Underwater detection and communication integrated signal waveform design method based on P4 coding technology

Abstract

The invention provides an underwater detection and communication integrated signal waveform design method based on a P4 coding technology, and the method employs the advantages of small calculation amount and flexible parameters of AFDM in a time-varying channel scene, employs an AFDM signal waveform as a carrier, and serves as the basis of an underwater detection and communication integrated system. The P4 coding has the characteristics of high correlation, simple coding mode and the like, and is used as a reference; however, phase disturbance is introduced to reduce coherence between signals and noise clutters, effectively suppress side lobes and improve signal detection performance by considering that P4 coding can cause side lobe increase and Doppler frequency shift destroys phase characteristics under an underwater multipath condition; and a disturbance sequence is optimized by using a particle swarm optimization (PSO) algorithm, so that the influence of AFDM signal peak sidelobe level increase and symbol error rate increase caused by phase disturbance on the overall performance is reduced, and the influence of phase disturbance on communication is reduced to the minimum while the detection performance is improved.

Description

Technical Field

[0001] The present invention belongs to the field of communication technology, and in particular relates to a method for designing an integrated underwater detection and communication signal waveform based on P4 coding technology. Background Art

[0002] Integrated Sensing and Communication (ISAC) has become a key technology for next-generation wireless communication systems. By enabling resource sharing on a single hardware platform, ISAC significantly improves spectrum efficiency and reduces hardware costs. In high-speed mobility and complex environments, ISAC technology not only meets the needs of efficient communication, but also enables high-precision target perception. However, in underwater environments, problems such as signal attenuation, complex multipath effects, and Doppler frequency shift severely limit the effectiveness of traditional independent sensing and communication systems, making traditional terrestrial ISACs unsuitable for the special underwater environment and not closely integrated with the underwater environment. Therefore, the development of an integrated underwater detection and communication (IUDC) system is particularly important.

[0003] IUDC systems have enormous potential for applications in areas such as marine resource exploration, underwater robot collaboration, underwater vehicle navigation, and marine environmental monitoring. The primary challenge lies in simultaneously meeting the performance requirements of high-precision perception and efficient communication in underwater dual-selective channels, while overcoming technical bottlenecks related to signal design, channel estimation, and interference suppression. Addressing these challenges requires developing waveform design techniques more suitable for underwater applications, laying a solid foundation for the practical application of IUDC systems.

[0004] In ISAC research, scholars have proposed three waveform design strategies: communication-first, perception-first, and joint optimization. These strategies provide a theoretical basis for achieving efficient signal transmission and target detection in underwater environments. Building on this foundation, some researchers have proposed affine frequency division multiplexing (AFDM) to overcome the limitations of traditional waveforms, such as orthogonal frequency division multiplexing (OFDM) or orthogonal time-frequency space (OTFS) algorithms, in detecting and communicating in high-speed mobile or complex underwater channels. AFDM, by utilizing the discrete affine Fourier transform (DAFT), efficiently represents channel characteristics in the delay-Doppler domain, making it particularly well-suited for ISAC systems. AFDM offers strong robustness to Doppler shift, low-complexity channel estimation, a dual-function waveform that supports both perception and communication, and optimal time-frequency diversity gain. Therefore, AFDM is also considered for use in IUDC systems to enhance the integrated capabilities of underwater perception and communication.

[0005] Despite its numerous advantages, AFDM also has some limitations when used in IUDC systems. Its reliance on time-frequency modulation makes it less robust to channel estimation errors and multipath interference. Furthermore, traditional AFDM demodulation methods are extremely sensitive to the time-varying characteristics of underwater channels, significantly degrading detection performance in rapidly changing environments. Summary of the Invention

[0006] Traditional AFDM demodulation methods are extremely sensitive to the time-varying characteristics of underwater channels, significantly degrading detection performance in rapidly changing environments. Improving the coding algorithm is an effective means of addressing these issues, increasing AFDM's adaptability to noise, multipath, and dynamic channel conditions. This is crucial for ensuring the reliability and efficiency of IUDC systems in complex underwater scenarios.

[0007] Therefore, in order to solve the problem of high sidelobe and reduced target detection accuracy of traditional AFDM waveform in IUDC system under underwater time-varying channel conditions, the present invention proposes a signal waveform design method for integrated underwater detection and communication based on P4 coding technology.

[0008] The inventive concept of the present invention is:

[0009] Firstly, this method takes advantage of AFDM's low computational complexity and flexible parameters in time-varying channel scenarios, and uses AFDM signal waveform as the carrier as the basis of the underwater detection and communication integrated system.

