A distributed OFDM base station cooperative sensing sequence design method

Abstract

The present invention discloses a distributed OFDM base station cooperative sensing sequence design method, comprising the following steps: setting parameters required for the problem; generating a signal sequence, a Fourier transform matrix, a frequency domain subcarrier selection matrix, and a zero padding matrix; generating a sidelobe level coefficient matrix and an autocorrelation ratio coefficient matrix; using an alternating iterative algorithm to obtain the optimal solution to the problem, solving the waveform optimal solution and limiting the peak-to-average power ratio, updating the matched filter and performing energy limitation, updating the frequency domain waveform, updating the dual variable, and calculating various residuals, objective functions, and waveform autocorrelation characteristics. After the iteration, the optimal waveform sequence is output, and various information such as residuals, objective functions, and autocorrelation characteristics are calculated. The present invention uses an alternating iterative algorithm to obtain the optimal solution to the problem, thereby maximally suppressing the autocorrelation sidelobe characteristics of multi-station waveforms and reducing interference of clutter on the communication system.

Description

Technical Field

[0001] The present invention relates to radar communication technology, and in particular to a distributed OFDM base station collaborative sensing sequence design technology. Background Art

[0002] In recent years, research on waveform optimization for collaborative sensing among distributed OFDM base stations has emerged, driven by the numerous challenges and demands faced by current wireless communication systems. It is a key development direction in modern wireless communication technology, aiming to improve the capacity, coverage, and efficiency of wireless networks. OFDM technology, with its strong resistance to multipath interference and frequency-selective fading, has been widely adopted in wireless communication systems such as Wi-Fi, 4G LTE, and 5G. With the rapid growth of user demand and data traffic, traditional centralized base station architectures face significant challenges in terms of capacity and coverage. A distributed base station architecture, by distributing multiple small base stations throughout the network coverage area and enabling collaborative operation between base stations, can provide greater coverage and higher system capacity. This architecture not only improves spectrum utilization but also reduces user terminal transmit power, extending battery life. Collaborative operation between base stations is key to distributed OFDM systems. By sharing information such as channel state information (CSI) and user location, base stations can dynamically adjust resource allocation and power control strategies to optimize system performance. Collaborative operation can also further improve system capacity and reliability through joint transmission and reception techniques. Despite the many advantages of distributed OFDM systems, their implementation also presents several technical challenges. For example, how to efficiently achieve collaboration between base stations, how to allocate resources and manage interference in dynamic environments, and how to design low-complexity channel estimation and detection algorithms. Solving these problems requires continuous exploration and innovation in both theoretical research and engineering practice. Wireless communication systems are often affected by multipath fading and frequency-selective interference. However, in a distributed environment, the coordinated operation of multiple base stations can affect system performance by various interferences and complex channel conditions. Distributed OFDM waveforms are expected to improve the system's ability to coordinate multi-user perception, increase spectrum efficiency, and enhance its resistance to interference, thereby promoting the development of communication systems in complex environments. In practical applications, high waveform correlation is required in OFDM multi-station systems to enhance the system's ability to resist clutter and improve target detection. Therefore, optimizing waveform design can not only improve system perception performance but also enhance its resistance to various types of interference, thereby improving overall system performance.

[0003] Research on waveform optimization for collaborative sensing in distributed OFDM base stations holds great promise in wireless communication systems. With the development of 5G and future 6G networks, the number of users and data demands are rapidly increasing, driving the need for efficient and stable communication systems. This research on waveform optimization for collaborative sensing in distributed OFDM base stations can not only significantly improve the performance of current wireless communication systems but also provide a solid technical foundation for the development of future networks and the realization of emerging applications. Through continuous research and innovation, we can drive wireless communication technology towards greater efficiency, intelligence, and environmental friendliness, injecting new vitality into its development. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a waveform design method in a distributed OFDM base station environment, which takes into account the unequal number of waveform points in the time and frequency domains due to hardware limitations, and can suppress the sidelobe characteristics of the radar to the greatest extent while ensuring communication quality and peak-to-average power ratio (PAPR) constraints, and can adjust the autocorrelation characteristics and the optimized ratio of the range sidelobe.

