ADMM-Based Low-Complexity Peak-to-Average Power Ratio Reduction Method for Multicarrier Modulation Signals

Abstract

The present invention discloses a low-complexity peak-to-average power ratio (PAPR) suppression method for multi-carrier modulation signals based on ADMM, belonging to the field of wireless communication. The method includes: introducing phase shifts to each sub-carrier in the signal transmission frequency domain of the multi-carrier modulation system; obtaining the time-domain waveform through oversampling and mathematically modeling the PAPR to obtain an optimization problem; in the Lagrangian function of the optimization problem, fixing the phase factor and the Lagrange multiplier, and then optimizing the optimization objective; fixing the optimization objective and the Lagrange multiplier of this optimization problem and using the fast Fourier transform (FFT) to optimize the phase factor; updating the Lagrange multiplier according to the optimized optimization objective, phase factor and constraint conditions, and iterating repeatedly until convergence, and optimizing the PAPR of the multi-carrier modulation through the optimized phase factor. The PAPR suppression method of the present invention has good PAPR optimization effect and low computational complexity.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular, to a method for suppressing the peak-to-average power ratio of a low-complexity multi-carrier modulation signal based on ADMM. Background Art

[0002] OFDM (Orthogonal Frequency Division Multiplexing) is an orthogonal frequency division multiplexing technology. In fact, OFDM is a type of multi-carrier modulation (MCM). It realizes parallel transmission of high-speed serial data through frequency division multiplexing. It has good anti-multipath fading ability and can support multi-user access. The OFDM technology is developed from multi-carrier modulation and is one of the implementation methods of multi-carrier transmission schemes. Its modulation and demodulation are respectively implemented based on IFFT and FFT, and it is a multi-carrier transmission scheme with the lowest implementation complexity and the widest application, and has an extremely important position in 4G and 5G communications.

[0003] The OFDM system can provide a larger coverage range, better transmission quality, higher data rate and spectral efficiency. However, since the OFDM symbol is composed of the superposition of multiple independently modulated sub-carrier signals, when the phases of each sub-carrier are the same or close, the superimposed signal will be modulated by the signal with the same initial phase, resulting in a large instantaneous power peak, and further bringing a relatively high peak-to-average power ratio (PAPR - Peak to Average Power Ratio), simply referred to as the peak-to-average ratio (PAPR). Since the dynamic range of a general power amplifier is limited, the OFDM signal with a large peak-to-average ratio is very likely to enter the non-linear region of the power amplifier, resulting in non-linear distortion of the signal, causing obvious spectral spreading interference and in-band signal distortion, and leading to a serious decline in the performance of the entire system. The high peak-to-average ratio has become a major technical obstacle for OFDM. Therefore, how to effectively reduce the PAPR of the OFDM system, that is, to optimize the target peak-to-average ratio through various algorithms, is a problem worthy of attention and is relatively crucial. Summary of the Invention

[0004] The present invention provides a method for suppressing the peak-to-average power ratio of a low-complexity multi-carrier modulation signal based on ADMM. This method can achieve the effect of directly optimizing the peak-to-average power ratio, so as to solve the technical problems that the existing peak-to-average ratio optimization often does not directly optimize the peak-to-average ratio, but takes it as a constraint condition, optimizes the signal distortion caused by the peak-to-average ratio optimization, and has a too high time complexity.

[0005] The first aspect of the present invention provides a method for suppressing the peak-to-average ratio of a multi-carrier modulation signal based on ADMM with low complexity, comprising the following steps: adding an initial phase to a plurality of subcarriers in the frequency domain of a multi-carrier modulation system signal transmission, and synthesizing the plurality of subcarriers after adding the initial phase to obtain a time domain waveform;

[0006] Oversampling the time domain waveform, using the added multiple initial phases to form a phase factor, and performing mathematical modeling based on the phase factor to obtain the problem to be optimized;

[0007] Obtaining a Lagrangian function of the problem to be optimized, which is composed of an optimization objective, the phase factor, and a Lagrangian multiplier; optimizing the optimization objective by fixing the phase factor and the Lagrangian multiplier using a cross-directional multiplier method; and updating the Lagrangian function using the optimized optimization objective;

[0008] Fixing the optimized optimization target and the Lagrangian multiplier, calculating the gradient of the phase factor in the Lagrangian function using a fast Fourier transform, optimizing the phase factor using a gradient descent method after searching for an optimal step size, and updating the Lagrangian function using the optimized phase factor;

[0009] The Lagrangian multiplier is updated according to the optimization objective, the optimized phase factor, and the constraints of the Lagrangian multiplier. The optimization objective, the phase factor, and the Lagrangian multiplier in the Lagrangian function of the problem to be optimized are iteratively updated multiple times until the iteration termination condition is met to output the optimal phase factor, and the peak-to-average ratio of the multiple subcarriers in the frequency domain of the multicarrier modulation system signal transmission is optimized using the optimal phase factor.