[0010] Secondly, P4 coding is used as the benchmark due to its strong correlation and simple coding method. However, considering that P4 coding will cause increased sidelobes and Doppler frequency shift to destroy the phase characteristics under underwater multipath conditions, phase perturbation is introduced to reduce the coherence between the signal and noise clutter, effectively suppress the sidelobes, and improve the signal detection performance. The perturbation sequence is optimized using the particle swarm optimization (PSO) algorithm to reduce the impact of the increased peak sidelobe level and symbol error rate of the AFDM signal caused by phase perturbation on the overall performance, thereby minimizing the impact of phase perturbation on communication while improving detection performance.

[0011] Through this method, an effective trade-off between sonar detection and communication performance can be achieved, and the broadband ambiguity function index of the AFDM communication signal can be improved, so that the signal has a stronger correlation, thereby obtaining more reliable communication and detection information.

[0012] The technical solution of the present invention is:

[0013] The method for designing an integrated underwater detection and communication signal waveform based on P4 coding technology comprises the following steps:

[0014] Step 1: In the DAFT domain, the communication information is coded and modulated by P4 coding to obtain the N-order symbol vector X in the DAFT domain. DAFT as a sequence of communication information;

[0015] Step 2: Add a pilot sequence P before the communication information sequence to form a new sequence, and add different phase perturbations θ[j] to each element of the new sequence to obtain a new symbol vector X′ DAFT :

[0016]

[0017] in, represents the Hadamard product, Θ represents the phase perturbation matrix composed of phase perturbations θ[j], P = [p[1] p[2] ... p[I]] represents the pilot sequence vector, j = 1, 2, ..., N + I; N represents the length of the coding sequence, and I represents the length of the pilot sequence;

[0018] Step 3: Establish an optimization problem for optimizing the phase perturbation matrix Θ:

[0019]

[0020] Where Q is an auxiliary variable, which represents the value of the weighted sidelobe level; is the peak normalized expression of the discrete broadband ambiguity function; WAF[m,β] is the discrete fuzzy function; W[m,β] is the discrete weighting function; θ max is the maximum threshold of phase disturbance;

[0021] Step 4: Use the optimization algorithm to solve the optimization problem of the phase perturbation matrix Θ established in step 3 to obtain the optimized phase perturbation matrix; use the optimized phase perturbation matrix to adjust X′ DAFT Get the final code

[0022] Step 5: According to the AFDM waveform design method, the code obtained in step 4 is Modulation is performed through inverse discrete affine Fourier transform to form the final integrated waveform.

[0023] Furthermore, the complex signal obtained by the P4 encoding is:

[0024]

[0025] Where N represents the length of the encoding sequence, φ n Indicates the phase of the nth signal.

[0026] Furthermore, a Zadoff-Chu sequence is used as a pilot sequence.

[0027] Furthermore, the discrete ambiguity function Ψ WAF [m,β] is obtained by deriving the continuous broadband ambiguity function:

[0028]

[0029] Where s[k] is the discrete time signal, m is the discrete time delay of the signal, and α β is the Doppler stretch factor, s * [α β (km)] is the complex conjugate of the signal under the action of discrete time delay and Doppler expansion factor.

[0030] Furthermore, the Doppler scaling factor is:

[0031]

[0032] where β is the discrete Doppler shift index.

[0033] Furthermore, the discrete weighting function W[m,β] is expressed as:

[0034]

[0035] Where m is the discrete signal delay and β is the discrete Doppler frequency shift index.

[0036] Furthermore, in step 4, the particle swarm optimization algorithm is used to solve the optimization problem of the phase perturbation matrix Θ established in step 3.

[0037] Furthermore, in step 5, the final integrated waveform is formed as follows:

[0038]

[0039] Where c1 and c2 are two AFDM parameters.

[0040] Beneficial effects

[0041] Compared with existing technologies, this paper designs a waveform suitable for an integrated underwater detection and communication system. This waveform uses an AFDM modulation waveform. To address the problem of reduced detection performance of traditional coding methods under underwater multipath conditions, P4 coding and random perturbations are introduced. The system also optimizes the random phase perturbation to improve detection and communication performance. Specifically, a particle swarm optimization (PSO) algorithm is used to determine the optimal value of the random phase perturbation to reduce the sidelobe level of the wideband ambiguity function (WAF), while simultaneously improving the signal's detection performance and radial velocity resolution.

