Distributed OFDM base station cooperative sensing sequence design method

Abstract

The invention discloses a distributed OFDM (Orthogonal Frequency Division Multiplexing) base station cooperative sensing sequence design method. The method comprises the following steps: setting parameters required by a 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 a self-cross-correlation proportionality coefficient matrix; an alternating iteration algorithm is adopted to solve the optimal solution of the problem, the waveform optimal solution is solved, the peak-to-average power ratio is limited, a matched filter is updated, energy limitation is carried out, frequency domain waveforms are updated, dual variables are updated, various residual errors, target functions and waveform self-cross-correlation characteristics are counted, iteration is finished, and an optimal waveform sequence is output; and carrying out statistics on various residual errors, objective functions, self-cross-correlation characteristics and other information. According to the method, the optimal solution of the problem is solved by adopting an alternating iteration algorithm, so that the self-cross-correlation sidelobe characteristic of the multi-station waveform is inhibited to the greatest extent, and the interference of clutters on a communication system is reduced.

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, the research on waveform optimization of distributed OFDM base station cooperative sensing stems from the many challenges and demands faced by current wireless communication systems. It is one of the important development directions of modern wireless communication technology, and its purpose is to improve the capacity, coverage and efficiency of wireless networks. OFDM technology has strong anti-multipath interference and frequency selective fading capabilities, so it is widely used in wireless communication systems such as Wi-Fi, 4G LTE and 5G. With the rapid growth of user demand and data traffic, the traditional centralized base station architecture faces huge challenges in capacity and coverage. The distributed base station architecture can provide a larger coverage and higher system capacity by distributing multiple small base stations in the network coverage area to achieve cooperative work between base stations. This architecture can not only improve spectrum utilization, but also reduce the transmit power of user terminals and extend battery life. The cooperative work between base stations is the 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. Cooperative work can also further improve the capacity and reliability of the system through joint transmission and reception technology. Although distributed OFDM systems have many advantages, they also face some technical challenges in their implementation. For example, how to efficiently achieve collaborative work between base stations, how to allocate resources and manage interference in a dynamic environment, how to design low-complexity channel estimation and detection algorithms, etc. The solution to these problems requires continuous exploration and innovation in theoretical research and engineering practice. Wireless communication systems are usually affected by multipath fading and frequency selective interference. However, in a distributed environment, the collaborative work of multiple base stations will cause the system performance to be affected by multiple interferences and complex channel conditions. Distributed OFDM waveforms are expected to improve the system's collaborative perception capabilities for multiple users, improve the system's spectrum utilization efficiency, and enhance the system's resistance to interference, thereby promoting the development of communication systems in complex environments. In actual engineering, in order to improve the system's anti-clutter capability and improve the ability to detect targets, the correlation requirements for the waveforms of OFDM multi-station systems are relatively high. Therefore, by optimizing the waveform design, not only can the system's perception performance be improved, but also its resistance to various types of interference can be enhanced, thereby improving the overall performance of the system.

[0003] The research on waveform optimization of cooperative sensing of distributed OFDM base stations shows broad prospects in wireless communication systems. With the development of 5G and future 6G networks, the number of users and data demand are growing rapidly, and the demand for efficient and stable communication systems is also increasing. The research on waveform optimization of cooperative sensing of 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, wireless communication technology will be promoted to develop in a more efficient, smarter and more environmentally friendly direction, injecting new vitality into the development of communication technology. Summary of the invention

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

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

[0006] Step 1, set the parameters required for the problem; including the number of base stations M, the length of the time domain signal sequence S N1, the effective length of the frequency domain signal sequence X N2, the FFT transformation 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, generating 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 the alternating iterative algorithm to find the optimal solution to the problem;

[0011] Solve the waveform optimal solution and limit the peak-to-average power ratio; first optimize the waveform without constraints, and then limit the peak-to-average power ratio of the updated waveform to meet the PAPR requirements in actual projects;

[0012] Update the matched filter and limit its energy; first update the matched filter by unconstrained optimization, and then limit 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 cycles, and the running time. Determine whether each of the output iteration parameters meets the preset conditions. If so, it indicates that the waveform optimal solution meets the PAPR constraint and low correlation performance. The iteration ends and the waveform optimal solution, that is, the optimal waveform sequence, is output to complete the perception waveform design. If not, return to step 5 to continue the iteration.

[0016] In step 5, considering that the objective functions of the models established for such problems are fourth-order and non-convex, it is generally difficult to directly obtain a closed 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 terms of realizing 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 a waveform and a 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 pth diagonal matrix Diag means constructing a diagonal matrix function, the pth angular frequency st represents the condition that the objective function satisfies; s is the vector form of S, s mn is the element in the mth row and nth column of S, variable m=1,2,...,M, variable n=1,...,N1, |·| is the absolute value; E m To select a matrix, its (m-1)N+1th to mNth elements 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, an alternating iterative algorithm ADMM is used to sequentially update the time domain waveform, the matched filter, the frequency domain waveform and the dual variable;

[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 cycles, and the running time. Determine 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.

[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 signals in adjacent frequency bands, and in-band distortion will cause rotation, attenuation and displacement of the received signal.

[0047] (4) The alternating iterative cycle algorithm ADMM overall framework adopted by 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 The present invention is a flow chart of the distributed OFDM base station collaborative sensing sequence design method.

