Multi-parameter modulation sonar waveform design method based on pulse width costas coding, sonar detection system and computer readable storage medium

Abstract

This application provides a method for designing multi-parameter modulated sonar waveforms based on pulse width Costas coding, a sonar detection system, and a computer-readable storage medium. It relates to the fields of underwater acoustic signal processing and waveform design technology, including system initialization and global parameter configuration; constructing a non-uniform time structure and pulse width coding, outputting the pulse width of sub-pulses and the absolute start time of the sub-pulses on the time axis; generating frequency coding sequences, phase coding sequences, and slope coding sequences to construct a multi-dimensional orthogonal modulation parameter space; outputting the complex baseband waveform of the sub-pulses based on global parameters, the pulse width of the sub-pulses, and the multi-dimensional orthogonal modulation parameter space combined with an adaptive slope adjustment strategy; and performing time-domain waveform synthesis based on the absolute start time of the sub-pulses on the time axis and the complex baseband waveform of the sub-pulses to obtain a multi-parameter modulated sonar waveform based on pulse width Costas coding. This application transforms periodic high grating lobes into low-level background noise by constructing a non-uniform time structure.

Description

Technical Field

[0001] This application relates to the field of underwater acoustic signal processing and waveform design technology, and more specifically, to a multi-parameter modulation sonar waveform design method based on pulse width Costas coding, a sonar detection system, and a computer-readable storage medium. Background Technology

[0002] Active sonar detection, particularly for target detection and identification in shallow sea environments, faces extremely severe challenges. The shallow sea acoustic channel exhibits complex boundary conditions; reflections from the sea surface and seabed lead to severe multipath effects, resulting in strong reverberation interference. Reverberation typically manifests as colored noise associated with the transmitted signal, and its intensity is often much higher than ambient noise, becoming a major bottleneck limiting the performance of shallow sea sonar. To effectively detect targets against a strong reverberant background, the transmitted waveform must possess extremely high signal processing gain and excellent sidelobe suppression capabilities.

[0003] Existing sonar waveform designs, such as linear frequency modulation (LFM) signals and their derivative waveforms (e.g., pulse trains, conventional coded modulation waveforms), while addressing range and velocity resolution to some extent, still have significant drawbacks. First, traditional pulse train waveforms typically employ a uniform time segmentation strategy. This strictly periodic structure inevitably introduces high-amplitude periodic grating lobes into the ambiguity function. Under the influence of strong direct waves or strong target echoes, these high lobes easily mask nearby weak targets, leading to "blind spots." Second, existing multi-parameter modulation methods often struggle to balance time-frequency resolution and sidelobe levels, especially in complex multipath environments like shallow seas. Single-dimensional parameter coding (e.g., only frequency or phase coding) lacks sufficient degrees of freedom to combat variable channel interference, resulting in insufficient reverberation immunity.

[0004] Therefore, in order to meet the detection needs of shallow sea environments with strong reverberation, it is urgent to break the periodic constraints of traditional waveform design and develop a new sonar waveform design method that can simultaneously achieve ultra-low distance sidelobes, high Doppler resolution, and strong anti-reverberation capability. Summary of the Invention

[0005] To address the aforementioned problems, this application adopts a multi-parameter modulated sonar waveform design method based on pulse width Costas coding, comprising the following steps:

[0006] Perform system initialization and global parameter configuration. Global parameters include the total waveform duration of the sonar detection system, the total bandwidth of the transmitted signal, the number of sub-pulse segments, and the sampling rate of the digital signal processing.

[0007] Based on the total waveform duration and the number of sub-pulse segments, a non-uniform time structure and pulse width coding are constructed to output the pulse width of the sub-pulse and the absolute start time of the sub-pulse on the time axis.

[0008] Generate frequency coding sequence, phase coding sequence and slope coding sequence, and construct a multidimensional orthogonal modulation parameter space by combining the number of sub-pulse segments, the total bandwidth of the transmitted signal and the pulse width of the sub-pulse;

[0009] The complex baseband waveform of the output sub-pulse is based on global parameters, the pulse width of the sub-pulse, and the multidimensional orthogonal modulation parameter space combined with an adaptive slope adjustment strategy.

[0010] Time-domain waveform synthesis is performed based on the absolute start time of the sub-pulse on the time axis and the complex baseband waveform of the sub-pulse to obtain a multi-parameter modulated sonar waveform based on pulse width Costas coding.

[0011] Optionally, constructing a non-uniform time structure and pulse width coding includes:

[0012] A Costas sequence of order N was selected as the pulse width coding sequence.

[0013] Summing the Costas sequence yields the total weight of the sequence;

[0014] The discrete integer sequence is mapped to a continuous time quantity using a normalization factor, and the pulse width of the sub-pulse is calculated.