[0042] The advantages of the present invention are as follows: (1) an optimized random phase perturbation P4 coding method suitable for underwater environments is proposed, which effectively improves the WAF characteristics, especially reduces the sidelobe level; (2) a strong anti-multipath and anti-Doppler characteristic is achieved through the AFDM waveform modulation method, thereby improving the waveform detection performance; (3) the improved waveform can significantly improve the resolution and detection accuracy of the detection signal under the condition of a slight increase in the communication bit error rate; (4) the introduced random phase perturbation can be implemented without additional receiving end processing, reducing the system complexity; (5) the designed waveform has flexible adaptability to the trade-off between detection and communication performance. It is suitable for complex underwater environments and effectively improves the accuracy of underwater detection and the robustness and reliability of communication.

[0043] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments with reference to the accompanying drawings, in which:

[0045] Figure 1 :Underwater detection and communication integrated system waveform design and transmission signal processing flow chart

[0046] Figure 2 :A flow chart for obtaining optimal coding based on particle swarm optimization algorithm

[0047] Figure 3 : Zero radial velocity (a) and zero delay (b) of AFDM signal based on P4 coding

[0048] Figure 4 : Zero radial velocity (a) and zero time delay (b) of AFDM signal based on ORP-P4 coding

[0049] Figure 5 : Comparison of autocorrelation performance of AFDM signals based on P4 and ORP-P4 coding

[0050] Figure 6 :Relationship between detection probability and signal-to-noise ratio for different coding methods

[0051] Figure 7 :The relationship between bit error rate and signal-to-noise ratio of different coding methods

[0052] Figure 8 :Relationship between different maximum disturbance limits, signal-to-noise ratio and bit error rate under ORP-P4 coding DETAILED DESCRIPTION

[0053] The specific embodiments of the present invention are further described in detail below with reference to the accompanying drawings and illustrated with reference to examples. The described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention:

[0054] As a waveform design for an integrated underwater detection and communication system, the basic idea is to first encode and modulate the communication information to obtain the baseband signal sequence to be sent, and then, according to the AFDM waveform design method, modulate the obtained baseband signal sequence through an inverse discrete affine Fourier transform to form the initial AFDM baseband waveform.

[0055] Despite its numerous advantages, AFDM also has limitations. Its reliance on time-frequency modulation makes it less robust to channel estimation errors and multipath interference. Furthermore, traditional AFDM demodulation methods are extremely sensitive to the time-varying characteristics of underwater channels, significantly degrading detection performance in rapidly changing environments. Addressing these issues requires improving coding algorithms to enhance AFDM's adaptability to noise, multipath, and dynamic channel conditions. These improvements are crucial to ensuring the reliability and efficiency of integrated detection and communication systems in complex underwater scenarios.

[0056] In this invention, P4 coding is used as the basis for encoding communication information. P4 coding is a special multi-phase coding sequence, widely used in scenarios such as ISAC due to its superior autocorrelation characteristics and anti-interference capabilities. This coding was originally used in radar detection scenarios to optimize range resolution and anti-interference performance. With the development of communication technology, P4 coding has gradually been applied to communication systems, especially ISAC systems. Its core concept is to suppress signal sidelobes through special phase design, thereby improving the system's resolution and anti-interference performance.

[0057] The P4 code is a polyphase sequence, the phase of the nth element of which is defined by the following formula:

[0058]

[0059] The corresponding complex signal is expressed as:

[0060]

[0061] Where N represents the length of the encoding sequence, φ n Indicates the phase of the nth signal.

[0062] Then use the simulated radio frequency division multiplexing signal as the carrier, encode and modulate the communication information through P4 coding in the DAFT domain, and obtain the N-order symbol vector X in the DAFT domain DAFT .

[0063] However, while P4 coding has excellent autocorrelation performance, its sidelobes can significantly increase under underwater multipath conditions, affecting detection accuracy. Doppler shift can disrupt the phase characteristics of P4 coding, reducing perception performance and communication reliability. Therefore, phase perturbation is considered to reduce the sidelobe amplitude of P4 coding. This maintains low autocorrelation sidelobes even in multipath conditions, thereby improving target detection accuracy.

