Orthogonal frequency division multiplexing (OFDM) communication perception integrated constellation probability shaping method for arbitrary filter

Abstract

The invention discloses an OFDM (Orthogonal Frequency Division Multiplexing) communication perception integrated constellation probability shaping method for any filter. The method comprises the following steps: establishing a unified perception processing model suitable for the filter; adopting an estimation mean square error of sensing channel state information as a sensing performance measurement index; according to the method, maximization of an information rate which can be realized by communication is taken as a communication performance target, and dynamic compromise between communication performance and sensing performance is realized by optimizing probability distribution of emission symbols under a preset sensing performance constraint condition; according to the method, the dynamic compromise performance of radar and communication is realized, so that guidance is provided for modulation parameter quantification under actual system requirements.

Description

Technical Field

[0001] This invention relates to the field of novel signal modulation technology for next-generation mobile communications (6G), specifically to a probabilistic constellation shaping method for OFDM communication sensing integration oriented to arbitrary filters. Background Technology

[0002] Among the many ISAC implementation paths, directly utilizing existing OFDM communication signals for radar sensing is the most cost-effective and easiest to deploy solution. Its basic principle is that while transmitting communication data, the base station or terminal captures echo signals reflected from environmental targets (such as vehicles or drones), and extracts information such as the target's distance and speed through signal processing.

[0003] However, directly using OFDM signals, originally designed for communication, for sensing faces the following contradictions: Communication randomness: To carry as much information as possible, the constellation modulation code of the communication signal should ideally be as random as possible (e.g., QAM) to maximize information entropy. Sensing determinism: An ideal radar waveform should have pulse-like, deterministic autocorrelation characteristics (i.e., a "thumbtack" ambiguity function) to achieve accurate target detection and differentiation. This conflict between "randomness" and "determinism" is the core bottleneck restricting the performance of OFDM-ISAC systems. Current technologies use uniform character modulation: all random symbols are generated with equal probability. Current practical modulation methods typically employ Phase Shift Keying (PSK) or Quadrature Amplitude Modulation (QAM), with the latter having a larger Euclidean distance between constellation symbols, thus offering better communication reliability (anti-jamming capability). However, for radar, the constant modulus specificity of PSK modulation leads to stronger radar main lobe resolution and lower sidelobe levels, which is significant for improving weak target detection capabilities and avoiding false alarms from "ghost" targets. Time-division multiplexing is another option. In practice, within a single frame of a transmitted communication signal, a portion can be modulated using PSK modulation, and another portion using QAM modulation—that is, time-division dynamic character modulation. Clearly, this method employs a "linear segmentation" time-sharing strategy, achieving a linear trade-off between radar and communication performance. This is based on probabilistic constellation shaping technology using matched filtering. Analysis of the randomness of the ambiguity function of OFDM signals reveals that randomness is determined by the fourth moment of the constellation symbols. By jointly optimizing this index and communication capacity, a trade-off between communication and sensing performance can be achieved using probabilistic constellation shaping technology. This scheme is most similar to the technology of this invention; however, its limitation lies in its applicability only to matched filtering, not to typical arbitrary filters such as reciprocal filtering and Wiener filtering.

[0004] Despite significant progress in existing technologies, the following key shortcomings remain: (1) The optimization metrics used in most current PCS-ISAC studies (such as the aforementioned work on matched filtering) are only effective for matched filtering. For arbitrary filters with superior performance, existing PCS schemes cannot be directly applied, lacking universality. (2) For uniformly distributed QAM and PSK, there is a "conflict" between radar sensing and communication performance. If this traditional scheme is adopted, either the best sensing performance and the worst communication performance (PSK) can be achieved simultaneously, or the worst sensing performance and the best communication performance (QAM) can be achieved. It is difficult to flexibly modulate between radar and communication performance, that is, it is impossible to achieve a performance trade-off. (3) For time-sharing strategies, this method can only achieve a linear trade-off between radar and communication performance, which can be regarded as the inner bound of the radar-communication performance trade-off, and the performance gain obtained is limited. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a probabilistic shaping method for OFDM communication-sensing integrated constellations oriented to arbitrary filters, thereby achieving a tighter outer boundary for radar-communication performance and thus obtaining greater gains relative to time-sharing strategies.