[0015] Based on the pulse width of each sub-pulse, the absolute start time of the sub-pulse on the transmission time axis is calculated recursively.

[0016] Optionally, constructing a multidimensional orthogonal modulation parameter space includes:

[0017] Frequency-coded sequences are generated using Costas sequences, sequence elements. The center frequencies of each sub-pulse are derived based on the following formula:

[0018] ;

[0019] In the formula, Let n be the baseband center frequency of the nth sub-pulse. The starting frequency, For the frequency jump step size, take In the formula, B represents the total bandwidth of the transmitted signal, and N represents the number of sub-pulse segments;

[0020] Phase-coded sequences are generated using pseudo-random binary sequences. Sequence elements ;

[0021] Use pseudo-random binary sequences to generate slope-coded sequences. Sequence elements ;

[0022] This leads to the four-dimensional modulation parameter vector in the multidimensional orthogonal modulation parameter space. , This represents the pulse width of the nth sub-pulse.

[0023] Optionally, the complex baseband waveform of the sub-pulse Represented as:

[0024] ;

[0025] In the formula, The function is a rectangular window function, indicating that the sub-pulse has a value only in local time; t represents the global continuous-time variable. Indicates the phase-coded value; This represents the frequency modulation slope of the nth sub-pulse. This represents the natural exponential function, where j is the imaginary unit.

[0026] Optionally, the frequency modulation slope of the nth sub-pulse The adaptive dynamic adjustment strategy is as follows:

[0027] Set the target effective bandwidth of each sub-pulse to ,have or ;

[0028] Based on the pulse width of the current sub-pulse Calculate the absolute value of the frequency modulation slope. ;

[0029] Combined with slope coding sequence Determine the slope polarity, and finally the frequency modulation slope. The calculation formula is:

[0030] .

[0031] Optionally, the specific expression for time-domain waveform synthesis is:

[0032] ;

[0033] in This indicates that the nth sub-pulse is delayed on the time axis. Waveform The total energy E is normalized to satisfy:

[0034] ;

[0035] The waveform also includes a windowing process before transmission, throughout the entire waveform. Apply a smoothing window function to both ends.

[0036] Optionally, the method also includes a step of performing matched filtering on the echo signal at the receiving end:

[0037] The receiver completely reproduces the multi-parameter modulated sonar waveform based on pulse width Costas coding at the transmitter as the local reference signal. A matched filter with the impulse response as the conjugate inversion of the local reference signal is constructed. The echo signal collected at the receiver is convolved with the impulse response to complete the matched filtering operation.

[0038] Optionally, the order N of the Costas sequence can take values ​​ranging from 1 to 2. And N is a prime number or a power of a prime number minus 1.

[0039] Optionally, sub-pulse bandwidth The setting also needs to satisfy the following constraint: if the spectra of each sub-pulse do not overlap in the frequency domain, then If the spectra of each sub-pulse are allowed to partially overlap in the frequency domain to improve spectral efficiency, then .

[0040] This application also provides a sonar detection system, characterized in that it includes:

[0041] Waveform generation module: It is equipped with a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it implements any of the aforementioned multi-parameter modulation sonar waveform design methods based on pulse width Costas coding and generates digital baseband waveform data.

[0042] Digital-to-analog converter module: used to convert digital baseband waveform data into analog electrical signals;

[0043] Transmitter module: Used to amplify and modulate analog electrical signals to drive underwater acoustic transducers to transmit sound waves underwater;

[0044] Receiver module: Used to receive echo signals reflected from underwater targets and perform preprocessing;

[0045] Signal processing module: Used to perform matched filtering and Doppler compensation processing on the received echo signal and the locally stored reference waveform to extract the target's distance and velocity information.

[0046] This application also provides a computer-readable storage medium storing a computer program thereon, characterized in that, when the program is executed by a processor, it implements any of the aforementioned multi-parameter modulated sonar waveform design methods based on pulse width Costas coding.

[0047] The advantages of the multi-parameter modulation sonar waveform design method, sonar detection system, and computer-readable storage medium based on pulse width Costas coding provided in this application are as follows:

[0048] (1) This method constructs a non-uniform time structure, making the pulse width and absolute start time of the time axis of the sub-pulses non-periodic, so that the cross-correlation functions between different sub-pulses cannot coincide and superimpose on the time axis, thus mathematically transforming the periodic high grid lobes into low-level background noise. Compared with traditional multi-parameter modulation waveforms, it can reduce the peak sidelobes by more than 3dB, significantly improve the sidelobe suppression ratio, and effectively solve the problem of missed detection of nearby weak targets in the background of strong direct waves or strong target echoes.

