obtain... The optimal output.

[0079] 14. End judgment.

[0080] 15. Output: Optimal phase shift matrix .

[0081] S522, via fixing ,optimization and .

[0082] First, after obtaining Then, fix it as a constant, and the objective function It can be converted into: .

[0083] at this time, It is still non-convex.

[0084] Secondly, for C 1. Based on the same method of removing the logarithm as in P2-1, further transform it into... And according to Schuler's complement theorem, the above inequality is transformed into the form of the following matrix inequality: .

[0085] Then, for and , by the binomial inequality is expressed as where is one fixed point in , denotes taking the real part, so can be expressed as ; similarly, can be expressed as: ; to further eliminate the coupling between and , we can further express as .

[0086] Finally, the optimal power allocation coefficients and precoding vectors are output by the algorithm 2 based on the LI-based precoding matrix optimization algorithm loop iteration.

[0087] Algorithm 2: LI-based precoding matrix optimization algorithm.

[0088] 1. Input: channel matrix , fixed phase shift matrix , auxiliary variable , maximum number of iterations and tolerance .

[0089] 2. Stage 1: initialization.

[0090] 3. Initialize variables , and .

[0091] 4. Substitute , , and into to obtain .

[0092] 5. Stage 2: iteration loop.

[0093] 6. For to , perform the following operations: 7. Given and , based on obtain .

[0094] 8. Update the auxiliary variable.

[0095] 9. .

[0096] 10. End the loop.

[0097] 11. Stage 3: Termination check.

[0098] 12. If or , then, 13. Exit loop, obtain optimal auxiliary variables .

[0099] 14. End of judgment.

[0100] 15. Output: Optimal power allocation factor and precoding matrix .

[0101] S53, based on TS and LI algorithm, form the overall joint optimization algorithm, solve the optimization method of MMF problem of received signal SINR, the specific content is as follows: 1. Input: Channel matrix , auxiliary variable .

[0102] 2. Initialize variables , , fixed variables and .

[0103] 3. Given , , based on TS algorithm to get .

[0104] 4. Given , and , based on LI algorithm to get .

[0105] 5. Output: Optimal power allocation factor , precoding matrix and phase shift matrix .

[0106] This embodiment verifies the influence of different system parameters on SINR through simulation experiment: As shown in Figure 4 , when the number of RIS units is different, the change of SINR.

[0107] As shown in Figure 5 , when the number of multipath is different, the change of BER with SINR.

[0108] As shown in Figure 6 , when the number of users is different, the change of SINR.

[0109] As shown in Figure 7As shown, the SINR changes when the maximum transmit power is different.

[0110] Therefore, the AFDM can adapt to the time-frequency dual selection channel by adjusting the DAFT parameters, realize channel path separation, obtain complete time and frequency diversity gain, and have strong anti-interference ability by using the above method. Meanwhile, the AFDM also has the characteristics of low modulation dimension and low pilot overhead, and is more efficient in resource utilization and signal processing. NOMA has higher system capacity, better user fairness and lower time delay than traditional OMA. By jointly optimizing the RIS phase, power allocation coefficient and precoding matrix, the parameter configuration of the multi-user received signal SINR can be optimized under the premise of meeting the fairness on the basis of original signal enhancement and user rate improvement.

[0111] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application but not to limit it, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that: the technical solutions of the present application can still be modified or replaced by equivalent, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. An optimization method for the MMF problem of the received signal SINR in a RIS-AFDM-NOMA system, characterized in that, Includes the following steps: S1. Construct a reconfigurable smart surface-simulated radio frequency multiplexing-non-orthogonal multiple access RIS-AFDM-NOMA uplink communication link; S2, for the first User terminals The discrete affine Fourier transform (DAFT) domain signal is subjected to inverse discrete affine Fourier transform (IDAFT) to generate the final transmission signal. S3. Based on the final transmitted signal from S2, establish a dual-selective channel model and obtain the signal from the user terminal at the transmitting end. The total received signal; S4. Perform Discrete Affine Fourier Transform (DAFT) on the total received signal and express it in matrix-vector form. Then sort the signals and perform Sequential Interference Cancellation (SIC). S5. Construct the maximum minimum fair MMF problem for the received signal interference-to-noise ratio (SINR), and perform joint optimization by adjusting the power allocation coefficient, precoding matrix, and RIS phase shift matrix variables.

