Signal decomposition-based anti-random symbol timing offset interference waveform generation method

Abstract

The application discloses a signal decomposition-based anti-random symbol timing offset interference waveform generation method, and belongs to the technical fields of wireless communication, spectrum security and intelligent signal processing. According to a target communication signal symbol rate, a plurality of time-shifted band-limited basis functions are configured, and an interference waveform is constructed by weighting and combining basis function coefficients; the basis function coefficient generation is converted into a finite time domain sequential decision, the waveform effect is evaluated under multiple symbol timing offset conditions in terms of an average bit error rate, a strategy gradient method is used to update the coefficient generation strategy, and an optimized coefficient sequence is obtained. In the online phase, the coefficient sequence is directly called to synthesize, normalize and output the interference waveform; when the target symbol rate or bandwidth changes, bandwidth adaptation is realized by adjusting the time scale of the basis function, and the coefficient sequence does not need to be re-optimized.

Description

Technical Field

[0001] This invention belongs to the fields of wireless communication, spectrum security and intelligent signal processing technology, and specifically relates to a method for generating waveforms that resist random symbol timing offset interference based on signal decomposition. Background Technology

[0002] With the development of cognitive radio and software-defined radio technologies, unauthorized spectrum occupation methods are becoming increasingly complex. In legally authorized spectrum control scenarios, physical-layer interference against unauthorized communication signals is a technical means to maintain order in spectrum use. Due to differences in modulation methods, symbol rates, and pulse shaping among different communication links, the impact of different interference waveforms on the target receiver varies significantly under the same power constraint. Therefore, designing interference waveforms adapted to the characteristics of the target communication signal is of great importance for improving interference effectiveness and power utilization efficiency.

[0003] Existing research on interference waveforms mainly includes two categories: offline theoretical design and online interactive optimization. Offline theoretical design methods typically determine the optimal interference waveform through theoretical analysis based on prior information such as the modulation scheme and symbol rate of the target communication signal. These methods can pre-design the waveform and directly call it in actual tasks. However, these methods are usually based on the assumption that the interference signal and the target communication signal are symbol-synchronized or that there is a definite symbol timing offset between them. When the interference signal generates an unknown symbol timing offset due to differences in the propagation path, the superposition relationship between the waveform structure and the target symbol changes with the offset, causing significant fluctuations in the performance of the pre-generated waveform under different offset conditions. Online optimization methods, on the other hand, interact with the target communication system in real time and continuously adjust the waveform parameters based on the feedback obtained. This allows for adaptive optimization for unknown but approximately constant symbol timing offsets during a single task. However, these methods require continuous waveform exploration, feedback acquisition, and strategy updates, resulting in long online optimization times that are difficult to meet the requirements of rapid response in spectrum control scenarios. Furthermore, the waveform optimized for the current offset conditions is often not directly applicable to other unknown offsets. In addition, most of the above methods use predefined digital modulation structures to construct candidate waveforms, and mainly search within the range of symbol-level parameters such as modulation mode, duty cycle, average power or pulse duration. The candidate waveform space is limited, making it difficult to make fine-grained adjustments to the local structure of the waveform in the continuous time domain.

[0004] Therefore, there is an urgent need for an interference waveform generation method that can break through the limitations of the predefined symbol-level waveform space, complete waveform optimization under multiple random symbol timing offsets, and can be directly called in actual tasks, so as to balance the ability to adapt to random time offsets and the speed of online response. Summary of the Invention

[0005] The purpose of this invention is to provide a method for generating waveforms that resist random symbol timing offset interference in spectrum control scenarios, in order to solve the problems that existing offline interference waveforms rely on symbol synchronization, waveforms designed for single symbol timing offsets are difficult to apply to other unknown offsets, and online interactive optimization is difficult to meet the requirements of rapid response.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for generating waveforms resistant to random symbol timing offset interference based on signal decomposition, comprising: Step 1: Establish a model of the target communication and jamming signal, using the symbol timing offset of the jamming signal relative to the target communication signal as a random variable, and using the bit error rate of the target receiver under the random symbol timing offset condition as the basis for evaluating the jamming effect. Step 2: Configure multiple time-shifted band-limited basis functions according to the symbol rate of the target communication signal, and weight and combine the multiple time-shifted band-limited basis functions according to their corresponding basis function coefficients to construct an interference waveform; Step 3: The joint generation of multiple basis function coefficients is transformed into a sequential decision process in the finite time domain, generating each basis function coefficient in turn to obtain a complete sequence of basis function coefficients; Step 4: Evaluate the interference waveforms generated by the complete basis function coefficient sequence under multiple symbol timing offset conditions, and determine the overall interference effect based on multiple bit error rates; Step 5: Based on the combined interference effect and the sampling trajectory formed by the sequential decision-making process, update the basis function coefficient generation strategy using the policy gradient method to obtain the optimized basis function coefficient sequence; Step 6: Save the optimized basis function coefficient sequence. In the online stage, call the optimized basis function coefficient sequence to synthesize the interference waveform, and output it after energy normalization and power scaling.

[0007] Compared with the prior art, the beneficial effects of the present invention are: (1) This invention utilizes a linear combination of multiple time-shifted band-limited basis functions to construct interference waveforms, expanding the design object of the interference waveform from predefined modulation methods, duty cycles and other symbol-level parameters to a sequence of basis function coefficients, thereby expanding the candidate waveform space and enabling fine-grained adjustment of local waveform structures smaller than the symbol period.