[0049] (2) The non-uniform pulse width results in different main lobe widths of the Doppler response of each sub-pulse (i.e., misalignment of the Sinc function zeros). After superposition, the side lobes of the Doppler dimension are effectively reduced, improving the sensitivity to low-speed targets. This makes the waveform have a stronger background clutter suppression capability when detecting low-Doppler targets. It improves the sensitivity to low-speed targets and the background clutter suppression capability, adapting to the detection needs of low-speed moving targets in shallow sea environments.

[0050] (3) This method generates frequency, phase, and slope encoded sequences, and constructs a four-dimensional orthogonal modulation parameter space of pulse width, frequency, phase, and slope by combining the sub-pulse pulse width, thus breaking the limitation of insufficient degrees of freedom in traditional single-dimensional parameter encoding. Each modulation parameter sequence is independent of each other and exhibits pseudo-random jump characteristics, giving the waveform rich time-frequency characteristics. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0052] Figure 1 This is an overall flowchart of the multi-parameter modulation sonar waveform design method based on pulse width Costas coding provided in the embodiments of this application;

[0053] Figure 2 It is a traditional uniform waveform time-domain structure diagram;

[0054] Figure 3 This is a time-domain structure diagram of a non-uniform waveform provided in an embodiment of this application. Detailed Implementation

[0055] To make the technical problems, technical solutions, and beneficial effects to be solved by this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the scope of this application.

[0056] Example 1

[0057] like Figure 1As shown, this application provides a method for designing multi-parameter modulated sonar waveforms based on pulse width Costas coding, including the following steps:

[0058] Perform system initialization and global parameter configuration. Global parameters include the total waveform duration of the sonar detection system. (Determines Doppler resolution), total transmitted signal bandwidth B (determines range resolution), number of subpulse segments N (determines coding complexity), and sampling rate of digital signal processing. ;

[0059] In this embodiment, the basic waveform parameters of the sonar detection system are first set. These parameters are the boundary conditions for waveform design and directly determine system performance such as detection range and resolution.

[0060] To simulate a medium-to-short-range high-precision detection scenario, the following parameters are set:

[0061] Total waveform duration: The long pulse width design is intended to achieve fine Doppler resolution. This helps to distinguish targets moving at low speeds.

[0062] Total bandwidth of transmitted signal: The corresponding time resolution is approximately Distance resolution .

[0063] Number of sub-pulse segments: N=10.

[0064] Digital signal processing sampling rate: It satisfies the Nyquist sampling theorem and is sufficient to cover the baseband signal bandwidth.

[0065] Based on the total waveform duration and the number of sub-pulse segments, a non-uniform time structure and pulse width coding are constructed to output the pulse width of the sub-pulse and the absolute start time of the sub-pulse on the time axis, specifically:

[0066] Generate a pulse width encoded sequence of length N (i.e., equal to the number of sub-pulse segments). The total duration of the waveform is determined using this sequence. Perform non-uniform segmentation and calculate the duration of each sub-pulse. and the absolute start time on the timeline .

[0067] A frequency-coded sequence, a phase-coded sequence, and a slope-coded sequence are generated. A multidimensional orthogonal modulation parameter space is constructed by combining the number of sub-pulse segments, the total bandwidth of the transmitted signal, and the pulse width of the sub-pulse. Specifically:

[0068] Generate frequency-coded sequence Phase-coded sequence and slope coding sequence This ensures that the parameter sequences have low cross-correlation characteristics.

[0069] The complex baseband waveform of the output sub-pulse is based on global parameters, the pulse width of the sub-pulse, and the multidimensional orthogonal modulation parameter space combined with an adaptive slope adjustment strategy.

[0070] The generation of linear frequency modulated sub-pulse signals with adaptive slope (complex baseband waveforms of the sub-pulses) is specifically based on the calculated pulse width (i.e., the duration of each sub-pulse). Using the generated multidimensional orthogonal modulation parameters, the complex baseband waveform of the nth sub-pulse is generated one by one. , where the frequency modulation slope It needs to be based on the pulse width of the current sub-pulse Adaptive dynamic adjustments are made to ensure the effective bandwidth of all sub-pulses. Maintain a constant or conform to preset spectral constraints.

[0071] Time-domain waveform synthesis is performed based on the absolute start time of the sub-pulse on the time axis and the complex baseband waveform of the sub-pulse to obtain a multi-parameter modulated sonar waveform based on pulse width Costas coding.

[0072] The generated N sub-pulses are strictly timed according to their start times. Seamlessly splicing is performed to generate a complete pulse width encoded multi-parameter modulation linear frequency modulation (PW-MPCM-LFM) waveform s(t), and after power normalization and digital up-conversion, the sonar transducer is driven to emit.