[0005] The technical solution adopted by the present invention to solve the above technical problems is a distributed OFDM base station cooperative sensing sequence design method:

[0006] Step 1: Set the parameters required for the problem, including the number of base stations M, the length N1 of the time domain signal sequence S, the effective length N2 of the frequency domain signal sequence X, the FFT transform dimension N, the parameter η that controls the peak-to-average power ratio (PAPR), and the signal average power P.

[0007] Step 2: Randomly generate an initial value of a time domain signal sequence S, a frequency domain signal sequence X=DFAS of S, a discrete Fourier transform matrix F, a frequency domain subcarrier selection matrix D, and a zero-padding matrix A;

[0008] Step 3: Generate a sidelobe level coefficient matrix Γ and an autocorrelation ratio coefficient matrix B;

[0009] Step 4: Considering the time-frequency domain constraints, PAPR constraints, and energy constraints, the waveform design and matched filter joint design problem of the distributed OFDM base station system is established with the goal of minimizing the weighted integrated sidelobe level (WISL) after the signal sequence passes through the matched filter.

[0010] Step 5: Use alternating iterative algorithm to find the optimal solution to the problem;

[0011] Obtain the optimal waveform solution and constrain the peak-to-average power ratio. First, optimize the waveform without constraints, then constrain the peak-to-average power ratio of the updated waveform to meet the PAPR requirements in actual projects.

[0012] Update the matched filter and impose energy constraints; first, update the matched filter through unconstrained optimization, and then constrain its energy;

[0013] Update the frequency domain waveform; use the updated time domain sequence to update the corresponding frequency domain sequence with different number of points;

[0014] Update the dual variables;

[0015] Step 6. Obtain the iteration parameters obtained by the current alternating iteration. The iteration parameters include the objective function value, the residual of each parameter, the number of loops, and the running time. Determine whether each of the output iteration parameters meets the preset conditions. If so, it indicates that the optimal waveform solution meets the PAPR constraint and low correlation performance. The iteration ends and the optimal waveform solution, that is, the optimal waveform sequence, is output to complete the perception waveform design. If not, return to step 5 to continue iteration.

[0016] In step 5, considering that the objective functions of the models established for such problems are all fourth-order and non-convex, it is generally difficult to directly obtain a closed-form solution, and directly optimizing the waveform will face the challenge of greater computational complexity. Therefore, it is further proposed to adopt the alternating iterative algorithm ADMM as a whole and use the generalized Lagrangian function to obtain the optimal solution to the problem. In order to implement the PAPR constraint problem, a method of projection into the PAPR constraint space is further proposed.

[0017] Specifically, in step 4, in the problem of jointly designing the waveform and the matched filter, the waveform WISL after the designed waveform passes through the matched filter is minimized and satisfies the following constraints:

[0018] 1) Limit the PAPR of the time domain waveform to meet the requirements of the transmit power amplifier;

[0019] 2) Energy constraints;

[0020] 3) Different requirements for autocorrelation performance in actual engineering.

[0021] Therefore, the joint design problem of OFDM signal waveform design and matched filter can be modeled as:

[0022]

[0023] stX=DFAS

[0024] |s mn | 2 ≤ηP, m=1,2,...,M,n=1,...,N1

[0025] s H E m s=1,m=1,...,M

[0026] Among them, ⊙ represents the Hadamard product, ||·||2 represents the L2 norm, and the intermediate quantity H represents the conjugate transpose, the p-th diagonal matrix Diag represents the construction of a diagonal matrix function, the pth angular frequency st represents the condition satisfied by the objective function; s is the vector form of S, s mn is the element in the mth row and nth column of S, with variables m=1,2,...,M, and n=1,...,N1, where |·| is the absolute value; E m To select a matrix, the elements from (m-1)N+1 to mN are 1, and the rest are 0;

[0027] Furthermore, by introducing the matched filter matrix Y, the waveform design and matched filter joint design problem of the distributed OFDM base station system is transformed into a convex problem:

[0028]

[0029] stY=S

[0030] X=DFAS

[0031] |s mn | 2 ≤ηP

[0032] e m H Y H Ye m =1

[0033] Among them, e m is a selection vector whose mth element is 1 and the rest are 0.

[0034] Specifically, in step 5, the alternating iterative algorithm ADMM is used to update the time domain waveform, matched filter, frequency domain waveform and dual variable in sequence;

[0035] Construct the augmented Lagrangian function for the above problem:

[0036]

[0037] I M represents the identity matrix whose diagonal elements are M; represents the Kronecker product, ρ u and ρ v is the penalty coefficient; y, x are the vector forms of the corresponding matrix variables Y, X, u, v are dual variables; ρ u and ρ v Both are penalty coefficients.