[0008] (2) This invention uses the symbol timing offset of the interference signal relative to the target communication signal as a random variable, and performs joint evaluation and offline optimization of the same interference waveform under multiple symbol timing offset conditions. The interference waveform obtained in this way does not depend on a certain symbol timing offset, and can still maintain a relatively stable interference effect under unknown random symbol timing offset conditions.

[0009] (3) The present invention transforms the joint optimization process of multiple basis function coefficients into a sequential decision process, and constructs a termination reward based on the comprehensive interference effect of the complete waveform under multiple symbol timing offsets, thereby enabling interference waveform optimization in a high-dimensional continuous coefficient space and reducing the difficulty of selecting all basis function coefficients at once.

[0010] (4) This invention adopts an offline training and online calling working mode. After training is completed, there is no need to estimate or compensate for the current symbol timing offset in the online stage, nor is there a need to re-interact and optimize with the target communication system online. It only needs to complete the basis function weighted synthesis and power adjustment based on the obtained coefficient sequence, thus improving the timeliness of interference waveform generation and output.

[0011] (5) The present invention can change the output waveform bandwidth by adjusting the time scale of the band-limited basis function while keeping the basis function coefficient sequence unchanged, so that the same set of optimization results can adapt to target communication signals with different bandwidths, reducing the need to retrain the waveform when the target signal parameters change.

[0012] To evaluate the interference performance of the proposed method, the simulation experiments of this invention selected impulse interference and noise interference as comparison schemes. Impulse interference refers to a symbol-level interference method that generates interference signals using a traditional digital modulation structure and optimizes the interference duty cycle using a linear slot machine algorithm based on Thompson Sampling. The interference modulation pattern is selected based on the theoretically optimal result. Noise interference refers to directly using Gaussian white noise as the interference signal under the same average power constraint, without modulation design or waveform parameter optimization. The former represents a traditional structured interference method with optimized parameters, while the latter represents a basic unstructured interference method that does not depend on the target signal structure. In the following text, "impulse interference" and "noise interference" refer to the two schemes mentioned above, respectively. Attached Figure Description

[0013] Figure 1 This is a flowchart of the present invention.

[0014] Figure 2 This is a system model diagram showing the target transmitter, target receiver, interference waveform generator, and noise signal superimposed in the channel.

[0015] Figure 3 The flowchart of the waveform coefficient optimization policy gradient algorithm based on signal decomposition is shown, illustrating the relationship between state input, policy network, sequential coefficient generation, environmental feedback, trajectory collection, and policy update.

[0016] Figure 4 The results show the comparison of bit error rates of the proposed method and the comparative scheme for binary phase shift keying target communication signals under different signal-to-noise ratio conditions.

[0017] Figure 5 The results show the comparison of bit error rate of the method of the present invention and the comparative scheme for the target communication signal of quadrature phase shift keying under different signal-to-noise ratio conditions.

[0018] Figure 6 The results show the comparison of bit error rates of the method of the present invention and the comparative scheme for hexadecimal quadrature amplitude modulation target communication signals under different signal-to-noise ratio conditions.

[0019] Figure 7 The results show the comparison of bit error rates of the proposed method and the comparative scheme for binary phase shift keying target communication signals under different symbol timing offset conditions when the signal-to-noise ratio is 10dB.

[0020] Figure 8 The results show the comparison of bit error rates of the proposed method and the comparative scheme for orthogonal phase shift keying target communication signals under different symbol timing offset conditions when the signal-to-noise ratio is 10dB.

[0021] Figure 9 The results show the bit error rate comparison between the method of this invention and the comparative scheme for hexadecimal quadrature amplitude modulation target communication signals under different symbol timing offset conditions when the signal-to-noise ratio is equal to 10dB.

[0022] Figure 10 The results show the comparison of bit error rates of the proposed method and the comparative scheme for binary phase shift keying target communication signals under different target signal bandwidth conditions when the signal-to-noise ratio is 10dB.

[0023] Figure 11 The results show the comparison of bit error rates of the method of the present invention and the comparative scheme for orthogonal phase shift keying target communication signals under different target signal bandwidth conditions when the signal-to-noise ratio is equal to 10dB.

[0024] Figure 12 The results show the comparison of bit error rates of the proposed method and the comparative scheme for hexadecimal quadrature amplitude modulation target communication signals under different target signal bandwidth conditions when the signal-to-noise ratio is 10dB. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] Example 1: Please see Figures 1-12This invention provides a method for generating waveforms resistant to random symbol timing offset interference based on signal decomposition, comprising the following steps: S1. Target communication and jamming signal modeling; S2. Band-limited basis function configuration and interference waveform construction based on signal decomposition; S3. Sequential decision modeling and generation of basis function coefficients; S4. Joint evaluation of waveform effects under multi-symbol timing offset; S5. Policy update based on coefficient generation of policy gradient; S6. Waveform online synthesis and output.

[0027] The following is a detailed explanation of each step.

[0028] S1. Target communication and jamming signal modeling, specifically: Please see Figure 2 .

[0029] Establish a system and signal model with random symbol timing offset. The system includes: target transmitter Tx, target receiver Rx, interference waveform generation terminal Jx, and training control module.

[0030] The target transmitter Tx sends the target communication signal to the target receiver Rx. The interference waveform generator Jx sends the designed interference waveform in a legally authorized environment. The target communication signal and the interference signal are superimposed through the channel and then reach the target receiver Rx.