[0073] like Figure 2 and Figure 3 As shown, unlike traditional waveform design which uniformly divides the time axis, this invention introduces a Costas sequence to non-uniformly divide the total signal duration, resulting in each sub-pulse having a different duration (pulse width). Based on this, frequency hopping, phase modulation, and positive / negative slope modulation are applied to each variable-length sub-pulse.

[0074] Due to the aperiodicity of the sub-pulse start time, the cross-correlation functions between different sub-pulses cannot coincide and superimpose on the time axis, thereby converting the periodic high gate lobes into low-level background noise and significantly improving the sidelobe suppression ratio (PSL). Theory and simulation show that, compared with traditional MPCM waveforms, this invention can reduce peak sidelobes by more than 3-5 dB.

[0075] The non-uniform pulse width results in varying main lobe widths in the Doppler response of each sub-pulse (i.e., misalignment of the Sinc function zeros). When superimposed, these differences effectively suppress the side lobes of the Doppler dimension, enhancing sensitivity to low-velocity targets. This gives the waveform stronger background clutter suppression capabilities when detecting low-Doppler targets.

[0076] By combining random jumps in four-dimensional (pulse width, frequency, phase, and slope) parameters, the enemy finds it difficult to sort and interfere with the signal, significantly improving the waveform's survivability in adversarial environments.

[0077] Constructing non-uniform time structures and pulse width coding includes:

[0078] A Costas sequence of order N is selected as the pulse width coding sequence. ,in This represents the nth element in the pulse width coding sequence, and is a positive integer.

[0079] Summing the Costas sequences yields the total weight of the sequences. ;

[0080] In the formula, This represents the sequence element corresponding to the temporary index k during the summation traversal;

[0081] Using a normalization factor to map a discrete integer sequence to a continuous time quantity, the pulse width of the nth sub-pulse... The calculation formula is:

[0082] ;

[0083] Based on the pulse width of each sub-pulse, recursively calculate the absolute start time of the nth sub-pulse on the transmission time axis. :

[0084] ;

[0085] In the formula, T k This represents the pulse width of the k-th sub-pulse;

[0086] The non-uniform time structure makes the time interval between any two sub-pulses n and m... ,exist The time exhibits a non-periodic distribution, thereby suppressing the periodic grating sidelobes in the distance ambiguity function.

[0087] This invention abandons the traditional uniform segmentation strategy of waveforms and adopts Costas sequence pairs. Non-uniform segmentation is performed. This is a key step in eliminating grating sidelobes.

[0088] In this embodiment, the following example calculations are performed:

[0089] (1) Sequence selection: The classic Costas sequence with length N=10 is selected as the pulse width coding sequence. Its specific value is:

[0090] ;

[0091] This sequence has ideal autocorrelation properties.

[0092] (2) Weighted summation: Calculate the normalized denominator :

[0093] ;

[0094] (3) Pulse width Calculate one by one: according to the formula When n=3, the calculation result is as follows (rounded to 5 decimal places):

[0095] ;

[0096] (4) Start time Step-by-step derivation: Calculate the absolute emission time of each sub-pulse using the recursive accumulation formula. When n=3:

[0097] ;

[0098] Observe the starting time sequence obtained from the above calculation. This allows us to detect the time interval between adjacent pulses (i.e., They are not equal at all. More importantly, the time difference between any two pulses... No longer presenting traditional waveforms ( This represents an integer multiple of the sub-pulse time difference in a traditional uniform waveform. This represents the fixed pulse width pattern of a traditional uniform sub-pulse. For example:

[0099] ;

[0100] This non-periodic time structure directly disrupts the physical condition that the cross-correlation terms in the fuzzy function are superimposed in phase at a specific time delay, thus eliminating the grating sidelobes at the mathematical root.

[0101] The construction of the multidimensional orthogonal modulation parameter space satisfies the following conditions:

[0102] Frequency-coded sequence Choose either Costas or Latin square sequences, sequence elements This is used to control the center frequency jump of each sub-pulse;

[0103] Phase-coded sequence A pseudo-random binary sequence is selected, and the sequence elements are... It is used to modulate the initial phase of each sub-pulse using binary phase keying (BPSK);

[0104] Slope coding sequence A pseudo-random binary sequence is selected, and the sequence elements are... It is used to control the positive and negative polarity of the frequency modulation slope of each sub-pulse;

[0105] In conclusion, , and The three are independent of each other, forming a four-dimensional modulation parameter vector. .

[0106] Multidimensional modulation parameter space and carrier frequency calculation: In order to further improve the anti-interference performance, this embodiment superimposes frequency, phase and slope coding on the non-uniform time structure.

