A method, medium and device for reducing peak-to-average ratio of an orthogonal frequency division multiplexing system

Abstract

Embodiments of the present disclosure relate to a method, medium and device for reducing a peak-to-average ratio of an orthogonal frequency division multiplexing system. The method comprises: receiving original data of a signal to be transmitted; generating a first carrier signal of the orthogonal frequency division multiplexing system according to the original data; generating a plurality of mutually independent second carrier signals through a generative adversarial network according to the first carrier signal; calculating peak-to-average ratios of the plurality of mutually independent second carrier signals, and selecting a second carrier signal with the smallest peak-to-average ratio for transmission; wherein the first carrier signal and the second carrier signal both carry information of the original data. The present disclosure generates a plurality of carrier signals with the same information through a generative adversarial network for calculation and comparison of peak-to-average ratios, selects a second carrier signal with the smallest peak-to-average ratio for transmission, and thus reduces the peak-to-average ratio. Since point multiplication of a frequency domain signal and a phase rotation factor and large-scale inverse fast Fourier transform operations are not required, the computational complexity is greatly reduced.

Description

Technical Field

[0001] This disclosure relates to the field of information and communication technology, and in particular to a method, medium, and device for reducing the peak-to-average power ratio (PAPR) of an orthogonal frequency division multiplexing (OFDM) system. Background Technology

[0002] To expand the breadth and depth of communication coverage and achieve highly reliable, low-latency global wireless communication, the future sixth-generation (6G) mobile system will integrate terrestrial and satellite communications to build an integrated air-space-ground-sea network, achieving seamless global coverage. Orthogonal frequency division multiplexing (OFDM) technology has advantages such as high spectral efficiency and resistance to multipath propagation, making it very suitable for integrated air interface designs. However, a high peak-to-average power ratio (PAPR) is a major drawback of OFDM. Excessive PAPR can lead to nonlinear distortion in high-power amplifiers and cause OFDM signals to face a high bit error rate after passing through nonlinear power amplifiers. Therefore, PAPR suppression algorithms for OFDM systems have always been a research hotspot. In 6G communication scenarios, PAPR suppression becomes even more important. On the one hand, with the introduction of terahertz technology, 6G will use more subcarriers for data transmission, further increasing the system PAPR. On the other hand, in space-to-ground communication, the high peak power places higher demands on the onboard power amplifier, which can lead to interference within and between adjacent frequency bands. Direct use of such amplifiers would reduce their efficiency and cause heat dissipation problems. Therefore, reducing the signal PAPR is an important issue in future research on integrated space-to-ground networks.

[0003] In related technologies, scholars both domestically and internationally have done extensive work on reducing PAPR in OFDM systems. These solutions can be categorized into two types: those using traditional methods and those incorporating deep learning. Traditional algorithms can be further divided into three main types based on their characteristics: pre-distortion algorithms, coding algorithms, and probabilistic algorithms. In recent years, deep learning has demonstrated superior performance in many fields, and PAPR suppression algorithms incorporating deep learning are considered a potential technology in 6G. Specifically, some methods use deep learning to adaptively determine the constellation mapping and demapping of symbols on each subcarrier, thereby simultaneously reducing the bit error rate and PAPR of the OFDM system. Others have proposed a model-driven tone reservation (TR) subcarrier algorithm, which, compared to the traditional TR scheme, reduces computational complexity and training costs while maintaining the same PAPR performance. However, the above methods are based on using Fast Fourier Transform (FFT) in OFDM systems to reduce PAPR. Research shows that using Discrete Wavelet Transform instead of the Fast Fourier Transform in traditional OFDM can also reduce the system's peak-to-average power ratio (PAPR).

[0004] In related technologies, a novel wavelet-based OFDM peak-to-average power ratio (PAPR) reduction technique has been proposed, which uses discrete wavelet transform instead of the fast Fourier transform in traditional OFDM. This technique is further combined with companding transform to achieve a further reduction in PAPR. Results show that wavelet-based OFDM can be integrated with other PAPR reduction techniques to further improve performance. A high-bandwidth-efficiency filtered-orthogonal wavelet division multiplexing (F-OWDM) system has also been proposed, and the PAPR and bit error rate of the F-OWDM system under additive white Gaussian noise and flat fading channels using different wavelets have been investigated. Results show that F-OWDM has a lower PAPR and lower bit error rate than traditional F-OFDM. Furthermore, to address the PAPR problem in OFDM systems, a wavelet-based OFDM system and partial transmission sequence techniques are used to reduce PAPR, and the bit error rate performance of the system with different modulation schemes is compared.

[0005] The aforementioned technical solutions still suffer from a high peak-to-average power ratio (PAPR) for orthogonal frequency division multiplexing (OFDM) systems, and also involve high computational complexity. They still cannot meet the low PAPR requirements of future 6G communication systems.

[0006] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.

