Low-complexity design method for MIMO-OFDM (Multiple Input Multiple Output-Orthogonal Frequency Division Multiplexing) system with constant peak to average power ratio

Abstract

The invention discloses a low-complexity design method for an MIMO-OFDM (Multiple Input Multiple Output-Orthogonal Frequency Division Multiplexing) system with a constant peak-to-average power ratio, which comprises the following steps of: defining a subcarrier set and a signal vector for data transmission for given base station configuration; processing the signal vector to obtain a frequency domain transmitting signal; performing inverse discrete Fourier transform (IDFT) on the frequency domain transmitting signal to obtain a time domain transmitting signal, and defining a baseband transmitting signal after OFDM modulation by adding a cyclic prefix to the time domain transmitting signal; the PAPR is adopted to measure the fluctuation of a baseband transmitting signal, the PAPR represents the ratio of the peak value to the mean value of the signal power, and a complementary cumulative distribution function is adopted to measure the PAPR; a non-convex optimization problem including OFDM modulation, multi-user precoding, inter-user interference and PAPR constraint is constructed by using the degree of freedom brought by a large-scale antenna array configured on a base station, and the non-convex optimization problem is solved. The method has remarkable advantages in the aspects of reducing the PAPR of a transmitted signal on each antenna and improving the symbol error probability of the whole system.

Description

Technical Field

[0001] The invention belongs to the field of wireless communications, and relates to a design method of a MIMO-OFDM system, and in particular to a low-complexity design method of a MIMO-OFDM system with a constant peak-to-average power ratio. Background Art

[0002] Massive multi-user multiple-input multiple-output (MIMO) technology is considered one of the key technologies in 5G. Massive antenna array technology can adapt to MIMO systems, thereby improving the spatial freedom of wireless channels and bringing higher data rates and transmission reliability. Orthogonal frequency division multiplexing (OFDM) is an important multi-carrier modulation technology. By decomposing broadband channels into several independent narrowband channels, it can effectively solve the problem of frequency selective fading. Combining OFDM technology with MIMO systems can give full play to the advantages of both, achieving faster communication rates and higher spectrum utilization. This system has been identified as a reliable technology for future generations of wireless communications.

[0003] However, as a multi-carrier technology, OFDM is prone to large signal envelope fluctuations when the spectrum of each carrier is the same or similar, which in turn leads to a high peak-to-average power ratio (PAPR) of the signal. High peak-to-average power ratio signals usually require power amplifiers with large feedback, which increases the complexity of analog-to-digital converters and digital-to-analog converters, and also places high requirements on the linearity of the amplifier in the transmitter, which may cause signal distortion, change the signal spectrum, and seriously deteriorate the performance of the system. When applying massive multi-user MIMO (MMU-MIMO) technology to engineering practice, base stations must use low-power RF links and low-power and power-efficient RF power amplifiers, which requires the transmitted signal to have a low PAPR. In order to meet the two requirements of using low-power and power-efficient power amplifiers and reducing interference between multiple users in MMU-MIMO technology, it is urgent to use more effective methods to reduce the PAPR of the system. Summary of the invention

[0004] Purpose of the invention: In order to overcome the deficiencies in the prior art, a low-complexity design method for a MIMO-OFDM system with a constant peak-to-average power ratio is provided, which can effectively suppress the PAPR of the transmitted signal in the downlink of a massive multi-user MIMO-OFDM system, while maintaining a good symbol error rate of the system. Compared with other methods, only a small number of iterations are required to achieve good results, and it has significant advantages in reducing the PAPR of the transmitted signal on each antenna and improving the symbol error probability (SER) of the entire system.

[0005] Technical solution: To achieve the above object, the present invention provides a low-complexity design method for a MIMO-OFDM system with a constant peak-to-average power ratio, comprising the following steps:

[0006] S1: For a given base station configuration, define the subcarrier set and signal vector used for data transmission;

[0007] S2: Process the signal vector to obtain a frequency domain transmission signal;

[0008] S3: Obtain a time domain transmit signal by performing an inverse discrete Fourier transform (IDFT) on the frequency domain transmit signal, and define a baseband transmit signal after OFDM modulation by adding a cyclic prefix (CP) to the time domain transmit signal;

[0009] S4: PAPR is used to measure the fluctuation of the baseband transmission signal. PAPR represents the ratio of the peak value to the mean value of the signal power. The complementary cumulative distribution function is used to measure PAPR.

