Fbmc-ss papr control method based on fountain code shift de-peaking and phase rotation

Abstract

This invention relates to the field of shortwave communication, and particularly to a peak-to-average power ratio (PAPR) control method for FBMC-SS based on fountain code shifting and phase rotation. This invention aims to minimize the overlap of peak signals from different subcarriers through shifting and phase rotation strategies, thereby reducing PAPR. Shifting alters the time-domain distribution of coded data packets on each subcarrier, while phase rotation alters the phase relationship of the coded data packets on each subcarrier. Encoded data packets with peak values ​​exceeding a threshold are multiplied by a phase rotation factor, and peak generation is avoided through fine-tuning the phase. Subsequent subcarriers undergo shifting and phase rotation sequentially, achieving a "peak-shaving and valley-filling" effect. This method not only effectively reduces the PAPR of filter bank multi-carrier spread spectrum systems and decreases nonlinear distortion, but also enhances the anti-interference capability of FBMC-SS systems in shortwave communication through fountain codes, ensuring communication reliability.

Description

Technical Field

[0001] This invention relates to the field of shortwave communication, and particularly to a peak-to-average power ratio (PAPR) control method for FBMC-SS systems based on fountain code (FC) shifting and phase rotation. This method not only effectively reduces the PAPR of filter bank multi-carrier spread spectrum (FBMC-SS) systems and decreases nonlinear distortion, but also enhances the anti-interference capability of FBMC-SS systems in shortwave communication by improving the fountain code, thus ensuring communication reliability. Background Technology

[0002] As a novel multi-carrier communication system, filter bank multi-carrier spread spectrum (FBMC) technology was first proposed in 2012. It combines the main advantages of FBMC and spread spectrum (SS) technologies, offering advantages such as low out-of-band power leakage and weak frequency offset sensitivity. It effectively addresses multipath fading and partial frequency band interference in complex shortwave channels, thus achieving reliable communication under low signal-to-noise ratio (SNR) conditions. FBMC-SS systems transmit data using a large number of parallel subcarriers, with all subcarriers transmitting the same information for maximum power ratio (MPR) combining at the receiver. Therefore, when the subcarrier signals are in phase, the combined signal at the transmitter often has a high peak power, which is one of the main drawbacks of multi-carrier systems. When the signal amplitude exceeds the linear operating range of the power amplifier, nonlinear distortion and out-of-band radiation occur. Furthermore, an excessively high peak-to-average power ratio (PAPR) requires power amplifiers, A / D converters, and D / A converters to have a large linear dynamic range, increasing the hardware implementation difficulty and energy consumption of multi-carrier systems. To reduce nonlinear distortion, lower the difficulty of hardware implementation, and enhance the practicality of FBMC-SS in shortwave communication, PAPR must be effectively suppressed.

[0003] Currently, PAPR suppression methods can be mainly divided into three types: pre-distortion, probabilistic, and coding. Pre-distortion methods suppress PAPR by performing nonlinear processing on the signal, such as amplitude limiting and companding. While these methods are simple in principle and have low complexity, they are prone to signal distortion and increased bit error rate. Probabilistic methods primarily process the original signal at the transmitting end, suppressing PAPR by reducing the probability of high-amplitude signals, such as Selected Mapping (SLM) and Partial Transmit Sequences (PTS). However, these methods tend to lead to higher system complexity and information redundancy. Coding methods encode data, selecting signals with lower PAPR for transmission. The main advantage of these methods is avoiding signal distortion caused by nonlinear operations such as clipping and compression, while also enhancing anti-interference capabilities through coding characteristics. Their disadvantages are that the encoded signal often incorporates redundant information, reducing the data transmission rate, and the encoding and decoding processes also increase computational complexity to some extent.

