Memory-free ISAC capacity-distortion balance estimation method based on data-driven neural network

Abstract

The invention discloses a memory-free ISAC capacity-distortion balance estimation method based on a data-driven neural network, and belongs to the technical field of machine learning and information theory crossing. In order to solve the problem of capacity-distortion relation calculation in a state dependent channel (SDMC), the method is realized through three parts of neural network modules: a conditional mutual information neural estimation module (CMINE) represents conditional mutual information between estimated input and output based on DV; a neural state estimation module (NSE / DNSE) estimates a channel state from the signal and minimizes distortion; an input distribution optimization module (NDT / PMFG) optimizes the input distribution under distortion constraints. The method comprises the following steps of: training CMINE and NSE / DNSE through an alternating optimization strategy training module: in a first stage, fixedly inputting a distribution optimization module; in the second stage, the first two are fixed, and the input distribution module is optimized. An explicit channel model or state distribution is not needed, the capacity-distortion curve is directly estimated from the data, the problem that a traditional method depends on a probability model is solved, and the method is suitable for continuous and discrete scenes.

Description

Technical Field

[0001] The present invention belongs to the interdisciplinary technical field of machine learning and information theory, and in particular relates to a memoryless ISAC capacity-distortion trade-off estimation method based on a data-driven neural network. Background Art

[0002] Synaesthesia integration, by integrating platforms and jointly designing waveforms to optimize spectrum and hardware resources, can improve overall system efficiency in numerous emerging applications and is widely considered a key technology for next-generation wireless systems. The information-theoretic limit of synaesthesia integration is generally expressed in terms of the capacity-distortion trade-off. While this trade-off has been fully characterized under the most general channel models, its computational challenges in specific channels remain. Specifically, traditional theoretical analysis methods and Blahut-Arimoto-type algorithms require an explicit probabilistic model of the system, making them impractical in complex engineering scenarios. Meanwhile, neural network estimation methods based on information metrics have demonstrated their potential in recent years. Summary of the Invention

[0003] Technical Problem: This invention aims to provide a memoryless ISAC capacity-distortion tradeoff estimation method based on a data-driven neural network, applicable to both continuous and discrete scenarios, when the state distribution or SDMC channel transition kernel is complex or unknown. This method requires estimating the communication rate and learning an optimal state estimator. Furthermore, the input distribution must be optimized to estimate the capacity-distortion tradeoff.

[0004] Technical solution: The technical solution adopted by the present invention is as follows:

[0005] A memoryless ISAC capacity-distortion trade-off estimation method based on a data-driven neural network is applicable to a memoryless state-dependent channel (SDMC) with generalized feedback, comprising the following steps:

[0006] Step 1: Construct a conditional mutual information neural estimation module to estimate the conditional mutual information between channel input and output;

[0007] Step 2: Construct a Neural State Estimator (NSE) module to estimate the channel state from the transmitted signal and the feedback signal. When the channel state is discrete, construct a Discrete Neural State Estimator (DNSE) to output the probability distribution of each possible state.

[0008] Step 3: Construct a channel input distribution optimization module to optimize the probability distribution of channel input while satisfying the state estimation distortion constraint;

[0009] Step 4. Use an alternating optimization strategy to train the above modules: train the conditional mutual information neural estimation module and the neural state estimation module under a fixed channel input distribution optimization module, and train the channel input distribution optimization module under a fixed conditional mutual information neural estimation module and the neural state estimation module; repeat the alternating training until convergence to obtain the maximum communication rate estimate under the distortion constraint, thereby determining the capacity-distortion trade-off relationship of the channel.

[0010] Furthermore, the Conditional Mutual Information Neural Estimation (CMINE) module in step 1 is constructed based on the Donsker-Varadhan (DV) mutual information representation, and the collected channel input, output and state data are trained through a neural network to obtain the conditional mutual information estimation value between the channel input and output. In terms of CMINE, the neural network g is defined as θ : where θ∈Θ, It is a d θ dimensional parameter space. Given a sample size of n (X n ,Y n ,S n )~P XYS , CMINE training needs to maximize the following objective function: in