[0007] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0008] The purpose of this disclosure is to provide a method, medium, and device for reducing the peak-to-average power ratio (PAPR) of an orthogonal frequency division multiplexing (OFDM) system, thereby solving at least one or more problems existing in the above-mentioned related technical solutions.

[0009] The objective of this invention is achieved through the following technical solution:

[0010] In a first aspect, the present invention provides a method for reducing the peak-to-average power ratio (PAPR) of an orthogonal frequency division multiplexing (OFDM) system, comprising:

[0011] Receive the raw data of the signal to be transmitted;

[0012] The first carrier signal of the orthogonal frequency division multiplexing system is generated based on the original data;

[0013] Based on the first carrier signal, a generative adversarial network generates multiple independent second carrier signals;

[0014] Calculate the peak-to-average power ratio (PAPR) of the plurality of independent second carrier signals, and select the second carrier signal with the smallest PAPR for transmission;

[0015] The original data is carried in both the first carrier signal and the second carrier signal.

[0016] Optionally, the step of generating the first carrier signal of the orthogonal frequency division multiplexing system based on the original data includes:

[0017] The first carrier signal is generated by using wavelet basis functions for frequency domain orthogonal multiplexing and then using time domain integer orthogonal time-shift multiplexing.

[0018] Optionally, the step of generating multiple independent second carrier signals based on the first carrier signal using a generative adversarial network includes:

[0019] Multiple third carrier signals are generated in the generative adversarial network based on the first carrier signal;

[0020] The third carrier signal is compared with the first carrier signal to determine whether it is true or false, and the third carrier signal that is determined to be true is taken as the second carrier signal.

[0021] Optionally, the step of generating multiple independent second carrier signals based on the first carrier signal using a generative adversarial network includes:

[0022] The process of generating and determining the third carrier signal is trained using a convolutional neural network.

[0023] Optionally, the step of training the process of generating and determining the third carrier signal using a convolutional neural network includes:

[0024] The third carrier signal and the first carrier signal are input into a convolutional neural network and a probability value is output. The probability value is normalized by a sigmoid activation function, and the third carrier signal with a value greater than 0.5 is judged as true.

[0025] Optionally, the step of training the process of generating and determining the third carrier signal using a convolutional neural network includes:

[0026] After training the decision-making process a preset number of times, the root mean square propagation algorithm is used as the optimization rule to train the generation process once.

[0027] Optionally, the step of generating multiple third carrier signals in the generative adversarial network based on the first carrier signal includes:

[0028] The sample distribution distance is used as a training condition for the generative adversarial network, and the loss function model is determined.

[0029] Optionally, the step of calculating the peak-to-average power ratio (PAPR) of the plurality of independent second carrier signals and selecting the second carrier signal with the smallest PAPR for transmission includes:

[0030] Formula for calculating peak-to-average power ratio (PAPR):

[0031]

[0032] Among them, PAPR dB is the peak-to-average power ratio; 10lgNdB is the theoretical peak-to-average power ratio with N subcarriers; s(t) is the symbol for the second carrier signal; E(|s(t)| 2 To find the expected value of the function; max|s(t)| 2 The function is for finding the maximum value.

[0033] In a second aspect, the present invention provides a computer-readable storage medium, comprising:

[0034] When executed by the processor, the program implements the steps of the method for reducing the peak-to-average power ratio of an orthogonal frequency division multiplexing system as described in any of the above embodiments.

[0035] Thirdly, the present invention provides an electronic device, comprising:

[0036] Processor; and

[0037] Memory for storing the executable instructions of the processor;

[0038] The processor is configured to perform the steps of the method for reducing the peak-to-average power ratio of an orthogonal frequency division multiplexing system described in any of the above embodiments by executing the executable instructions.

[0039] The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects:

[0040] In the embodiments of this disclosure, on the one hand, multiple carrier signals with the same information are generated by using a generative adversarial network for the calculation and comparison of peak-to-average power ratio (PAPR), and the one with the smallest PAPR is selected for transmission, thereby achieving the purpose of reducing PAPR; on the other hand, since the dot product of frequency domain signal and phase rotation factor and large-scale fast Fourier inverse transform operation are not required, the computational complexity is greatly reduced.

[0041] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0042] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0043] Figure 1 A flowchart illustrating a method for reducing the peak-to-average power ratio (PAPR) of an orthogonal frequency division multiplexing system according to an exemplary embodiment of the present disclosure is shown.

[0044] Figure 2 A schematic diagram showing a comparison of PAPR performance between conventional OFDM and WOFDM in an exemplary embodiment of this disclosure;

[0045] Figure 3 A schematic diagram illustrating the principle of the SLM algorithm in an exemplary embodiment of this disclosure is shown;

[0046] Figure 4 A schematic diagram illustrating the PAPR suppression performance of a WOFDM system employing the SLM algorithm in an exemplary embodiment of this disclosure;

[0047] Figure 5 This diagram illustrates the overall framework of the WGAN-SLM method in an exemplary embodiment of this disclosure.

[0048] Figure 6 This diagram illustrates the structure of the WGAN model in an exemplary embodiment of this disclosure.