[0004] Fountain codes, first proposed in 1998, currently include Luby Transform (LT) codes, Raptor codes, and Spinal codes. The transmitting end generates a continuous stream of coded data packets, like a fountain; the receiving end only needs to collect enough "drops" (i.e., coded data packets) to recover the original data, much like filling a glass with water and then drinking it, without needing to know which drops. This encoding method has advantages such as no feedback required from the receiver, no fixed code rate, and ease of user acceptance, making it very suitable for broadcasts with a large number of communication targets or in harsh channel environments. Although the encoded signal often contains some redundant information, reducing the data transmission rate, it effectively avoids signal distortion caused by pre-distortion methods. Since the FBMC-SS system mainly focuses on applications in shortwave communication, and the data transmission rate of shortwave communication is generally low, adopting the fountain code method will not excessively affect communication performance. Furthermore, because fountain codes have a certain error correction capability, they can enhance anti-interference capabilities and improve the reliability of the FBMC-SS system in shortwave communication.

[0005] Currently, research on reducing peak-to-average power ratio (PAPR) based on fountain codes mainly focuses on Orthogonal Frequency Division Multiplexing (OFDM). The main idea is to generate multiple candidate OFDM symbols using fountain codes at the transmitter and filter them using a preset threshold. If the value is below the threshold, the symbol is transmitted; otherwise, it is discarded. Essentially, this method combines the variable code rate characteristic of fountain codes with probabilistic filtering. The more candidate signals there are, the better the PAPR suppression effect tends to be, but this also leads to a significant increase in system complexity and coding delay. Although FBMC-SS has some similarities to OFDM, all subcarriers in FBMC-SS transmit the same information for maximum ratio combining at the receiver. Therefore, traditional methods cannot be directly applied; targeted improvements must be made based on the structural characteristics of FBMC-SS. Summary of the Invention

[0006] To address the aforementioned problems, this invention proposes a peak-to-average power ratio (PAPR) control method for FBMC-SS based on fountain code shifting and phase rotation. Analogous to the classic game "Tetris," which requires avoiding excessive stacking of blocks in the same column, this invention, through shifting and phase rotation strategies, aims to minimize the overlap of peak signals from different subcarriers, thereby reducing PAPR. Figure 1 As shown: Peak shifting alters the temporal distribution of coded data packets on each subcarrier, similar to the "shifting" in Tetris, i.e., "coarse adjustment"; phase rotation alters the phase relationship of coded data packets on each subcarrier, similar to the "rotation" in Tetris, i.e., "fine adjustment". Using the coded data packets on the first subcarrier as the reference layer (green coded data packets), when a large peak occurs at certain times, the second subcarrier sequentially selects data packets at relatively low amplitude troughs (blue coded data packets) and places them at the same time. Simultaneously, individual coded data packets with peaks exceeding a threshold (red coded data packets) are multiplied by a phase rotation factor to fine-tune the phase and avoid peak generation. Subsequent subcarriers undergo peak shifting and phase rotation sequentially, achieving the effect of "peak smoothing and valley filling". Furthermore, due to the unordered recovery characteristic of fountain codes, the receiver only needs to collect a sufficient number of coded data packets to recover the original information, regardless of the receiving order. Although the coded data packets on each subcarrier have different arrangements, they are all from the same group of coded data packets; therefore, the FBMC-SS receiver can perform maximum ratio combining to ensure reliability.

[0007] The technical solution adopted in this invention is: the FBMC-SS peak-to-average power ratio control method based on fountain code shifting and phase rotation, wherein the fountain code adopts the classic LT code and the modulation method adopts binary phase shift keying (BPSK). Figure 2The encoding process of LT codes is demonstrated. Figure 3 The structure and related processing flow of the FBMC-SS system transmitter are demonstrated. The method consists of the following steps:

[0008] S1 performs LT encoding and BPSK modulation on the original information bits s[n]; the details are as follows:

[0009] S1.1 Divide the original information bits s[n] evenly into r original data packets and determine the degree distribution function μ(d);

[0010] Let r represent the number of raw data packets; u represent the capacity of each raw data packet, that is, each raw data packet contains u bits;

[0011] Define μ(d) as the degree distribution function, using the classic Robust Soliton Distribution (RSD) of LT codes, and its expression is:

[0012]

[0013] Where ρ(d) represents the ideal solitary wave distribution, τ(d) represents the parameter-adjustable distribution, and d is the index of the degree variable, d=1,2,…,r.