[0010] S5: By utilizing the degrees of freedom brought by the massive antenna array configured on the base station, a non-convex optimization problem including OFDM modulation, multi-user (MU) precoding, multi-user interference (MUI) and PAPR constraints is constructed and solved.

[0011] Furthermore, the step S1 specifically includes:

[0012] Assume that the base station is configured with M transmitting antennas to serve K single-antenna mobile users, and K < < M, the number of OFDM subcarriers is N, and the signal vector s n ∈Θ K Contains information transmitted to K users, n = 1, 2, ..., N is the OFDM carrier index, Θ is the complex-valued constellation set, s n，k ∈Θ represents the symbol sent to user k on carrier n; the subcarrier set used for data transmission is defined as Γ, and its complementary set Γ c Used for band protection, that is, when n∈Γ c When there is a signal vector s n =0 K×1 .

[0013] Furthermore, the step S2 specifically includes:

[0014] Signal vector s n First, N precoding vectors are generated by using a precoder designed based on the mean square error minimization criterion. to a n Normalization is performed to obtain the normalized precoding vector w n , reorder them according to the direction from the user to the transmitting antenna, and obtain the frequency domain transmitted signal [x1,…,xm ]=P[w1,…,w n ], where P represents the corresponding sorting matrix, and the N-dimensional vector x m It is the frequency domain signal transmitted from the mth transmitting antenna.

[0015] Furthermore, the step S3 specifically includes:

[0016] Frequency domain transmitted signal x m Perform inverse discrete Fourier transform to obtain the time domain transmission signal y m , that is, y m =IDFT(x m ), for the time domain transmitted signal y m Adding CP, the frequency domain signal vector received by the receiver is expressed as: n =H n w n +b n , n = 1, ..., N, where r n is the nth received signal vector, H n represents the channel matrix of the nth subcarrier of MIMO-OFDM, b n is an independent and identically distributed complex Gaussian noise, each of which has a mean of 0 and a variance of N0;

[0017] For a given frequency domain signal The baseband transmit signal after OFDM modulation is expressed as:

[0018]

[0019] in, T is the OFDM symbol time, Δf is the subcarrier frequency spacing, and N is the number of subcarriers.

[0020] Furthermore, the PAPR in step S4 is defined as follows:

[0021]

[0022] In actual OFDM systems, discrete signals are used to calculate PAPR:

[0023]

[0024] Further, the complementary cumulative distribution function in step S4 is expressed as:

[0025] CCDF(α)=Pr{PAPR>α}=1-(1-e -α ) N (4)

[0026] Among them, α represents the specified PAPR threshold, N is the number of OFDM signal subcarriers, and Pr represents the probability that the PAPR exceeds the threshold.

[0027] Furthermore, the construction of the non-convex optimization problem in step S5 includes:

[0028] A1: Taking minimizing MUI as the objective function, taking the PAPR of each antenna and the transmit power of each antenna less than the preset threshold as constraints, a non-convex optimization model including OFDM modulation, multi-user precoding, multi-user interference (MUI) and PAPR constraints is constructed:

[0029] The precoded signal satisfies:

[0030]

[0031] The frequency domain signal on the guard band satisfies:

[0032]

[0033] Combining the above constraints into:

[0034]

[0035] in, Yes k , k∈Ω and Ω c 's collection of associations; is a block diagonal matrix whose diagonal elements are H k , for all k∈Ω, and For all k∈Ω c ;

[0036] Using equation PP T =I M，K , the precoding constraint and OFDM modulation are jointly expressed as:

[0037]

[0038] in Is The former KM t A submatrix consisting of columns;

[0039] A2: The downlink transmission scheme is described as the following optimization problem:

[0040]

[0041] In formula (9), the constraint condition and are the PAPR and total transmit power constraints for each antenna, respectively, where ζ i and P max These are all pre-given thresholds;

[0042] A3: Assuming x and y are two auxiliary variables, equation (9) can be equivalently expressed as the following optimization problem:

[0043]