[0049] Figure 7 This diagram illustrates the network structure of the generation process in an exemplary embodiment of this disclosure.

[0050] Figure 8 This diagram illustrates the network structure of the determination process in an exemplary embodiment of this disclosure.

[0051] Figure 9 A schematic diagram showing a comparison of PAPR performance (K=16) of different algorithms in an exemplary embodiment of this disclosure;

[0052] Figure 10 A schematic diagram showing the CCDF curves (K takes different values) of SLM and WGAN-SLM in an exemplary embodiment of this disclosure;

[0053] Figure 11 A schematic diagram showing a comparison of PAPR performance (K=16) of different generative adversarial network algorithms in an exemplary embodiment of this disclosure;

[0054] Figure 12 A schematic diagram showing a comparison of the bit error rate performance (K=16) of different algorithms in an exemplary embodiment of this disclosure;

[0055] Figure 13 A schematic diagram showing a comparison of loss functions for different models in exemplary embodiments of this disclosure;

[0056] Figure 14 A schematic diagram of a storage medium according to an exemplary embodiment of the present disclosure is shown;

[0057] Figure 15 This diagram illustrates an electronic device according to an exemplary embodiment of the present disclosure. Detailed Implementation

[0058] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0059] Furthermore, the accompanying drawings are merely illustrative of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0060] This example implementation first provides a method for reducing the peak-to-average power ratio (PAPR) of an orthogonal frequency division multiplexing (OFDM) system. (See reference...) Figure 1 As shown, the steps include:

[0061] Step S100: Receive the raw data of the signal to be transmitted.

[0062] Step S200: Generate the first carrier signal of the orthogonal frequency division multiplexing system based on the original data.

[0063] Step S300: Generate multiple independent second carrier signals based on the first carrier signal using a generative adversarial network.

[0064] Step S400: Calculate the peak-to-average power ratio (PAPR) of multiple independent second carrier signals, and select the second carrier signal with the smallest PAPR for transmission.

[0065] Both the first carrier signal and the second carrier signal carry information about the original data.

[0066] It is important to understand that, in order to meet the low peak-to-average power ratio (PAPR) requirement of future integrated space-ground networks, a method combining the Selective Mapping (SLM) algorithm from probabilistic algorithms with Wavelet OFDM (WOFDM) technology has been proposed to improve PAPR performance. However, this method has limited PAPR reduction and high computational complexity. To address these issues, this disclosure proposes the WGAN-SLM algorithm, which incorporates a Wasserstein generative adversarial network (WGAN), based on the SLM algorithm. The main idea is to use the WGAN network to generate K WOFDM signals with identical information for PAPR calculation and comparison, eliminating the dot product of frequency domain signals and phase rotation factors, as well as the large-scale inverse fast Fourier transform (IFFT) operation, thus significantly reducing computational complexity. A convolutional neural network (CNN) is used as the basic network structure of the WGAN generator, and Wasserstein distance is used as the loss function, making the model more stable during training. Simulation results and computational complexity analysis show that, compared with the traditional SLM algorithm, this algorithm has a much smaller computational load, and at the same time, it can effectively reduce the system PAPR without increasing the system bit error rate.

[0067] It's also important to understand that Generative Adversarial Networks (GANs) borrow ideas from game theory, using adversarial training to ensure that the samples generated by the network conform to the distribution of real samples. Both the first and second carrier signals can be called OFDM signals. The second carrier signal can also be called a WGAN signal.

[0068] It's also important to understand that a wavelet function refers to a function that has a very short duration (tight support) in the time domain and an average value of zero (no DC component). It is generally represented by ψ(t) and defined by the following formula:

[0069]

[0070] The function ψ(t) is called the mother wavelet function. However, not all functions ψ(t) that satisfy the above equation can be used as the mother wavelet function. To ensure the existence of the inverse transform in wavelet transform, a constraint condition needs to be imposed, namely the wavelet admissibility condition. Assuming ψ(t) is the mother wavelet function, its Fourier transform ψ(ω) should satisfy:

[0071]

[0072] As can be seen from the above equation, wavelets possess compact support in the time domain. Generally, any wavelet satisfying the admissibility condition in space L... 2 All functions of (R) can be used as wavelet mother functions; for ω=0, ψ(ω)=0 must be true. If we consider the function ψ(ω) as a filter, then ψ(ω) is a non-low-pass filter and should be a band-pass filter.

[0073] Based on the above analysis, we can see that ψ(t), which can be used as the mother function of the wavelet, should have bandpass properties; and since its mean is zero, it should be reflected as an oscillating and decaying waveform in the image.

[0074] The continuous wavelet function is defined as follows: Taking the wavelet mother function ψ(t) and performing a scaling and translation transformation, let its scaling parameter be a and its translation coefficient be τ, and let its scaled and translated function form be ψ(t). a,τ If (t), then definition (2) can be expressed as follows:

[0075]

[0076] ψ a,τ (t) is a sequence of functions obtained by scaling and translating the same mother wavelet function ψ(t).