[0031] Target communication waveform It can be represented as: in, The pulse shaping function used by the transmitting end. For symbol period, Symbol rate, Data symbols obtained from PSK, QAM, or other digital modulation constellations.

[0032] Therefore, the target communication waveform Data symbols Pulse shaping function After pulse shaping, in each symbol period It is formed by stacking the elements one by one.

[0033] Taking an Additive White Gaussian Noise (AWGN) channel as an example, assuming the receiver is coherent and the transmitter and receiver are perfectly synchronized, the signal received by the target receiver Rx... Represented as: in, and These are the target signal power and the interference signal power, respectively. To normalize the interference waveform, With a mean of 0 and a variance of noise, Defined as the timing offset of random symbols, it represents the timing offset of unknown symbols caused by differences in propagation paths.

[0034] As can be seen from the above received signal model, the signal received by the target receiver Rx consists of the target communication signal, interference signals with random symbol timing offsets, and noise signals. The distortion caused by interference signals and noise will produce errors during demodulation, thereby reducing the communication quality of the target link between the target transmitter Tx and the target receiver Rx.

[0035] In the above system model, the objective of this invention is to design an interference waveform that can maximize the bit error rate (BER) of the target receiver under given power constraints and random symbol timing offset conditions.

[0036] After completing the target communication and interference signal modeling, proceed to step S2 to construct the interference waveform based on signal decomposition.

[0037] S2. Construction of interference waveforms based on signal decomposition, specifically as follows: To expand the candidate interference waveform space and search for effective waveforms under random symbol timing offset conditions, this embodiment uses a signal decomposition-based method to construct interference waveforms.

[0038] According to signal representation theory, any continuous-time signal can be mapped to a finite-dimensional signal space. Given a set of basis functions: ; arbitrary signal All can be expanded as follows: in express In basis functions The projection onto the surface. Therefore, both the target communication signal and the jamming signal can be represented by basis function expansion.

[0039] According to the above definition, when two signals are represented in the signal space expanded by the same basis function, their correlation can be effectively enhanced, thereby improving interference performance.

[0040] According to the Nyquist-Shannon sampling theorem, any band-limited signal can be represented as a linear expansion of a time-shifted sinc function. Since target signals in practical applications typically exhibit band-limited characteristics, the time-shifted sinc function can serve as the fundamental function for waveform construction. Furthermore, by adjusting the time scaling factor of the sinc function, the bandwidth of the final generated signal can be flexibly controlled to meet different interference requirements.

[0041] Therefore, normalized interference waveform This can be expressed as a linear expansion of the time-shifted sinc basis function: , in, Indicates the first The weight coefficients of each basis function The time interval between adjacent basis functions. The time scale factor of the sinc function is based on the target symbol rate. Configure the settings to match the bandwidth of the generated waveform with the bandwidth of the target signal. This is done by adjusting the coefficients. It can adjust the waveform shape with a finer time resolution than symbol-level modulation structures.

[0042] Compared with existing symbol-level interference waveforms designed based on digital modulation signal structures, this embodiment constructs interference waveforms from the perspective of signal decomposition. It describes the interference waveform structure through a linear combination of multiple time-shifted sinc basis functions, enabling the interference waveform to be adjusted with finer granularity in the continuous time domain. This allows for more flexible construction of interference waveforms even when symbol timing offsets exist.

[0043] Under power constraints, the coefficient sequence of the above basis functions needs to be jointly optimized to maximize the interference effect.

[0044] Because the target communication signal has cyclic stationary characteristics, the interference waveform can be designed within a single waveform segment and then repeated periodically to form a continuous interference signal, thus reducing design complexity while maintaining the interference effect.

[0045] Specifically, the duration is selected as Given a waveform segment, use K basis functions within the waveform segment, and the corresponding basis function coefficients form a coefficient vector: ; Based on the coefficient vector The corresponding interference waveform segment is generated and optimized. After optimization, the interference waveform segment is repeated periodically to form a continuous interference signal.

[0046] Subsequently, the generated interference waveform is normalized in energy and scaled in power to reduce the interference signal power. Not exceeding the preset maximum power .

[0047] Therefore, the specific optimization objective of the basis function coefficient sequence is expressed as: The constraints are: in, Indicates the use of coefficient sequence And in time offset Bit error rate of the target receiver at that time. This represents the expectation on a preset random timed offset distribution.

[0048] The above optimization objective indicates that, under the interference signal power Not exceeding the preset maximum power Under the condition of, for the basis function coefficient sequence Optimization is performed to maximize the expected bit error rate of the target receiver under a preset random symbol timing offset distribution, thereby obtaining the optimal coefficient sequence. .

[0049] Due to the presence of random symbol timing offsets, it is difficult for the interference waveform generator to analytically model the objective function used for interference waveform optimization. To address this issue, this invention reformulates the parameter optimization problem as a reinforcement learning (RL) problem to learn an effective interference waveform, and further, in step S3, the basis function coefficient sequence... The generation is decomposed into a sequential decision-making process in the finite time domain.

[0050] S3. Sequential decision modeling and generation of basis function coefficients, specifically: In step S2, the interference waveform It is obtained by linear combination of multiple time-shifted sinc basis functions, and its waveform structure is composed of the basis function coefficient sequence. Sure.

[0051] Since joint optimization of K basis function coefficients simultaneously will form a high-dimensional continuous parameter space, and the interference effect of the coefficient sequence can only be evaluated by the bit error rate of the target receiver after all basis function coefficients are determined and the complete interference waveform is generated, this embodiment transforms the problem of generating the interference waveform into a reinforcement learning problem, and decomposes the generation process of the coefficient sequence θ into a sequential decision process in the finite time domain.