[0044] Furthermore, in step S5, a CPAPR-LADMM algorithm is constructed to solve the non-convex optimization problem, and the construction method specifically includes:

[0045] Construct the augmented Lagrangian function:

[0046]

[0047] In the formula, is the scaled dual variable, λ>0 is a penalty parameter;

[0048] Constraints and The feasible regions of are defined as Γ and Φ respectively, and CPAPR-LADMM performs the following iterations:

[0049]

[0050]

[0051] z k+1 =argminL λ (x k+1 ,y k+1 ,z,u k , v k ) (14)

[0052] u k+1 =u k +x k+1 -y k+1 (15)

[0053] v k+1 =v k +z k+1 -Ay k+1 (16).

[0054] Furthermore, the process of solving the non-convex optimization problem by the CPAPR-LADMM algorithm in step S5 includes:

[0055] B1: Solve subproblems (12)

[0056] Subproblem (12) is equivalent to solving the following optimization subproblem:

[0057]

[0058] Problem (17) is a problem involving M t The quadratic constrained quadratic program (QCQP) with 2 constraints is equivalently converted to an M with only one constraint. t A quadratically constrained quadratic programming (QCQP-1) is used to obtain the optimal solution; Problem (17) is equivalent to:

[0059]

[0060] Problem (18) is decomposed into M t QCQP-1 subproblems:

[0061]

[0062] Let x i =α i c i , and α i >0 and Then problem (19) is equivalent to the following optimization problem:

[0063]

[0064] in,

[0065] The objective function is to maximize the inner product while satisfying the constraints. To get the minimum value:

[0066]

[0067] Introducing the penalty coefficient η k > 0 is used to penalize violations of equality constraints. The problem is reformulated as follows:

[0068]

[0069] We obtain the solution by setting the derivative of the objective function to zero and projecting the solution onto the corresponding feasible set.

[0070]

[0071] Among them, the symbol express The phase of; using the bisection method, the optimal η can be obtained efficiently k ; Then, c i Substituting into equation (20) and simplifying, we can obtain iThe quadratic problem of i The optimal solution is as follows:

[0072]

[0073] Will and Substitute into x i =α i c i In, get Through parallel calculation, we get:

[0074]

[0075] B2: Solve subproblem (13)

[0076] Subproblem (13) is equivalent to:

[0077]

[0078] By setting the derivative of the objective function to zero and projecting the solution onto Solve the above problem on the feasible domain of ; the solution of the unconstrained optimization problem of problem (26) is:

[0079]

[0080] Since the dimension of the inverse matrix is ​​JKM t , The computational complexity of is very high, approximately To solve this problem, a linearization method is used to approximate the quadratic terms in the subproblem

[0081] set up have:

[0082]

[0083] in, It is at point y k The gradient of the function f(y), and β>0 is the penalty parameter;

[0084] Substituting equation (28) into equation (26) and ignoring the constant term in equation (26), equation (26) is transformed into:

[0085]

[0086] By setting the derivative of the objective function to zero, the solution to the unconstrained optimization problem is:

[0087]

[0088] Next, project the solution onto On the feasible domain of , the solution of formula (29) is:

[0089]

[0090] B3: Solve subproblems (14)

[0091] Subproblem (14) is formulated as the following optimization problem:

[0092]

[0093] The optimal solution of formula (32) is obtained by setting the derivative of the objective function to zero:

[0094]

[0095] Furthermore, the method for solving the non-convex optimization problem using the CPAPR-LADMM algorithm in step S5 includes:

[0096] C1: input s, A, λ, β;

[0097] C2: Initialization: x 1 ,y 1 , z 1 ,u 1 , v 1 is a feasible solution; set the maximum number of iterations K max ;

[0098] C3: Whilek ≤ K max ; Carry out M t parallel computing;

[0099] C4: Obtain c using the dichotomy method using formula (23) i ;

[0100] C5: through formula (24) Update alpha i ;

[0101] C6: Pass x i =α i c i Update x i ; End parallel computing and get x k+1 ;

[0102] C7: through formula (31) Update y k+1 ;

[0103] C8: Through formula (33) Update z k+1 ;

[0104] C9: through formula (15)uk+1 =u k +x k+1 -y k+1 Update k+1 ;

[0105] C10: through formula (16) v k+1 =v k +z k+1 -Ay k+1 Update v k+1 ;

[0106] C11: End While:

[0107] C12: Output: x k+1 .