[0107] The variables are defined as follows:

[0108] Frequency jump step size.

[0109] Baseband start frequency.

[0110] : Frequency-coded Costas sequence.

[0111] : The center frequency of the nth sub-pulse.

[0112] Phase and slope encoding sequence.

[0113] In this embodiment, the following example calculations are performed:

[0114] (1) Frequency parameter calculation:

[0115] Step length .

[0116] Starting frequency .

[0117] Another set of Costas sequences was selected as the frequency encoding:

[0118] ;

[0119] (2) Center frequency Step-by-step derivation: Substituting into the formula :

[0120] The center frequency of each sub-pulse is at Pseudo-random transitions were implemented within the range, and the transition mode was decoupled from the pulse width variation mode, which greatly increased the complexity of the waveform and the anti-reconnaissance capability.

[0121] (3) Setting the phase and slope encoding sequence:

[0122] Phase sequence : Select a variant of Barker code and introduce Phase modulation:

[0123] ;

[0124] Corresponding phase value: .

[0125] slope sequence A pseudo-random binary sequence is selected to control the frequency modulation direction.

[0126] ;

[0127] Where 1 represents negative frequency modulation and 0 represents positive frequency modulation.

[0128] Complex baseband waveform of sub-pulse (i.e., the nth sub-pulse) The mathematical model of ) is expressed as:

[0129] ;

[0130] In the formula, The function is a rectangular window function, indicating that the sub-pulse has a value only in local time; t represents the global continuous-time variable. Indicates the phase-coded value; This represents the frequency modulation slope of the nth sub-pulse. This represents the natural exponential function, where j is the imaginary unit.

[0131] Let be the baseband center frequency of the nth sub-pulse, and its calculation formula is:

[0132] ;

[0133] In the above formula The starting frequency, The frequency jump step size is usually taken as... ; The frequency modulation slope of the nth sub-pulse is determined by the slope encoding. and pulse width A joint decision.

[0134] The frequency modulation slope of the nth sub-pulse The adaptive dynamic adjustment strategy is as follows:

[0135] Set the target effective bandwidth of each sub-pulse to ,in It is a preset constant, preferably or ;

[0136] Based on the pulse width of the current sub-pulse Calculate the absolute value of the frequency modulation slope. ;

[0137] Combined with slope coding sequence Determine the slope polarity, and finally the frequency modulation slope. The calculation formula is:

[0138] .

[0139] This strategy ensures that the pulse width is within acceptable limits. Even with drastic changes in the Costas sequence, all sub-pulses maintain a consistent bandwidth coverage in the frequency domain, avoiding spectral holes or excessive overlap caused by pulse width variations.

[0140] In LFM signals, bandwidth In this embodiment, the pulse width from arrive Dramatic changes. Using a fixed slope would result in extremely large bandwidths for long pulses and extremely small bandwidths for short pulses, leading to uneven spectral coverage and spectral holes. Therefore, it is necessary to adjust the slope according to... Dynamic adjustment This ensures that the bandwidth of all sub-pulses is consistent.

[0141] Set target sub-pulse bandwidth The following calculations will be performed one by one. When n=4, This is the longest pulse, and the absolute value of the slope should be the smallest:

[0142] ;

[0143] When n=6 , ;

[0144] The calculation results clearly demonstrate the effectiveness of the "adaptive slope" strategy: in order to maintain the same... Bandwidth, the frequency modulation slope of the shortest pulse ( ) is the longest pulse slope ( It is 10 times that of a traditional single LFM waveform. This dramatic dynamic adjustment of parameters is not present in traditional single LFM waveforms, demonstrating the technological advancement of this invention in maintaining spectral flatness.

[0145] The specific expression for time-domain waveform synthesis is:

[0146] ;

[0147] in This indicates that the nth sub-pulse is delayed on the time axis. Waveform The total energy E is normalized to satisfy:

[0148] ;

[0149] The waveform also includes a windowing process before transmission, throughout the entire waveform. A smoothing window function is applied to both ends of the transmitted waveform to suppress out-of-band spectral leakage caused by transient switching of the transmitted waveform.

[0150] Substitute all the parameters obtained from the above calculations into the sub-pulse model and then concatenate them.

[0151] The mathematical expression for the nth sub-pulse is specified as follows:

[0152] ;

[0153] For example, substituting the parameter n=9, we obtain the specific expression for the last segment of the waveform:

[0154] ;

[0155] This subpulse occurs only in local time. efficient.

[0156] Final synthesized waveform for:

[0157] ;

[0158] This expression describes a complex waveform with a duration of 0.1s, which is composed of 10 LFM signals of different lengths, frequencies, slopes, and phases seamlessly spliced ​​together.