[0010] Optionally, in one embodiment of the present invention, the time domain waveform is:

[0011]

[0012] Among them, θ i ,i=1,...,N is the initial phase of the increase, α i is the amplitude of the i-th subcarrier, N is the number of sampling points, and M is the frequency value.

[0013] Optionally, in one embodiment of the present invention, oversampling the time domain waveform includes:

[0014] Select the oversampling factor O and the sampling rate f s =OM, sampling period Let t = nT s , the time domain waveform after sampling is:

[0015]

[0016] where \(n = 1,\cdots,L\), and \(L\) is the number of oversampling points.

[0017] Optionally, in an embodiment of the present invention, a phase factor is composed of a plurality of increased initial phases, and a problem to be optimized is obtained through mathematical modeling based on the phase factor, including:

[0018] Extracting the common term in the time-domain waveform after sampling Composing the phase factor

[0019] And constructing \(L\) row vectors where \(l = 1,\cdots,L\);

[0020] Constructing the problem to be optimized according to the phase factor and the row vectors:

[0021]

[0022] That is, optimizing the maximum peak value, where and Satisfy:

[0023]

[0024] The problem to be optimized is transformed into:

[0025]

[0026] Optionally, in an embodiment of the present invention, a Lagrangian function of the problem to be optimized composed of an optimization objective, the phase factor, and a Lagrange multiplier is obtained, the phase factor and the Lagrange multiplier are fixed, the optimization objective is optimized, and the Lagrangian function is updated using the optimized optimization objective, including:

[0027] Obtaining the Lagrangian function of the problem to be optimized:

[0028]

[0029] where, is the Lagrange multiplier, is the phase factor, and \(t\) is the optimization objective;

[0030] Let the partial derivative of the Lagrangian function be equal to 0 to obtain the constraint condition of the Lagrange multiplier :

[0031]

[0032] Fixing the phase factor and the Lagrange multiplier Transform the Lagrangian function into a function that only depends on the optimization objective t k and update the optimization objective t with the point that minimizes the Lagrangian function . k+1 .

[0033] Optionally, in an embodiment of the present invention, fix the optimized optimization objective and the Lagrange multiplier, use the fast Fourier transform to find the gradient of the phase factor in the Lagrangian function, search for the optimal step size, and then use the gradient descent method to optimize the optimization variable. Update the Lagrangian function with the optimized phase factor, including:

[0034] The Lagrangian function updated with the optimized optimization objective is:

[0035]

[0036] Take the derivative with respect to the initial phase angle θ n of each subcarrier, and let the vector The Lagrangian function is:

[0037]

[0038] Let the partial derivative of the Lagrangian function with respect to θ be equal to 0: n

[0039]

[0040] Let the inside of the brackets be equal to F(n, l):

[0041]

[0042] where Get:

[0043]

[0044] Perform a fast Fourier transform to get:

[0045]

[0046] where is the FFT of with a length of ON, that is:

[0047]

[0048] After finding the partial derivative of the Lagrangian function with respect to θ n , the gradient of L at this point is obtained:

[0049]

[0050] Update it using the gradient descent method: where a is the optimal step size found.

[0051]

[0052] where a is the optimal step size found.

[0053] Optionally, in an embodiment of the present invention, updating the Lagrange multiplier according to the optimization objective, the optimized phase factor, and the preset constraint conditions includes:

[0054] For the problem to be optimized When the inequality constraint in the constraint condition takes the less-than sign, i.e., at this time, the Lagrange multiplier τ l = 0; when the inequality constraint takes the equal sign, i.e., at this time, the Lagrange multiplier τ l > 0, and the final Lagrange multiplier τ is obtained through the constraint condition l constraint condition:

[0055]

[0056] Use the constraint condition of the final Lagrange multiplier τ l to update τ l and assign different weights to τ according to the magnitude of each l :

[0057]

[0058] Optionally, in an embodiment of the present invention, the iteration termination condition is:

[0059] the gradient of the phase factor is 0; or

[0060] the peaks of subcarriers in adjacent preset numbers of iterations are equal.

[0061] An embodiment of the second aspect of the present invention provides an electronic device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor executes the program to perform the low-complexity peak-to-average ratio suppression method for multi-carrier modulation signals based on ADMM as described in the above embodiments.

[0062] An embodiment of the third aspect of the present invention provides a computer-readable storage medium, on which a computer program is stored, and the program is executed by a processor to perform the low-complexity peak-to-average ratio suppression method for multi-carrier modulation signals based on ADMM as described in the above embodiments.