[0014] The expression for the ideal solitary wave distribution ρ(d) is:

[0015]

[0016] The expression for the parameter-tunable distribution τ(d) is:

[0017]

[0018] Where S represents the size of the preprocessing set after each iteration of decoding. c is a constant set by the user, 0≤c≤1, usually set to c=0.03; δ represents the upper limit of the decoding failure probability, 0≤δ≤1, usually set to δ=0.5.

[0019] S1.2 Randomly select the degree value d according to the degree distribution function μ(d);

[0020] S1.3 Randomly select d different original data packets from all the original data packets and perform an XOR operation to generate encoded data packets;

[0021] S1.4 repeats S1.2 and S1.3 to generate a continuous stream of encoded data packets until the encoded length reaches the preset maximum number of encoded data packets K;

[0022] S1.5 modulates all encoded data packets using BPSK.

[0023] S2 performs shifting and peak offsetting on the BPSK modulated encoded data packets; specifically as follows:

[0024] The shifting and peak shifting refers to selecting the optimal time domain position for the coded data packet on each subcarrier, aligning its peak value with the valley value of the already placed coded data packet, thus achieving "peak shaving and valley filling," or "coarse adjustment."

[0025] S2.1 Initialize the reference layer subcarriers;

[0026] All BPSK modulated coded data packets are placed sequentially on the first subcarrier as the reference layer in the original generation order.

[0027] S2.2 Generate a set of candidate encoded data packets;

[0028] Based on the degree value d of different encoded data packets, they are sorted in ascending order from low to high to form a set of candidate encoded data packets. According to the characteristics of robust solitary wave distribution, the main range of their degree values ​​is usually 1-10, and the vast majority of the probability is concentrated at lower degree values; for example, the proportion of encoded data packets with a degree value d≤6 is usually greater than 95%. To enhance computational efficiency and practicality, subsequent steps will primarily focus on optimally shifting encoded data packets with d≤6, while other encoded data packets will be placed sequentially to fill in the remaining positions.

[0029] S2.3 Calculate the optimal shift amount;

[0030] To evaluate the peak-shaving effect of each candidate shift, for each candidate shift τ, the instantaneous power of the coded data packet after shift and its superposition with the existing signal is calculated. :

[0031]

[0032] The first term is the accumulated signal of the first k-1 subcarriers. Indicates time-domain shift The first item is the l-th coded data packet on the m-th subcarrier; the second item is the (l-1)-th coded data packets already placed on the current subcarrier. Indicates time-domain shift The third item is the v-th coded data packet on the k-th subcarrier; the fourth item is the l-th coded data packet to be placed. This represents the l-th coded data packet to be placed on the k-th subcarrier; t is the time series index, τ is the candidate shift; m is the subcarrier sequence index, used to calculate the cumulative signal of the first k-1 subcarriers, m=1,2,…,k-1; k is the subcarrier sequence index, used to calculate the total signal of all subcarriers, k=1,2,…,N, where N is the number of subcarriers; v is the sequence index of the placed coded data packets, used to calculate the first l-1 coded data packets on the k-th subcarrier, v=1,2,…,l-1; l is the sequence index of the coded data packet to be placed, used to calculate the l-th coded data packet to be placed on the k-th subcarrier. There are coded data packets, l=1,2,…,K; The center frequency f of the k-th subcarrier is represented. k That is, up-conversion.

[0033] definition Indicates the optimal shift amount:

[0034]

[0035] S2.4 Shift and place packages one by one;

[0036] The optimal shift amount is calculated using S2.3. Then, from the candidate coded data packet set generated in S2.2, the coded data packets with d≤6 are shifted and placed one by one, that is, the l-th coded data packet to be placed on the k-th subcarrier is represented as...

[0037]

[0038] Repeat steps S2.2 to S2.4. When the coded data packets with d≤6 have been placed, fill the remaining positions with coded data packets with d>6 in sequence until all coded data packets on the subcarrier have been shifted and placed.