[0006] Technical solution: The present invention provides a probabilistic shaping method for an integrated sensing constellation of OFDM communication oriented to arbitrary filters, comprising the following steps:

[0007] (1) Establish a unified sensing processing model applicable to filters;

[0008] (2) The mean square error of the estimation of the sensing channel state information is used as the sensing performance metric.

[0009] (3) With maximizing the achievable information rate as the communication performance target, and under the condition of satisfying the preset perception performance constraints, a dynamic trade-off between communication performance and perception performance is achieved by optimizing the probability distribution of transmitted symbols.

[0010] Furthermore, in step (1), the filter includes, but is not limited to, a reciprocal filter, a Wiener filter, or a matched filter.

[0011] Furthermore, in step (3), the probability distribution of the emitted symbol is optimized as the input probability distribution defined on a finite set of constellation points.

[0012] Furthermore, the optimized probability distribution can be dynamically adjusted according to preset sensing performance constraints: when the requirements for sensing performance are increased, the optimized probability distribution causes the characteristics of the transmitted signal to approach the constant mode modulation signal, i.e., the PSK signal; when the requirements for communication performance are increased, the optimized probability distribution approaches the QAM signal.

[0013] Furthermore, in step (3), the preset perception performance constraint threshold value is between the mean square error corresponding to the constant mode modulation signal and the mean square error corresponding to the uniform distribution modulation signal.

[0014] Furthermore, in step (3), the performance trade-off is achieved by optimizing the probability distribution of the emitted symbols, which is solved using an optimization algorithm based on alternating iteration.

[0015] Furthermore, the optimization algorithm based on alternating iteration introduces an auxiliary variable, decomposing the original optimization problem into two sub-problems concerning the probability distribution of emitted symbols and the auxiliary variable, and performing alternating optimization until the convergence condition is met.

[0016] The present invention discloses an OFDM communication sensing integrated constellation probabilistic shaping system for arbitrary filters, comprising:

[0017] Unified Sensing Processing Module: Used to establish a unified sensing processing model suitable for filters;

[0018] Sensing performance metrics module: Used to measure the mean square error of the estimation of sensing channel state information as a sensing performance metric.

[0019] Dynamic trade-off module: Used to achieve a dynamic trade-off between communication performance and sensing performance by optimizing the probability distribution of transmitted symbols, with the goal of maximizing the achievable information rate of communication, while meeting preset sensing performance constraints.

[0020] An electronic device according to the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method as described in any one of claims 1-7.

[0021] The present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method as described in any one of claims 1-7.

[0022] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: This invention proposes a more universal PCS waveform design method, enabling it to be compatible with and uniformly optimize various radar receiving schemes, including MF and higher-performance arbitrary filters (such as reciprocal filters (RF) and Wiener filters (WF), thus overcoming the bottleneck of poor universality in existing technologies. The core objective of this invention is to introduce and establish the mean square error (MSE) of the estimation of channel state information (CSI) as a more fundamental and comprehensive measure of sensing performance. By directly targeting the reduction of MSE, this invention aims to synergistically suppress sidelobe effects caused by signal randomness and noise amplification effects introduced by arbitrary filters, thereby more effectively improving radar sensing accuracy without significantly reducing communication performance. This invention achieves a dynamic trade-off between radar and communication performance, thus providing guidance for the quantification of modulation parameters under practical system requirements. Attached Figure Description

[0023] Figure 1 The dynamic range of the present invention varies under different filtering schemes. Variation curves (N=64, M=32);

[0024] Figure 2 The NMSE varies under different filtering schemes of this invention. Change curve;

[0025] Figure 3 The constellation distribution of the non-uniform finite character optimization result of this invention is shown in the example of 64-QAM.