[0011] Furthermore, in step 2, the NSE maps the transmitted signal and the feedback signal into an estimated value of the channel state through a neural network, and is trained by minimizing the distortion between the state estimate and the actual state; when the channel state takes a discrete value, the DNSE outputs the probability distribution of each possible state as the state estimation result. In terms of NSE, the following neural network mapping t is defined ψ :X×Z→S, where ψ∈Ψ is the parameter of the neural network, Indicates the corresponding d ψ dimensional parameter space. Given a sample set of size n NSE training requires minimizing the following objective function: Where d(·,·) is a given distortion function. In terms of DNSE, the neural network t is defined as follows ξ : Among them, ξ∈Ξ represents the parameters of the neural network, is the corresponding d ξdimensional parameter space; Represents a probability simplex of dimension |S|. Based on n samples (X n ,S n ,Z n ,S n ), DNSE training needs to minimize the following objective function:

[0012] Furthermore, the channel input distribution optimization module described in step 3 is implemented using a neural distribution transformer (NDT) when the input signal is continuous, and characterizes the input distribution by mapping a random vector that obeys a uniform distribution into a continuous channel input sample; when the input signal is discrete, it is implemented using a probability mass function generator (PMFG), and characterizes the input distribution by parameterizing the probability mass function of discrete input symbols. In terms of NDT, the following neural network h is defined: φ : Among them, U i ~P U For the definition on a compact set The uniform distribution on Represents the channel input sample. In order to constrain the channel input cost to a given B, the following normalization operation is performed: Let X n,φ represents the unconstrained output sample generated by NDT, considering the following empirical cost The final normalized output X i By the original output Scaling is performed to obtain NDT training needs to maximize the following objective function: Among them, λ≥0 is a preset hyperparameter, and D is a given distortion level. As for PMFG, it consists of a single layer with a dimension of d x The neural network is composed of a parameter υ, where Represents the corresponding parameter space. The input of PMFG is a constant 1. The output of PMFG is the element-by-element probability distribution of the parameter vector after the softmax operation: To train PMFG, we need to maximize the objective function:

[0013] Furthermore, the alternating optimization strategy described in step 4 includes two training phases: in the first phase, the channel input distribution optimization module is fixed, and only the conditional mutual information neural estimation module and the neural state estimation module are trained to improve the mutual information estimation accuracy and obtain a near-optimal state estimation; in the second phase, the conditional mutual information neural estimation module and the neural state estimation module are fixed, and the channel input distribution optimization module is trained to improve the mutual information estimation value under the condition of satisfying the preset state distortion constraint. In the continuous case, the following steps are included:

[0014] Step 1.1: Given SDMC P YZ|XS , state source P S , cost constraint B, distortion constraint D; initialize CMINE parameter θ, NDT parameter φ, NSE parameter ψ, learning rate γ, penalty coefficient λ, and training batch size m;

[0015] Step 1.2: Sample NDT input With unknown state samples

[0016] Step 1.3: Generate channel input X using NDT m,φ ;

[0017] Step 1.4, Sampling SDMC P YZ|XS Channel output Y m With the feedback signal Z m ;

[0018] Step 1.5: Use CMINE to calculate the current communication rate Use NSE to calculate the current distortion

[0019] Step 1.6: If it is the first stage, update the CMINE parameters: Update NSE parameters:

[0020] Step 1.7: If it is the second stage, calculate the NDT objective function And update the NDT parameters:

[0021] Step 1.8: If the algorithm does not converge, return to step 1.2 and repeat the above steps;

[0022] Step 1.9: Obtain the capacity estimation result under the current distortion and cost constraints

[0023] In the discrete case, the following steps are involved:

[0024] Step 1.1: Given SDMC P YZ|XS , state source P S, distortion constraint D; initialize CMINE parameter θ, PMFG parameter υ, DNSE parameter ξ, learning rate γ, penalty coefficient λ, and training batch size m;

[0025] Step 1.2: Sampling unknown state samples

[0026] Step 1.3: Use PMFG to get the channel input PMF p υ ;

[0027] Step 1.4, Sampling SDMC P YZ|XS Channel output Y m With the feedback signal Z m ;

[0028] Step 1.5: Use CMINE to calculate the current communication rate Calculated using DNSE

[0029] Step 1.6: If it is the first stage, update the CMINE parameters: Update DNSE parameters:

[0030] Step 1.7: If it is the second stage, calculate the PMFG objective function L PMFG (X n ,Y n ,S n ,Z n ,υ), and update the PMFG parameters:

[0031] Step 1.8: If the algorithm does not converge, return to step 2 and repeat the above steps;

[0032] Step 1.9: Obtain the capacity estimation result under the current distortion and cost constraints