[0064] When adding random perturbations to the code and optimizing the random perturbations, considering the possible channel estimation or signal recovery at the signal receiving end, the simplest and most effective implementation method is to add a pilot sequence P with high autocorrelation performance before the communication information sequence. In this embodiment, the Zadoff-Chu sequence is used as the pilot sequence of the signal. Then, the symbol vector X of order N in the DAFT domain is DAFT Combined with the pilot sequence P into a new sequence, and adding different phase perturbations θ[j] to each element in the new sequence, a new symbol vector X′ is obtained DAFT ,Right now:

[0065]

[0066] in, represents the Hadamard product, Θ represents the phase perturbation matrix composed of phase perturbations θ[j], P = [p[1] p[2] ... p[I]] represents the pilot sequence vector, and j = 1, 2, …, N + I.

[0067] From the perspective of sonar and IUDC, in order to improve the detection performance of integrated detection and communication, it is necessary to reduce the side lobes of the broadband ambiguity function. In general, the ambiguity function of the waveform is determined only by the communication information to be transmitted, that is, X DAFT Phase perturbation provides an additional degree of freedom for the waveform, making it possible to reduce the sidelobes of the ambiguity function. The waveform can be optimized by adjusting each element of the phase perturbation matrix Θ. Furthermore, when processed by the communication receiver, the phase perturbation is treated as noise, eliminating the need to modify the IUDC receiver processing system.

[0068] Of course, the phase disturbance also needs to be limited and cannot be unlimitedly large. Therefore, it is necessary to assume that the phase disturbance θ[j] has a maximum threshold θ max Obviously, as θ max As the random phase perturbation improves the P4 algorithm, the side lobes of the broadband ambiguity function of the AFDM signal will gradually decrease, but the symbol error rate loss in communication symbol recognition will also increase. Therefore, the variable that needs to be optimized is the phase perturbation matrix Θ, and its goal is to optimize the method proposed in this invention at the maximum phase perturbation threshold θ max Under this condition, the sidelobes of the broadband ambiguity function are minimized. Then the optimization problem of optimizing the phase perturbation matrix Θ is expressed as:

[0069]

[0070] Where g(Θ) represents the weighted sidelobe level of the measured sonar broadband ambiguity function. The expression of g(Θ) is:

[0071]

[0072] in, is the peak-normalized expression of the discrete broadband ambiguity function. WAF [m,β] represents the discrete ambiguity function, which can be derived from the continuous broadband ambiguity function as follows:

[0073]

[0074] In the formula is the Doppler factor, c is the underwater sound speed, v m is the radial velocity. Next, discretize the formula to obtain

[0075]

[0076] Where s[k] is the discrete time signal and m is the discrete time delay of the signal. β is the Doppler stretch factor, where β is the discrete Doppler shift index. * [α β (km)] is the complex conjugate of the signal under the action of discrete time delay and Doppler expansion factor.

[0077] In the formula, W[m,β] represents a discrete weighting function that adjusts the impact of different delays and frequency shifts on performance. For example, when sidelobes are more sensitive at low delays and low frequency shifts, they can be given a higher weight. In this embodiment, W[m,β] is expressed as:

[0078]

[0079] This allows the optimization of the sidelobes for any region of interest in the delay-Doppler plane of the discrete wideband ambiguity function.

[0080] The above optimization problem can be rewritten as:

[0081]

[0082] Among them, Q is an auxiliary variable, which represents the value of the weighted sidelobe level. The rewritten optimization problem is a nonlinear optimization problem with many local minima.

[0083] In this embodiment, a particle swarm optimization algorithm (PSO) is used to solve the nonlinear optimization problem. Compared with other algorithms, the PSO algorithm has the advantages of simple implementation, flexible handling of constraints, global search capabilities, and insensitivity to initial values. In particular, the simplicity of the algorithm implementation is consistent with the integration of IUDC, saving node space and reducing node energy consumption. The specific algorithm is as follows. First, the particle position and velocity are defined:

[0084] D i =(Q,Θ)

[0085] V i =(ΔQ,ΔΘ)

[0086] Among them, D i represents the particle position, and the auxiliary variable Q is the desired value, i.e., the target variable. The phase perturbation matrix Θ is a sequence of angle variables, satisfying |θ[j]|<θ max . V i Represents the particle velocity, ΔQ is the scalar velocity, and ΔΘ represents the angular variable velocity. The velocity is usually limited to a range to prevent particles from jumping out of the search space. The update formulas are:

[0087] D i (t+1)=Di (t)+V i (t+1)

[0088] V i (t+1)=ωV i (t)+e1r1(p best -D i (t))+e2r2(g best -D i (t))