[0026] Figure 4 This is the radar communication performance trade-off curve of the present invention;

[0027] Figure 5 This is the integrated testing scenario of the present invention;

[0028] Figure 6 This is the effect of the distance perception performance optimization of the present invention;

[0029] Figure 7 This is the speed perception performance optimization effect of the present invention. Detailed Implementation

[0030] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0031] like Figure 1 As shown, this embodiment of the invention provides a probabilistic shaping method for an integrated sensing constellation of OFDM communication oriented to arbitrary filters, including the following steps: wherein, lowercase bold variables represent vectors, and uppercase bold variables represent matrices. ,and These represent conjugate, transpose, and conjugate transpose, respectively. It represents the mathematical expectation.

[0032] (1) Constructing an integrated OFDM signal model: Based on the standard OFDM signal framework, assuming that the OFDM signal contains M symbols and N subcarriers, the transmitted baseband signal can be represented as:

[0033]

[0034] The m-th transmitted symbol is:

[0035]

[0036] Here, A finite number of characters representing modulation. Indicates the length of the cyclic prefix. Indicates the length of the symbol. Indicates the subcarrier frequency spacing. express A rectangular window inside.

[0037] Ultimately, the actual transmitted signal of the ISAC system is ,in Where is the carrier frequency. The echo signal transmitted through the channel is represented as:

[0038]

[0039] in and Represented as the first The time delay and Doppler frequency corresponding to the distance to each target Expressed as the return attenuation coefficient, it is usually assumed to follow a zero mean and variance of . A Gaussian random process. Furthermore... The zero mean and variance are The noise.

[0040] For radar sensing, the original OFDM echo signal, after preprocessing and sampling, can be represented in time-frequency matrix form as follows:

[0041]

[0042] in , Represented as a random sign matrix and a noise matrix, respectively. It represents the Hadamah accumulation. Represented as a perceived channel state information (CSI) matrix, it is shown as follows:

[0043]

[0044] here and represents the steering vectors for time delay and Doppler, respectively, and Q represents the number of radar targets.

[0045] (2) Constructing a unified sensing processing framework for matched / arbitrary filters: The ultimate goal of radar sensing is to obtain the data compression result of delay-Doppler (DD), i.e. .here Represents an N-dimensional DFT matrix. Yes The estimated matrix is ​​denoted as

[0046]

[0047] in, This is represented as a time-frequency filtering matrix. Consider three typical filters: matched filtering, reciprocal filtering, and Wiener filtering. The specific form is as follows:

[0048]

[0049] In the above formula, This represents the input signal-to-noise ratio before filtering. (Definition) The filtered spectrum is shown in the following form:

[0050]

[0051] in express The element in the nth row and mth column.

[0052] because The randomness of the signal means that this invention uses its expected value to measure the average performance of radar sensing. For ease of analysis, the following explanation uses the filtering results for a single target (i.e., Q=1, ignoring the subscript q):

[0053]

[0054] The above formula reveals the composition of the time-delay-Doppler filtering result: Base interference: Composed of two parts, caused by signal randomness (the first term of equation (c) above) and filtered noise (the third term of equation (c) above). This base determines the weakest detectable target. Target main lobe signal: i.e., the second term of equation (c) above, ideally with a sinc function shape, its peak power is... Proportional.

[0055] Dynamic range (DR) is used as a metric for perceptual performance and is defined as follows:

[0056]

[0057] in, This represents the region far from the target main lobe in the range-Doppler domain. It can be seen that dynamic range is influenced by the input signal-to-noise ratio, the randomness of the modulation symbols, and the filtering method used. Therefore, DR is the most intuitive performance indicator for characterizing filtering performance.

[0058] Figure 1 The dynamic range as a function of the input signal-to-noise ratio is presented under various filtering schemes (MF, RF, WF) and typical data modulation methods (QAM, PSK). The changing curve shows that, to obtain an ideal range-Doppler profile (i.e., the lowest sidelobes and the strongest noise immunity), the transmitted signal must strictly satisfy the constant mode constraint, i.e., PSK.