[0159] It also includes the step of performing matched filtering on the echo signal at the receiving end:

[0160] The receiver completely reproduces the multi-parameter modulated sonar waveform based on pulse width Costas coding at the transmitter as the local reference signal. A matched filter with the impulse response as the conjugate inversion of the local reference signal is constructed. The echo signal collected at the receiver is convolved with the impulse response to complete the matched filtering operation.

[0161] The step of performing matched filtering on the echo signal at the receiving end utilizes the broadband ambiguity function characteristics of the PW-MPCM-LFM waveform:

[0162] Broadband ambiguity function of waveform Defined as:

[0163] ;

[0164] in For time delay, This is the Doppler scaling factor. The distance ambiguity function of this waveform ( (Slice) The peak value of the main lobe is located at At that point, its side petals are composed of It is composed of the superposition of several cross-correlation terms. Let the Doppler factor... Distance ambiguity function Expanded to the sum of the autocorrelation and cross-correlation of the sub-pulses:

[0165] ;

[0166] Autocorrelation terms (Main lobe source) This is the matched filter output of each sub-pulse. Since each sub-pulse is an LFM signal, its output approximates a Sinc function:

[0167] ;

[0168] All sub-pulses in When these pulses overlap, they form a sharp main peak. The width of the main peak is determined by the bandwidth of the sub-pulse. The decision, the magnitude of which is determined by the total duration Decide.

[0169] Cross-correlation terms (Sidelobe origin and fusion advantages) This is the misalignment correlation between the nth pulse and the mth pulse.

[0170] ;

[0171] Since the pulse widths between sub-pulses are not the same in the PW-MPCM-LFM waveform, the time difference is determined by the Costas sequence:

[0172] ;

[0173] because It is a non-uniform change. For different The combination is completely random and aperiodic. This means that the energy of the cross-correlation function is "spread" and "pasted" across the entire time axis, making it impossible to form a coherent superposition at a specific location.

[0174] Final distance ambiguity formula:

[0175] ;

[0176] Due to the introduction of the non-uniform time structure in step S2, the time delay difference between any two sub-pulses The non-periodic distribution prevents the cross-correlation terms from coherently superimposing on the time axis, thereby eliminating the periodic grating lobes and causing the range sidelobes to exhibit a noise-like distribution, in which the periodic grating lobe terms are completely eliminated.

[0177] make , investigation Caused Doppler frequency shift .

[0178] ;

[0179] Integral result:

[0180] ;

[0181] In traditional waveforms The Sinc envelope zeros of all sub-items coincide. However, in PW-MPCM-LFM, due to... They are all different, and each sub-item is different. Zero-point misalignment. When one sub-item is at the sidelobe peak, another may be near the zero point. When they are superimposed, they cancel each other out, thus suppressing the Doppler sidelobe.

[0182] Phase Term Includes non-uniform start times This introduces additional random phase rotation on the Doppler axis, further suppressing energy focusing at non-zero Doppler positions.

[0183] Sharpening for Doppler resolution includes:

[0184] Utilizing non-uniform pulse width This makes the response function of each sub-pulse in the Doppler domain... The zero points do not coincide; when the echo signal has a non-zero Doppler frequency shift At that time, the Doppler responses of different sub-pulses undergo incoherent cancellation during superposition, suppressing the Doppler sidelobes; simultaneously, combined with the non-uniform start time determined in step S2... A phase rotation factor was introduced. This factor changes nonlinearly with n, further disrupting the coherent focusing of the Doppler domain energy and giving the waveform the characteristics of a thumbtack-type ambiguity function.

[0185] The order N of the Costas sequence ranges from 1 to 1. Furthermore, N is preferably a prime number or a power of a prime minus 1 to ensure the existence of the Costas sequence and optimal autocorrelation sidelobe performance; the Costas sequence satisfies the finite field condition. The fundamental root property ensures that its difference triangle property is ideal, that is, the difference between any two elements is unique in the whole sequence, thereby maximizing the randomness of non-uniform time intervals.

[0186] Sub-pulse bandwidth The settings also need to satisfy the power spectrum flatness constraint after waveform synthesis: if the spectra of each sub-pulse do not overlap in the frequency domain, then If the spectra of each sub-pulse are allowed to partially overlap in the frequency domain to improve spectral efficiency, then .

[0187] The method also includes an adaptive waveform parameter adjustment step for reverberant environments: in strong reverberant environments, this is achieved by reducing the pulse width coding sequence. The variance of the sub-pulse width distribution is optimized to achieve a more uniform distribution while maintaining a slight aperiodicity, thus balancing Doppler resolution with signal-to-mixing ratio (SCR) in a reverberant environment. In multi-target interference environments, this is achieved by increasing the pulse width coding sequence. The variance is increased by increasing the ratio of the shortest pulse width to the longest pulse width to maximize the discriminative power of the Doppler dimension and improve the ability to resolve nearby velocity targets.