[0063] The method for suppressing the peak-to-average power ratio of a low-complexity multi-carrier modulation signal based on ADMM, electronic device, and storage medium according to the embodiments of the present invention have the following beneficial effects:

[0064] 1) The method of introducing phase shift is adopted to optimize the peak-to-average power ratio of multi-carrier modulation. Introducing phase shift does not increase the average power of the system. It can directly optimize the target peak-to-average power ratio by optimizing the target peak value, and introducing phase shift, i.e., selective mapping (SLM), does not sacrifice the sub-carriers of the original data compared with methods such as tone reservation (TR);

[0065] 2) The algorithm proposed based on the alternating direction method of multipliers can ensure convergence to a great extent. At the same time, FFT is introduced during gradient descent, with a fast convergence speed and low time complexity, and the overall running speed of the algorithm is faster than that of other algorithms;

[0066] 3) The proposed method has a good final optimization effect and can achieve the optimization effect at the level of the most advanced software in the current relevant foreign fields such as WinIQSIM2 TM level.

[0067] The additional aspects and advantages of the present invention will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the present invention. Description of the Drawings

[0068] The above-mentioned and / or additional aspects and advantages of the present invention will become obvious and easy to understand from the following description of the embodiments in conjunction with the drawings, where:

[0069] Figure 1 is a flowchart of a method for suppressing the peak-to-average power ratio of a low-complexity multi-carrier modulation signal based on ADMM according to an embodiment of the present invention;

[0070] Figure 2 is a schematic diagram of the effect of suppressing the peak-to-average power ratio of a multi-carrier modulation signal according to an embodiment of the present invention;

[0071] Figure 3 is a schematic diagram of the execution process of a method for suppressing the peak-to-average power ratio of a low-complexity multi-carrier modulation signal based on ADMM according to an embodiment of the present invention;

[0072] Figure 4 is a comparison diagram of the peak-to-average power ratio of multi-carrier modulation before and after optimization when the number of sub-carriers is 2000 according to an embodiment of the present invention;

[0073] Figure 5 is a comparison diagram of the peak-to-average power ratio of multi-carrier modulation before and after optimization when the number of sub-carriers is 5000 according to an embodiment of the present invention;

[0074] Figure 6It is a comparison chart before and after the peak-to-average power ratio (PAPR) optimization of multi-carrier modulation when the number of sub-carriers is 10,000 according to an embodiment of the present invention;

[0075] Figure 7 It is a schematic structural diagram of an electronic device provided by an embodiment of the invention. Detailed implementation manners

[0076] The embodiments of the present invention will be described in detail below. The examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements with the same or similar functions from beginning to end. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0077] The method for suppressing the peak-to-average power ratio of low-complexity multi-carrier modulation signals based on ADMM, an electronic device, and a storage medium according to an embodiment of the present invention will be described below with reference to the accompanying drawings. Regarding the problem mentioned in the above background technology that when the phases of each sub-carrier are the same or similar, the superimposed signal will be modulated by the signals with the same initial phase, resulting in a large instantaneous power peak, causing nonlinear distortion of the signal, obvious spectral spreading interference, and in-band signal distortion, leading to a serious decline in the performance of the entire system. And the existing peak-to-average power ratio optimization often does not directly optimize the peak-to-average power ratio, but takes it as a constraint condition to optimize the signal distortion caused by the peak-to-average power ratio optimization and has a too high time complexity. The present invention provides a method for suppressing the peak-to-average power ratio of low-complexity multi-carrier modulation signals based on ADMM. In this method, the target peak-to-average power ratio is directly optimized by introducing phase shifts to each sub-carrier in the signal transmission frequency domain of the multi-carrier modulation system, and the cross-direction multiplier method is used to solve this optimization problem. Thus, the problem that the existing peak-to-average power ratio optimization often does not directly optimize the peak-to-average power ratio, but takes it as a constraint condition to optimize the signal distortion caused by the peak-to-average power ratio optimization and has a too high time complexity is solved.

[0078] Specifically, Figure 1 It is a flowchart of a method for suppressing the peak-to-average power ratio of low-complexity multi-carrier modulation signals based on ADMM according to an embodiment of the present invention.

[0079] As Figure 1 shown, the method for suppressing the peak-to-average power ratio of low-complexity multi-carrier modulation signals based on ADMM includes the following steps:

[0080] In step S101, initial phases are respectively added to multiple sub-carriers in the signal transmission frequency domain of the multi-carrier modulation system, and the multiple sub-carriers after adding the initial phases are synthesized to obtain a time-domain waveform.