[0108] Beneficial effects: Compared with the prior art, the present invention proposes a low-complexity CPAPR-LADMM method for the problem of high PAPR values ​​in massive multi-user MIMO-OFDM systems. The core is to use the degrees of freedom brought by the massive antenna array configured on the base station to construct a non-convex optimization problem including OFDM modulation, multi-user precoding, multi-user interference (MUI) and PAPR constraints, and solve it, which can reduce interference between multiple users and maintain a constant PAPR value. Using the CPAPR-LADMM method, fewer iterations are required to reduce the PAPR of the transmitted signal, improve the system operation efficiency, and improve the system's SER performance, which is more in line with the application in engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] Figure 1 It is the downlink diagram of massive multi-user MIMO-OFDM system;

[0110] Figure 2 This is a comparison chart of reducing the PAPR of the transmitted signal under different methods and different numbers of iterations;

[0111] Figure 3 This is a comparison chart of SER of different methods. DETAILED DESCRIPTION

[0112] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0113] The present invention provides a low-complexity design method for a MIMO-OFDM system with a constant peak-to-average power ratio, comprising the following steps:

[0114] S1: For a given base station configuration, define the subcarrier set and signal vector used for data transmission;

[0115] Reference Figure 1 , assume that the base station is configured with M transmitting antennas to serve K single-antenna mobile users, and K<<M, the number of OFDM subcarriers is N, and the signal vector s n ∈Θ K Contains information transmitted to K users, n = 1, 2, ..., N is the OFDM carrier index, Θ is the complex-valued constellation set, s n，k ∈Θ represents the symbol sent to user k on carrier n; the subcarrier set used for data transmission is defined as Γ, and its complementary set Γ c Used for band protection, that is, when n∈Γ c When there is a signal vector s n =0 K×1 .

[0116] S2: Process the signal vector to obtain a frequency domain transmission signal;

[0117] Signal vector s n First, N precoding vectors are generated by using a precoder designed based on the mean square error minimization criterion. n∈1,2,...,N,for a n Normalization is performed to obtain the normalized precoding vector w n , reorder them according to the direction from the user to the transmitting antenna, and obtain the frequency domain transmitted signal [x1,…,x m ]=P[w1,…,w n ], where P represents the corresponding sorting matrix, and the N-dimensional vector x m It is the frequency domain signal transmitted from the mth transmitting antenna.

[0118] S3: Obtain a time domain transmit signal by performing an inverse discrete Fourier transform (IDFT) on the frequency domain transmit signal, and define a baseband transmit signal after OFDM modulation by adding a cyclic prefix (CP) to the time domain transmit signal;

[0119] Frequency domain transmitted signal x m Perform inverse discrete Fourier transform to obtain the time domain transmission signal y m , that is, y m =IDFT(x m ), for the time domain transmitted signal y m Adding CP, the frequency domain signal vector received by the receiver is expressed as: n =H n w n +b n , n = 1, ..., N, where r nis the nth received signal vector, H n represents the channel matrix of the nth subcarrier of MIMO-OFDM, b n is an independent and identically distributed complex Gaussian noise, each of which has a mean of O and a variance of N0;

[0120] For a given frequency domain signal The baseband transmit signal after OFDM modulation is expressed as:

[0121]

[0122] in, T is the OFDM symbol time, Δf is the subcarrier frequency spacing, and N is the number of subcarriers.

[0123] S4: PAPR is used to measure the fluctuation of the baseband transmission signal. PAPR represents the ratio of the peak value to the mean value of the signal power. The complementary cumulative distribution function is used to measure PAPR.

[0124] The definition of PAPR is as follows:

[0125]

[0126] In actual OFDM systems, discrete signals are used to calculate PAPR:

[0127]

[0128] In actual systems, the complementary cumulative distribution function is used to measure the performance of PAPR, which is defined as:

[0129] CCDF(α)=Pr{PAPR>α} (4)

[0130] Among them, α represents the PAPR threshold value specified by the system, Pr represents the probability that the PAPR exceeds the threshold value, and N is the number of subcarriers of the OFDM signal. The purpose of reducing the PAPR of the transmitted signal is to make the high-power amplifier at the transmitting end always work within its linear range, thereby reducing the nonlinear distortion of the power amplifier to ensure that the signal at the receiving end has a better bit error rate.