[0077] The integer time-shift orthogonality property of wavelets can be expressed as:

[0078] For each n≥0, we have

[0079] <W n (tm),W n (tk)>=δ(km)I r×r ,m,k∈Z (4)

[0080] Figure 2 This is the complementary cumulative distribution function (CCDF) of traditional OFDM and WOFDM. (See reference...) Figure 2 As shown, at CCDF = 1.0 × 10 -4 At that time, the PAPR of the WOFDM system was 8dB, lower than that of the traditional OFDM system. The WOFDM system uses multi-wavelet packet transform instead of FFT / IFFT, retaining most of the advantages of the traditional OFDM system, and has better spectral efficiency and lower PAPR performance. By combining the traditional PAPR suppression algorithm with the WOFDM system, the PAPR can be further reduced to meet the PAPR requirements of future integrated space-ground networks.

[0081] It is also necessary to understand that reference Figure 3 As shown, the basic idea of ​​the SLM algorithm is to reduce the probability of peak signals occurring by increasing the number of transmitted signals, thereby reducing the PAPR of the system.

[0082] At the transmitting end, the unprocessed OFDM frequency domain data X is copied into K identical paths. Then, K random phase sequence vectors P, each of length N, are generated. u =[P u (0),…,P u [(N-1)],(u=1,2,…,K), where and It follows a uniform distribution in the range [0, 2π). Then, a dot product is performed with it to obtain the following equation:

[0083] X k =[X(0)P k (0),…,X(N-1)P k (N-1)] (5)

[0084] Then, perform an IFFT operation on each group of signals to obtain the different output sequence signals x after K rotations. k As shown in the following formula:

[0085] x k =IFFT(X k =IFFT(X⊙P) k ), 1≤k≤K (6)

[0086] Finally, from the K groups of time-domain signals x k Select the signal x with the smallest PAPR value. k As a transmitted signal. (Reference) Figure 4 The CCDF curve of the WOFDM system after processing with the SLM algorithm is shown. The PAPR value of the signal after SLM processing is significantly reduced, but as the number of groups increases, the improvement in PAPR suppression performance becomes less significant, and the computational complexity of the system increases substantially. Based on the principle of the SLM algorithm and combined with generative adversarial network technology, this disclosure proposes a WGAN-SLM peak-to-average ratio suppression algorithm, which reduces the PAPR of the WOFDM system while reducing the computational complexity.

[0087] It is also necessary to understand that reference Figure 5As shown, the algorithm consists of three modules: multi-wavelet packet signal generation, WGAN, and PAPR calculation. The principle of this algorithm is to use a generative adversarial network to generate K independent statistically identical WOFDM signals, and then select the signal with the smallest PAPR for transmission, thereby reducing the system's peak-to-average power ratio (PAPR). The WGAN-SLM algorithm generates candidate signals by optimizing the waveform of the transmitted signal without changing the information carried by the original signal, and the entire process requires only one IFFT module, resulting in low computational complexity.

[0088] According to the above method, on the one hand, multiple carrier signals with the same information are generated by using generative adversarial networks for the calculation and comparison of peak-to-average power ratio (PAPR), and the one with the smallest PAPR is selected for transmission, thereby achieving the purpose of reducing PAPR; on the other hand, since the dot product of frequency domain signal and phase rotation factor and large-scale fast inverse Fourier transform operation are not required, the computational complexity is greatly reduced.

[0089] Below, for reference Figures 1 to 13 The above method in this example embodiment will be described in more detail as shown in the figure.

[0090] refer to Figure 5 As shown, optionally, step S200 includes the following steps:

[0091] Step S210: The first carrier signal is generated by using wavelet basis functions for frequency domain orthogonal multiplexing and then time domain integer orthogonal time-shift multiplexing.

[0092] It's important to understand that OFDM technology essentially modulates information onto orthogonal Fourier bases (subcarriers) at different frequencies, achieving precise frequency domain division. However, it lacks control in the time domain. Consequently, an excessive number of subcarriers leads to an excessively high peak-to-average power ratio (PAPR) in the OFDM signal time domain. WOFDM, in addition to implementing traditional frequency division multiplexing in the frequency domain, utilizes the integer time-shift characteristics of multiple wavelet bases in the time domain to achieve orthogonal multiplexing. This allows for the transmission of the same data rate with fewer subcarriers, mitigating the PAPR problem caused by a large number of subcarriers.

[0093] Traditional OFDM signals based on Fourier basis can be represented as:

[0094]

[0095] Where, d k It is an information symbol, T is the symbol time, N is the number of subcarriers, and the subcarrier frequency is f. k = t / T, k = 0, 1, ... N.

[0096] When wavelet basis functions are used instead of Fourier basis functions, OFDM transmission signals based on frequency domain orthogonal multiplexing can be expressed as:

[0097]

[0098] Where N is the number of subcarriers, p k (t) is a multi-wavelet subfunction. Common wavelet bases include Haar wavelet, Meyer wavelet, and Daubechies wavelet. This disclosure uses the Db2 wavelet with a vanishing moment of 2 as the wavelet base function.