[0059] However, using DR as the radar perception optimization metric for PCS design has a significant drawback: it leads to non-convexity in the optimization. Specifically, perception performance is typically constrained by the following conditions:

[0060]

[0061] This constraint, which is a quadratic function minus an affine function greater than or equal to 0, forms a non-convex set, leading to the non-convexity of the PCS model. Therefore, DR can be used as a perceptual performance metric, but it is not suitable for PCS optimization. This limitation forces the search for another perceptual metric, the perceptual CSI mean square error (MSE), denoted as:

[0062]

[0063] The final perceptual mean square errors of the three filters are as follows:

[0064]

[0065] Even considering the absolute fairness of performance comparisons between different filters, the inherent scale variation problem still exists. For example, under PSK modulation, theoretically, the sensing performance (measured by DR) of MF, RF, and WF is exactly the same, but the calculated absolute values ​​of MSE differ. This problem can be explained using the Normalized Mean Square Error (NMSE). Specifically, by normalizing the MSE using the effective signal power, the effect of scale variation is eliminated. Here, NMSE is defined as... .

[0066] Because NMSE is a scale-invariant metric, it makes it possible to conduct consistent and meaningful performance comparisons between different filtering schemes. For example, under PSK modulation, the NMSE values ​​of MF, RF, and WF are exactly the same, such as... Figure 2 As shown, this proves the fairness of NMSE.

[0067] Furthermore, through further simplification and calculation, a clear mathematical relationship between NMSE and DR was revealed:

[0068]

[0069] Based on this relationship, we can re-examine the optimization objective of perception performance. If DR is used as the metric, the optimization problem can be formulated as:

[0070]

[0071] Among them, the constraints are used to assess the effectiveness of the signal energy.

[0072] Based on the relationship between NMSE and DR, this constrained optimization problem can be reconstructed into an equivalent unconstrained optimization problem:

[0073]

[0074] Wherein, the penalty function and the parameter terms are respectively , In other words, within the perceptual performance optimization framework, the NMSE of perceptual CSI can be viewed as a penalty function version of DR.

[0075] However, similar to DR, NMSE, when applied to PCS, leads to non-convex constraints. Note that while MSE cannot be directly used for performance comparisons between different filters due to scale issues, the goal is to independently optimize PCS for each specific filter. Therefore, this invention ultimately adopts MSE as the perceptual optimization metric for PCS.

[0076] (3) Constructing a communication-sensing integrated constellation shaping model

[0077] For a typical time-frequency dual-select fading communication channel, the matrix model of the received communication signal can be assumed to be:

[0078]

[0079] in, and Representing the channel matrix and zero mean, respectively, with power as... The noise.

[0080] The Realizable Information Rate (AIR) is used as a metric for communication performance and is expressed as:

[0081]

[0082] in, Similarly, scalars represent the corresponding elements of each matrix.

[0083] Below, by optimizing the probability distribution of transmitted symbols, the system's communication capability is maximized while strictly meeting the preset sensing performance (measured by MSE), as specifically expressed as follows:

[0084]

[0085] Wherein, objective function It is the achievable information rate (AIR) of the communication link, which serves as a metric for communication performance. Input the probability distribution of the constellation points to be optimized.

[0086] In core constraints It is calculated based on the specific target filter (MF, RF, or WF) and its corresponding MSE expression. It is an adjustable MSE threshold, whose value ranges between the MSE corresponding to the ideal constant modulus signal (PSK, optimal for sensing, lowest MSE) and the uniformly distributed QAM signal (optimal for communication, highest MSE).

[0087] (4) For the integrated communication and sensing constellation shaping model: This invention employs an improved Blahut-Arimoto algorithm. This algorithm introduces a posterior probability distribution. As an auxiliary variable, the original problem is transformed into a problem about and The problem of alternating iterative optimization.

[0088] For the k-th iteration, the alternating optimization steps are as follows:

[0089] A. Given independent variables Regarding latent variables Maximize mutual information to obtain The optimal solution is:

[0090]

[0091] B. Given ,about Maximizing mutual information: Solving using the Lagrange multiplier method, thus obtaining... The optimal solution is:

[0092]

[0093] In the results of the kth alternation optimization above, and It is still an unknown quantity and requires further solution. Substituting these into the first two constraints of the optimization model, we obtain... and The required system of two nonlinear equations needs to be satisfied. This can be solved using classical numerical algorithms, such as Newton's method or the bisection method. and The final result is obtained. The (k+1)th iteration is repeated until the mean square error between two consecutive iterations is sufficiently small, at which point the iteration process is complete.