[0188] Waveforms generated based on the above specific embodiments Through fuzzy functions Theoretical verification yields the following specific technical effects:

[0189] Mathematical proof for eliminating grating sidelobes in the distance dimension:

[0190] Theoretical criterion: According to the definition of fuzzy function, the distance dimension ( The cross-correlation sidelobes of () are determined by the following formula:

[0191] ;

[0192] in Let be the sub-pulse cross-correlation function. The necessary and sufficient condition for grating sidelobes to occur is that there exist multiple distinct sub-pulse pairs (n, m) with time differences... Equal values ​​result in multiple cross-correlation peaks occurring at the same time. In-phase superposition. Superposition gain. .

[0193] Traditional waveform (counterexample) verification: If uniform segmentation is used, ,but .for ,exist Pair pulses satisfy At this point, the sidelobe amplitude is 9 times that of a single pulse, forming a strong grating sidelobe.

[0194] Numerical proof in this embodiment (positive example): Substituting the values ​​obtained in step 2... sequence:

[0195] ;

[0196] Calculate the set of all possible sub-pulse time differences Consider the first-order adjacent time difference (i.e., m = n - 1):

[0197] ;

[0198] Observation reveals that no two values ​​in the above set are equal. Further examination of the second-order interval (i.e., m = n - 2):

[0199] ;

[0200] After traversal and calculation, the set The elements in the dataset exhibit high sparsity and non-repetition (approximately Golomb's rule property). This means that for any observation time... ,satisfy There is at most one pair of sub-pulses.

[0201] Quantitative conclusion: In traditional waveforms, The superposition gain at any point is 9; while in the waveform of this invention, the gain at any point is 9. The superposition gain at that point is only 1. The theoretical improvement in peak sidelobe suppression is:

[0202] ;

[0203] Considering the cross-correlation sidelobe tail of the actual signal (i.e. (It is not zero in itself), and the improvement in actual simulation is usually in the range of 3-8dB. Moreover, the originally sharp periodic grating side lobes are completely broken into a flat noise-like background, which greatly improves the detection capability of weak targets.

[0204] Doppler: Significantly sharpens resolution.

[0205] This embodiment includes from arrive Multiple pulse widths.

[0206] Long pulse It provides an extremely narrow Doppler main lobe (zero bandwidth) ).

[0207] short pulse It provides a wider Doppler main lobe (zero-point bandwidth) When the two are superimposed, the main lobe width is dominated by the long pulse (ensuring high resolution), while the side lobes cancel each other out due to the misalignment of the zeros of the Sinc function with different widths.

[0208] In summary, by introducing a Costas sequence to construct a non-uniform time structure and supplementing it with adaptive slope adjustment, this invention successfully eliminates the periodic grating sidelobes from a mathematical perspective while retaining the anti-interference advantages of multi-parameter modulation, thus achieving a comprehensive improvement in sonar waveform performance.

[0209] This application also provides a sonar detection system, including:

[0210] Waveform generation module: It is equipped with a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it implements the multi-parameter modulation sonar waveform design method based on pulse width Costas coding as described above, and generates digital baseband waveform data.

[0211] Digital-to-analog converter module: used to convert digital baseband waveform data into analog electrical signals;

[0212] Transmitter module: Used to amplify and modulate analog electrical signals to drive underwater acoustic transducers to transmit sound waves underwater;

[0213] Receiver module: Used to receive echo signals reflected from underwater targets and perform preprocessing;

[0214] Signal processing module: Used to perform matched filtering and Doppler compensation processing on the received echo signal and the locally stored reference waveform to extract the target's distance and velocity information.

[0215] This application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the multi-parameter modulated sonar waveform design method based on pulse width Costas coding as described in any of the preceding claims.