[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] In order to better describe the embodiments of the present invention, the following definitions are first made:

[0054] OFDM waveform: Regarding the design of the waveform for collaborative sensing of distributed OFDM base stations, since the OFDM system is a multi-carrier system, the signals of each subcarrier will be superimposed in the time domain. If the subcarriers have the same symbol phase, it will bring a very high peak-to-average power ratio. Such a transmission power will exceed the operating range of the transmitter power amplifier, reduce the efficiency of the power amplifier, and easily cause signal distortion. It is difficult and costly to increase the operating range of the power amplifier from the hardware equipment. Therefore, it is necessary to adopt certain PAPR suppression technology for the transmission waveform. At the same time, in order to prevent the distortion of the signal shape caused by factors such as nonlinear devices and channel distortion, the waveform mode is constrained. Of course, in the OFDM system, the differences between single stations and multiple stations must also be considered. The key issue in OFDM waveform design is the design of OFDM orthogonal waveforms. A single base station only needs to consider its own autocorrelation, but for a multi-station system, the cross-correlation between waveforms must also be considered to construct a more appropriate optimization target.

[0055] MIMO radar: Multiple-input multiple-output radar, that is, a radar with multiple transmitting antennas and multiple receiving antennas. It can be seen as a further development of phased array radar. The signal waveform emitted by this radar has strong flexibility and is easy to expand. Generally speaking, the signal waveforms emitted by this radar need to have good orthogonal characteristics.

[0056] Orthogonal waveform: In the pulse system, the linear convolution method is generally used to calculate the matched filtering result, and the classic matched filtering autocorrelation sidelobe is high; and when the transmission bandwidth of the OFDM signal is limited, the sidelobe of the matched filter is further increased. At the same time, in order to make the algorithm suitable for more scenarios, weights are added, and the algorithm is designed with the weighted integrated sidelobe level WISL as the objective function to meet the detection requirements of the waveform of the distributed OFDM base station cooperative perception for weak targets.

[0057] ADMM algorithm: decompose and reorganize the problem, convert the original problem into a series of sub-problems to solve, and then use alternating iterations to approach the optimal solution. In each iteration, ADMM introduces Lagrange multipliers to convert the original problem into a set of sub-problems that can be independently or iteratively corrected.

[0058] Lagrange multiplier algorithm: Lagrange multiplier algorithm is a widely used optimization algorithm, which transforms the constrained optimization problem into an unconstrained optimization problem, greatly simplifying the problem-solving process. In particular, the present invention will use the Lagrange multiplier method and KKT conditions to construct a new Lagrangian function so that its derivative is zero, thereby obtaining the best solution.

[0059] Weighted Integrated Range Sidelobe WISL: WISL is a performance indicator for measuring the sidelobe energy of signals in radar or communication systems. In wireless communication and radar systems, the 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 the sidelobe, so the waveform needs to be optimized to minimize the sidelobe level. WISL is an important indicator for measuring the sidelobe energy of a waveform. By weighted integration of the sidelobe energy of the autocorrelation function, it can effectively evaluate and optimize the performance of the waveform. In radar and wireless communication systems, by minimizing WISL, a better waveform can be designed to improve the system's anti-interference ability 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 of the time domain sequence S N1, the effective length of the frequency domain sequence X N2, the FFT transformation dimension N, the parameter η for controlling the peak-to-average power ratio PAPR, and the signal average power P.

[0062] Step 2: In order to ensure the versatility and robustness of the system, a time domain signal sequence is randomly generated. Middle Columns m Represents the time domain signal sequence of the mth base station, m = 1, 2, ..., M. Due to hardware limitations, N1 is required to be less than N2. In actual operation, the time domain sequence is padded with zeros to a length of N, then transformed to the frequency domain and the frequency domain waveform X with an intermediate length of N2 is intercepted in the frequency domain, and the frequency domain sequence at other positions is set to zero; the frequency domain waveform is transformed into a time domain waveform by IFFT, and the first N1 length is intercepted as a time domain waveform, and the PAPR is 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 ratio 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; s 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) is * Take the derivative, * represents conjugate, and set its derivative to 0, and we get:

[0092]

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

[0094] The time domain waveform s can be updated by equation (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 is solved mn Update according to the following formula, Composition signal new As the solution result of this signal s.

[0095]

[0096] 5-4 Update Y

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

[0098]

[0099] The matched filter y can be updated by equation (12) and the projection space is obtained according to the energy constraint. Then the signal y of the mth station 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 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 cycles, and the running time. Determine 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 perceptual orthogonal waveform design is completed; if not, return to step 5 to continue the iteration.

[0109] The following is the performance verification of the waveform designed based on the above-mentioned distributed OFDM base station collaborative 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 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 of the distributed OFDM base station system.

Claims

1. A distributed OFDM base station cooperative sensing sequence design method, characterized in that: Includes 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 transformation dimension N, the parameter η for controlling the peak-to-average power ratio PAPR, and the signal average power P; Step 2: randomly generate initial values ​​of the time domain signal sequences 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, generating 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 filtering 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, variable m=1,2,...,M, variable n=1,...,N1, |·| is the absolute value; E m To select a matrix, its (m-1)N+1th to mNth elements 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, characterized in that: 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, characterized in that: 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, u, v are dual variables; ρ u and ρ v Both are penalty coefficients.

4. The method according to claim 3, characterized in that: For the augmented Lagrangian function The solution is solved by the alternating iterative algorithm ADMM, by minimizing 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, characterized in that: 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, v is:

6. The method according to claim 5, characterized in that 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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