Communication and perception integrated waveform design method based on KL divergence

Abstract

The present invention provides a communication-perception integrated waveform design method based on KL divergence, which belongs to the field of communication-perception integration. The method comprises: step S1, constructing a scenario model of an ISAC system, including an ISAC base station, an unmanned aerial vehicle (UAV) target, and a communication user, obtaining a KL divergence index for unified performance characterization of the ISAC system, wherein the KL divergence index is composed of a KL divergence expression of the communication performance of the ISAC system and a KL divergence expression of the perception performance of the ISAC system; step S2, designing an optimization problem for a transmit constellation diagram of the ISAC system based on the KL divergence index for unified performance characterization, solving the problem using a neural network to obtain a transmit constellation diagram, and the base station using the constellation diagram to perform integrated waveform mapping to form an integrated waveform; step S3, using the KL divergence index for unified performance characterization to perform beamforming design on the integrated waveform to achieve reasonable allocation of system resources. The present invention can achieve a compromise between communication and perception performance in the ISAC system.

Description

Technical Field

[0001] The present invention belongs to the field of communication and perception integration, and particularly relates to a communication and perception integration waveform design method based on KL divergence. Background Art

[0002] Integrated Sensing and Communication (ISAC) technology can effectively reduce hardware costs while improving spectrum utilization, and is considered a key technology in future 6G communications. To achieve efficient resource allocation and meet the performance requirements of practical projects, it is necessary to study a unified representation of the overall communication and perception performance of the integrated system to guide integrated waveform design. In this context, F. Liu et al. pioneered the study of beamforming in ISAC systems, using the signal-to-interference-plus-noise ratio (SINR) at the synaesthesia user and the transmitted beam pattern as indicators of communication and perception performance, respectively. Given the limited intuitiveness of the transmitted beam pattern in representing perception performance, F. Liu, X. Wang et al. used the Cramer-Rao Bound (CRB) to measure perception performance. They studied the beamforming problem in both fully digital and hybrid analog-digital ISAC systems, respectively. Their results demonstrate that the CRB can effectively characterize the performance of the perception subsystem in ISAC systems. To characterize the communication performance of ISAC systems, X. Wang and J. Johnston studied beamforming using communication rate and bit error rate (BER) as metrics, respectively. Y. Xiong further evaluated the communication rate and perceived CRB of ISAC systems under Gaussian channels from an information theory perspective.

[0003] Although the research on integrated waveform design under different communication and perception performance indicators in ISAC systems is relatively mature, due to the different quantification methods of different indicators, the integrated waveform design is highly complex and cannot meet the performance indicators of the ISAC system. Therefore, further research is needed on the unified representation of communication and perception performance and integrated waveform design in ISAC systems. Summary of the Invention

[0004] The purpose of this invention is to propose a communication-perception integrated waveform design method based on KL divergence, which can achieve a trade-off between communication and perception performance in the ISAC system, solve the problems of difficult waveform design and complex performance trade-offs, and provide a new ISAC waveform design method.

[0005] The present invention is achieved through the following technical solutions:

[0006] The communication-awareness integrated waveform design method based on KL divergence includes the following steps:

[0007] Step S1: Construct a scenario model of the ISAC system, which includes an ISAC base station, a drone target to be sensed and detected by the ISAC base station, and a communication user, and obtain a KL divergence index for the unified performance representation of the ISAC system. The KL divergence index is composed of a KL divergence expression of the ISAC system's communication performance and a KL divergence expression of the ISAC system's perception performance.

[0008] Step S2: Designing an ISAC system transmit constellation optimization problem based on the KL divergence index of the unified performance representation obtained in step S1, and solving the problem using a neural network to obtain a transmit constellation. The base station uses the constellation to perform integrated waveform mapping to form an integrated waveform.

[0009] Step S3: Using the KL divergence index of the unified performance representation obtained in step S1, beamforming design is performed for the integrated waveform in step S2 to achieve reasonable allocation of system resources.

[0010] Furthermore, in step S1, there are K scattering points on the fuselage of the UAV target, there are K sensing links between the UAV target and the ISAC base station, and there is a direct path and P between the communication user and the ISAC base station. l The states of the communication user and the UAV remain unchanged within a time slot. During this time slot, the signal received by the communication user is The perceived echo is Where ρ0 represents the path loss per unit distance, d c and d t They represent the distances of the communication user and the drone target to be detected by the base station from the ISAC base station, θ c ,θ p and θ k They represent the departure angles of the direct path communication link, the non-direct path communication link and the sensing link corresponding to the kth scattering point, α p represents the small-scale fading coefficient of the pth non-direct path communication link, n c Represents the Gaussian white noise of the communication link, which has a mean of zero and a variance of Gaussian distribution, n r Represents the Gaussian white noise of the sensing link, which has a mean of zero and a variance of Gaussian distribution, w represents the signal beamforming vector, s represents the signal sent by the ISAC base station, a(·) represents the antenna steering vector, reflecting multiple antennas, a * (·) means taking the conjugate of a(·), a H(·) represents the conjugate transpose of a(·).