[0039] definition This represents the signal after the k-th subcarrier has completed shifting and peak offsetting:

[0040]

[0041] in, This represents the signal of the l-th coded data packet on the k-th subcarrier after time-domain shifting. Let represent the shift amount of the l-th coded data packet on the k-th subcarrier; let Indicates the shift amount for the remaining positions. The expression is

[0042]

[0043] S3 performs phase rotation on critical data packets; the details are as follows:

[0044] After completing the shifting and peak offsetting in step S2, it is necessary to identify the key data packets through peak detection and multiply the key data packets by the phase rotation factor γ. k Further reduce peak power, i.e., "fine-tuning":

[0045] S3.1 peak detection;

[0046] definition This represents the total signal after the shifting and peak offsetting are completed:

[0047]

[0048] definition This indicates the calculation of the instantaneous power of the current signal:

[0049]

[0050] Define P th This represents the peak detection threshold, used to identify significant power peaks.

[0051]

[0052] Where λ represents the threshold coefficient, i.e., reaching λ times the average power P. avg The time at which λ is considered the peak time that needs optimization is typically set to 2.5; T total This indicates the total transmission time.

[0053] definition Represents the peak time t p The set of:

[0054]

[0055] S3.2 Identify key data packets;

[0056] For each peak moment, it is necessary to analyze the directional contribution of each encoded data packet to the peak, thereby identifying the main contributor as the "critical data packet" for targeted phase adjustment, while keeping the phase of other encoded data packets unchanged.

[0057] definition This indicates that the l-th coded data packet on the k-th subcarrier is at time l. Directed contribution:

[0058]

[0059] The conjugate operation eliminates the phase shift of the total signal, resulting in the relative phase relationship between the encoded data packet and the total signal.

[0060] Define contribution range Used to measure the magnitude of the impact of encoded data packets:

[0061]

[0062] Based on directional contribution and contribution range The encoded data packets that make the main contribution to the peak value are identified as key data packets. :

[0063]

[0064] in, Indicates the threshold for positive contribution. A th Indicates the contribution magnitude threshold. ; This represents the threshold coefficient, which can usually be set to 0. .

[0065] S3.3 Determine the set of candidate phase rotation factors;

[0066] definition Represents the set of candidate phase rotation factors:

[0067]

[0068] S3.4 Search for the optimal phase rotation factor:

[0069] S3.4.1 Phase rotation factor for all encoded data packets Initialize to 1:

[0070]

[0071] S3.4.2 Calculate the phase rotation factor that minimizes the peak power of the critical data packet;

[0072] For each key data packet Test all candidate phases sequentially; for each candidate phase rotation factor Calculate the peak power after using the phase rotation factor. :

[0073]

[0074] definition The phase rotation factor that minimizes peak power:

[0075]

[0076] S3.4.3 updates the phase rotation factor for critical data packets on this subcarrier, while keeping the phase rotation factor at 1 for other coded data packets:

[0077]

[0078] S4 generates the transmit signal of the FBMC-SS system through shaping filtering and up-conversion;

[0079] S5 calculates the PAPR of the transmitted signal of the FBMC-SS system.

[0080] Furthermore, in S4, the process of generating the transmit signal of the FBMC-SS system through shaping filtering and up-conversion is as follows:

[0081] Define s k [n] represents the transmitted symbol on the k-th subcarrier after the original information bits s[n] have undergone steps S1, S2, and S3. Define s k [t] represents s k [n] The transmitted symbol obtained after L-fold upsampling:

[0082]

[0083] Among them, T s For symbol period, Indicates T s It is a periodic impulse function.

[0084] Define x(t) as the transmitted signal of the FBMC-SS system, which is composed of the s signals on each subcarrier. k [n] is obtained by upsampling, shaping filtering, and upconversion, followed by time-domain superposition:

[0085]

[0086] Where h(t) represents the prototype filter.

[0087] Furthermore, S5 calculates the PAPR of the transmitted signal of the FBMC-SS system, as follows:

[0088] Peak-to-average power ratio (PAPR) is defined as the ratio of the peak power to the average power of the signal over the total transmission time.