[0038] By minimizing Update variables. At the k+1th iteration, the algorithm consists of the following update process:

[0039]

[0040] u (k+1) =u (k) +s (k+1) -y (k+1)

[0041]

[0042] Step 6: Output the iteration parameters obtained by the current alternating iteration. The iteration parameters include the objective function value, the residual of each parameter, the number of loops, and the running time. Determine whether each of the output iteration parameters meets the preset conditions. If so, it indicates that the waveform of signal S meets the PAPR constraint and low correlation performance. The iteration ends, the optimal waveform sequence is output, and the perception waveform design is completed. If not, return to step 5 to continue iteration.

[0043] The beneficial effects of the present invention are:

[0044] (1) Based on the low-correlation waveform design in the distributed OFDM base station cooperative sensing environment under strong clutter environment, the signal can overcome the influence of clutter in the system, reduce the autocorrelation performance, and improve the system detection performance.

[0045] (2) During the design process, the original complex fourth-order convex optimization problem is transformed into a second-order problem by introducing equivalent variables, which simplifies the optimization problem and improves the solution efficiency;

[0046] (3) While overcoming the influence of the clutter environment, the optimized multi-station waveform can ensure low range sidelobes of autocorrelation and cross-correlation, and strong ability to detect small targets. At the same time, it can ensure a low peak-to-average power ratio to prevent out-of-band radiation and in-band distortion caused by the nonlinearity of the power amplifier. Out-of-band radiation will affect the signals in the adjacent frequency bands, and in-band distortion will cause the received signal to rotate, attenuate and shift.

[0047] (4) The alternating iterative loop algorithm ADMM overall framework adopted in the present invention is used for complex convex optimization problems. It can show good robustness when dealing with large-scale problems and has higher computational efficiency and scalability. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a flow chart of the distributed OFDM base station collaborative sensing sequence design method of the present invention.

[0049] Figure 2Comparison of ISL correlation performance for initial random data, data optimized for autocorrelation ratio 5:1, and data optimized for autocorrelation ratio 50:1, M=3, N1=64, N2=128, N=1024,

[0050] Figure 3 Comparison of ISL autocorrelation performance for initial random data, data optimized for autocorrelation ratio 5:1, and data optimized for autocorrelation ratio 50:1, M=3, N1=64, N2=128, N=1024,

[0051] Figure 4 Comparison of WISL correlation performance for initial random data, data optimized for autocorrelation ratio 5:1, and data optimized for autocorrelation ratio 50:1, M=3, N1=64, N2=128, N=1024,

[0052] Figure 5 Comparison of WISL autocorrelation performance for initial random data, data optimized for autocorrelation ratio 5:1, and data optimized for autocorrelation ratio 50:1, M=3, N1=64, N2=128, N=1024, DETAILED DESCRIPTION

[0053] To better describe the embodiments of the present invention, the following definitions are first made:

[0054] OFDM Waveform: Regarding the waveform design for collaborative sensing by distributed OFDM base stations, since OFDM systems are multi-carrier systems, the individual subcarrier signals will overlap in the time domain. If the subcarriers have the same symbol phase, this will result in a very high peak-to-average power ratio (PAPR). This transmit power exceeds the operating range of the transmitter's power amplifier, reducing its efficiency and potentially causing signal distortion. Increasing the operating range of the power amplifier through hardware is difficult and costly. Therefore, certain PAPR reduction techniques are required for the transmit waveform. Furthermore, waveform mode constraints are imposed to account for signal distortion caused by factors such as nonlinear devices and channel distortion. Of course, OFDM systems also require consideration of the differences between single-station and multi-station systems. A key issue in OFDM waveform design is the design of orthogonal OFDM waveforms. While a single-station system only needs to consider its own autocorrelation, a multi-station system also requires consideration of the cross-correlation between waveforms to construct a more appropriate optimization objective.

[0055] MIMO radar: Multiple-Input, Multiple-Output radar, or MIMO radar, is a radar with multiple transmit and receive antennas. It can be considered a further development of phased array radar. The signal waveforms transmitted by this radar are highly flexible and easily scalable. Generally, the signal waveforms transmitted by this radar must exhibit good orthogonality.