[0099] Based on frequency domain orthogonal multiplexing and equation (8), the WOFDM symbol after further adopting the time domain integer orthogonal time-shift multiplexing scheme can be expressed as:

[0100]

[0101] Here, N is the number of subcarriers, and M is the time-domain support length of the multi-wavelet.

[0102] For an OFDM system with N subcarriers, the theoretical peak-to-average power ratio (PAPR) is 10lgNdB. For WOFDM, if the basis function support length is an integer M, the number of subcarriers can be reduced to N / M. Theoretically, when the frame length is infinite, the PAPR is 10lg(N / M) = 10lgN - 10lgM, which is 10lgMdB lower than that of traditional OFDM.

[0103] refer to Figure 6 As shown, step S300 may optionally include the following steps:

[0104] Step S310: Generate multiple third carrier signals in the generative adversarial network based on the first carrier signal;

[0105] Step S320: Compare the third carrier signal with the first carrier signal to determine whether it is true or false, and use the third carrier signal that is determined to be true as the second carrier signal.

[0106] It's important to understand that by using CNNs as the basic network structure for both generators and discriminators, robust features can be extracted from complex data, enhancing the WGAN model's ability to extract sample features. This makes the probability distribution of generated samples closer to the probability distribution of real samples, thus ensuring the quality of the generated samples. Research shows that deep CNNs generally have better learning capabilities and image feature representation capabilities than shallow CNNs. However, as the number of CNN layers increases, the number of network parameters also grows exponentially. This can lead to gradient explosion or gradient vanishing, causing instability in the training process, difficulty in network convergence, and ultimately, overfitting.

[0107] refer to Figure 7 As shown, step S300 may optionally include the following steps:

[0108] Step S330: Train the process of generating and determining the third carrier signal by using a convolutional neural network.

[0109] It's important to understand that the generator's role is to generate fake data that resembles the original data, making it difficult for the discriminator to distinguish between the original and fake input. Analysis of the data sample distribution reveals that the real data used in this disclosure consists of two-dimensional data points representing signal amplitudes at specific times. Therefore, the generator network does not need to be overly complex; its structure is as follows... Figure 7 As shown, k represents the kernel size, n is the number of filters, and s is the stride. In the generative network, except for the last layer with a 3×3 kernel, all other layers have a 5×5 kernel size and a fixed stride of 1. Batch normalization (BN) layers and ReLU activation functions are added after each convolutional layer to accelerate training convergence. Finally, a tanh function model is used to mitigate the gradient vanishing problem.

[0110] refer to Figure 8 As shown, optionally, step S330 includes the following steps:

[0111] Step S331: Input the third carrier signal and the first carrier signal into the convolutional neural network and output the probability value; normalize the probability value through the sigmoid activation function, and judge the third carrier signal greater than 0.5 as true.

[0112] It's important to understand that the discriminator network primarily handles binary classification. Its input consists of real signals and fake signals generated by the generator network. Since the discriminator needs to understand the feature point distribution of the real signals, its construction is more complex than that of the generator. It contains four one-dimensional convolutional layers with a kernel size of 4×4, a fixed stride of 2, and filters of 64, 128, and 256 respectively. A batch normalization (BN) layer and a LeakyReLU nonlinear activation function are added after each convolutional layer to prevent neurons from malfunctioning when the ReLU function enters the negative range. The output uses a sigmoid activation function to compress the input probability values ​​to the range (0,1). When the probability value is greater than 0.5, it is classified as Real; otherwise, it is classified as Fake.

[0113] refer to Figure 5 As shown, optionally, step S330 includes the following steps:

[0114] Step S332: After training the decision-making process a preset number of times, the root mean square propagation algorithm is used as the optimization rule to train the generation process once.

[0115] It's important to understand that the training method for the WGAN network model in this paper is as follows: the loss is measured using Wasserstein distance, and the optimization algorithm is RMSProp. Using the Adam optimization algorithm would lead to training instability. During training, a nested loop approach is adopted, with the generator trained once after each iteration of the discriminator training. After the weights are updated, numerical pruning is performed to fix the values ​​within a certain range. The specific implementation process of WGAN is shown in the WGAN algorithm.

[0116] WGAN algorithm:

[0117] Initialize the discriminator parameters w0, the generator parameters θ0, and the learning rate α;

[0118] 1) while generator parameters have not converged do

[0119] 2) for t=1,L,n critic

[0120] 3) for i = 1, ..., m

[0121] 4) Sample x ~ P(x) from real data and z ~ P(z) from noisy data to generate a random number ε: uniform[0,1].

[0122] 5) Generate mixed samples

[0123] 6)

[0124] 7)w←w+α·RMSProp(w,g w )

[0125] 8) w←clip(w,-c,c)

[0126] 9)end for

[0127] 10) Sample x ~ P(x) from real data, and sample z ~ P(z) from noisy data.