[0089] Where t is the current iteration number and T is the maximum iteration number. e1 and e2 are learning factors, which represent the acceleration factors of the particle approaching its own historical optimal solution and the global optimal solution respectively, and are usually set to 1.5 to 2. r1 and r2 are random numbers used to introduce randomness and increase the diversity of the search. best represents the historical optimal solution of each particle, g best Represents the global optimal solution for each particle. This ensures that each particle approaches its own historical optimal solution and the global optimal solution. ω represents the inertia weight. When its value is large, it retains the particle's inertia (global search), and when it is small, it weakens the inertia (local search). Initially, a large value (0.8 to 1.0) encourages global search. Later, a small value (0.4 to 0.6) encourages local search and convergence. The dynamic change formula can be used:

[0090]

[0091] In this way, Q and Θ can be obtained, and |θ[j]|<θ max The optimal solution under these constraints is obtained. At this point, we can obtain an integrated underwater detection and communication signal encoding method based on P4 coding and PSO optimized perturbation. This method is called the Optimized Random Perturbation P4 (ORP-P4) algorithm.

[0092] Finally, the final encoding is obtained using the optimized phase perturbation matrix Substitute the discrete time domain waveform generation formula of the AFDM signal into:

[0093]

[0094] Where c1 and c2 are two AFDM parameters, c1 determines the chirp slope. The resulting waveform is the integrated waveform based on AFDM waveform and ORP-P4 coding technology, suitable for IUDC systems, as demonstrated in this example.

[0095] To illustrate the improvement of the detection performance of the integrated detection and communication signal waveform by the proposed ORP-P4 algorithm, the zero radial velocity and zero time delay graphs of the signal before and after random perturbation optimization, as well as the autocorrelation performance of the obtained waveform, are compared to show the improvement of detection performance. Figure 3 and Figure 4 The ambiguity of signals transmitted using traditional P4 coding and ORP-P4 coding is shown, with the two figures showing the WAF at zero radial velocity and zero time delay, respectively. The proposed ORP-P4 algorithm produces a unique "thumbnail-shaped" WAF that decays rapidly in all directions, enhancing radial velocity and delay resolution. It also reduces the interference observed outside the origin with traditional P4 coding, alleviating the adverse effects of time delay and radial velocity on detection. This demonstrates the superior performance of ORP-P4 in IUDC detection over signals without optimized coding. In addition, Figure 5 It is confirmed that ORP-P4 coding has stronger autocorrelation and lower autocorrelation sidelobes than traditional P4 coding.

[0096] To illustrate the improvement of the detection probability performance of the integrated detection and communication signal waveform of the proposed ORP-P4 algorithm, the detection probability of various coding methods is compared using the peak-to-average ratio detection method under the conditions of a false alarm probability of 0.05 and an AFDM symbol time of 10ms. Specifically, the detector is based on the cross-correlation between the received and transmitted waveforms, and uses the ratio of the peak value to the average value of the cross-correlation as the test statistic. Under a certain signal-to-noise ratio, multiple independent transmissions are performed. For each trial, the peak-to-average ratio of the cross-correlation is calculated and compared with a predetermined false alarm probability value to obtain the detection threshold under this signal-to-noise ratio. The detection probability is calculated as the ratio of the number of trials in which the target is detected to the total number of trials. As Figure 6 As shown, ORP-P4 outperforms 16-QAM and traditional P4 encoding due to its enhanced WAF performance.

[0097] In order to illustrate the impact of the proposed ORP-P4 algorithm on the communication performance of the integrated detection and communication signal waveform, the bit error rates of different coding methods under different signal-to-noise ratio conditions are compared. Figure 7 The figure shows the bit error rate under different signal-to-noise ratio conditions. Standard P4 coding and 16-QAM alone exhibit the same bit error rate performance under the same signal-to-noise ratio. However, the ORP-P4 coding proposed in this example uses phase perturbation to improve detection performance, which introduces noise at the receiver. This makes it difficult to decode and process information, thereby reducing communication performance, but it is still within an acceptable range. Figure 7 It also shows the ORP-P4 at different θ max It can be seen that when θ max As the value increases, performance decreases. Figure 8 This provides some reference for selecting the maximum random perturbation value when using this algorithm for coding and waveform design.

