A method for reducing peak-to-average ratio of an OFDM system

Abstract

This invention relates to a method for reducing the peak-to-average power ratio (PAPR) of an OFDM system. It involves extending reserved subcarriers to the data subcarrier frequency band, constraining the maximum error vector of the system, and reducing the PAPR. The method includes: first, establishing an primal optimization problem with the OFDM signal PAPR as the objective function and the maximum error vector on the data subcarriers and the power of the reserved subcarriers as constraints; second, decomposing the primal problem into three subproblems using the ADMM algorithm, alternately solving each subproblem and iterating repeatedly until the globally optimal solution is obtained. Compared with existing technologies, this invention has advantages such as avoiding excessive interference that leads to an increase in the system's bit error rate and achieving better PAPR reduction.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a method for reducing the peak-to-average power ratio (PAPR) of an OFDM system. Background Technology

[0002] The basic idea of ​​OFDM is to convert a high-speed serial data stream into multiple low-speed parallel sub-data streams through serial-to-parallel (S / P) conversion, and then modulate them onto multiple orthogonal subcarriers for parallel transmission. This parallel transmission system greatly extends the pulse width of the symbol and improves performance against harsh transmission conditions such as multipath fading. OFDM system signals are composed of multiple subcarrier signals superimposed. When the phases of the subcarriers are close or identical, the inverse Fourier transform process will cause subcarrier superposition, resulting in a high-power signal and a large peak-to-average power ratio (PAPR). This places high demands on the linearity of the amplifier within the transmitter. If the peak value of the signal waveform is outside the linear dynamic range of the power amplifier, it will introduce signal distortion, causing changes in the spectrum of the superimposed signal. This will disrupt the orthogonality between the sub-channel signals, resulting in mutual interference and affecting the overall system performance.

[0003] The TR algorithm (Reserved Subcarrier Technique) is a widely used PAPR suppression algorithm. It divides N subcarriers into data subcarriers and reserved subcarriers. The data subcarriers are used to transmit information, while the reserved subcarriers are used to generate peak cancellation signals to reduce the PAPR of the final signal. At the receiving end, only the signal at the data subcarrier position needs to be demodulated, unaffected by the reserved subcarrier. However, the traditional TR algorithm has high computational complexity and limited PAPR reduction capability, necessitating a feasible method to improve the TR algorithm. Summary of the Invention

[0004] The purpose of this invention is to overcome the defects of the prior art and provide a method for reducing the peak-to-average power ratio of an OFDM system.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A method for reducing the peak-to-average power ratio (PAPR) of an OFDM system, comprising the following steps:

[0007] S1: Perform OFDM modulation on the original signal.

[0008] S2: Use TR technology to suppress PAPR and extend the frequency domain cancellation signal C to the data subcarriers. Add the maximum EVM constraint to the interference of the frequency domain cancellation signal C on the data subcarriers to obtain the vector D on the data subcarrier set. Combining the maximum in-band distortion constraint on the data subcarriers and the power constraint on the reserved subcarriers, define the TR problem based on the maximum EVM constraint in the OFDM system.

[0009] S3: Input the original OFDM frequency domain signal X and time domain signal x, the vector D of the frequency domain peak cancellation signal C on the data subcarrier set, the vector B on the reserved subcarrier set, the time domain transmitted signal y after TR, and the initial value of the Lagrange multiplier u (D). 1 B 1 ,y 1 ,u 1 EVM preset threshold, power preset threshold, penalty coefficient (α,β,ρ), simplified IFFT matrix Q D and Q B Given the total number of iterations K, the frequency domain peak cancellation signal C is calculated and obtained using the TR algorithm based on the maximum EVM constraint.

[0010] Furthermore, the specific content of S1 is as follows:

[0011] For the original frequency domain signal X = [X0, X1, ..., X...] N-1 ] T OFDM modulation is performed to obtain the frequency domain OFDM signal, and then IFFT transformation is performed on it to obtain the time domain OFDM signal.