[0131] S5: By exploiting the degrees of freedom provided by the massive antenna array configured on the base station, a non-convex optimization problem including OFDM modulation, multi-user (MU) precoding, multi-user interference (MUI) and PAPR constraints is constructed and solved;

[0132] The formulation of the non-convex optimization problem involves:

[0133] A1: Taking minimizing MUI as the objective function, taking the PAPR of each antenna and the transmit power of each antenna less than the preset threshold as constraints, a non-convex optimization model including OFDM modulation, multi-user precoding, multi-user interference (MUI) and PAPR constraints is constructed:

[0134] The precoded signal satisfies:

[0135]

[0136] The frequency domain signal on the guard band satisfies:

[0137]

[0138] Combining the above constraints into:

[0139]

[0140] in, Yes k , k∈Ω and Ω c 's collection of associations; is a block diagonal matrix whose diagonal elements are H k , for all k∈Ω, and For all k∈Ω c ;

[0141] Using equation PP T =I M，K , the precoding constraint and OFDM modulation are jointly expressed as:

[0142]

[0143] in Is The former KM t A submatrix consisting of columns;

[0144] A2: The downlink transmission scheme is described as the following optimization problem:

[0145]

[0146] In formula (9), the constraint condition and are the PAPR and total transmit power constraints for each antenna, respectively, where ζ i and P max These are all pre-given thresholds;

[0147] A3: Assuming x and y are two auxiliary variables, equation (9) can be equivalently expressed as the following optimization problem:

[0148]

[0149] The non-convex optimization problem is solved by constructing the CPAPR-LADMM algorithm. The construction method specifically includes:

[0150] Construct the augmented Lagrangian function:

[0151]

[0152] In the formula, is the scaled dual variable, λ>0 is a penalty parameter;

[0153] Constraints and The feasible regions of are defined as Γ and Φ respectively, and CPAPR-LADMM performs the following iterations:

[0154]

[0155] u k+1 =u k +x k+1 -y k+1 (15)

[0156] v k+1 =v k +z k+1 -Ay k+1 (16)

[0157] The process of CPAPR-LADMM algorithm to solve non-convex optimization problems includes:

[0158] B1: Solve subproblems (12)

[0159] Subproblem (12) is equivalent to solving the following optimization subproblem:

[0160]

[0161] Problem (17) is a problem involving M t The quadratic constrained quadratic program (QCQP) with 2 constraints is equivalently converted to an M with only one constraint. t A quadratically constrained quadratic programming (QCQP-1) is used to obtain the optimal solution; Problem (17) is equivalent to:

[0162]

[0163] Problem (18) is decomposed into M t QCQP-1 subproblems:

[0164]

[0165] Let x i =α i c i , and α i >0 and Then problem (19) is equivalent to the following optimization problem:

[0166]

[0167] in,

[0168] The objective function is to maximize the inner product while satisfying the constraints. To get the minimum value:

[0169]

[0170] Introducing the penalty coefficient η k > 0 is used to penalize violations of equality constraints. The problem is reformulated as follows:

[0171]

[0172] We obtain the solution by setting the derivative of the objective function to zero and projecting the solution onto the corresponding feasible set.

[0173]

[0174] Among them, the symbol express The phase of; using the bisection method, the optimal η can be obtained efficiently k ; Then, c i Substituting into equation (20) and simplifying, we can obtain i The quadratic problem of i The optimal solution is as follows:

[0175]

[0176] Will and Substitute into x i =α i c i In, get Through parallel calculation, we get:

[0177]

[0178] B2: Solve subproblem (13)

[0179] Subproblem (13) is equivalent to:

[0180]

[0181] By setting the derivative of the objective function to zero and projecting the solution onto Solve the above problem on the feasible domain of ; the solution of the unconstrained optimization problem of problem (26) is:

[0182]

[0183] Since the dimension of the inverse matrix is ​​JKM t , The computational complexity of is very high, approximately To solve this problem, a linearization method is used to approximate the quadratic terms in the subproblem