[0128] 11)

[0129] 12)θ←θ-α·RMSProp(θ,g θ )

[0130] 13) end for

[0131] 14) end while

[0132] The Root Mean Square Propagation (RMSProp) algorithm, based on an exponentially weighted average of gradients, introduces the square and square root, making it suitable for handling non-stationary objectives. RMSProp helps reduce oscillations on the path to the minimum and allows for a larger learning rate, thus accelerating the algorithm's learning speed. The specific implementation process of the RMSProp algorithm is as follows:

[0133] RMSProp algorithm:

[0134] Initialize the cumulative variable r = 0, the global learning rate ε, the decay rate ρ, the initial parameter θ, and the small constant δ.

[0135] 1) while the stopping criterion is not met, do

[0136] 2) Collect m samples {x} from the training set. 1 ,…x m The small batch size corresponds to the target y. i

[0137] 3) Calculate the gradient

[0138] 4) Cumulative squared gradient r←ρr+(1-ρ)ge g

[0139] 5) Calculation parameter update

[0140] 6) Application update θ←θ+Δθ

[0141] 7) end while

[0142] refer to Figure 5 As shown, step S310 may optionally include the following steps:

[0143] Step S311: Use the sample distribution distance as a training condition for the generative adversarial network and determine the loss function model.

[0144] It is important to understand that the original generative adversarial network (GAN) has the objective function shown in equation (10). Where P... d P represents the probability distribution of the real data. g This represents the probability distribution of the generated data.

[0145]

[0146] However, traditional GANs suffer from problems such as training instability, slow convergence, and gradient vanishing. Therefore, this paper proposes using Wasserstein distance as the loss function, which solves the problem of the original GAN's difficulty in convergence during adversarial training. The Wasserstein distance is specifically defined as:

[0147]

[0148] Among them, Π(P d ,P g ) represents P d and P g The set of all joint distributions. inf is the lower bound function.

[0149] By incorporating the Wasserstein distance into the GAN and transforming its form, we obtain:

[0150]

[0151] Where the constant C is greater than or equal to 0. The above equation represents the Lipschitz constant ||f|| in the function D(x). L Given that the condition does not exceed C, for all possible values ​​of D(x) that satisfy the condition... The upper boundary.

[0152] The loss function of WGAN can be obtained as shown in equation (13).

[0153]

[0154] That is, the distance between sample distributions is used as a training condition for the generative adversarial network, and the loss function model is determined.

[0155] Optionally, step S400 includes:

[0156] Formula for calculating peak-to-average power ratio (PAPR):

[0157]

[0158] Among them, PAPR dB is the peak-to-average power ratio; 10lgNdB is the theoretical peak-to-average power ratio with N subcarriers; s(t) is the symbol for the second carrier signal; E(|s(t)| 2 To find the expected value of the function; max|s(t)| 2 The function is for finding the maximum value.

[0159] It's important to understand that for an OFDM system with N subcarriers, the theoretical peak-to-average power ratio (PAPR) is 10lgN dB. For WOFDM, if the basis function support length is an integer M, the number of subcarriers can be reduced to N / M. Theoretically, when the frame length is infinitely long, the PAPR is 10lg(N / M) = 10lgN - 10lgM, which is 10lgM dB lower than that of traditional OFDM.

[0160] In exemplary embodiments of this disclosure, a computer-readable storage medium is also provided, having stored thereon a computer program that, when executed by, for example, a processor, can implement the steps of the method for reducing the peak-to-average power ratio (PAPR) of an orthogonal frequency division multiplexing (OFDM) system described in any of the above embodiments. In some possible embodiments, various aspects of the invention can also be implemented as a program product comprising program code that, when run on a terminal device, causes the terminal device to perform the steps described in the above-described method for reducing the PAPR of an OFDM system according to various exemplary embodiments of the invention.

[0161] Based on the above embodiments, the present invention also provides specific verification methods and experimental results.

[0162] To verify the effectiveness of the proposed algorithm, this disclosure uses the computational complexity reduction ratio (CCRR) to represent the improvement in computational complexity. The mathematical expression for CCRR is:

[0163]

[0164] Where C represents the algorithm complexity.

[0165] Assuming N is the number of subcarriers in the system and K is the number of IFFTs, then for the traditional SLM scheme, performing K IFFTs generates K time-domain candidate signals, requiring a total of NKlog2N complex addition operations. This involves multiple complex multiplication operations. However, for the WGAN-SLM algorithm, once the number of generated time-domain candidate signals exceeds 4, the training time of the WGAN network becomes negligible compared to the required IFFT operation time. Therefore, the WGAN-SLM scheme can be considered to generate candidate time-domain signals with only one IFFT transformation. When the number of subcarriers = 128, the computational complexity and CCRR of these two SLM algorithms are shown in Table 1. It can be seen that compared with the traditional SLM algorithm, the WGAN-SLM algorithm significantly reduces the computational complexity of the system; the larger K is, the greater the reduction.