[0094] To illustrate the technical effects of this invention, a simulation experiment was conducted. Simulation experiment: The distribution of symbols with a finite number of characters is as follows... Figure 3 As can be seen intuitively, after optimization, the smaller the value of c0, the higher the requirement for perception performance, and the closer the optimization result of the non-uniform constellation is to PSK; conversely, the closer it is to QAM. Figure 4 The proposed method demonstrates the trade-off between radar communication performance and performance: Overall, after optimization, the communication sensing performance trade-off of the matched / arbitrary filter is significantly better than that of the traditional time-division method.

[0095] Actual measurement data: A prototype of the integrated radar and communication system was built and field tests were conducted. Figure 5 ), by transmitting and receiving actual test data, MF, RF, and WF were performed sequentially, and the test results are as follows. Figure 6 , Figure 7 As shown, after non-uniform finite character optimization, the sidelobes of the matched filter range image are significantly reduced compared to the traditional uniform QAM results, with a maximum performance gain of about 3-4 dB.

Claims

1. A probabilistic shaping method for an integrated sensing constellation in OFDM communication oriented towards arbitrary filters, characterized in that, Includes the following steps: (1) Establish a unified sensing processing model applicable to filters; (2) The mean square error of the estimation of the sensing channel state information is used as the sensing performance metric. (3) With maximizing the achievable information rate as the communication performance target, and under the condition of satisfying the preset perception performance constraints, a dynamic trade-off between communication performance and perception performance is achieved by optimizing the probability distribution of transmitted symbols.

2. The OFDM communication sensing integrated constellation probabilistic shaping method for arbitrary filters according to claim 1, characterized in that, In step (1), the filter includes, but is not limited to, a reciprocal filter, a Wiener filter, or a matched filter.

3. The OFDM communication sensing integrated constellation probabilistic shaping method for arbitrary filters according to claim 1, characterized in that, In step (3), optimizing the probability distribution of the emitted symbols is to optimize the input probability distribution defined on a finite set of constellation points.

4. The OFDM communication sensing integrated constellation probabilistic shaping method for arbitrary filters according to claim 3, characterized in that, The optimized probability distribution can be dynamically adjusted according to preset sensing performance constraints: when the requirements for sensing performance are increased, the optimized probability distribution makes the characteristics of the transmitted signal approach the constant mode modulation signal, i.e., the PSK signal; when the requirements for communication performance are increased, the optimized probability distribution approaches the QAM signal.

5. The OFDM communication sensing integrated constellation probabilistic shaping method for arbitrary filters according to claim 1, characterized in that, In step (3), the preset sensing performance constraint threshold value is between the mean square error corresponding to the constant mode modulation signal and the mean square error corresponding to the uniform distribution modulation signal.

6. The OFDM communication sensing integrated constellation probabilistic shaping method for arbitrary filters according to claim 1, characterized in that, In step (3), the performance trade-off is achieved by optimizing the probability distribution of the emitted symbols, which is solved by using an optimization algorithm based on alternating iteration.

7. The OFDM communication sensing integrated constellation probabilistic shaping method for arbitrary filters according to claim 6, characterized in that, Alternating iteration-based optimization algorithms introduce auxiliary variables to decompose the original optimization problem into two subproblems: the probability distribution of emitted symbols and the auxiliary variables. These subproblems are then optimized alternately until the convergence condition is met.

8. A probabilistic constellation shaping system for OFDM communication sensing, characterized in that, include: Unified Sensing Processing Module: Used to establish a unified sensing processing model suitable for filters; Sensing performance metrics module: Used to measure the mean square error of the estimation of sensing channel state information as a sensing performance metric. Dynamic trade-off module: Used to achieve a dynamic trade-off between communication performance and sensing performance by optimizing the probability distribution of transmitted symbols, with the goal of maximizing the achievable information rate of communication, while meeting preset sensing performance constraints.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1-7.

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