[0089]

[0090] The beneficial effects of this invention are as follows:

[0091] ① This invention draws inspiration from the stacking avoidance concept in the game "Tetris" and proposes a layered PAPR optimization method: first, the temporal distribution of the encoded data packets is adjusted by shifting and peak shifting ("coarse adjustment"), and then the phase relationship is finely adjusted by phase rotation ("fine adjustment"), thereby avoiding the overlap of peaks from multiple signals and achieving "peak shifting and valley filling". This method utilizes the unordered recovery characteristics of fountain codes, requiring only a sufficient number of data packets for decoding at the receiver, and combines maximum ratio combining to improve signal quality.

[0092] ② This invention fully utilizes the out-of-order recovery characteristics and error correction capabilities of fountain codes, achieving good compatibility with the FBMC-SS system. Specifically, the out-of-order recovery characteristics of fountain codes can be well adapted to the maximum ratio combining structure at the receiver, and their inherent error correction capability enhances the system's anti-interference ability in shortwave channels, ensuring communication reliability. Simulation results show that this invention can significantly reduce PAPR with acceptable complexity while maintaining good bit error rate performance, demonstrating excellent overall performance advantages. Attached Figure Description

[0093] Figure 1 : A schematic diagram of the staggered shifting and phase rotation process of fountain code data packets;

[0094] Figure 2 : A schematic diagram of the encoding process of LT code;

[0095] Figure 3 : Transmitter of FBMC-SS system based on fountain code shifting and phase rotation;

[0096] Figure 4 : A flowchart of the method described in this invention;

[0097] Figure 5 Comparison of PAPR performance of different methods in FBMC-SS system;

[0098] Figure 6 Comparison of bit error rate performance of different methods in FBMC-SS system;

[0099] Figure 7 Comparison of complexity and performance of different methods in the FBMC-SS system. Detailed Implementation

[0100] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0101] Figure 4 This is a flowchart of the method described in this invention. This invention proposes a peak-to-average power ratio control method for FBMC-SS based on fountain code shifting and phase rotation, which consists of the following steps:

[0102] S1 performs LT encoding and BPSK modulation on the original information bits s[n]:

[0103] S1.1 Divide the original information bits s[n] evenly into r original data packets and determine the degree distribution function μ(d);

[0104] S1.2 Randomly select the degree value d according to the degree distribution function μ(d);

[0105] S1.3 Randomly select d different original data packets from all the original data packets and perform an XOR operation to generate encoded data packets;

[0106] S1.4 repeats S1.2 and S1.3 to generate a continuous stream of encoded data packets until the encoded length reaches the preset maximum number of encoded data packets K;

[0107] S1.5 modulates all encoded data packets using BPSK.

[0108] S2 performs shifting and peak shifting on the BPSK modulated encoded data packets:

[0109] S2.1 Initialize the reference layer subcarriers;

[0110] S2.2 Generate a set of candidate encoded data packets;

[0111] S2.3 Calculate the optimal shift amount;

[0112] S2.4 Shift and place packages one by one;

[0113] S3 performs phase rotation on critical data packets:

[0114] S3.1 peak detection;

[0115] S3.2 Identify key data packets;

[0116] S3.3 Determine the set of candidate phase rotation factors;

[0117] S3.4 Search for the optimal phase rotation factor:

[0118] S3.4.1 Phase rotation factor γ of all encoded data packets k,l Initialize to 1;

[0119] S3.4.2 Calculate the phase rotation factor that minimizes the peak power of the critical data packet;

[0120] S3.4.3 updates the phase rotation factor for key data packets on this subcarrier, while keeping the phase rotation factor of other coded data packets at 1;

[0121] S4 generates the transmit signal of the FBMC-SS system through shaping filtering and up-conversion;

[0122] S5 calculates the PAPR of the transmitted signal of the FBMC-SS system.

[0123] This section analyzes the performance of the peak-to-average power ratio (PAPR) control method based on fountain code shifting and phase rotation in the FBMC-SS system through multiple sets of numerical simulation results. The basic parameter configuration of the FBMC-SS system is shown in Table 1. It transmits a total of 1000 bits (800 information bits + 200 pilot bits) using block pilots. Each original data packet consists of 1 pilot bit and 4 information bits. The capacity of the fountain code encoded data packet is the same as that of the original data packet. The number of encoded data packets, K, is usually set to 1.5 times the number of original data packets, r, to maintain sufficient redundancy. Since this invention mainly focuses on PAPR suppression at the transmitter, the receiver can be reverse-engineered based on the transmitter structure and maximum ratio combining can be added; this will not be elaborated further here.