[0052] Specifically, the process of generating a complete coefficient sequence is divided into K decision steps. In the i-th decision step, the current state is constructed based on the basis function coefficients determined in the previous decision steps. The agent selects an action based on the current interference strategy π. And use the action to determine the coefficients corresponding to the i-th sinc basis function. After the current coefficients are determined, the state changes from... Transition to the next state This process is repeated until a complete coefficient sequence is obtained. The specific states, actions, and state update methods in the sequential decision-making process are as follows: State construction: Due to the The coefficients of the basis functions The selection is based on the fact that the coefficients of the preceding basis functions have already been determined, therefore, in the... At each decision step, the current state vector will be... Defined as: Wherein, the state vector The dimension is equal to the length of the design coefficient sequence K.

[0053] In the state vector In the above, the first i elements are used to record the basis function coefficients that have been determined in the preceding decision steps.

[0054] The rest are still undetermined The positions corresponding to the basis function coefficients are filled with 0.

[0055] Therefore, the state vector It can characterize the selection of basis function coefficients that have been completed before the current decision step.

[0056] In the initial decision step i=0, since no basis function coefficients have been generated yet, the initial state is: As the decision-making process proceeds, the determined basis function coefficients are sequentially written into the corresponding positions of the state vector; For example: in determining coefficients Then, the status of the next decision step is updated as follows: Thus, the coefficients obtained from this decision Reserved for the next decision-making step.

[0057] Action generation: In the i-th decision step, the action Defined as the coefficient corresponding to the i-th sinc basis function, i.e.: Therefore, each time an action selection is performed, the weight coefficient of a sinc basis function is determined.

[0058] Since the basis function coefficients take continuous values, this embodiment uses a continuous action space to generate the basis function coefficients, thereby enabling fine control of the interference waveform structure.

[0059] In the i-th decision step, the agent determines the current state. The action distribution corresponding to the interference strategy π output is used to select actions from the action distribution. Thus we obtain: Then Write the current coefficient sequence and update the state. .

[0060] Follow the steps outlined above: It can then be generated step by step: Finally, the complete sequence of basis function coefficients is obtained: After completing all K decision steps, the obtained coefficient sequence θ is weighted and combined with the corresponding time-shifted sinc basis function according to the interference signal synthesis formula in step S2 to generate a complete interference waveform.

[0061] Since the bit error rate corresponding to the target receiver can only be obtained after all K coefficients have been generated and synthesized into a complete interference waveform, after the sequential generation of coefficients is completed, step S4 is entered to jointly evaluate the generated interference waveform under multiple symbol timing offset conditions.

[0062] S4. Joint evaluation of waveform effects under multi-symbol timing offset, specifically: To address the issue of unknown random symbol timing offset between the interference signal and the target communication signal, this embodiment does not evaluate and optimize the generated interference waveform for a specific symbol timing offset. Instead, it uses the symbol timing offset τ as a random variable, selects multiple different symbol timing offsets within a preset symbol timing offset range, and evaluates the interference effect on the same interference waveform generated in step S3.

[0063] For each training epoch, after the sequential generation of K basis function coefficients is completed, based on the complete coefficient sequence: , and synthesize a complete interference waveform.

[0064] Subsequently, multiple different timing offsets are set within a preset random symbol timing offset range, and the corresponding timing offsets are applied to the interference waveform to obtain the bit error rate of the target receiver under different timing offset conditions.

[0065] Let the timing offsets of the selected symbols be: The corresponding measured bit error rates of the target receiver are as follows: Where L represents the number of symbol timing offsets selected in a single training round.

[0066] The bit error rates obtained under the above multiple symbol timing offset conditions are jointly evaluated, and their average value is taken as the bit error rate corresponding to the current complete interference waveform. That is: Therefore, the evaluation results reflect the current coefficient sequence. The overall interference effect under multiple symbol timing offsets is reflected, rather than just its interference performance under a single fixed symbol timing offset.

[0067] Since the bit error rate can only be calculated by the target receiver after all K basis function coefficients have been generated and synthesized into a complete interference waveform during the sequential generation process, the first K-1 decision steps cannot obtain a complete evaluation of the interference effect.

[0068] Based on this, this embodiment uses a terminal reward method to construct instant rewards. .

[0069] The immediate reward obtained by the agent in the i-th decision step Defined as: in This represents the bit error rate (BER) at the receiver, which is calculated after the complete interference waveform is generated. A positive reward scaling factor is used to amplify the reward value, thereby promoting stable convergence of the algorithm.

[0070] Therefore, in the first K−1 decision steps: In the final decision-making step, namely: At that time, the complete basis function coefficient sequence has been generated, and the complete interference waveform can be synthesized. Therefore, the bit error rate obtained from the joint evaluation can be used to... As feedback from the terminal, the following was obtained: The above reward structure ensures that all basis function coefficients in a training round collectively correspond to the overall interference performance of the final interference waveform, rather than calculating the interference effect independently for each individual basis function coefficient.

[0071] After K consecutive decision-making steps, the sampling trajectory formed in a complete training round is represented as: in, This represents a complete trajectory obtained by strategy π sampling; This represents the termination state after all K basis function coefficients have been generated.

[0072] After defining the state, action, and reward, this embodiment aims to maximize the cumulative return of the entire sequential decision-making process, so that the interference waveform corresponding to the generated basis function coefficient sequence has a better comprehensive interference effect.