[0166] Table 1 Comparison of computational complexity between traditional SLM and WGAN-SLM

[0167]

[0168] To verify the feasibility of applying the WGAN-SLM algorithm to a spaceborne multi-wavelet OFDM system, this disclosure presents simulation analyses of the WGAN-SLM algorithm's peak-to-average power ratio (PAPR), bit error rate (BER), and model stability. Simulation parameters were set based on the TR38.811 satellite scenario, with the satellite at an orbital altitude of 1500 km and a carrier frequency of 20 GHz. Referring to the subcarrier spacing specifications in the non-terrestrial network portion of the 5G NR communication protocol: when the synchronization signal bandwidth is no greater than 5 MHz, the subcarrier spacing is defined as 15 kHz; when the synchronization signal bandwidth is no greater than 10 MHz, the subcarrier spacing is defined as 30 kHz; when the synchronization signal bandwidth is no greater than 40 MHz, the subcarrier spacing is defined as 120 kHz; and when the synchronization signal bandwidth is no greater than 80 MHz, the subcarrier spacing is defined as 240 kHz. Considering the generally large bandwidth in satellite communication scenarios, a subcarrier spacing of 240 kHz was used in the simulation. The simulation parameter settings are shown in Table 2.

[0169] Table 2. Matlab simulation parameters for the peak-to-average ratio suppression algorithm.

[0170]

[0171] refer to Figure 9 As shown, the CCDF performance curves of the traditional SLM algorithm, CF algorithm, TR algorithm, and WGAN-SLM algorithm are presented when K=16. (CCDF = 1.0 × 10⁻⁶) -4 At that time, WGAN-SLM significantly outperformed the traditional SLM and CF algorithms in reducing the PAPR of the WOFDM system, with a corresponding PAPR of approximately 6.0 dB; compared to the TR algorithm, the PAPR suppression performance was slightly improved. Simulation results showed that the proposed algorithm has good peak-to-average ratio (PAPR) suppression performance.

[0172] refer to Figure 10 As shown, the CCDF performance curves of the traditional SLM algorithm and the WGAN-SLM algorithm are displayed when K is 4, 8, and 16. The peak-to-average ratio (PAR) of the WGAN-SLM algorithm decreases with increasing K. When K is relatively small, the PAR decreases more significantly. However, as K increases, the PAR decreases gradually, consistent with the traditional SLM algorithm.

[0173] refer to Figure 11As shown, the CCDF performance curves of the WOFDM system after passing through the traditional SLM algorithm, GAN-SLM algorithm, WGAN-SLM algorithm, and WGAN-SLM algorithm are presented when K=16. The WGAN-SLM algorithm significantly outperforms the GAN-SLM and WGAN-SLM algorithms in reducing the PAPR of the WOFDM system.

[0174] refer to Figure 12 The figure shows a comparison of the system bit error rate (BER) of several algorithms when K=16. The BER curves of the traditional SLM algorithm, GAN-SLM algorithm, WGAN-SLM algorithm, and WGAN-SLM algorithm are very similar, which indicates that the algorithm proposed in this paper reduces PAPR while almost not increasing the system BER.

[0175] refer to Figure 13 As shown, the loss function changes of GAN-SLM and WGAN-SLM on the WOFDM signal training set after different numbers of iterations are presented. The loss value of WGAN-SLM gradually stabilizes after 800 iterations; GAN-SLM converges relatively slowly, only stabilizing after 1500 iterations. Therefore, compared with GAN-SLM, the WGAN-SLM model has the advantages of faster convergence and easier training.

[0176] Based on the simulation results above, the method proposed in this disclosure can effectively reduce the PAPR of WOFDM signals while ensuring low bit error rate and computational complexity. For example, the WGAN-SLM algorithm performs well with a bit error rate of 16 and a CCDF of 1.0 × 10⁻⁶. -4 At this time, the corresponding PAPR is approximately 6.0 dB. Compared with the SLM algorithm, the PAPR is reduced by approximately 0.5 dB, the computational complexity is reduced by 93.7%, and the bit error rate remains essentially unchanged.

[0177] refer to Figure 14 As shown, a program product 500 for implementing the above-described method according to an embodiment of the present invention is described. It may employ a portable compact disc read-only memory (CD-ROM) and include program code, and may run on a terminal device, such as a personal computer. However, the program product of the present invention is not limited thereto. In this document, the readable storage medium may be any tangible medium containing or storing a program that may be used by or in conjunction with an instruction execution system, apparatus, or device.

[0178] The program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0179] The computer-readable storage medium may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. The readable storage medium may also be any readable medium other than a readable storage medium, capable of transmitting, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0180] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0181] In exemplary embodiments of this disclosure, an electronic device is also provided, which may include a processor and a memory for storing executable instructions of the processor. The processor is configured to perform the steps of the method for reducing the peak-to-average power ratio of an orthogonal frequency division multiplexing system described in any of the above embodiments by executing the executable instructions.