[0124]

[0125] Table 2 and Figure 5 This paper presents a comparison of PAPR performance of different methods in FBMC-SS systems. "Orig" represents standard FBMC-SS, without PAPR optimization measures and LT coding, providing a PAPR performance benchmark for comparison with other schemes; "SLM" represents the selection mapping method; "PTS" represents the partial transmission sequence method; "PDFT-S" represents Pruned Discrete Fourier Transform-Spread (PDFT-S); and "FC" represents the fountain code shifting and phase rotation method proposed in this invention. Since the same information is transmitted on each row of subcarriers in FBMC-SS, the CCDF curve of Orig is linear, and the PAPR under statistical characteristics is relatively high. Figure 5As shown, various PAPR suppression methods have improved the peak-to-average power ratio (PAPR) of FBMC-SS systems to some extent. SLM controls PAPR by reducing the probability of peak occurrence, and the average PAPR value can be reduced to 5.24 dB. However, this method has large fluctuations (maximum value 8.58, minimum value 2.64, fluctuation range reaches nearly 6 dB), so from the statistical characteristics of the CCDF curve, it only reduces the PAPR by about 2 dB. However, due to the limited accuracy of the generation and selection mechanism of the phase factor, the PAPR suppression effect of SLM is not ideal. PTS further reduces the probability of high peak values ​​by subcarrier grouping, achieving the best average PAPR performance and optimization magnitude among all methods (3.59 dB and 64.75%↓ in Table 2), but it also leads to an exponential increase in its computational complexity. Especially when the number of subcarriers is large, the excessive complexity will greatly limit its practical application. PDFT-S has a lower average PAPR performance than SLM, but it is more stable in statistical characteristics, reaching 6.6 dB on the order of 10⁻³ probability. The FC proposed in this invention achieves suboptimal PAPR performance (average 4.59 dB, an improvement of 54.93%) through the joint optimization of peak shifting and phase rotation, and its statistical characteristics are also relatively stable.

[0126]

[0127] Figure 6 This paper compares the bit error rate (BER) performance of different methods in the FBMC-SS system. The BER performance of Orig, SLM, and PTS is very similar (the BER of all three methods can reach 10 dB at SNR = -8 dB). -3 The error rate (ERR) is on the order of magnitude because SLM and PTS only reduce PAPR by changing the phase; their design does not enhance anti-interference capability and mainly relies on the reliability of the FBMC-SS system itself. Among all methods, FC exhibits the best bit error rate performance (the bit error rate can reach 10^-10 dB at SNR = -12 dB). -3 (On the order of magnitude). This is because the redundancy of the fountain code enhances error correction capability and improves reliability to some extent. Although PDFT-S achieves improved PAPR performance through pruning operations, the reduction in the number of subcarriers also reduces the maximum ratio combining gain, leading to a decrease in bit error rate performance and a significant weakening of anti-interference capability (bit error rate reaches 10). -3 The required level is SNR = -4dB.

[0128] Table 3 and Figure 7This paper compares the complexity and performance of different methods in the FBMC-SS system. While the PTS technique exhibits the best PAPR performance, its computational complexity increases exponentially with the number of subcarriers, easily leading to excessive computational burden when the number of subcarriers is large, severely limiting practical applications. In contrast, the FC method performs second best in PAPR while achieving the best BER performance; although its shifting and phase rotation operations introduce some signaling overhead, its complexity is far lower than the exponential level of PTS and remains within an acceptable range. Although SLM has the lowest complexity, its PAPR and bit error rate performance are not ideal, failing to meet expectations. While PDFT-S achieves good PAPR performance, its complexity increases linearly with the number of subcarriers because the receiver needs to know which subcarriers are active to perform correct combining and demodulation, which also increases signaling overhead and system complexity.