[0073] The objective function corresponding to strategy π is defined as follows: Where Eν∼π[⋅] represents the expectation of the trajectory ν sampled by policy π, γ represents the discount factor, and satisfies: This represents the discount factor.

[0074] Therefore, by maximizing the objective function This gradually leads the strategy to generate a sequence of basis function coefficients that can achieve a higher average bit error rate under multiple random symbol timing offsets.

[0075] Due to terminal bit error rate The evaluation results are based on multiple symbol timing offset conditions. Therefore, this evaluation method enables the coefficient generation strategy to be optimized for random symbol timing offset distributions, rather than being bound to a fixed symbol timing offset condition.

[0076] After completing the joint evaluation of the multi-symbol timing offset and obtaining the terminal reward and complete sampling trajectory, the sampling trajectory will be used for subsequent policy parameter updates, as explained in step S5, policy update based on policy gradient coefficient generation.

[0077] S5. Policy update based on coefficient generation of policy gradient, specifically: Please see Figure 3 .

[0078] In step S3, the sequential generation of basis function coefficients is completed, and in step S4, the bit error rate feedback under multiple symbol timing offset conditions is obtained. After obtaining the complete sampling trajectory ν, the interference strategy is updated using the sampling trajectory.

[0079] Specifically, the interference policy network and policy update process are as follows: To effectively process continuous state spaces and output continuous actions, this embodiment uses a neural network to parameterize and approximate the interference strategy, denoted as: ; Where ω represents the policy network parameters.

[0080] The policy network uses the current state vector As input, it outputs the parameters of a Gaussian distribution, including the mean. and standard deviation .

[0081] The policy network first processes the input state vector through a shared hidden layer. Feature extraction is performed, and then two independent output heads are set up: the mean output head and the standard deviation output head.

[0082] The mean output header is used to output the mean of the Gaussian distribution. The output range of the mean is constrained by a scaled Tanh activation function; the standard deviation output header is used to output the standard deviation corresponding to the Gaussian distribution. The Softplus activation function is used to ensure that the standard deviation of the output is positive.

[0083] Based on the Gaussian distribution output by the policy network, the coefficients of each basis function are generated sequentially according to the method described in step S3. After completing all K decision steps, the complete interference waveform is synthesized according to the method described in step S2, and the bit error rate feedback is obtained according to the method described in step S4. The corresponding complete sampling trajectory ν is used for subsequent policy network parameter updates.

[0084] Since the agent only receives an evaluation reward at the end of one training round, this embodiment uses a Monte Carlo reward-based policy gradient method to update the policy network parameters ω using the complete sampled trajectory ν.

[0085] The gradient of the policy network parameter ω is expressed as: in, The cumulative reward starting from the i-th decision step is defined as: in, As a discount factor, The immediate reward obtained at the k-th decision step.

[0086] According to the reward settings in step S4, only the termination decision step receives a delay reward based on the interference performance of the complete interference waveform, while intermediate decision steps do not receive an immediate reward. Since the terminal bit error rate feedback reflects the interference performance of the entire basis function coefficient sequence, and there is no positional deviation between the basis function coefficients in the decision steps, this embodiment sets: With γ=1 and only the termination decision step provides a reward, each state-action pair receives the same cumulative reward based on the bit error rate feedback, i.e.: in, The positive reward scaling factor mentioned in step S4. The bit error rate feedback is obtained by joint evaluation under multiple symbol timing offset conditions.

[0087] For finitely sampled trajectories, the policy gradient needs to be estimated using the sampled trajectories. Due to the randomness of the interference environment, Monte Carlo rewards... There are significant fluctuations, which in turn leads to a high variance in the gradient estimate.

[0088] To reduce the variance of gradient estimation, this embodiment introduces a baseline b, which is defined as the mean of the terminal reward in the preceding training rounds.

[0089] Because it satisfies: Therefore, introducing a baseline b can center the return value and reduce the variance of the gradient estimate without introducing bias.

[0090] To perform gradient updates of the policy network parameters, a loss function L(ω) is constructed. For a complete training epoch, the loss function is defined as: The gradient descent optimizer is used to minimize the loss function L(ω) in order to update the policy network parameters ω.

[0091] After completing a policy update, the updated policy is used to continue executing steps S3 and S4, repeating the sequential generation of basis function coefficients, joint evaluation of waveform effects under multi-symbol timing offset, and policy update, until the preset number of training rounds, average bit error rate convergence, or performance improvement is less than the preset threshold is reached.

[0092] After training, the policy network can be fixed and deterministic coefficients can be output, for example, by directly using the mean of the Gaussian distribution corresponding to each decision step; alternatively, the best-performing basis function coefficient sequence during training can be saved for direct use in the online waveform synthesis in step S6.

[0093] S6. Waveform online synthesis and output, specifically: After completing the offline training in step S5, the optimized basis function coefficient sequence is saved, and the basis function coefficient sequence is called to generate interference waveforms during the online phase.

[0094] Specifically, the basis function coefficient sequence with the highest average bit error rate can be selected from the training records, and the basis function coefficient sequence, basis function interval, training symbol rate, power normalization parameter, and applicable modulation scheme are written into the waveform configuration file. During the online phase, the waveform configuration file is read, the corresponding basis functions are configured according to the target communication signal parameters, and the saved basis function coefficient sequence is directly called.