[0081] If N sampling points are uniformly taken between 0 and MHz in the frequency domain, the spectral lines of OFDM are respectively: The waveform y(t) in the time domain after synthesis can be obtained from these spectral lines. An initial phase θ is added to each waveform i , i = 1, ..., N, to obtain the optimized time-domain waveform y(t).

[0082] The initial multi-carrier time-domain waveform without optimization is as follows:

[0083]

[0084] Optimizing the peak-to-average power ratio (PAPR) of the final time-domain waveform by introducing the method of phase shift does not bring additional power. Therefore, the essence of this PAPR optimization problem is to optimize the peak value of the final synthesized waveform. By adding an initial phase θ to each waveform i , i = 1, ..., N to optimize the PAPR, the finally synthesized time-domain waveform is as follows:

[0085]

[0086] In step S102, oversampling is performed on the time-domain waveform. Multiple added initial phases are used to form a phase factor, and a mathematical model is established according to the phase factor to obtain the problem to be optimized.

[0087] The oversampling factor is selected as O, that is, O-fold oversampling. Therefore, the sampling rate f s = OM, and the sampling period Let t = nT s The time-domain points after sampling are:

[0088]

[0089] where n = 1, ..., L. Considering that sampling one period of the waveform with the largest period can obtain the sampling points of at least one period of all waveforms, sampling one period of the waveform with the smallest frequency, that is of the waveform, so the number of sampling points is So far, the problem is transformed into optimizing the PAPR of y(n). The common term ejθ i is taken out:

[0090]

[0091] And L row vectors are constructed where l = 1, ..., L, and let Then obviously the optimization problem is:

[0092]

[0093] That is, optimizing the maximum peak value, where and satisfy:

[0094]

[0095] The optimization problem can be further written in the following form:

[0096]

[0097] In step S103, obtain the Lagrangian function of the optimization problem to be optimized, which consists of an optimization objective, a phase factor, and a Lagrange multiplier. Using the alternating direction method of multipliers (ADMM), fix the phase factor and the Lagrange multiplier, optimize the optimization objective, and update the Lagrangian function using the optimized optimization objective.

[0098] The ADMM algorithm (alternating direction method of multipliers) provides a framework for solving optimization problems with linear equality constraints, facilitating the decomposition of the original optimization problem into several relatively easy-to-solve sub-optimization problems for iterative solution. This "decomposition" function is the core essence of the ADMM algorithm. The essence of the ADMM algorithm is to update only one variable at each step while fixing the other two variables, and repeat this alternating update until convergence. This algorithm has been proven to have a very low time complexity and can guarantee convergence to a certain extent.

[0099] First, write out the Lagrangian function of this optimization problem where is the Lagrange multiplier. First, fix and to turn it into a function only about t, and use the point that makes the smallest to update t.

[0100] Optionally, in an embodiment of the present invention, obtain the Lagrangian function of the optimization problem to be optimized:

[0101]

[0102] where is the Lagrange multiplier, is the phase factor, and t is the optimization objective;

[0103] Let the partial derivative of the Lagrangian function be equal to 0 to obtain the constraint condition of the Lagrange multiplier :

[0104]

[0105] This is the constraint condition regarding and cannot obtain the updated t k+1 . It is observed that when and are fixed, the original optimization problem then becomes: The result of this problem can be obtained through search, and the objective function is the updated t k+1 .

[0106] Fixed phase factor and Lagrange multiplier Transform the Lagrangian function into a function only about the optimization objective t k of, and use the point that makes the Lagrangian function the smallest to update the optimization objective t k+1 .

[0107] In step S104, fix the optimized optimization objective and Lagrange multiplier, calculate the gradient of the phase factor in the Lagrangian function using the fast Fourier transform, search for the optimal step size, and then optimize the phase factor using the gradient descent method. Update the Lagrangian function using the optimized phase factor.

[0108] The Lagrangian function updated using the optimized optimization objective is:[[]]

[0109]

[0110] Note that taking the derivative of complex numbers is relatively complicated. Take the derivative directly with respect to the initial phase angle θ n of each subcarrier, and let the vector At this time, the Lagrangian function is:[[]]

[0111]

[0112] After that, let the partial derivative of this Lagrangian function with respect to θ n be equal to 0:[[]]

[0113]

[0114] Note that the two terms inside the brackets are conjugate to each other. Further simplify it. Let the inside of the brackets be equal to F(n, l), then we have:[[]]

[0115]

[0116] where The following simplified formula is obtained:[[]]

[0117]

[0118] It is observed that the time complexity of the above formula is too high, and the time complexity of calculating the gradient is O(N*N*L), that is, O(N 3 ). Make it into the following FFT form to obtain a faster speed:[[]]

[0119]

[0120] where It can be regarded as performing an FFT of length ON on , that is:

[0121]