[0184] set up have:

[0185]

[0186] in, It is at point y k The gradient of the function f(y), and β>0 is the penalty parameter;

[0187] Substituting equation (28) into equation (26) and ignoring the constant term in equation (26), equation (26) is transformed into:

[0188]

[0189] By setting the derivative of the objective function to zero, the solution to the unconstrained optimization problem is:

[0190]

[0191] Next, project the solution onto On the feasible domain of , the solution of formula (29) is:

[0192]

[0193] B3: Solve subproblems (14)

[0194] Subproblem (14) is formulated as the following optimization problem:

[0195]

[0196] The optimal solution of formula (32) is obtained by setting the derivative of the objective function to zero:

[0197]

[0198] The method of CPAPR-LADMM algorithm to solve non-convex optimization problems can be summarized as follows:

[0199] C1: input s, A, λ, β;

[0200] C2: Initialization: x 1 ,y 1 , z 1 ,u 1 , v 1 is a feasible solution; set the maximum number of iterations K max ;

[0201] C3: Whilek ≤ K max ; Carry out M t parallel computing;

[0202] C4: Obtain c using the dichotomy method using formula (23) i ;

[0203] C5: through formula (24) Update alpha i ;

[0204] C6: Pass x i =α i c i Update x i ; End parallel computing and get x k+1 ;

[0205] C7: through formula (31) Update y k+1 ;

[0206] C8: Through formula (33) Update z k+1 ;

[0207] C9: through formula (15)u k+1 =u k +x k+1 -y k+1 Update k+1 ;

[0208] C10: through formula (16) v k+1 =v k +z k+1 -Ay k+1 Update v k+1 ;

[0209] C11: End While;

[0210] C12: Output the optimal solution of optimization problem (9): x k+1 .

[0211] Based on the above scheme, in order to verify the effect of the method of the present invention, this embodiment conducts a simulation experiment of the algorithm, uses the software MATLAB to perform simulation, and verifies the theoretical analysis. The specific simulation results and analysis are as follows:

[0212] like Figure 2 The comparison diagram of reducing the PAPR of the transmitted signal under different methods and different iteration times shows that the CPAPR-LADMM algorithm designed by the present invention achieves a PAPR of 2dB. Compared with LADMM, FITRA, APGM, PADMM, ZF and MF precoding, CPAPR-LADMM can improve the performance by 0.2dB, 0.8dB, 0.8dB, 2.4dB, 11.1dB and 11.1dB respectively. More importantly, the CCDF curve of CPAPR-LADMM shows obvious cutoff characteristics, which means that based on the CPAPR-LADMM method provided by the present invention, the optimal solution to problem (9) can be solved, so as to obtain a transmitted signal with a constant PAPR (the threshold value specified by the system) and meeting the system power requirements. Therefore, this method can effectively suppress the increase of the PAPR value, thereby avoiding the nonlinear distortion of the power amplifier and the degradation of SER performance caused by excessively high PAPR values. However, for other methods such as LADMM, FITRA, APGM, PADMM, ZF, and MF precoding, this cutoff feature is clearly missing in their CCDF curves.

[0213] like Figure 3 The SER effect diagram of different methods is shown. -3 When the SNR performance of the CPAPR-LADMM algorithm is about 0.05 dB compared with the ideal linear ZF precoding, the algorithm of the present invention achieves 2.55 dB, 3.15 dB, 3.35 dB and 5.15 dB improvement compared with LADMM, FITRA, APGM and PADMM, respectively. In particular, the ZF and MF precoding methods lack PAPR optimization, resulting in severe nonlinear distortion of the power amplifier and unacceptable SER performance.

[0214] From the above simulation experiments, it can be seen that the CPAPR-LADMM algorithm has lower complexity and faster convergence speed. Only a small number of iterations are needed to obtain lower SER and better PAPR suppression effect. Therefore, the CPAPR-LADMM method is more efficient than other existing methods and is more conducive to application in actual engineering.