[0182] Those skilled in the art will understand that various aspects of the present invention can be implemented as systems, methods, or program products. Therefore, various aspects of the present invention can be specifically implemented in the following forms: entirely hardware implementations, entirely software implementations (including firmware, microcode, etc.), or implementations combining hardware and software aspects, collectively referred to herein as “circuits,” “modules,” or “systems.”

[0183] The following reference Figure 15 To describe an electronic device 600 according to this embodiment of the present invention. Figure 15 The electronic device 600 shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of the present invention.

[0184] like Figure 15 As shown, the electronic device 600 is presented in the form of a general-purpose computing device. The components of the electronic device 600 may include, but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different system components (including storage unit 620 and processing unit 610), a display unit 640, etc.

[0185] The storage unit stores program code that can be executed by the processing unit 610, causing the processing unit 610 to perform the steps described in the above-described section of this specification regarding methods for reducing the peak-to-average power ratio (PAPR) of an orthogonal frequency division multiplexing (OFDM) system, according to various exemplary embodiments of the present invention. For example, the processing unit 610 can perform actions such as... Figure 1 The steps are shown in the figure.

[0186] The storage unit 620 may include a readable medium in the form of a volatile storage unit, such as a random access memory unit (RAM) 6201 and / or a cache storage unit 6202, and may further include a read-only memory unit (ROM) 6203.

[0187] The storage unit 620 may also include a program / utility 6204 having a set (at least one) program module 6205, such program module 6205 including but not limited to: an operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0188] Bus 630 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the various bus structures.

[0189] Electronic device 600 can also communicate with one or more external devices 700 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 600, and / or with any device that enables electronic device 600 to communicate with one or more other computing devices (e.g., router, modem, etc.). This communication can be performed via input / output (I / O) interface 650. Furthermore, electronic device 600 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 660. Network adapter 660 can communicate with other modules of electronic device 600 via bus 630. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0190] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, or network device, etc.) to execute the above-described method for reducing the peak-to-average power ratio of an orthogonal frequency division multiplexing system according to the embodiments of this disclosure.

[0191] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A method for reducing the peak-to-average power ratio (PAPR) of an orthogonal frequency division multiplexing (OFDM) system, characterized in that, include: Receive the raw data of the signal to be transmitted; The first carrier signal of the orthogonal frequency division multiplexing system is generated based on the original data; wherein, the first carrier signal is generated by using wavelet basis functions on the basis of frequency domain orthogonal multiplexing and then time domain integer orthogonal time-shift multiplexing. Based on the first carrier signal, a generative adversarial network generates multiple independent second carrier signals; Calculate the peak-to-average power ratio (PAPR) of the plurality of independent second carrier signals, and select the second carrier signal with the smallest PAPR for transmission; The original data is carried in both the first carrier signal and the second carrier signal. The step of generating multiple independent second carrier signals based on the first carrier signal using a generative adversarial network includes: Multiple third carrier signals are generated in the generative adversarial network based on the first carrier signal; wherein the sample distribution distance is used as the training condition of the generative adversarial network, and the loss function model is determined. The third carrier signal is compared with the first carrier signal to determine whether it is true or false, and the third carrier signal that is determined to be true is taken as the second carrier signal.

2. The method according to claim 1, characterized in that, The step of generating multiple independent second carrier signals based on the first carrier signal using a generative adversarial network includes: The process of generating and determining the third carrier signal is trained using a convolutional neural network.

3. The method according to claim 2, characterized in that, The step of training the process of generating and determining the third carrier signal using a convolutional neural network includes: The third carrier signal and the first carrier signal are input into a convolutional neural network and a probability value is output. The probability value is normalized by a sigmoid activation function, and the third carrier signal with a value greater than 0.5 is judged as true.

4. The method according to claim 2, characterized in that, The step of training the process of generating and determining the third carrier signal using a convolutional neural network includes: After training the decision-making process a preset number of times, the root mean square propagation algorithm is used as the optimization rule to train the generation process once.

5. The method according to any one of claims 1-4, characterized in that, The step of calculating the peak-to-average power ratio (PAPR) of the plurality of independent second carrier signals and selecting the second carrier signal with the smallest PAPR for transmission includes: Formula for calculating peak-to-average power ratio (PAPR): Among them, PAPR dB is the peak-to-average power ratio; 10lgNdB is the theoretical peak-to-average power ratio with N subcarriers; s(t) is the symbol for the second carrier signal; E(|s(t)| 2 To find the expected value of the function; max│s(t)│ 2 The function is for finding the maximum value.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method for reducing the peak-to-average power ratio of an orthogonal frequency division multiplexing system as described in any one of claims 1 to 5.

7. An electronic device, characterized in that, include: processor; as well as Memory for storing the executable instructions of the processor; The processor is configured to perform the steps of the method for reducing the peak-to-average power ratio of an orthogonal frequency division multiplexing system according to any one of claims 1 to 5 by executing the executable instructions.

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