[0056] Orthogonal waveforms: In pulsed systems, linear convolution is generally used to calculate matched filtering results. However, classic matched filtering results in high autocorrelation sidelobes. Furthermore, when the transmitted OFDM signal bandwidth is limited, the sidelobes of matched filtering increase further. To expand the algorithm's suitability for a wider range of scenarios, weights are added, and the algorithm is designed using the weighted integrated sidelobe level (WISL) as the objective function. This meets the waveform requirements for collaborative sensing of distributed OFDM base stations for detecting small targets.

[0057] The ADMM algorithm breaks down and restructures the problem, converting it into a series of subproblems to solve. It then uses alternating iterations to approximate the optimal solution. During each iteration, ADMM introduces Lagrange multipliers to transform the original problem into a set of subproblems that can be independently or iteratively corrected.

[0058] Lagrange Multiplier Algorithm: The Lagrange Multiplier Algorithm is a widely used optimization algorithm that transforms constrained optimization problems into unconstrained ones, greatly simplifying the problem-solving process. Specifically, this paper utilizes the Lagrange Multiplier method and the KKT condition to construct a new Lagrangian function whose derivative is zero, thereby obtaining the optimal solution.

[0059] Weighted Integrated Range Sidelobe (WISL): WISL is a performance metric that measures the sidelobe energy of signals in radar or communication systems. In wireless communications and radar systems, an ideal waveform should have a low sidelobe level to avoid unnecessary interference and false detection. However, in actual waveform design, it is impossible to completely eliminate sidelobes, so waveform optimization is required to minimize the sidelobe level. WISL, as an important metric for measuring waveform sidelobe energy, can effectively evaluate and optimize waveform performance by weightedly integrating the sidelobe energy of the autocross-correlation function. In radar and wireless communication systems, minimizing WISL allows for the design of more optimal waveforms, improving the system's anti-interference capability and signal detection accuracy.

[0060] In the embodiment of the present invention, the overall idea of ​​the distributed OFDM base station cooperative sensing sequence design is to model and solve the waveform optimization problem of low correlation performance in the distributed OFDM system. The specific steps are as follows: Figure 1 As shown:

[0061] Step 1: Set the number of base stations M, the length N1 of the time domain sequence S, the effective length N2 of the frequency domain sequence X, the FFT transform dimension N, the parameter η that controls the peak-to-average power ratio (PAPR), and the signal average power P.

[0062] Step 2: To ensure the versatility and robustness of the system, randomly generate a time domain signal sequence. Column s m represents the time domain signal sequence of the mth base station, where m = 1, 2, ..., M. Due to hardware limitations, N1 must be less than N2. In practice, the time domain sequence is padded with zeros to a length of N, then transformed to the frequency domain. The middle portion of the frequency domain waveform X, with a length of N2, is cut off, and the frequency domain sequence at all other locations is set to zero. An IFFT transform is performed on the frequency domain waveform to convert it to a time domain waveform, and the first N1 length is cut off as the time domain waveform, with PAPR limited.

[0063] The time domain signal is recorded as The relationship between time-frequency domain signals can be expressed as:

[0064] X=DFAS (1)

[0065] in is the frequency domain subcarrier selection matrix, is the discrete Fourier transform DFT matrix, is the sequence zero-padding matrix.

[0066] Step 3: Generate sidelobe level coefficient matrix and the autocorrelation coefficient matrix

[0067] Step 4: Construct an optimization target by describing the relevant performance of the waveform of the distributed OFDM base station system, and establish an optimization problem by considering the time-frequency domain constraints, PAPR constraints, and energy constraints.

[0068] Based on the distributed OFDM base station system, the expression of weighted integrated sidelobe level WISL can be written as:

[0069]

[0070] ||·||2 represents the L2 norm, ε r represents WISL, c represents a constant;

[0071]

[0072] Among them, Diag represents the function of constructing a diagonal matrix,

[0073] In the problem of jointly designing waveforms and matched filters, we expect that the waveform WISL after the designed waveform passes through the matched filter is minimized and satisfies the following constraints:

[0074] 1) Limit the PAPR of the time domain waveform to meet the requirements of the transmit power amplifier;

[0075] 2) Energy constraints;

[0076] 3) Different requirements for autocorrelation performance in actual engineering.