[0122] Let For the convenience of performing convolution operations, first reverse and fold the sequence g of length ON: g1 = filp(g), where the flip function means folding the sequence along the center; then construct a new sequence of length 2N through g1:

[0123] g new = [g1((O - 1)*N + 1:O*N) g1(1:N - 1)]

[0124] Then the expression inside the square brackets in the above gradient formula result can be written as:

[0125]

[0126] where represents the convolution operation, S(n) = conv(g_new, f, `valid'), and the conv function means only returning the convolution part of the calculation without zero-padding the edges. The time complexity of calculating the gradient once is O(NlogN), which is greatly reduced compared to before. After obtaining the partial derivative of the Lagrangian function with respect to θ n , the gradient of L at this point is obtained:

[0127]

[0128] After that, the gradient descent method is used to update :

[0129]

[0130] where a is the best step size found by the search. It is observed that the gradient formula contains this factor. Combining the constraint on in step three, it is found that only when the inequality constraint in the original problem is active (the inequality holds with equality) will it affect the gradient, which is consistent with the macroscopic understanding, that is, optimizing the points where the peak value can exactly reach t k+1 . However, it should be noted that when choosing the step size in actual optimization, it is necessary to avoid the original inactive (the inequality does not hold with equality) points, that is, the points where the original peak value is less than t k+1 but the peak value after optimization exceeds t k+1 .

[0131] In step S105, the Lagrange multiplier is updated according to the optimization objective, the optimized phase factor, and the constraint conditions of the Lagrange multiplier. By performing multiple iterative updates on the optimization objective, the phase factor, and the Lagrange multiplier in the Lagrange function of the problem to be optimized until the iteration termination condition is satisfied, the optimal phase factor is output, and the peak-to-average power ratio of multiple subcarriers in the signal transmission frequency domain of the multi-carrier modulation system is optimized using the optimal phase factor.

[0132] Optionally, in an embodiment of the present invention, the iteration termination condition is:

[0133] The gradient of the phase factor is 0; or

[0134] The peak values of subcarriers in adjacent preset numbers of iterations are equal.

[0135] Regarding the previously obtained constraint conditions According to the complementary slackness, when the inequality constraint in the optimization problem constraint condition takes the less-than sign, that is, at this time, the Lagrange multiplier τ l = 0; when the inequality constraint takes the equal sign, that is, at this time, the Lagrange multiplier τ l > 0. Therefore, through the constraint condition the final constraint condition of the Lagrange multiplier τ l can be obtained:

[0136]

[0137] Use the above formula to update τ l and assign different weights to τ according to the magnitude of each l . The specific process is as follows:

[0138]

[0139]

[0140] Thus, one iteration is completed. Repeat steps S103 - S105 until convergence to obtain the final phase factor and then obtain the finally optimized time-domain waveform y(n).

[0141] Through the above introduction, the alternating direction method of multipliers (ADMM) method used in the present invention is: for k = 1, 2, 3,... repeat the following steps until convergence:

[0142] 1. First, fix and and turn it into a function only about t k and update t with the point that makes the smallest.k+1 ;

[0143] 2. Fix and the updated t k+1 , turning it into a function only about , and updating with the point that minimizes

[0144] 3. Update k+1 and to update

[0145] The low - complexity peak - to - average power ratio (PAPR) reduction method for multi - carrier modulation signals based on ADMM of the present invention will be described in detail through a specific embodiment below.

[0146] As Figure 2 shown in the multi - carrier modulation system, there are N sub - carriers in the frequency domain, the highest carrier frequency is M Hz, and the carrier spacing is Before optimization, the peak of the final synthesized waveform in the time domain is very high and the PAPR is very large; after introducing phase shift optimization, the peak of the waveform in the time domain is low and the PAPR is reduced. By using the PAPR reduction algorithm for multi - carrier modulation signals proposed in the present invention, the optimal phase multiplier can be obtained according to multi - carrier modulation systems with different parameters, and finally the target PAPR optimization can be achieved. As Figure 3 shown, the specific steps are as follows:

[0147] Step 1, the multi - carrier modulation system has N sub - carriers, the highest frequency M, the oversampling factor O is set to 4, the sampling frequency f s = 4M, the sampling period The amplitudes of the sub - carriers are all 1, the number of sampling points L = 4N, and the original data waveform before optimization after sampling is:

[0148]

[0149] Step 2, let the constant Ea = 0.5, where Ea represents a relatively small constant value. To avoid subsequent optimization, the initial value of the phase factor is given the Neumann phase, that is, the initial phase given to the i - th sub - carrier is θ i = (i * i * π / N), the initial value of tausize is set to 0, the initial value of the gradient descent step size a is set to 0.0001, and the initial value of the phase factor the Lagrange multiplier τ l is assigned an initial value through the following formula:

[0150]

[0151]

[0152] Step 3: Start iterative solution, that is, use the Alternating Direction Method of Multipliers (ADMM) for solution. First, solve the gradient of the phase factor in this iteration through the following formula:

[0153]

[0154] where \(S(n)=\text{conv}(g_{new}, f, 'valid')\), and the conv function represents returning only the convolution part of the calculation without zero-padding the edges. Among them, \(g_{new}=[g1(3*N + 1:4*N) g1(1:N - 1)]\). Let That is, perform an FFT of \(4N\) points on the sequence Then \(g1 = \text{filp}(g)\), and the flip function represents folding the sequence along the center; finally, \(g_{new}\) is obtained. In \(S(n)\), This step is essentially to first perform an FFT and then fold the obtained sequence, and perform a convolution operation without zero-padding the edges after folding. After finding the partial derivative of the Lagrangian function with respect to \(\theta\) n the gradient of \(L\) at this point is obtained:

[0155]

[0156] Step 4: Search for the optimal step size \(a\) through the following iterative algorithm:

[0157] Before all iterations, set the flag label2 to be inactive. In each iteration, update according to for to obtain a new phase factor through the gradient descent method. The optimized time-domain waveform can be obtained through the phase factor. In each iteration, set the flag label1 to be inactive. If the optimized time-domain peak value in this iteration is greater than the optimized time-domain peak value in the previous iteration, then activate label1. If label1 is already activated, continue to judge. If label2 is not activated, then halve the step size and continue the next iteration; if label2 is already activated, then divide the step size by 1.05, and take the phase factor as the previous result, jump out of all iterations, and obtain the final step size and phase factor. If label1 is not activated, then set the inactive set and the active set, which represent satisfying the inequality with the less-than sign (\(\tau\) l = 0) and the inequality with the equal sign (\(\tau\) lA total of L time-domain data sets greater than 0). If the peak value of the inactive set is greater than the peak value of the active set at this time, the step size is divided by 2. If label2 has been activated, the iteration is terminated, and the current value is taken as the final step size and phase factor. Otherwise, the next iteration continues; if the peak value of the inactive set is less than the peak value of the active set at this time, the step size is increased to 1.05 times, and label2 is activated at the same time; if the peak value of the inactive set is equal to the peak value of the active set at this time, the iteration is terminated, and the current value is taken as the final step size and phase factor.

[0158] The algorithm mainly considers the following situations: If the optimized result is not as good as the previous optimization, it means that the step size is too large, and the step size needs to be appropriately reduced at this time; if the result decreases after optimization, but the data in the inactive set comes up and exceeds the original active set to become the new active set, it means that the step size is too large and needs to be appropriately reduced; if the data in the inactive set does not come up, it means that the optimization effect at this time is better than the previous optimization effect, and the step size can be further increased to observe whether the optimization effect can be further improved. Through the above algorithm, the optimal step size a of the gradient descent method is finally searched, and the optimal phase factor in this iteration is obtained.

[0159] Step 5, through the obtained phase factor Update t and

[0160]

[0161]

[0162]

[0163] And it is judged whether the optimized peak value in this iteration is lower than the peak value of the previous optimization. If so, the parameters and peak values are stored, and the iterations in steps 3 - 5 are repeated until the gradient drops to 0 or the peak values stored in several adjacent times are equal, then the iteration is terminated and the final result is obtained. The finally optimized waveform y(n) is obtained by the following formula:

[0164]

[0165] Figure 4The time-domain waveform comparison before and after the optimization of the low-complexity peak-to-average power ratio (PAPR) suppression algorithm for multi-carrier modulation signals based on the alternating direction method of multipliers (ADMM) proposed in the present invention is compared under the conditions that the number of sub-carriers is 2000, the highest frequency is 1 MHz (the increase in bandwidth does not affect the optimal solution of the algorithm of the present invention), and the modulus values of the sub-carriers are all 1. Since introducing phase shift does not add new power, reducing the PAPR of the multi-carrier modulation system is to reduce the waveform in the time domain. It can be seen from the figure that the peak value in the time domain is reduced from 2000 to 49.5877, and the PAPR of the system is optimized by 32.06 dB, fully reaching the level of foreign software WinIQSIM2 TM . At the same time, the optimization time is shorter than that of WinIQSIM2 TM , only 18.75 s is needed.

[0166] Figure 5 The time-domain waveform comparison before and after the optimization of the low-complexity peak-to-average power ratio (PAPR) suppression algorithm for multi-carrier modulation signals based on the alternating direction method of multipliers (ADMM) proposed in the present invention is compared under the conditions that the number of sub-carriers is 5000, the highest frequency is 1 MHz, and the modulus values of the sub-carriers are all 1. It can be seen from the figure that the peak value in the time domain is reduced from 5000 to 79.117, and the PAPR of the system is optimized by 36.01 dB. At the same time, the time used is short, only 100.59 s is needed.