2. The optimization method for the MMF problem of the received signal SINR of the RIS-AFDM-NOMA system according to claim 1, characterized in that, The uplink communication link in S1 is specifically as follows: The transmitter is Single-antenna user terminal The receiving end is a single-antenna access point (AP), and one includes... Each RIS of the reflection unit acts as a relay for coordinated communication.

3. The optimization method for the MMF problem of the received signal SINR of the RIS-AFDM-NOMA system according to claim 2, characterized in that, S2 specifically refers to: S21, regarding the first User terminals DAFT domain signal It performs non-orthogonal multiple access (NOMA) power allocation, precoding processing, and serial-to-parallel conversion operations to obtain intermediate signals. ; S22, For intermediate signals Perform IDAFT to obtain the time-domain signal. ; S23, Regarding time-domain signals Add the chirped periodic prefix CPP, and after performing the parallel / serial conversion operation, obtain the first... User terminals The final transmitted signal .

4. The optimization method for the MMF problem of the received signal SINR of the RIS-AFDM-NOMA system according to claim 3, characterized in that, S3 specifically refers to: S31. Define a dual-selectivity channel in Point channel response The matrix form is ;in, Indicates the number of paths; , and They represent the first Channel gain coefficient, delay factor, and Doppler factor for each propagation path; Represents the delay matrix; Represents the Doppler frequency shift matrix; S32. Based on S31, the dual-selective channel, after removing the chirped periodic prefix (CPP) at the receiver, receives the signal from the transmitter... User terminals The signals can be divided into: (1) Direct Link The received signal is shown below: ;in, It is the symbol for the imaginary unit; ; It is the first of the transmitting end User terminals The final transmitted signal after P / S conversion, excluding CPP; Indicates the first One multipath propagation component; It is the total number of multipath propagation components; , and They are the first Channel gain coefficient, delay coefficient, and Doppler coefficient of each multipath propagation component; yes exist Additive white Gaussian noise (AWGN) generated at the point; (2) Reflection Link The received signal from RIS-AP is shown below: ； in, It is the first in RIS The phase coefficients on each reflecting unit, where... ; This represents the total number of reflection units in the RIS. It is the first in RIS-AP The first reflector unit The delay coefficient of each multipath propagation component; yes The total number of multipath propagation components in the middle; , and They are respectively The Middle The first reflector unit Channel gain coefficient, delay coefficient, and Doppler coefficient of each multipath propagation component; and They are and RIS-AP Additive white Gaussian noise (AWGN) generated at each moment; S33, Based on S32, the total received signal is As shown below: ； in, It is the sum of additive white Gaussian noise (AWGN) in the direct link and the reflected link.

5. The optimization method for the MMF problem of the received signal SINR of the RIS-AFDM-NOMA system according to claim 4, characterized in that, S4 specifically refers to: S41, Total Received Signal Perform a Discrete Affine Fourier Transform (DAFT) to obtain the DAFT domain signal; S42, Establish the first User terminals Matrix-vector form of the DAFT domain received signal ; S43. Matrix-vector form of the received signal in the DAFT domain of S42 ,right One from the transmitter user terminal UTs The signals are superimposed to obtain the total received signal. : ； in, It is the original signal vector in the DAFT domain; It is the power distribution factor; It is a precoding matrix; and They are Channel and The channel response matrix; Θ and G are respectively The RIS phase shift matrix and RIS-AP channel response matrix formed by the reflection units; v is The sum of the time-domain signal vectors of each AWGN; S44, The total received signal in S43 ,Will The user terminals (UTs) are sorted in descending order according to channel conditions, and then the SIC operation is performed to decode the total received signal from the transmitting user terminals (UTs). ; S45. Define two performance metrics for UTS: (1) From the transmitting end The signal-to-interference-plus-noise ratio (SINR) of the received signal is: ;in, yes The variance of the additive white Gaussian noise (AWGN) term; , They represent The power allocation coefficients and precoding matrix, ; , They represent the first User terminals The corresponding direct channel matrix and reflection channel matrix; (2) Receiving end Total rate of UTs for: ;in, yes The rate.