[0129]

[0130] From the above comparative analysis, it is clear that while PTS has the best performance, its exponentially increasing complexity greatly limits its practical application; SLM has the lowest complexity, but its PAPR and bit error rate performance are relatively weak, making it suitable for scenarios with lower performance requirements; PDFT-S, due to its pruning operation, has PAPR and bit error rate performance that affect each other, requiring careful consideration of the pruning ratio and system performance; the FC proposed in this invention maintains suboptimal PAPR performance and optimal anti-interference capability in the above comparisons, while its complexity remains within an acceptable range, demonstrating a significant overall cost-performance advantage in the FBMC-SS system.

Claims

1. A method for controlling the peak-to-average power ratio of FBMC-SS based on fountain code shift de-peaking and phase rotation, characterized in that, This method consists of the following steps: S1 performs LT encoding and BPSK modulation on the original information bits s[n]; the details are as follows: S1.1 Divide the original information bits s[n] evenly into r original data packets and determine the degree distribution function μ(d); Let r represent the number of raw data packets; u represent the capacity of each raw data packet, that is, each raw data packet contains u bits; Define μ(d) as the degree distribution function, using the classic robust solitary wave distribution of LT codes, and its expression is: ， Where ρ(d) represents the ideal solitary wave distribution, τ(d) represents the parameter-adjustable distribution, and d is the index of the degree variable, d=1,2,…,r; The expression for the ideal solitary wave distribution ρ(d) is: ， The expression for the parameter-tunable distribution τ(d) is: ， Where S represents the size of the preprocessing set after each iteration of decoding. c is a human-set constant, 0≤c≤1; δ represents the upper limit of the decoding failure probability, 0≤δ≤1; S1.2 Randomly select the degree value d according to the degree distribution function μ(d); S1.3 Randomly select d different original data packets from all the original data packets and perform an XOR operation to generate encoded data packets; S1.4 repeats S1.2 and S1.3 to generate a continuous stream of encoded data packets until the encoded length reaches the preset maximum number of encoded data packets K; S1.5 modulates all encoded data packets using BPSK. S2 performs shifting and peak offsetting on the BPSK modulated encoded data packets; specifically as follows: S2.1 Initialize the reference layer subcarriers; All BPSK modulated coded data packets are placed sequentially on the first subcarrier as the reference layer in the original generation order; S2.2 Generate a set of candidate encoded data packets; Based on the degree value d of different encoded data packets, they are sorted in ascending order from low to high to form a set of candidate encoded data packets; S2.3 Calculate the optimal shift amount; To evaluate the de-peaking effect of each candidate shift, for each candidate shift τ, the instantaneous power of the encoded data packet shifted and superimposed with the existing signal is computed : ， The first term is the accumulated signal of the first k-1 subcarriers. Indicates time-domain shift The first item is the l-th coded data packet on the m-th subcarrier; the second item is the (l-1)-th coded data packets already placed on the current subcarrier. Indicates time-domain shift The third item is the v-th coded data packet on the k-th subcarrier; the fourth item is the l-th coded data packet to be placed. This represents the l-th coded data packet to be placed on the k-th subcarrier; t is the time series index, τ is the candidate shift; m is the subcarrier sequence index, used to calculate the cumulative signal of the first k-1 subcarriers, m=1,2,…, k-1; k is the subcarrier sequence index, used to calculate the total signal of all subcarriers, k=1,2,…, N, where N is the number of subcarriers; v is the sequence index of the placed coded data packets, used to calculate the first l-1 coded data packets on the k-th subcarrier, v=1,2,…, l-1; l is the sequence index of the coded data packet to be placed, used to calculate the l-th coded data packet to be placed on the k-th subcarrier. There are coded data packets, l=1,2,…,K; The center frequency f of the k-th subcarrier is represented. k That is, up-conversion; Definitions denotes the optimal shift amount: ， S2.4 Shift and place packages one by one; The optimal shift amount is calculated using S2.

3. Then, from the candidate coded data packet set generated in S2.2, the coded data packets with d≤6 are shifted and placed one by one. That is, the l-th coded data packet to be placed on the k-th subcarrier is represented as: ， Repeat steps S2.2 to S2.