[0077] Therefore, the joint design problem of band-limited OFDM signal waveform design and matched filter design can be modeled as:

[0078]

[0079] Where ⊙ represents the Hadamard product, H represents conjugate transpose; E m To select a matrix, its (m-1)N+1th to mNth elements are 1, and the rest of the elements are 0.

[0080] Step 5: Use the alternating iterative algorithm ADMM to update the time domain waveform, matched filter, frequency domain waveform and dual variable in sequence.

[0081] 5-1 Equivalent transformation, simplified optimization model:

[0082] In order to solve the above-mentioned quartic optimization function about the S variable, a new variable Y is introduced to reduce the degree of the objective function, and the fourth-order non-convex problem is transformed into a convex problem. The optimization problem can be transformed into:

[0083]

[0084] in, is a selection vector whose mth element is 1 and the rest are 0; mn is the element in the mth row and nth column of S; |·| is the absolute value.

[0085] 5-2 Construct the augmented Lagrangian function for the above problem:

[0086]

[0087] Among them, I M represents the identity matrix of dimension M; represents the Kronecker product, ρ u and ρ v is the penalty coefficient; s, y, x are the vector forms of the corresponding matrix variables S, Y, X, and u and v are dual variables;

[0088] By minimizing Update variables. At the k+1th iteration, the algorithm consists of the following update process:

[0089]

[0090] 5-3 Update S

[0091] The conjugate s of the variable s in equation (7) * Take the derivative, * represents conjugate, and let its derivative be 0, and we get:

[0092]

[0093] Among them, vec represents the matrix steering function;

[0094] The time domain waveform s can be updated by formula (9), and the projection space is obtained according to the peak-to-average power ratio PAPR constraint. Then the signal s of each sampling point in s obtained by solution is mn Update according to the following formula, Composition signal s new As the solution result of this signal s.

[0095]

[0096] 5-4 Update Y

[0097] Regarding the variable y in formula (7) * Taking the derivative and setting it to 0, we get:

[0098]

[0099] The matched filter y can be updated by formula (12), and the projection space is obtained according to the energy constraint Then the mth station signal y in the solved y is m Update according to the following formula, m=1,...,M,y m That is, the mth column of Y, the vector consisting of the (m-1)N1+1th to mN1th elements of y, which is updated by Composition signal y new As the solution result of this signal y.

[0100]

[0101] 5-5 Update X

[0102] The augmented Lagrangian function of equation (7) with respect to the variable x * Taking the derivative and setting it to 0, we get:

[0103]

[0104] The frequency domain waveform x can be updated according to formula (15).

[0105] 5-6 Update the dual variable

[0106]

[0107] The dual variables u and v can be updated according to formula (16).

[0108] Step 6: Output the iteration parameters obtained by the current alternating iteration. The iteration parameters include the objective function value, the residual of each parameter, the number of loops, and the running time. Determine whether each of the output iteration parameters meets the preset conditions. If so, it indicates that the waveform of signal S meets the PAPR constraint and low correlation performance. The iteration ends, the optimal waveform sequence is output, and the perceptual orthogonal waveform design is completed. If not, return to step 5 to continue iteration.

[0109] The following is the performance verification of the waveform designed based on the above-mentioned distributed OFDM base station cooperative sensing sequence design method. Figure 2 This is an overall comparison of the correlation performance of the ISL optimized waveform and the initial random sequence with autocorrelation ratios of 5:1 and 50:1 respectively. It can be seen that the autocorrelation performance of the optimized sequence is improved compared with the initial sequence; Figure 3 is Figure 2 Based on the autocorrelation r 22 From the enlarged image, we can see that the autocorrelation sidelobes of the three ISL waveforms are significantly different. The initial sequence is about -13dB, the sequence with an autocorrelation ratio of 5:1 is about -14dB, and the sequence with an autocorrelation ratio of 50:1 is about -32dB. The autocorrelation performance is greatly improved. Figure 4 This is an overall comparison of the correlation performance of the WISL optimized waveform and the initial random sequence with autocorrelation ratios of 5:1 and 50:1 respectively. It can be seen that the autocorrelation performance of the optimized sequence is improved compared with the initial sequence; Figure 5 is Figure 4 Based on the autocorrelation r 22 From the enlarged image, we can see that the autocorrelation sidelobes of the three WISL waveforms have a significant difference in the specified distance sidelobe area [-10, 10]. The initial sequence is about -14dB, the sequence with an autocorrelation ratio of 5:1 is about -20dB, and the sequence with an autocorrelation ratio of 50:1 is about -86dB. In the specified area, the autocorrelation performance is greatly improved compared to the ISL waveform.