6. The optimization method for the MMF problem of the received signal SINR of the RIS-AFDM-NOMA system according to claim 5, characterized in that, S5 specifically refers to: S51. Establish the maximum minimum fair MMF multi-parameter joint optimization problem for the received signal SINR. S52. Using the alternating optimization AO method, the MMF multi-parameter joint optimization problem of the received signal SINR is decomposed into two sub-problems and solved one by one. S521, By fixing the power distribution coefficient With precoding matrix By introducing auxiliary variables and eliminating non-affine variables using binomial inequalities, and then obtaining the values ​​one by one using the auxiliary angle formulas in trigonometric functions, we can find the values ​​one by one. The optimal phase angle of each reflection unit is determined, and the optimal phase shift matrix of RIS is obtained. The entire optimization process is based on the phase shift matrix optimization algorithm of TS. S522: By fixing the RIS optimal phase shift matrix in S521, the non-affineness and coupling between variables are removed by using the binomial inequality, the basic inequality, and the Schul complement theorem, respectively; the entire optimization process is based on the LI precoding matrix optimization algorithm. S53. Based on the TS-based and LI-based algorithms in S521 and S522 respectively, a general joint optimization algorithm is formed to solve the optimization problem of MMF of the received signal SINR.

7. The optimization method for the MMF problem of the received signal SINR of the RIS-AFDM-NOMA system according to claim 6, characterized in that, S51 specifically refers to: First, based on the power allocation factor Precoding matrix Together with the optimal phase shift matrix Θ of RIS, we establish the joint optimization problem of maximum-minimum-fairness MMF, as shown below: ； ； ； ； ； in, , and They represent Rate constraints, power allocation coefficient constraints, and power constraints of the precoding matrix; , and These represent the lower limit of the rate, the upper limit of the power allocation coefficient, and the upper limit of the precoding matrix power, respectively. Represents any reflection unit in the phase shift matrix Θ of the RIS. Phase constraint; express The total channel response matrix; express The total channel response matrix; express The noise standard deviation; Then, auxiliary variables are introduced. And let the auxiliary variable be set. From the transmitting end The minimum SINR value received by each user terminal UTs; therefore, P1 can be transformed into: ； ； 。 8. The optimization method for the MMF problem of the received signal SINR of the RIS-AFDM-NOMA system according to claim 7, characterized in that, S521 specifically refers to: First, by fixing the power allocation coefficient and precoding matrix In S51 Transformed into the RIS optimal phase shift matrix Θ and auxiliary variables For the subproblems of the optimization object; Secondly, for Perform logarithmic elimination operation to obtain the result. Equivalent linear constraints; Then, for any phase shift parameter variable in the subproblem The phase shift parameter variables are obtained by using the binomial inequality and the auxiliary angle formula in trigonometric functions. The corresponding optimal phase shift parameters ; Finally, we obtain the result through iterative loops. The optimal phase shift parameters of each reflecting unit are determined, and the optimal phase shift matrix is ​​then output. .

9. The method for optimizing the MMF problem of the received signal SINR of the RIS-AFDM-NOMA system according to claim 8, characterized in that, S522 specifically refers to: First, the optimal phase shift matrix obtained in step S521 is... The objective function in S521 is fixed as a constant. Convert to power allocation factor Precoding matrix And auxiliary variables are subproblems that are the objects of optimization; Secondly, for non-convex constraints First, eliminate the logarithm, then use Schuler's complement theorem to define the non-convex constraint. Inequalities containing non-affine terms are equivalently transformed into matrix inequalities that do not contain non-affine terms. Then, for and Approximate equivalent transformations are performed using binomial inequalities and basic inequalities respectively to eliminate... The sum of non-affine terms of the square of a single variable Bivariate coupled product terms; Finally, by performing alternating LI using a cyclic iterative LI precoding matrix optimization algorithm, the optimal power allocation coefficient is output. and optimal precoding vector .

10. The optimization method for the MMF problem of the received signal SINR of the RIS-AFDM-NOMA system according to claim 9, characterized in that, S53 specifically refers to: The first step is to input the initial parameters: channel matrix and auxiliary variables. ; The second step is to initialize the auxiliary variables. Channel matrix, power allocation coefficient and precoding matrix ; The third step is to fix the initialized power allocation coefficients based on the given channel matrix. and precoding matrix The optimal phase shift matrix is ​​obtained by calling the TS algorithm. The fourth step is to fix the optimal phase shift matrix based on the given channel matrix. The LI algorithm is called to obtain the optimal power allocation coefficient. and optimal precoding vector ; Step 5: Output the optimal power allocation coefficient Optimal precoding vector and the optimal phase shift matrix The optimization results of the maximum minimum fairness MMF problem for signal-to-interference-plus-noise ratio (SINR) are obtained.

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