[0033] Beneficial effects: 1. In step 1, CMINE is designed to estimate the conditional mutual information without explicit calculation; 2. In step 2, NSE and DNSE are novelly proposed to learn the optimal estimator without theoretical deduction; 3. In step 3, NDT and PMFG and the corresponding proposed objective function are used to optimize the channel input distribution under the distortion constraint without explicit optimization; 4. The above modules are combined into a joint framework in step 4 and trained using the alternating optimization method. It does not require a known channel transition probability model or state distribution and can be solved as a whole in a data-driven manner, overcoming the difficulties of traditional analytical methods and the Blahut-Arimoto algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is the overall structure of the present invention in a continuous situation;

[0035] Figure 2 It is the overall architecture of the present invention in a discrete situation;

[0036] Figure 3 The estimated capacity-distortion trade-off relationship in the application example of the present invention in the continuous case;

[0037] Figure 4 The estimated capacity-distortion trade-off relationship in a discrete application example of the present invention is shown in FIG. DETAILED DESCRIPTION

[0038] The technical solution of the present invention is described in detail below, but the protection scope of the present invention is not limited to the embodiments.

[0039] like Figure 1 and Figure 2 As shown, the present invention discloses a capacity-distortion trade-off relationship estimation method for a memoryless synaesthesia integrated system based on a data-driven neural network, which can directly calculate the capacity-distortion curve from samples in continuous and discrete scenarios when the channel or state distribution is complex or unknown.

[0040] The following are examples for continuous and discrete cases:

[0041] In the continuous case, considering a real Gaussian channel with Nakagami-2 fading, its model can be expressed as: Y = SX + N, where and in and Assuming ideal feedback, that is, Z = Y, and considering the quadratic distortion function, that is The cost constraint is Assume B = 10dB. Then, the specific steps include:

[0042] Step 1: Given SDMC P YZ|XS , state source P S , cost constraint B, distortion constraint D; initialize CMINE parameter θ, NDT parameter φ, NSE parameter ψ, learning rate γ, penalty coefficient λ, and training batch size m;

[0043] Step 2: Sample NDT input With unknown state samples

[0044] Step 3: Generate channel input X using NDT m,φ ;

[0045] Step 4: Sample SDMC P YZ|XS Channel output Ym With the feedback signal Z m ;

[0046] Step 5. Use CMINE to calculate the current communication rate Use NSE to calculate the current distortion

[0047] Step 6. If it is the first stage, update the CMINE parameters: Update NSE parameters:

[0048] Step 7: If it is the second stage, calculate the NDT objective function And update the NDT parameters:

[0049] Step 8: If the algorithm does not converge, return to step 1.2 and repeat the above steps;

[0050] Step 9: Obtain the capacity estimation result under the current distortion and cost constraints

[0051] Figure 3 The estimated channel capacity C is shown in the above steps after fixing different distortion constraints D. B (D) Results. This characterizes a series of performance points on the capacity-distortion plane, namely Figure 3 The solid points are connected by dashed lines in the figure. In this application example, the obtained results lie between the known internal and external environments, which is the first meaningful characterization of the capacity-weight trade-off in this case.

[0052] In the discrete case, consider a binary channel with multiplicative Bernoulli states, i.e., Y = SX, where X = Y = S = {0, 1}, and the state S follows a Bernoulli distribution with parameter q, i.e., Pr{S = 1} = q∈(0, 1). Assuming ideal feedback, i.e., Z = Y, and considering the Hamming distortion function, i.e., in It is a binary XOR operation. Then, the specific steps include:

[0053] Step 1: Given SDMC P YZ|XS , state source P S , distortion constraint D; initialize CMINE parameter θ, PMFG parameter υ, DNSE parameter ξ, learning rate γ, penalty coefficient λ, and training batch size m;

[0054] Step 2: Sampling unknown state samples

[0055] Step 3: Use PMFG to get the channel input PMF p υ ;

[0056] Step 4: Sample SDMC P YZ|XS Channel output Y m With the feedback signal Z m ;

[0057] Step 5. Use CMINE to calculate the current communication rate Calculated using DNSE

[0058] Step 6. If it is the first stage, update the CMINE parameters: Update DNSE parameters:

[0059] Step 7: If it is the second stage, calculate the PMFG objective function L PMFG (X n ,Y n ,S n ,Z n ,υ), and update the PMFG parameters:

[0060] Step 8: If the algorithm does not converge, return to step 2 and repeat the above steps;

[0061] Step 9: Obtain the capacity estimation result under the current distortion and cost constraints

[0062] Figure 4 The results of the estimated channel capacity C(D) obtained by the above steps are shown after fixing different distortion constraints D. This depicts a series of performance points on the capacity-distortion plane, namely Figure 4 In this application example, the obtained results reproduce the existing theoretical characterization, namely Figure 4 The solid line in , verifies the effectiveness and correctness of the present invention.