Claims

1. A low-complexity design method for a MIMO-OFDM system with a constant peak-to-average power ratio, characterized in that: The steps include: S1: For a given base station configuration, define the subcarrier set and signal vector used for data transmission; S2: Process the signal vector to obtain a frequency domain transmission signal; S3: Obtain a time domain transmit signal by performing an inverse discrete Fourier transform on the frequency domain transmit signal, and define a baseband transmit signal after OFDM modulation by adding a cyclic prefix to the time domain transmit signal; S4: PAPR is used to measure the fluctuation of the baseband transmission signal. PAPR represents the ratio of the peak value to the mean value of the signal power. The complementary cumulative distribution function is used to measure PAPR. S5: By utilizing the degrees of freedom brought by the massive antenna array configured on the base station, a non-convex optimization problem including OFDM modulation, multi-user precoding, multi-user interference and PAPR constraints is constructed and solved.

2. The low-complexity design method for a MIMO-OFDM system with a constant peak-to-average power ratio according to claim 1, characterized in that: The step S1 specifically includes: Assume that the base station is configured with M transmitting antennas to serve K single-antenna mobile users, and K < < M, the number of OFDM subcarriers is N, and the signal vector s n ∈Θ K Contains information transmitted to K users, n = 1, 2, ..., N is the OFDM carrier index, Θ is the complex-valued constellation set, s n,k ∈Θ represents the symbol sent to user k on carrier n; the subcarrier set used for data transmission is defined as Γ, and its complementary set Γ c Used for band protection, that is, when n∈Γ c When there is a signal vector s n =0 K×1 .

3. The low-complexity design method for a MIMO-OFDM system with a constant peak-to-average power ratio according to claim 2, characterized in that: The step S2 specifically includes: Signal vector s n First, N precoding vectors are generated by using a precoder designed based on the mean square error minimization criterion. to a n Normalization is performed to obtain the normalized precoding vector w n , reorder them according to the direction from the user to the transmitting antenna, and obtain the frequency domain transmitted signal [x1,…,x m ]=P[w1,…,w n ], where P represents the corresponding sorting matrix, and the N-dimensional vector x m It is the frequency domain signal transmitted from the mth transmitting antenna.

4. The low-complexity design method for a MIMO-OFDM system with a constant peak-to-average power ratio according to claim 3, characterized in that: The step S3 specifically includes: Frequency domain transmitted signal x m Perform inverse discrete Fourier transform to obtain the time domain transmission signal y m , that is, y m =IDFT(x m ), for the time domain transmitted signal y m Adding CP, the frequency domain signal vector received by the receiver is expressed as: n =H n w n +b n ,n=1,...,N, where r n is the nth received signal vector, H n represents the channel matrix of the nth subcarrier of MIMO-OFDM, b n is an independent and identically distributed complex Gaussian noise, each of which has a mean of 0 and a variance of N0; For a given frequency domain signal The baseband transmission signal after OFDM modulation is expressed as: in, T is the OFDM symbol time, Δf is the subcarrier frequency spacing, and N is the number of subcarriers.

5. The low-complexity design method for a MIMO-OFDM system with a constant peak-to-average power ratio according to claim 4, characterized in that: The definition of PAPR in step S4 is as follows: In actual OFDM systems, discrete signals are used to calculate PAPR:

6. The low-complexity design method for a MIMO-OFDM system with a constant peak-to-average power ratio according to claim 5, characterized in that: The complementary cumulative distribution function in step S4 is expressed as: CCDF(α)=Pr{PAPR>α}=1-(1-e -α ) N (4) Among them, α represents the specified PAPR threshold, N is the number of OFDM signal subcarriers, and Pr represents the probability that the PAPR exceeds the threshold.

7. The low-complexity design method for a MIMO-OFDM system with a constant peak-to-average power ratio according to claim 5, characterized in that: The construction of the non-convex optimization problem in step S5 includes: A1: Taking minimizing MUI as the objective function, taking the PAPR of each antenna and the transmit power of each antenna less than the preset threshold as constraints, a non-convex optimization model including OFDM modulation, multi-user precoding, multi-user interference (MUI) and PAPR constraints is constructed: The precoded signal satisfies: The frequency domain signal on the guard band satisfies: Combining the above constraints into: in, Yes k , k∈Ω and Ω c 's collection of associations; is a block diagonal matrix whose diagonal elements are H k , for all k∈Ω, and For all k∈Ω c ; Using equations The precoding constraint and OFDM modulation are jointly expressed as: in Is The former KM t A submatrix consisting of columns; A2: The downlink transmission scheme is described as the following optimization problem: In formula (9), the constraint condition and are the PAPR and total transmit power constraints for each antenna, respectively, where ζ i and P max These are all pre-given thresholds; A3: Assuming x and y are two auxiliary variables, equation (9) can be equivalently expressed as the following optimization problem:

8. The low-complexity design method for a MIMO-OFDM system with a constant peak-to-average power ratio according to claim 7, characterized in that: In step S5, a CPAPR-LADMM algorithm is constructed to solve the non-convex optimization problem. The construction method specifically includes: Construct the augmented Lagrangian function: In the formula, is the scaled dual variable, λ>0 is a penalty parameter; Constraints and The feasible regions of are defined as Γ and Φ respectively, and CPAPR-LADMM performs the following iterations: from k+1 =argminL λ (x k+1 ,y k+1 ,from,to k ,in k ) (14) u k+1 =u k +x k+1 -y k+1 (15) v k+1 =v k +z k+1 -Yes k+1 (16).

9. A low-complexity design method for a MIMO-OFDM system with a constant peak-to-average power ratio according to claim 8, characterized in that: The process of using the CPAPR-LADMM algorithm to solve the non-convex optimization problem in step S5 includes: B1: Solve subproblems (12) Subproblem (12) is equivalent to solving the following optimization subproblem: Problem (17) is a problem involving M t The quadratic constrained quadratic programming with 2 constraints is equivalent to converting it into an M with only one constraint. t A quadratic constrained quadratic programming is performed to obtain the optimal solution; Problem (17) is equivalent to: Problem (18) is decomposed into M t QCQP-1 subproblems: Let x i =α i c i , and α i >0 and Then problem (19) is equivalent to the following optimization problem: in, The objective function is to maximize the inner product while satisfying the constraints. To get the minimum value: Introducing the penalty coefficient η k > 0 is used to penalize violations of equality constraints. The problem is reformulated as follows: We obtain the solution by setting the derivative of the objective function to zero and projecting the solution onto the corresponding feasible set. Among them, the symbol express The phase of ; using the dichotomy method, we can get the optimal η k ; Then, c i Substituting into equation (20) and simplifying, we can obtain i The quadratic problem of i The optimal solution is as follows: Will and Substitute into x i =α i c i In, get Through parallel calculation, we get: B2: Solve subproblems (13) Subproblem (13) is equivalent to: By setting the derivative of the objective function to zero and projecting the solution onto Solve the above problem on the feasible domain of ; the solution of the unconstrained optimization problem of problem (26) is: Use linearization methods to approximate quadratic terms in subproblems set up have: in, It is at point y k The gradient of the function f(y), and β>0 is the penalty parameter; Substituting equation (28) into equation (26) and ignoring the constant term in equation (26), equation (26) is transformed into: By setting the derivative of the objective function to zero, the solution to the unconstrained optimization problem is: Next, project the solution onto On the feasible domain of , the solution of formula (29) is: B3: Solve subproblems (14) Subproblem (14) is formulated as the following optimization problem: The optimal solution of formula (32) is obtained by setting the derivative of the objective function to zero:

10. The low-complexity design method for a MIMO-OFDM system with a constant peak-to-average power ratio according to claim 9, characterized in that: The method for solving the non-convex optimization problem using the CPAPR-LADMM algorithm in step S5 includes: C1: input s, A, λ, β; C2: Initialization: x 1 ,y 1 ,z 1 ,u 1 ,v 1 is a feasible solution; set the maximum number of iterations K max ; C3: While k ≤ K max ; Carry out M t parallel computing; C4: Obtain c using the dichotomy method through formula (23) i ; C5: through formula (24) Update alpha i ; C6: through x i =α i c i Update x i ; End parallel computing and get x k+1 ; C7: through formula (31) Update y k+1 ; C8: Through formula (33) Update z k+1 ; C9: through formula (15)u k+1 =u k +x k+1 -y k+1 Update k+1 ; C10: through formula (16) v k+1 =v k +z k+1 -Ay k+1 Update v k+1 ; C11: End While; C12: Output: x k+1 .

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