[0216] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A multi-parameter modulated sonar waveform design method based on pulse width Costas coding, characterized in that, Includes the following steps: Perform system initialization and global parameter configuration, the global parameters including the total waveform duration of the sonar detection system, the total bandwidth of the transmitted signal, the number of sub-pulse segments, and the sampling rate of the digital signal processing; Based on the total duration of the waveform and the number of sub-pulse segments, a non-uniform time structure and pulse width coding are constructed to output the pulse width of the sub-pulse and the absolute start time of the sub-pulse on the time axis. Generate frequency coding sequence, phase coding sequence and slope coding sequence, and construct a multidimensional orthogonal modulation parameter space by combining the number of sub-pulse segments, the total bandwidth of the transmitted signal and the pulse width of the sub-pulse; Based on the global parameters, the pulse width of the sub-pulse, and the multidimensional orthogonal modulation parameter space, combined with an adaptive slope adjustment strategy, the complex baseband waveform of the sub-pulse is output. Time-domain waveform synthesis is performed based on the absolute start time of the subpulse on the time axis and the complex baseband waveform of the subpulse to obtain a multi-parameter modulated sonar waveform based on pulse width Costas coding. The construction of the multidimensional orthogonal modulation parameter space includes: Frequency-coded sequences are generated using Costas sequences, sequence elements. The center frequencies of each sub-pulse are derived based on the following formula: ； In the formula, Let n be the baseband center frequency of the nth sub-pulse. The starting frequency, For the frequency jump step size, take In the formula, B represents the total bandwidth of the transmitted signal, and N represents the number of sub-pulse segments; Phase-coded sequences are generated using pseudo-random binary sequences. Sequence elements ; Use pseudo-random binary sequences to generate slope-coded sequences. Sequence elements ; This leads to the four-dimensional modulation parameter vector in the multidimensional orthogonal modulation parameter space. , This represents the pulse width of the nth sub-pulse; The complex baseband waveform of the sub-pulse Represented as: ； In the formula, The function is a rectangular window function, indicating that the sub-pulse has a value only in local time; t represents the global continuous-time variable. Indicates the phase-coded value; This represents the frequency modulation slope of the nth sub-pulse. This represents the natural exponential function, where j is the imaginary unit; The frequency modulation slope of the nth sub-pulse The adaptive dynamic adjustment strategy is as follows: Set the target effective bandwidth of each sub-pulse to ,have or ; Based on the pulse width of the current sub-pulse Calculate the absolute value of the frequency modulation slope. ; Combined with slope coding sequence Determine the slope polarity, and finally the frequency modulation slope. The calculation formula is: 。 2. The multi-parameter modulated sonar waveform design method based on pulse width Costas coding according to claim 1, characterized in that: The construction of the non-uniform time structure and pulse width coding includes: A Costas sequence of order N was selected as the pulse width coding sequence. Summing the Costas sequence yields the total weight of the sequence; The discrete integer sequence is mapped to a continuous time quantity using a normalization factor, and the pulse width of the sub-pulse is calculated. Based on the pulse width of each sub-pulse, the absolute start time of the sub-pulse on the transmission time axis is calculated recursively.

3. The multi-parameter modulated sonar waveform design method based on pulse width Costas coding according to claim 1, characterized in that: The specific expression for the time-domain waveform synthesis is as follows: ； in This indicates that the nth sub-pulse is delayed on the time axis. The waveform The total energy E is normalized to satisfy: ； The waveform also includes a windowing process before transmission, covering the entire waveform. Apply a smoothing window function to both ends.

4. The multi-parameter modulated sonar waveform design method based on pulse width Costas coding according to claim 1, characterized in that: It also includes the step of performing matched filtering on the echo signal at the receiving end: The receiver completely reproduces the multi-parameter modulated sonar waveform based on pulse width Costas coding at the transmitter as a local reference signal. A matched filter with the impulse response being the conjugate inversion of the local reference signal is constructed. The echo signal collected at the receiver is convolved with the impulse response to complete the matched filtering operation.

5. The multi-parameter modulated sonar waveform design method based on pulse width Costas coding according to claim 2, characterized in that: The order N of the Costas sequence takes values ​​in the range of: And N is a prime number or a power of a prime number minus 1.

6. The multi-parameter modulated sonar waveform design method based on pulse width Costas coding according to claim 1, characterized in that: The sub-pulse bandwidth The setting also needs to satisfy the following constraint: if the spectra of each sub-pulse do not overlap in the frequency domain, then If the spectra of each sub-pulse are allowed to partially overlap in the frequency domain to improve spectral efficiency, then .

7. A sonar detection system, characterized in that, include: Waveform generation module: configured with a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the multi-parameter modulation sonar waveform design method based on pulse width Costas coding as described in any one of claims 1-6, and generates digital baseband waveform data; Digital-to-analog converter module: used to convert the digital baseband waveform data into analog electrical signals; Transmitter module: used to amplify the power and modulate the carrier of the analog electrical signal, driving the underwater acoustic transducer to transmit sound waves underwater; Receiver module: Used to receive echo signals reflected from underwater targets and perform preprocessing; Signal processing module: Used to perform matched filtering and Doppler compensation processing on the received echo signal and the locally stored reference waveform to extract the target's distance and velocity information.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the multi-parameter modulation sonar waveform design method based on pulse width Costas coding as described in any one of claims 1-6.

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