[0098] In summary, the present invention provides a method for designing an integrated signal waveform for underwater multi-base detection communication based on P4 coding technology. At the transmitting end, the communication information is first channel-coded and modulated to obtain a baseband signal sequence to be transmitted; then, according to the AFDM waveform design method, the baseband signal sequence is modulated by inverse discrete affine Fourier transform to form an initial AFDM baseband waveform. Further utilizing the P4 coding sequence with good autocorrelation characteristics, a random phase perturbation optimized by the PSO algorithm is introduced on each element, thereby effectively reducing the broadband ambiguity function sidelobe level of the transmitted signal and improving the detection performance. At the same time, in order to facilitate channel estimation and disturbance compensation at the receiving end, a pilot signal is inserted at the transmitting end. Finally, the generated integrated waveform is amplified by digital-to-analog conversion and a power amplifier, and then sent to the complex underwater acoustic channel through the sonar transmitting array. The advantages of the present invention are: (1) it realizes the integrated design of underwater detection and communication functions, and fully utilizes the detection signal energy; (2) it proposes a signal processing method corresponding to the optimized waveform; (3) it can still ensure excellent detection effect under the condition of high communication bit error rate; (4) it significantly reduces the sidelobe level of the broadband ambiguity function and improves the resolution of the integrated signal; (5) the introduced random phase disturbance can be implemented without additional receiving end processing, which reduces the system complexity.

[0099] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A method for designing an integrated underwater detection and communication signal waveform based on P4 coding technology, characterized by: The following steps are involved: Step 1: In the DAFT domain, the communication information is coded and modulated by P4 coding to obtain the N-order symbol vector X in the DAFT domain. DAFT as a sequence of communication information; Step 2: Add a pilot sequence P before the communication information sequence to form a new sequence, and add different phase perturbations θ[j] to each element of the new sequence to obtain a new symbol vector X′ DAFT : in, represents the Hadamard product, Θ represents the phase perturbation matrix composed of phase perturbations θ[j], P = [p[1] p[2] ... p[I]] represents the pilot sequence vector, j = 1, 2, ..., N + I; N represents the length of the coding sequence, and I represents the length of the pilot sequence; Step 3: Establish an optimization problem for optimizing the phase perturbation matrix Θ: |θ[j]|<θ max Where Q is an auxiliary variable, which represents the value of the weighted sidelobe level; is the peak normalized expression of the discrete broadband ambiguity function; WAF [m,β] is the discrete fuzzy function; W[m,β] is the discrete weighting function; θ max is the maximum threshold of phase disturbance; Step 4: Use the optimization algorithm to solve the optimization problem of the phase perturbation matrix Θ established in step 3 to obtain the optimized phase perturbation matrix; use the optimized phase perturbation matrix to adjust X′ DAFT Get the final code Step 5: According to the AFDM waveform design method, the code obtained in step 4 is Modulation is performed through inverse discrete affine Fourier transform to form the final integrated waveform.

2. The method for designing an integrated underwater detection and communication signal waveform based on P4 coding technology according to claim 1, characterized in that: The complex signal obtained by the P4 encoding is: Where N represents the length of the encoding sequence, φ n Indicates the phase of the nth signal.

3. The method for designing an integrated underwater detection and communication signal waveform based on P4 coding technology according to claim 1, characterized in that: The Zadoff-Chu sequence is used as the pilot sequence.

4. The method for designing an integrated underwater detection and communication signal waveform based on P4 coding technology according to claim 1, characterized in that: Discrete ambiguity function Ψ WAF [m,β] is obtained by deriving the continuous broadband ambiguity function: Where s[k] is the discrete time signal, m is the discrete time delay of the signal, and α β is the Doppler stretch factor, s * [α β (km)] is the complex conjugate of the signal under the action of discrete time delay and Doppler expansion factor.

5. The method for designing an integrated underwater detection and communication signal waveform based on P4 coding technology according to claim 4, characterized in that: The Doppler stretch factor is: where β is the discrete Doppler shift index.

6. The method for designing an integrated underwater detection and communication signal waveform based on P4 coding technology according to claim 1, characterized in that: The discrete weighting function W[m,β] is expressed as: Where m is the discrete signal delay and β is the discrete Doppler frequency shift index.

7. The method for designing an integrated underwater detection and communication signal waveform based on P4 coding technology according to claim 1, characterized in that: In step 4, the particle swarm optimization algorithm is used to solve the optimization problem of the phase perturbation matrix Θ established in step 3.

8. The method for designing an integrated underwater detection and communication signal waveform based on P4 coding technology according to claim 1, characterized in that: In step 5, the final integrated waveform is formed as follows: Where c1 and c2 are two AFDM parameters.

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