Claims

1. A memoryless ISAC capacity-distortion trade-off estimation method based on data-driven neural network, suitable for memoryless state-dependent channel SDMC with generalized feedback, characterized by: The following steps are involved: Step 1: Construct a conditional mutual information neural estimation module (CMINE) to train the channel input, output, and state data through a neural network to estimate the conditional mutual information between input and output. Step 2: Construct a neural state estimation module (NSE) to estimate the channel state from the transmitted signal and the feedback signal and minimize the estimated distortion. When the channel state is discrete, construct a discrete neural state estimator (DNSE) to output the probability distribution of each possible state. Step 3: Construct a channel input distribution optimization module. When the input is continuous, the neural distribution transformer (NDT) generates input samples that meet the cost constraint. When the input is discrete, the probability mass function generator (PMFG) generates the probability distribution of discrete symbols. Step 4: Use alternating optimization strategy to train the module: Phase 1: Fix the input distribution optimization module and train the CMINE and NSE / DNSE to improve the mutual information estimation accuracy and reduce state distortion; Phase 2: Fix the CMINE and NSE / DNSE and train the input distribution optimization module to maximize the communication rate under the distortion constraint; The first and second stages are repeated until convergence, and a capacity-distortion trade-off curve is output.

2. The method according to claim 1, wherein: The CMINE described in step 1 is constructed based on the Donsker-Varadhan mutual information representation, whose goal is to maximize the conditional mutual information estimate, and its training needs to rely on the first stage of the alternating optimization in step 4.

3. The method according to claim 1, wherein: In step 2, the NSE is trained by minimizing the distortion between the state estimate and the true state, and the DNSE is trained by minimizing the cross entropy loss of the discrete state probability distribution; the training of the NSE / DNSE needs to be synchronized with the CMINE in step 1 in the first stage of the alternating optimization.

4. The method according to claim 1, wherein: In step 3, the NDT constrains the generation of input samples through normalization operations to meet the preset cost limit; the PMFG generates the probability distribution of discrete symbols through softmax operation; the parameter update of the NDT / PMFG needs to be completed in the second stage of the alternating optimization in step 4.

5. The method according to claim 1, wherein: In the alternating optimization strategy of step 4, the first and second stages are performed according to the following logical association: In the first stage, the input distribution optimization module of step 3 is fixed, and the CMINE of step 1 and the NSE / DNSE of step 2 are updated using the data generated by the current input distribution; In the second stage, based on the updated CMINE and NSE / DNSE, the input distribution of step 3 is optimized to improve the communication rate.

6. The method according to claim 5, wherein: In a continuous scenario, the alternating optimization includes: Initialize the CMINE of step 1, the NSE of step 2, and the NDT parameters of step 3; In the first phase, input samples are generated by NDT and channel outputs are sampled to update CMINE and NSE parameters; In the second stage, based on the updated CMINE and NSE, the NDT parameters are optimized to generate an input distribution with a higher communication rate.

7. The method according to claim 6, wherein: In a discrete scenario, the alternating optimization includes: Initialize the CMINE of step 1, the DNSE of step 2, and the PMFG parameters of step 3; In the first stage, discrete input distribution is generated by PMFG and channel output is sampled to update CMINE and DNSE parameters; In the second stage, based on the updated CMINE and DNSE, the PMFG parameters are optimized to generate an input distribution that satisfies the distortion constraints.

8. The method according to claim 1, wherein: The convergence conditions for step 4 include: The change range of the communication rate estimation value output by CMINE in step 1 is lower than the first threshold; The state distortion change amplitude of the NSE / DNSE output in step 2 is lower than the second threshold; The parameter update of the input distribution optimization module in step 3 tends to be stable.

9. The method according to claim 4, wherein: The normalization operation of the NDT in step 3 is achieved by scaling the unconstrained output samples, and the scaling ratio is dynamically adjusted by the preset input cost constraint; the softmax operation of the PMFG directly acts on the single-layer neural network parameters to generate a discrete probability distribution.

10. The method according to claim 1, wherein: The method achieves the following correlation through the collaborative training of steps 1 to 4: The CMINE of step 1 provides a communication rate estimation benchmark for the alternating optimization of step 4; The NSE / DNSE in step 2 provides distortion constraint verification for the alternating optimization in step 4; The input distribution optimization module in step 3 iteratively optimizes the input distribution based on the output results of steps 1 and 2 to approach the capacity-distortion limit.

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