[0012] Furthermore, in S2, the frequency-domain OFDM signal has N subcarriers, divided into N... r One reserved subcarrier and NN r Given several data subcarriers, and incorporating a maximum EVM constraint to limit the maximum in-band distortion caused by introduced interference in the data subcarriers, we obtain the original optimization problem:

[0013]

[0014]

[0015]

[0016] In the formula, α is the preset threshold for EVM, β is the preset threshold for power, and matrix M D and M R All are binary diagonal matrices, each with a dimension of N×N, corresponding to the data subcarrier position and the reserved subcarrier position, respectively;

[0017] Define a simplified IFFT matrix Q D and QB The dimensions are LN×(NN) r ) and LN×N r The optimization variable C is decomposed into a vector D on the data subcarrier set and a vector B on the reserved subcarrier set. The optimization variables of the original problem do not satisfy the conditions for using the ADMM algorithm, so variable substitution is performed, and the equality constraint y = x + Q is introduced. D D+Q B B, leading to the equivalent problem:

[0018]

[0019]

[0020]

[0021] y = x + Q D D+Q B B.

[0022] Furthermore, in S3, the augmented Lagrangian function of the original problem is decomposed into a function of three variables, D, B, and y. The three objective functions are solved alternately and iterated repeatedly until the global optimum is obtained. The expression for the Lagrangian function is:

[0023]

[0024] The iterative steps are as follows:

[0025]

[0026]

[0027]

[0028] u k+1 :=u k +x+Q D D k+1 +Q B B k+1 -y k+1 .

[0029] The specific steps of the TR algorithm based on the maximum EVM constraint include:

[0030] A) Input the original OFDM frequency domain signal X and time domain signal x, the vector D of the frequency domain peak cancellation signal C on the data subcarrier set, the vector B on the reserved subcarrier set, the time domain transmitted signal y after TR, and the initial value of the Lagrange multiplier u (D). 1 B 1 ,y 1 ,u 1EVM preset threshold, power preset threshold, penalty coefficient (α,β,ρ), simplified IFFT matrix Q D and Q B and the total number of iterations K;

[0031] B) Let k = 1, 2, ..., K, and perform iteration;

[0032] C) Solve subproblem a, and update D. k+1 ;

[0033] D) Solve subproblem b and update B. k+1 ;

[0034] E) Solve subproblem c and update y. k+1 ;

[0035] F) Calculate u k+1 =u k +x+Q D D k+1 +Q B B k+1 -y k+1 ;

[0036] G) Output D K+1 B K+1 .

[0037] Furthermore, solve subproblem a and update D. k+1 The specific steps include:

[0038] C1) Calculate v k =xy k +u k / ρ;

[0039] C2) Let i = 1, 2, ..., N r Iterate;

[0040] C3) Calculation

[0041] Furthermore, solve subproblem b and update B. k+1 The specific steps include:

[0042] D1) Calculation

[0043] D2) Calculation

[0044] D3) Calculation

[0045] Furthermore, solve subproblem c and update y. k+1 The specific steps include:

[0046] E1) Calculate p k =Q D D k+1 +Q B B k+1 +x+u k / ρ;

[0047] E2) Calculate y using the linear Bregman algorithm k+1 .

[0048] The method for reducing the peak-to-average power ratio (PAPR) of an OFDM system provided by this invention has at least the following advantages compared to existing technologies:

[0049] This invention adds a maximum EVM constraint to the interference of the frequency domain peak cancellation signal on the data subcarrier, that is, limits the maximum error vector amplitude deviation on the data subcarrier to a certain range, thereby improving the peak-to-average power ratio (PAPR) reduction effect with minimal impact on the bit error rate at the receiver. At the same time, it combines ADMM with the TR method to propose a suboptimal solution algorithm with low computational complexity for the original optimization problem. The main operation of each iteration process is matrix and vector multiplication. Therefore, the proposed method based on the maximum EVM constraint TR algorithm can achieve effective PAPR reduction performance with low complexity and can still converge after multiple iterations. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the reserved subcarrier technology in the method for reducing the peak-to-average power ratio of the OFDM system of the present invention in the embodiment;

[0051] Figure 2 The flowchart shows the TR algorithm based on the maximum EVM constraint for reducing the peak-to-average power ratio of the OFDM system of the present invention in the embodiment. Detailed Implementation

[0052] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0053] Example

[0054] Error Vector Magnitude (EVM) is a measure of in-band distortion of a signal. It is the deviation of a constellation point Z from the original frequency domain signal X, and is defined as the ratio of the square root of the average power of the error vector signal to the square root of the average power of the reference signal.