4. When the coded data packets with d≤6 have been placed, fill the remaining positions with coded data packets with d>6 in sequence until all coded data packets on this subcarrier have been shifted and placed. Definitions denotes the signal after the kth subcarrier has been shifted to de-peak. ， in, This represents the signal of the l-th coded data packet on the k-th subcarrier after time-domain shifting. Let represent the shift amount of the l-th coded data packet on the k-th subcarrier; let Indicates the amount of shift for the remaining positions. The expression is: ， S3 performs phase rotation on critical data packets; the details are as follows: After the step S2, the key data packet is combed out by peak detection and multiplied by the phase rotation factor γ k Further reduce the peak power, namely "fine adjustment" S3.1 peak detection; Definitions Total signal after completion of shift de-peaking: ， Definitions denotes the calculation of the instantaneous power of the current signal: ， Definition P th denotes a peak detection threshold for identifying significant power peaks: ， where λ represents a threshold coefficient, i.e. the moment of time at which the peak value is considered to be optimized is the moment of time at which the power P avg reaches λ times the average power P total represents the total transmission time; Definitions representing the peak time t p the set of ， S3.2 Identify key data packets; For each peak moment, it is necessary to analyze the directional contribution of each encoded data packet to the peak, so as to identify the main contributor as the "critical data packet" for targeted phase adjustment, while keeping the phase of other encoded data packets unchanged; Definitions denotes the directed contribution of the kth subcarrier and the lth encoded data packet at time instant t. ， The conjugate operation eliminates the phase shift of the total signal, resulting in the relative phase relationship between the encoded data packet and the total signal. Define contribution range Used to measure the magnitude of the impact of encoded data packets: ， Based on directional contribution and contribution range The encoded data packets that make the main contribution to the peak value are identified as key data packets. : ， wherein, represents a positive contribution degree threshold value, ; A th represents a contribution amplitude threshold value, ; represents a threshold coefficient; S3.3 Determine the set of candidate phase rotation factors; Definitions denotes a set of candidate phase rotation factors: ， S3.4 Search for the optimal phase rotation factor: S3.4.1 Rotating the phase factor of all encoded data packets by to 1: ， S3.4.2 Calculate the phase rotation factor that minimizes the peak power of the critical data packet; for each key packet , test all candidate phases in turn; for each candidate phase rotate the factor , compute the peak power after using the phase rotate factor : ， Definitions denotes the phase rotation factor that minimizes the peak power: ， S3.4.3 updates the phase rotation factor for critical data packets on this subcarrier, while keeping the phase rotation factor at 1 for other coded data packets: ， S4 generates the transmit signal of the FBMC-SS system through shaping filtering and up-conversion; S5 calculates the PAPR of the transmitted signal of the FBMC-SS system.

2. The FBMC-SS peak-to-average power ratio control method based on fountain code shifting and phase rotation according to claim 1, characterized in that: In S4, the process of generating the transmit signal of the FBMC-SS system through shaping filtering and up-conversion is as follows: Definition of s k [n] represents the transmission symbol of the original information bit s[n] on the kth subcarrier after the S1, S2 and S3 steps, and s k [t] represents the transmission symbol of s k [n] after L times up-sampling: ， where T s is a symbol period, represents an impulse function with a period of T s . The definition x(t) represents the transmitted signal of the FBMC-SS system, resulting from the sum in the time domain of s k [n] after upsampling, shaping filtering and upconversion. ， Where h(t) represents the prototype filter.

3. The method according to claim 1, wherein the method is characterized in that: S5 calculates the PAPR of the transmitted signal of the FBMC-SS system as follows: The peak-to-average power ratio is defined as the ratio of the peak power to the average power of the signal over the total transmission time. 。 4. The method according to claim 1, wherein the method is characterized in that: In S1.1, the artificially set constant c is set to c=0.03, and the upper limit of the decoding failure probability δ is set to δ=0.

5.

5. The method according to claim 1, wherein the method is characterized in that: To enhance computational efficiency and practicality, the encoded data packets with d≤6 are optimally shifted, while other encoded data packets are sequentially filled with empty spaces in the remaining positions.

6. The method of claim 1, wherein the method is characterized by: In S3.1, the threshold coefficient λ = 2.

5.

7. The method according to claim 1, wherein the method is characterized in that: In S3.2, the threshold coefficient is set to .

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