[0095] Subsequently, following the interference waveform construction method described in step S2, basis function weighted synthesis is completed based on the saved basis function coefficient sequence, and the generated interference waveform is subjected to energy normalization and power scaling to ensure that the interference signal power meets the preset maximum power constraint. After completing the above processing, the interference waveform will be output.

[0096] Since the basis function coefficient sequence called has been jointly optimized for multiple symbol timing offsets during offline training, there is no need to estimate or compensate for the current symbol timing offset in the online stage, nor is there a need to perform online interactive optimization for the current symbol timing offset again. The interference waveform synthesis, power normalization and output can be completed directly based on the already saved basis function coefficient sequence.

[0097] Furthermore, when the symbol rate or bandwidth of the target communication signal changes, the already trained basis function coefficient sequence θ remains unchanged, and the signal is adjusted according to the new target symbol rate. Adjust the time scale of the basis functions and set the sampling rate and the time interval Δt between adjacent basis functions accordingly to make the digital implementation satisfy the Nyquist sampling condition.

[0098] After completing the above parameter adjustments, the interference waveform is re-synthesized in the manner described in step S2, and energy normalization and power scaling are re-executed, so that the generated interference waveform can be adapted to target communication signals with different symbol rates or bandwidths without re-optimizing the basis function coefficient sequence.

[0099] Thus, through steps S1-S6, the offline optimization and online generation process of the waveform resisting random symbol timing offset interference based on signal decomposition is completed.

[0100] Example 2: Offline training under single communication conditions: This embodiment establishes a target communication link in an AWGN channel. The target communication signal uses Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), and 16-ary Quadrature Amplitude (16-QAM), respectively.

[0101] Target symbol rate Set as Baud rate, corresponding to symbol period The target transmitter and receiver employ root raised cosine (RRC) pulse shaping and matched filtering. The interference-to-noise ratio (JNR) is fixed at 10 dB, and the target signal-to-noise ratio (SNR) is varied to obtain different communication conditions.

[0102] Set the interference waveform segment as described in step S2 of Example 1. Waveform segment duration. The timescale is set to 0.2 milliseconds, and the interval Δt between adjacent sinc basis functions is set to 10 microseconds. Therefore, K coefficients to be optimized are set within a segment, corresponding to the segment's coverage. The timescale of each basis function is determined by... Confirmed. After waveform synthesis is complete, the waveform is normalized according to the average power, and then the waveform segments are repeated periodically to form a continuous interference signal.

[0103] The policy network employs a shared hidden layer with 64 neurons, activated using linear transformation and rectified linear unit (ReLU) activation. Following the hidden layer are mean and standard deviation output heads: the mean output head uses scaled Tanh activation to constrain the range of values; the standard deviation output head uses Softplus activation. The training optimizer uses Adam with a learning rate of [missing information - likely a specific value]. The discount factor γ is set to 1.

[0104] In each training round, K basis function coefficients are generated sequentially according to step S3 in Example 1, and a complete interference waveform is synthesized based on the complete basis function coefficient sequence. The target transmitter sends a target signal lasting 0.1 seconds. One symbol period is divided into 10 equally spaced time offset points, with an interval of [missing information]. The bit error rate (BER) at each of the 10 time offset points was calculated, and the average BER at each of the 10 time offset points was used as the termination feedback for the current training round, as described in step S4 of Example 1. The training process consisted of 2500 rounds.

[0105] For different target modulation methods and different SNR conditions, the above training process can be performed separately, and the corresponding basis function coefficient sequences can be saved.

[0106] After training, the basis function coefficient sequence with the highest average bit error rate is selected from the training records, and the coefficient sequence, basis function interval, training symbol rate, power normalization parameter and applicable modulation method are written into the waveform configuration file.

[0107] During the online phase, the waveform configuration file is read, and the corresponding interference waveform is directly synthesized and output in accordance with the method described in step S6 of Embodiment 1.

[0108] Please see Figures 4-6 , Figures 4-6 The results show the comparison of the bit error rate of the method of the present invention and the comparative scheme for different modulated signals under different signal-to-noise ratio conditions. Figure 4 , Figure 5 and Figure 6 These correspond to binary phase shift keying, quadrature phase shift keying, and hexadecimal quadrature amplitude modulation target signals, respectively.

[0109] Simulation results show that, under binary phase-shift keying (BPSK), quadrature phase-shift keying (QPSK), and hexadecimal quadrature amplitude modulation (QAM) target communication signal conditions, the interference waveform generated by this invention exhibits good interference performance under different signal-to-noise ratios (SNRs) and random symbol timing offsets. Taking a SNR of 10 dB as an example, compared with the theoretically optimal pulse interference, this invention improves the bit error rate for the three modulation signals by approximately 30.7%, 20.7%, and 16.9%, respectively.

[0110] Please see Figures 7-9 , Figures 7-9 The results show the comparison of the bit error rate of the proposed method and the comparative scheme for different modulated signals under different symbol timing offsets when the signal-to-noise ratio is 10dB. Figure 7 , Figure 8 and Figure 9 These correspond to binary phase shift keying, quadrature phase shift keying, and hexadecimal quadrature amplitude modulation target signals, respectively.

[0111] When the symbol timing offset changes within one symbol period, the interference effect of the present invention remains generally stable, while the pulse interference decreases at an offset of 0.5 symbol periods, indicating that the present invention has good adaptability to random symbol timing offsets.

[0112] Example 3: Adaptation under different target bandwidths; This embodiment, based on Embodiment 1 and Embodiment 2, provides a detailed explanation of the waveform adaptation process when the target communication signal symbol rate or bandwidth changes.