[0055]

[0056] The core of the ADMM algorithm is to transform a complex optimization problem into several easier-to-solve subproblems, and then solve each subproblem alternately and iterate repeatedly until the global optimum is obtained. It mainly solves the following constrained convex optimization problems:

[0057]

[0058] stAx+By=C

[0059] in, and Let f(x) and g(y) be the parameters of the equality constraints, and let f(x) and g(y) be two convex functions. ADMM decomposes the original problem into minimizing two objective functions f(x) and g(y), and then performs alternating optimization on the two variables until the optimal solution is obtained: p * =inf{f(x)+g(y)|Ax+By=C}.

[0060] Based on the above, this invention relates to a method for reducing the peak-to-average power ratio (PAPR) of an OFDM system. This method is based on the maximum error vector constraint of the data subcarriers, such as... Figure 1 As shown, the specific steps include the following:

[0061] Step 1: Modulate the original signal using OFDM.

[0062] Each symbol consists of N subcarriers. The original frequency domain signal can be represented as X = [X0, X1, ..., X...]. N-1 ] T X k This is the frequency domain representation of the signal modulated by the k-th subcarrier, where k = 0, 1, ..., N-1. The frequency domain representation of the baseband transmit signal modulated by OFDM is:

[0063]

[0064] Where L is the oversampling factor, typically four times oversampled for discrete signals to approximate the PAPR of continuous signals. Performing an IFFT transform on the frequency domain signal yields the modulated time domain signal:

[0065] x = IFFT(X) = QX

[0066] Where Q is an LN×N dimensional IFFT transform matrix, and the elements of the matrix are:

[0067]

[0068] Step 2: Utilize TR (Transmission of Error) technology to suppress PAPR (Parallel Parallel Propagation), and extend the frequency-domain cancellation signal vector C to the data subcarriers to ensure it also has an effective value. To control the interference introduced on the data subcarriers and prevent excessive interference from causing a sharp increase in the receiver's bit error rate, a maximum EVM (Effective Virtual Machine) constraint is added to the interference C on the data subcarriers, limiting the maximum error vector amplitude deviation on the data subcarriers to a certain range. Considering both the maximum in-band distortion constraint on the data subcarriers and the power constraint on the reserved subcarriers, the TR problem based on the maximum EVM constraint in the OFDM system is defined.

[0069] In traditional TR technology, the set of reserved subcarriers With data subcarrier set They are mutually orthogonal, meaning the frequency domain peak cancellation signal vector C has an effective value of 0 on the data subcarrier set. The time-domain transmitted signal y after TR technology can be expressed as:

[0070] y = IFFT(X + C) = x + QC

[0071] PAPR is defined as the ratio of the maximum instantaneous power to the average power of a signal. The PAPR of signal y can be expressed as:

[0072]

[0073] In practical applications, it is usually required that the power of C be much smaller than the signal power, i.e. Therefore and Very close, and reducing the peak-to-average power ratio (PAPR) mainly involves reducing the maximum peak value of the signal, therefore we can define To approximate PAPR(y).

[0074] Error Vector Magnitude (EVM) is a measure of in-band distortion of a signal. It is the deviation of a constellation point Z from the original frequency domain signal X, and is defined as the ratio of the square root of the average power of the error vector signal to the square root of the average power of the reference signal.

[0075]

[0076] To improve the reduction effect of PAPR, we consider extending C to the set of data subcarriers, meaning that C has an effective value on all subcarriers. Extending the peak cancellation signal C to the data subcarriers obviously introduces interference to the original data signal, thereby increasing the system's bit error rate. Therefore, a maximum EVM (error vector amplitude) constraint is added to the TR problem to constrain the maximum distortion within the signal band, ensuring that the impact on the receiver's bit error rate is minimal.

[0077] like Figure 2As shown, the primal optimization problem is defined by combining the minimization of signal PAPR, the maximum in-band distortion constraint, and the reserved subcarrier power constraint:

[0078]

[0079]

[0080]

[0081] Where α is the preset threshold for EVM, β is the preset threshold for power, and matrix M D and M R All are binary diagonal matrices with dimensions of N×N, corresponding to the data subcarrier positions and reserved subcarrier positions, respectively.