[0167] Figure 6 The time-domain waveform comparison before and after the optimization of the low-complexity peak-to-average power ratio (PAPR) suppression algorithm for multi-carrier modulation signals based on the alternating direction method of multipliers (ADMM) proposed in the present invention is compared under the conditions that the number of sub-carriers is 10000, the highest frequency is 1 MHz, and the modulus values of the sub-carriers are all 1. It can be seen from the figure that the peak value in the time domain is reduced from 10000 to 113.0826, and the PAPR of the system is optimized by 38.93 dB. At the same time, the time used is short, only 2072.01 s is needed. Figures 4-6 It can be seen that the algorithm proposed in the present invention has the bearing capacity for a certain large number of sub-carriers. When the number of sub-carriers increases, the optimization effect is better, and the optimization time used is shorter than that of foreign software WinIQSIM2 TM . The algorithm optimization speed is faster.

[0168] According to the low-complexity peak-to-average power ratio (PAPR) suppression method for multi-carrier modulation signals based on ADMM proposed in the embodiment of the present invention, the target PAPR is directly optimized by introducing phase shifts to each sub-carrier in the signal transmission frequency domain of the multi-carrier modulation system, and this optimization problem is solved by the alternating direction method of multipliers. This algorithm can ensure a certain convergence, and finally has a good optimization effect, and the computational complexity of the algorithm is low and the time used is less compared with foreign software, and the solution speed is faster.

[0169] Figure 7Schematic diagram of the structure of the electronic device provided by the embodiment of the present invention. The electronic device may include:

[0170] A memory 701, a processor 702, and a computer program stored on the memory 701 and executable on the processor 702.

[0171] When the processor 702 executes the program, it implements the low-complexity peak-to-average ratio suppression method for multi-carrier modulation signals based on ADMM provided in the above embodiment.

[0172] Furthermore, the electronic device further includes:

[0173] A communication interface 703 for communication between the memory 701 and the processor 702.

[0174] The memory 701 is used to store a computer program executable on the processor 702.

[0175] The memory 701 may include a high-speed RAM memory, and may also include a non-volatile memory, such as at least one disk memory.

[0176] If the memory 701, the processor 702, and the communication interface 703 are implemented independently, the communication interface 703, the memory 701, and the processor 702 may be interconnected through a bus and communicate with each other. The bus may be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. The bus may be divided into an address bus, a data bus, a control bus, etc. For the sake of simplicity of representation, Figure 7 only a thick line is used to represent it in the figure, but it does not mean that there is only one bus or one type of bus.

[0177] Optionally, in a specific implementation, if the memory 701, the processor 702, and the communication interface 703 are integrated on a chip, the memory 701, the processor 702, and the communication interface 703 may communicate with each other through an internal interface.

[0178] The processor 702 may be a Central Processing Unit (CPU), or an Application Specific Integrated Circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present invention.

[0179] This embodiment also provides a computer-readable storage medium, on which a computer program is stored, and the program, when executed by a processor, implements the above-described method for suppressing the peak-to-average power ratio of a low-complexity multi-carrier modulation signal based on ADMM.

[0180] In the description of this specification, the descriptions with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc., mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any one or N embodiments or examples in a suitable manner. In addition, without contradiction, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples.

[0181] In addition, the terms "first" and "second" are used for descriptive purposes only and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "N" is at least two, such as two, three, etc., unless otherwise specifically defined.

[0182] Any process or method description in the flowchart or described in other ways herein may be understood to represent a module, segment, or portion of code including one or more executable instructions for implementing a customized logic function or process, and the scope of the preferred embodiments of the present invention includes additional implementations, where the functions may be executed in a substantially simultaneous manner or in a reverse order according to the involved functions, rather than in the order shown or discussed, which should be understood by those skilled in the art to which the embodiments of the present invention belong.

[0183] It should be understood that each part of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above embodiments, the N steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, any one of the following techniques known in the art or a combination thereof can be used: discrete logic circuits having logic gate circuits for implementing logical functions on data signals, application specific integrated circuits having suitable combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.

[0184] Those of ordinary skill in the art can understand that all or part of the steps carried by the method of the above embodiments can be completed by instructing relevant hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiments.