[0113] First, with a target bandwidth of 75kHz, offline training was completed as described in Example 2, and the trained basis function coefficient sequence was saved. .

[0114] When faced with target communication signals with different symbol rates or different bandwidths, maintain the already trained basis function coefficient sequence. Unchanged, and according to the new target symbol rate. Adjust the time scale factor in the basis functions, and at the same time, set the sampling rate and the time interval Δt between adjacent sinc basis functions accordingly, so that the digital implementation satisfies the Nyquist sampling condition.

[0115] After completing the above parameter adjustments, continue to use the original basis function coefficient sequence θ to synthesize the interference waveform, and re-execute energy normalization and power scaling.

[0116] In the simulation experiment of this embodiment, the target signal bandwidth is extended to 300kHz.

[0117] Tests were conducted on target communication signals for binary phase shift keying, quadrature phase shift keying, and hexadecimal quadrature amplitude modulation, respectively.

[0118] Please see Figures 10-12 , Figures 10-12 The results show the comparison of the bit error rate of the method of the present invention and the comparative scheme for different modulated signals under different target signal bandwidth conditions when the signal-to-noise ratio is equal to 10dB. Figure 10 , Figure 11 and Figure 12 These correspond to binary phase shift keying, quadrature phase shift keying, and hexadecimal quadrature amplitude modulation target signals, respectively.

[0119] Simulation results show that under binary phase shift keying, quadrature phase shift keying, and hexadecimal quadrature amplitude modulation conditions, the bit error rate curves of the present invention, impulse interference, and noise interference remain generally stable with the change of target bandwidth. The present invention maintains the highest bit error rate throughout the entire test range.

[0120] This demonstrates that after training the basis function coefficient sequence under a fixed target bandwidth, when the symbol rate or bandwidth of the target communication signal changes, the basis function coefficient sequence θ can remain unchanged. Only the time scale of the basis function needs to be adjusted, along with the sampling rate and Δt, to adapt the generated interference waveform to the new target communication signal bandwidth, without requiring re-optimization of the basis function coefficient sequence. This illustrates that the design approach of "coefficients describing waveform structure and basis function scale matching bandwidth" in this invention possesses bandwidth adaptability.

[0121] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for generating waveforms resistant to random symbol timing offset interference based on signal decomposition, characterized in that, include: Step 1: Establish a model of the target communication and jamming signal, using the symbol timing offset of the jamming signal relative to the target communication signal as a random variable, and using the bit error rate of the target receiver under the random symbol timing offset condition as the basis for evaluating the jamming effect. Step 2: Configure multiple time-shifted band-limited basis functions according to the symbol rate of the target communication signal, and weight and combine the multiple time-shifted band-limited basis functions according to their corresponding basis function coefficients to construct an interference waveform; Step 3: The joint generation of multiple basis function coefficients is transformed into a sequential decision process in the finite time domain, generating each basis function coefficient in turn to obtain a complete sequence of basis function coefficients; Step 4: Evaluate the interference waveforms generated by the complete basis function coefficient sequence under multiple symbol timing offset conditions, and determine the overall interference effect based on multiple bit error rates; Step 5: Based on the combined interference effect and the sampling trajectory formed by the sequential decision-making process, update the basis function coefficient generation strategy using the policy gradient method to obtain the optimized basis function coefficient sequence; Step 6: Save the optimized basis function coefficient sequence. In the online stage, call the optimized basis function coefficient sequence to synthesize the interference waveform, and output it after energy normalization and power scaling.

2. The method for generating waveforms against random symbol timing offset interference based on signal decomposition according to claim 1, characterized in that: The specific process of target communication and interference signal modeling in step one is as follows: The target communication waveform is constructed based on the data symbols obtained from the digital modulation constellation, the pulse shaping function, and the symbol period of the target communication signal, wherein the symbol period is determined according to the symbol rate of the target communication signal; Under additive white Gaussian noise channel conditions, the target communication signal, interference signal and noise are superimposed to obtain the received signal of the target receiver. Among them, the interference signal has a random symbol timing offset relative to the target communication signal due to the difference in propagation path. Given a power constraint on the interference signal, the design objective of the interference waveform is to maximize the bit error rate of the target receiver under random symbol timing offset conditions.

3. The method for generating waveforms against random symbol timing offset interference based on signal decomposition according to claim 1, characterized in that: The specific process of configuring the band-limited basis function and constructing the interference waveform based on signal decomposition in step two is as follows: Based on the signal representation method where band-limited signals can be linearly expanded using time-shifted sampling basis functions, multiple time-shifted band-limited basis functions are used to construct interference waveforms, with the weights corresponding to each time-shifted band-limited basis function serving as basis function coefficients. The time interval between adjacent time-shifted band-limited basis functions is set, and the time scale of the time-shifted band-limited basis functions is set according to the symbol rate of the target communication signal, so that the bandwidth of the generated interference waveform matches the bandwidth of the target communication signal. A waveform segment of a preset duration is selected, and multiple time-shifted band-limited basis functions are configured within the waveform segment. The corresponding basis function coefficients are jointly optimized, and the optimized waveform segment is periodically repeated to form a continuous interference signal, ensuring that the continuous interference signal meets a preset maximum power constraint.