[0082]

[0083] According to the definition:

[0084] M D +M R =I

[0085] M D M R =0

[0086] Step 3: Input the original OFDM frequency domain signal X and time domain signal x, the vector D of the frequency domain peak cancellation signal C on the data subcarrier set, the vector B on the reserved subcarrier set, the time domain transmitted signal y after TR processing, and the initial value of the Lagrange multiplier u (D). 1 B 1 ,y 1 ,u 1 EVM preset threshold, power preset threshold and penalty coefficient (α,β,ρ), simplified IFFT matrix Q D and Q B The total number of iterations K is used to calculate the frequency domain peak cancellation signal C based on the proposed TR algorithm based on maximum EVM constraints.

[0087] To simplify the calculation, a simplified IFFT matrix Q is defined. D and Q B The dimensions are LN×(NN) r ) and LN×N r The optimization variable C is decomposed into a vector D on the data subcarrier set and a vector B on the reserved subcarrier set. r Let NN be the dimension of vector B. r Let Q be the dimension of vector D. Matrix Q D and Q BEach column corresponds to the position of the data subcarrier set and the reserved subcarrier set, respectively, then QC = Q D D+Q B B. The optimization variables of the original problem do not meet the conditions for using the ADMM algorithm. Therefore, variable substitution is performed, and the equality constraint y = x + Q is introduced. D D+Q B B, leading to the equivalent problem:

[0088]

[0089]

[0090]

[0091] y = x + Q D D+Q B B

[0092] Its augmented Lagrangian function is:

[0093]

[0094] Where ρ is the penalty parameter, These are Lagrange multipliers. The ADMM algorithm is used to decompose the original problem into three subproblems concerning D, B, and y. In each iteration, the optimal solution D to each of these three subproblems is solved sequentially. K+1 B K+1 and y K+1 Then update the dual variable u. K+1 This process continues until the stopping criterion is met, at which point the global optimal solution is obtained. The formula for the update iteration steps is:

[0095]

[0096]

[0097]

[0098] u k+1 :=u k +x+Q D D k+1 +Q B B k+1 -y k+1

[0099] definition Let subproblem a be the solution to subproblem a. Solving subproblem a yields D. K+1 The update is as follows:

[0100]

[0101] definition Let B be a subproblem b. Solving subproblem b yields B. K+1 The update is as follows:

[0102]

[0103] definition Let y be a subproblem c. Solve subproblem c using the linear Bregman algorithm to obtain y. K+1 Update.

[0104] Finally, according to u k+1 :=u k +x+Q D D k+1 +Q B B k+1 -y k+1 Update the dual variable.

[0105] The overall algorithm flow is shown in the table below:

[0106] Table 1 Algorithm Flow

[0107]

[0108]

[0109] Furthermore, the algorithm principles are supplemented as follows:

[0110] ADMM primarily addresses the following constrained convex optimization problems:

[0111] in, and Let f(x) and g(y) be the parameters of the equality constraints, and let f(x) and g(y) be two convex functions. ADMM can decompose the original problem into minimizing two objective functions f(x) and g(y), and then alternately optimize the two variables until the optimal solution is obtained: p * =inf{f(x)+g(y)|Ax+By=C}.

[0112] Solving the original problem using the augmented Lagrange method, the augmented Lagrange function of the original problem can be expressed as: Where λ>0 is the dual variable, and ρ>0 is the parameter of the penalty term.

[0113] In each iteration, ADMM alternately seeks the optimal solution for the local objective function with respect to x and y, and then updates the dual variable λ. Let k be the iteration number, then its optimization solution steps can be expressed as:

[0114]

[0115]

[0116] λ k+1 :=λ k +ρ(Ax k+1 +By k+1 -C)

[0117] The original optimization problem considering the maximum EVM constraint is:

[0118]

[0119]

[0120]

[0121] y = x + Q D D+Q B B

[0122] Its augmented Lagrangian function is:

[0123]

[0124] Where ρ > 0 is the penalty parameter. These are Lagrange multipliers. The ADMM algorithm is used to decompose this problem into three subproblems concerning D, B, and y. In each iteration, the optimal solution D to each of these three subproblems is solved sequentially. K+1 B K+1 and y K+1 Then update the dual variable u. k+1 The process continues until the stopping criterion is met, thus obtaining the globally optimal price. The update iteration formula is as follows:

[0125]

[0126]

[0127]

[0128] u k+1 :=u k +x+Q D D k+1 +Q B B k+1 -y k+1

[0129] Where k is the iteration counter.