[0110] The above simulation experiments verify the effectiveness of this method.

[0111] In summary, the distributed OFDM base station cooperative sensing sequence design method solves the problem of high waveform sidelobes in the presence of clutter, and provides assistance for target detection and other tasks in the distributed OFDM base station system.

Claims

1. A distributed OFDM base station cooperative sensing sequence design method, characterized in that: Including steps: Step 1: Set the number of base stations M, the length N1 of the time domain signal sequence S, the effective length N2 of the frequency domain signal sequence X, the FFT transform dimension N, the parameter η that controls the peak-to-average power ratio (PAPR), and the signal average power P. Step 2: Randomly generate initial values ​​of the time domain signal sequence S of M base stations, and obtain the initial value of the frequency domain signal sequence X=DFAS of S, where D is the frequency domain subcarrier selection matrix, F is the discrete Fourier transform matrix, and A is the sequence zero padding matrix; Step 3: Generate a sidelobe level coefficient matrix Γ and an autocorrelation ratio coefficient matrix B; Step 4: Considering the time-frequency domain constraints, PAPR constraints, and energy constraints, the waveform design and matched filter joint design problem of the distributed OFDM base station system is established with the goal of minimizing the weighted integrated sidelobe level (WISL) after the signal sequence passes through the matched filter: Among them, ⊙ represents the Hadamard product, ||·||2 represents the L2 norm, and the intermediate quantity H represents the conjugate transpose, the pth diagonal matrix Diag means constructing a diagonal matrix function, the pth angular frequency p=0,1,...,2N1-1; st represents the condition satisfied by the objective function; s is the vector form of S, s mn is the element in the mth row and nth column of S, with variables m=1,2,...,M, and n=1,...,N1, where |·| is the absolute value; E m To select a matrix, the elements from (m-1)N+1 to mN are 1, and the rest are 0; Step 5: Solve the problem in step 4 and output the calculated time domain signal sequence S; Step 6: When the time-domain signal sequence S meets the preset conditions, it is output as the optimal waveform sequence, and the perception waveform design is completed.

2. The method according to claim 1, wherein: Step 5: The specific method for solving the waveform design and matched filter joint design problem of the distributed OFDM base station system is: By introducing the matched filter matrix Y, the waveform design and matched filter joint design problem of the distributed OFDM base station system is transformed into a convex problem: Among them, e m is a selection vector whose mth element is 1 and the rest are 0.

3. The method according to claim 2, wherein: When solving convex problems, first construct the augmented Lagrangian function of the optimization problem Among them, I M represents the identity matrix of dimension M; represents the Kronecker product, ρ u and ρ v is the penalty coefficient; y, x are the vector forms of the corresponding matrix variables Y, X, and u, v are both dual variables.

4. The method according to claim 3, wherein: For the augmented Lagrangian function The solution is solved by the alternating iterative algorithm ADMM, which minimizes the augmented Lagrangian function The objective function value composed of the vector form s of the time domain signal sequence, the form y of the matched filter matrix, the vector form x of the frequency domain signal sequence and the dual variables u, v is updated in sequence, and the updated s is the updated time domain signal sequence S.

5. The method according to claim 4, wherein: At the k+1th iteration, by minimizing the augmented Lagrangian function The specific method of sequentially updating the vector form s of the time domain signal sequence, the form y of the matched filter matrix, the vector form x of the frequency domain signal sequence, and the dual variables u and v is as follows:

6. The method according to claim 5, wherein: In step 6, the iteration parameters obtained by the current alternating iteration are obtained. The iteration parameters include the objective function value, the residual of each parameter, the number of cycles, and the running time. It is judged whether each of the output iteration parameters meets the preset conditions. If so, it indicates that the waveform of the signal S meets the PAPR constraint and low correlation performance. The iteration ends, the optimal waveform sequence is output, and the perception waveform design is completed; if not, return to step 5 to continue the iteration.

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