Claims

1. A low-complexity peak-to-average power ratio (PAPR) reduction method for multi-carrier modulation signals based on ADMM, characterized in that, It includes the following steps: Add initial phases to multiple subcarriers in the signal transmission frequency domain of a multi-carrier modulation system respectively, and synthesize the multiple subcarriers with the added initial phases to obtain a time-domain waveform; Oversample the time-domain waveform, use the added multiple initial phases to form a phase factor, and perform mathematical modeling according to the phase factor to obtain a problem to be optimized; Obtain the Lagrangian function of the problem to be optimized composed of an optimization objective, the phase factor and a Lagrange multiplier, use the alternating direction method of multipliers, fix the phase factor and the Lagrange multiplier, optimize the optimization objective, and update the Lagrangian function with the optimized optimization objective; Fix the optimized optimization objective and the Lagrange multiplier, use the fast Fourier transform to calculate the gradient of the phase factor in the Lagrangian function, search for the optimal step size, and then use the gradient descent method to optimize the phase factor, and update the Lagrangian function with the optimized phase factor; Update the Lagrange multiplier according to the optimization objective, the optimized phase factor and the constraint conditions of the Lagrange multiplier. Through multiple iterative updates of the optimization objective, the phase factor and the Lagrange multiplier in the Lagrangian function of the problem to be optimized, until the iteration termination condition is satisfied, output the optimal phase factor, and use the optimal phase factor to optimize the peak-to-average power ratio of the multiple subcarriers in the signal transmission frequency domain of the multi-carrier modulation system; The time-domain waveform is: where θ i , i = 1, ..., N is the added initial phase, α i is the amplitude of the i-th subcarrier, N is the number of sampling points, and M is the frequency value; Oversampling the time-domain waveform includes: Select the oversampling factor O and the sampling rate f s = OM, sampling period Let t = nT s , and the time-domain waveform after sampling is as follows: where n = 1,..., L, and L is the number of oversampling points; Using the added multiple initial phases to form a phase factor, and performing mathematical modeling according to the phase factor to obtain a problem to be optimized, including: Extract the common terms in the time-domain waveform after sampling Form the phase factor And construct L row vectors where l = 1,... L; Constructing the problem to be optimized according to the phase factor and the row vector: That is, optimize the maximum peak value, where and Satisfy: The problem to be optimized is transformed into:

2. The method according to claim 1, wherein Obtaining the Lagrangian function of the problem to be optimized composed of an optimization objective, the phase factor and a Lagrange multiplier, fixing the phase factor and the Lagrange multiplier, optimizing the optimization objective, and updating the Lagrangian function with the optimized optimization objective, including: Obtaining the Lagrangian function of the problem to be optimized: wherein, is the Lagrange multiplier, is the phase factor, and t is the optimization objective; Setting the partial derivatives of the Lagrangian function equal to 0 gives the Lagrange multipliers The constraint conditions of: Fix the phase factor and the Lagrange multiplier Transform the Lagrange function into a function only about the optimization objective t k such that the Lagrange function The smallest point to update and optimize the target t k+1 .

3. The method according to claim 2, wherein Fix the optimized optimization objective and the Lagrange multiplier, use the fast Fourier transform to find the gradient of the phase factor in the Lagrangian function, search for the optimal step size, and then use the gradient descent method to optimize the optimization objective, and update the Lagrangian function with the optimized phase factor, including: The Lagrangian function updated with the optimized optimization objective is: The initial phase angle θ of each subcarrier n Derive, and let the vector The Lagrangian function is as follows: Set the partial derivative of the Lagrangian function with respect to θ n equal to 0: Let the content inside the square brackets be equal to F(n, l): Among them, obtain: Performing a fast Fourier transform to obtain: Among them, To perform an FFT of length ON on That is: Find the partial derivative of the Lagrangian function with respect to θ n After that, the gradient of L at this point is obtained: Update using the gradient descent method: where a is the optimal step size searched.

4. The method according to claim 3, characterized in that Updating the Lagrange multiplier according to the optimization objective, the optimized phase factor and the preset constraint conditions, including: The problem to be optimized When the inequality constraint in the constraint conditions takes the less-than sign, that is At this time, the Lagrange multiplier τ l = 0; when the inequality constraint takes the equal sign, that is At this time, the Lagrange multiplier τ l > 0, through the constraint conditions The final constraint condition for the Lagrange multiplier τ l is as follows: Using the constraint condition of the final Lagrange multiplier τ l to update τ l and assign different weights to τ according to the magnitude of each l :

5. The method according to any one of claims 4, characterized in that The iteration termination condition is: The gradient of the phase factor is 0; or The peaks of subcarriers at adjacent preset numbers are equal in multiple iterations.

6. An electronic device, characterized in that, It includes: A memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the ADMM-based low-complexity peak-to-average power ratio (PAPR) reduction method for multi-carrier modulation signals according to any one of claims 1-5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the ADMM-based low-complexity peak-to-average power ratio (PAPR) reduction method for multi-carrier modulation signals according to any one of claims 1-5.

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