[0130] Solving subproblem a, according to the augmented Lagrangian function, subproblem a can be simplified to the following equivalent problem:

[0131]

[0132]

[0133] in, make Further simplification yields the following equivalent problem:

[0134]

[0135]

[0136] Because the objective function and constraints are related to D i It is separable, therefore it can be decomposed into NT. r There are several parallel subproblems, and the optimal solution is found for each subproblem:

[0137]

[0138] st|D i | 2 ≤α

[0139] The problem is a convex quadratic function with convex constraints. The optimal solution can be obtained by first finding the stationary point where the gradient of the objective function is 0, then projecting this stationary point onto the feasible region, and calculating D. k+1 The update is as follows:

[0140]

[0141] Solving subproblem b, according to the augmented Lagrangian function, subproblem b can be simplified to the following equivalent problem:

[0142]

[0143]

[0144] in,

[0145] This problem is a convex problem with inequality constraints, and its closed-form solution can be obtained using the Lagrange multiplier method. Its Lagrange function is: Where, μ k ≥0 represents a Lagrange multiplier. Its objective function and constraint functions are differentiable. According to the Lagrange multiplier method, the optimal solution is B. k+1 and the optimal Lagrange multiplier μ k* Should meet Right now:

[0146] Then B K+1 The update is as follows:

[0147]

[0148] Solving subproblem c, according to the augmented Lagrangian function, subproblem c can be equivalent to the following problem:

[0149]

[0150] Where, p k =Q D D k+1 +Q B B k+1 +x+u k / ρ.

[0151] make y can be represented as This can be transformed into solving an optimization problem with respect to m:

[0152]

[0153] Where λ is the coefficient of the introduced penalty term. This transforms the original solution for y in the complex field into a solution for m in the positive real field. This optimization problem is an approximate point operator of the infinite norm, which can be computed in linear time using a linearized Bregman algorithm. The relevant derivation is as follows:

[0154] Let J(m) = λ||m|| ∞ and Furthermore, the Bregman distance between points m and n is defined as follows:

[0155] Where p∈J(n) is the subgradient of J at point n, and <p,mn> is the inner product operation. In the linearized Bregman algorithm, H(m) is linearly expanded to obtain:

[0156]

[0157] in, Let H(m) be the quadratic term of the Taylor expansion. Then the optimization problem with respect to m can be transformed into solving:

[0158]

[0159] The solution is obtained iteratively by substituting the defined Bregman distance and simplifying to obtain:

[0160]

[0161] Where C is a constant for p k+1 Simplify:

[0162]

[0163] definition Then we have: p k Substitute m k+1 The formula, when rearranged, yields: in, Differentiate with respect to m, where m is separable:

[0164]

[0165] Because r k =r k-1 +(zm k After sorting, we get:

[0166]

[0167] Then y can be finally obtained. i =m i ·sign(v i The approximate point operators for solving the infinite norm using the linear Bregman algorithm are summarized in the following table:

[0168] Table 2. Flowchart of the approximate point operator for solving the infinite norm using the linear Bregman algorithm.

[0169]

[0170] By using the linear Bregman algorithm, the update of variable y can be obtained. k+1 Finally, through u k+1 :=u k +x+Q D D k+1 +Q B B k+1 -y k+1 After updating the dual variable, we obtain u. k+1 Repeat the above steps until the maximum number of iterations is reached.