4. The method for generating waveforms against random symbol timing offset interference based on signal decomposition according to claim 1, characterized in that: The specific process of sequential decision modeling and generation of basis function coefficients in step three is as follows: The generation of the complete basis function coefficient sequence is divided into multiple decision steps corresponding to the number of basis function coefficients to be generated. Each decision step constructs the current state based on the basis function coefficients determined in the previous decision steps, and the basis function coefficient generation strategy determines the current action based on the current state. The basis function coefficients corresponding to the current time-shifted band-limited basis function are determined by the current action. After determining the current basis function coefficients, update the current basis function coefficient sequence and state, and proceed to the next decision step. Determine each basis function coefficient in sequence according to the above method until a complete basis function coefficient sequence is generated, wherein each basis function coefficient takes continuous values.

5. The method for generating waveforms against random symbol timing offset interference based on signal decomposition according to claim 4, characterized in that: The process of determining the state and action during the sequential generation of the basis function coefficients is as follows: Set the dimension of the state vector to be the same as the length of the sequence of basis function coefficients to be designed. In any decision step, fill the corresponding positions in the state vector with the already determined basis function coefficients and fill the positions corresponding to the undetermined basis function coefficients with zero values. In the initial decision-making step, each position in the state vector is set to zero. The action corresponding to each decision step is defined as the basis function coefficient of the time-shifted band-limited basis function to be determined in that decision step. The action is determined based on the current state and the basis function coefficient generation strategy. After determining the corresponding basis function coefficient, it is written into the state vector to form the state corresponding to the next decision step.

6. The method for generating waveforms against random symbol timing offset interference based on signal decomposition according to claim 1, characterized in that: The specific process for the joint evaluation of waveform effects under multi-symbol timing offset in step four is as follows: In each training round, after the sequential generation of all basis function coefficients and the synthesis of the complete interference waveform are completed, multiple different symbol timing offsets are set within the preset random symbol timing offset range, so that the same complete interference waveform is applied to each symbol timing offset condition, and the bit error rate corresponding to the target receiver is obtained respectively. The bit error rate obtained under multiple symbol timing offset conditions is jointly evaluated, and the average value of the multiple bit error rates is taken as the comprehensive interference effect corresponding to the current complete interference waveform. This allows the basis function coefficient generation strategy to be optimized for random symbol timing offset distribution, rather than being bound to a single symbol timing offset condition.

7. The method for generating waveforms against random symbol timing offset interference based on signal decomposition according to claim 6, characterized in that: The process of constructing the reward and sampling trajectory after the joint evaluation of the waveform effect is as follows: Since the comprehensive interference effect is obtained only after all basis function coefficients are generated and the complete interference waveform is synthesized, the immediate reward corresponding to each decision step before the last decision step is set to zero, and a termination reward is set according to the comprehensive interference effect in the last decision step, and the termination reward is scaled using a positive reward scaling factor. The state, action, and immediate reward corresponding to each decision step are recorded in the order of decision-making, and together with the termination state after all basis function coefficients are generated, they constitute the complete sampling trajectory of a training round, so that all basis function coefficients in a training round correspond to the final interference performance of the complete interference waveform.

8. The method for generating waveforms against random symbol timing offset interference based on signal decomposition according to claim 5, characterized in that: The construction process of the basis function coefficient generation strategy in step five is as follows: The basis function coefficient generation strategy is parameterized using a neural network. The state vector of the current decision step is used as the input of the neural network. Feature extraction is performed through a shared hidden layer, and mean output header and standard deviation output header are set after the shared hidden layer. The mean output head uses a scaled hyperbolic tangent activation function to constrain the output range, and the standard deviation output head uses a smooth activation function to ensure that the output result is positive. A Gaussian probability distribution is constructed based on the outputs of the mean output head and the standard deviation output head, and the action of the current decision step is sampled from the Gaussian probability distribution to determine the corresponding basis function coefficients.

9. The method for generating waveforms against random symbol timing offset interference based on signal decomposition according to claim 8, characterized in that: The specific process of generating policy updates based on policy gradient coefficients is as follows: A policy gradient method based on Monte Carlo rewards is adopted to update the basis function coefficient generation policy using the complete sampling trajectory formed in one training round; Since the termination reward is only obtained in the last decision step based on the interference performance of the complete interference waveform, the discount factor is set to one so that each state and action in a training round receives the same cumulative reward. Using the mean of the termination reward from previous training rounds as a baseline, the cumulative reward is centered to reduce the variance of the policy gradient estimation. A loss function is constructed based on the probability of the action corresponding to each decision step under the current basis function coefficient generation policy and the difference between the termination reward and the baseline. The basis function coefficient generation policy is updated by minimizing the loss function.

10. The method for generating waveforms against random symbol timing offset interference based on signal decomposition according to claim 3, characterized in that: The specific process of online waveform synthesis and output in step six is ​​as follows: After completing offline training, the basis function coefficient sequence with the best overall interference effect is selected from the training process, and the basis function coefficient sequence, basis function interval, training symbol rate, power normalization parameter and applicable modulation method are written into the waveform configuration file. During the online phase, the waveform configuration file is read, and the corresponding time-shifted band-limited basis function is configured according to the target communication signal parameters. The saved basis function coefficient sequence is called to complete the interference waveform synthesis, energy normalization and power scaling before output, without the need to estimate or compensate for the current symbol timing offset. When the symbol rate or bandwidth of the target communication signal changes, the stored basis function coefficient sequence remains unchanged. The time scale of the time-shifted band-limited basis function is adjusted according to the changed target symbol rate, and the sampling rate and the time interval between adjacent basis functions are adjusted accordingly to achieve bandwidth adaptation of the interference waveform without re-optimizing the basis function coefficient sequence.

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