[0171] In summary, the OFDM system peak-to-average power ratio (PAPR) reduction method provided by this invention is based on the constraint of the maximum error vector on the data subcarrier. It extends the reserved subcarrier to the data subcarrier frequency band, constraining the maximum error vector of the system and reducing the system PAPR. The method includes: First, establishing an original optimization problem with the OFDM signal PAPR as the objective function and the maximum error vector on the data subcarrier and the power of the reserved subcarrier as constraints; second, using the ADMM algorithm to decompose the original problem into three subproblems, solving each subproblem alternately and iterating repeatedly until the global optimal solution is obtained. This invention controls the maximum error vector introduced by the reserved subcarrier onto the data subcarrier, avoiding excessive interference that could lead to an increase in the system bit error rate, thus achieving a better PAPR reduction effect.

[0172] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for reducing the peak-to-average power ratio (PAPR) of an OFDM system, characterized in that, Includes the following steps: 1) Perform OFDM modulation on the original signal; 2) Use TR technology to suppress PAPR and extend the frequency domain cancellation signal C to the data subcarriers. Add the maximum EVM constraint to the interference of the frequency domain cancellation signal C on the data subcarriers to obtain the vector D on the data subcarrier set. Combining the maximum in-band distortion constraint on the data subcarriers and the power constraint on the reserved subcarriers, define the TR problem based on the maximum EVM constraint in the OFDM system. 3) Input the original OFDM frequency domain signal and time domain signals The frequency-domain peak cancellation signal C is represented by vector D on the data subcarrier set, vector B on the reserved subcarrier set, and the time-domain transmitted signal after TR. Lagrange multipliers initial value EVM preset threshold, power preset threshold, penalty coefficient Simplified IFFT matrix and and total number of iterations The frequency domain peak cancellation signal C is calculated and obtained based on the TR algorithm based on the maximum EVM constraint. In step 2), the frequency domain OFDM signal has N subcarriers, divided into... One reserved subcarrier and Given several data subcarriers, and incorporating a maximum EVM constraint to limit the maximum in-band distortion caused by introduced interference in the data subcarriers, we obtain the original optimization problem: In the formula, Set a threshold for EVM. To preset a power threshold, the matrix and All are binary diagonal matrices, with dimensions of 1. These correspond to the data subcarrier position and the reserved subcarrier position, respectively; Define a simplified IFFT matrix and The dimensions are respectively and The optimization variable C is decomposed into a vector D on the data subcarrier set and a vector B on the reserved subcarrier set. The optimization variables of the original problem do not meet the conditions for using the ADMM algorithm, so variable substitution is performed and equality constraints are introduced. This leads to the equivalent problem: In step 3), the augmented Lagrangian function of the original problem is decomposed into a function relating to... , and A function of three variables is solved alternately and iterated over three objective functions until the global optimum is obtained. The expression for the Lagrange function is: The iterative steps are as follows: 。 2. The method for reducing the peak-to-average power ratio of an OFDM system according to claim 1, characterized in that, The specific content of step 1) is as follows: For the original frequency domain signal OFDM modulation is performed to obtain the frequency domain OFDM signal, and then IFFT transformation is performed on it to obtain the time domain OFDM signal.

3. The method for reducing the peak-to-average power ratio of an OFDM system according to claim 1, characterized in that, In step 3), the specific steps of the TR algorithm based on the maximum EVM constraint include: A) Input the original OFDM frequency domain signal and time domain signals The frequency-domain peak cancellation signal C is represented by vector D on the data subcarrier set, vector B on the reserved subcarrier set, and the time-domain transmitted signal after TR. Lagrange multipliers initial value EVM preset threshold, power preset threshold, penalty coefficient Simplified IFFT matrix and and total number of iterations ; B) Let Iterate; C) Solve subproblem a, update ; D) Solve subproblem b and update ; E) Solve subproblem c, update ; F) Calculation ; G) Output , .

4. The method for reducing the peak-to-average power ratio of an OFDM system according to claim 3, characterized in that, Solve subproblem a, update The specific steps include: C1) Calculation ; C2) Let Iterate; C3) Calculation .

5. The method for reducing the peak-to-average power ratio of an OFDM system according to claim 3, characterized in that, Solve subproblem b and update. The specific steps include: D1) Calculation ; D2) Calculation ; D3) Calculation .

6. The method for reducing the peak-to-average power ratio of an OFDM system according to claim 3, characterized in that, Solve subproblem c and update. The specific steps include: E1) Calculation ; E2) Calculate using the linear Bregman algorithm .

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