[0011] Furthermore, according to whether there is a sensing target in the echo after the signal transmitted by the ISAC base station is reflected by the UAV target, the sensing echo is expressed as a binary hypothesis problem. in, Indicates that there is no perceived target in the target echo, only noise, and Indicates that the perceived target is successfully detected in the target echo.

[0012] Furthermore, in step S1, the KL divergence index of the unified performance characterization is KLD I =(1-η1)KLD c +η1KLD r , where η1 is a weight factor used to balance communication performance and perception performance, is the KL divergence expression of perceptual performance, W=ww H , Q means that the ISAC base station transmits a Q-order modulated signal, I M represents the identity matrix of order M, P r (·) represents probability, c m It represents the complex representation of the mth constellation point in the Q-order constellation diagram, Represents Σ n The square root of the inverse matrix of is the KL divergence expression of communication performance, m represents the subscript corresponding to the m-th constellation point in the Q-order constellation diagram, n represents the subscript corresponding to the n-th constellation point in the Q-order constellation diagram, μ m represents the intermediate variable corresponding to the mth constellation point, μ n represents the intermediate variable corresponding to the nth constellation point, c n Represents the complex number representation of the nth constellation point in the Qth order constellation diagram.

[0013] Furthermore, in step S2, the transmit constellation optimization problem is

[0014] Furthermore, in step S2, the neural network includes two multi-layer perceptron networks, and the two multi-layer perceptron networks respectively optimize the complex number c m The real part c m,r and the imaginary part c m,i , both multilayer perceptrons use ReLU function as activation function, for the complex number c composed of real and imaginary parts generated by the two multilayer perceptrons m , modified using the normalization layer, the corresponding modification function is tanh(·) is used to map complex magnitudes to an interval.

[0015] Furthermore, in step S2, for the transmit constellation optimization problem, the KL divergence expression KLD of the perceptual performance r Follow Monotonically increasing, the transmit constellation optimization problem is transformed into This formula is used as the loss function of the neural network, and the neural network is trained by the back propagation algorithm to obtain the required constellation diagram, where c n Represents the nth constellation point in the Q-order constellation diagram, Represents the average energy of the Q-order constellation point.

[0016] Furthermore, in step S3, the KL divergence expression KLD of the perceptual performance is firstly r And the KL divergence expression of communication performance KLD c The Pareto frontier problem between Then transform the problem into Finally, the semi-positive programming method is used to solve the transformed problem and obtain the optimal beamforming vector based on the KL divergence unified performance characterization, where D r =AA H , express When KLD c The value of h c represents the steering vector for the communication user, P represents the transmission power, and η2 is used for KLD r With KLD c Distribution of performance between.

[0017] The present invention has the following beneficial effects:

[0018] 1. The present invention first obtains the KL divergence index based on the unified performance representation of communication performance and perception performance, then obtains the SAC system transmit constellation optimization problem based on the KL divergence index, and uses a neural network to solve the problem to obtain the transmit constellation diagram. While generating an integrated signal, it also senses and detects drones and provides communication services for communication users. Finally, the KL divergence index is used to design beamforming for the integrated waveform. That is, to address the problem of inconsistent integrated waveform design indicators of the ISAC system, an ISAC performance evaluation model based on KL divergence is established, enabling the base station to flexibly provide integrated services for communication users and detection drones according to different needs, optimizing resource allocation, and proposing a beamforming method based on the unified performance representation of KL divergence. The Pareto frontier of the ISAC system's communication performance and perception performance is clarified, revealing the essence of the ISAC system's performance trade-off, and providing an important theoretical basis for future ISAC system resource and performance allocation. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The present invention will be further described in detail below with reference to the accompanying drawings.

[0020] Figure 1 Flowchart of the present invention.

[0021] Figure 2 This is the result diagram of the constellation diagram optimization of the present invention.

[0022] Figure 3 It is the KL divergence diagram of the communication performance and perception performance of the present invention.

[0023] Figure 4 This is a result diagram of the Pareto frontier of communication performance and perception performance related indicators of the present invention. DETAILED DESCRIPTION

[0024] like Figure 1 As shown in FIG, the communication-awareness integrated waveform design method based on KL divergence includes the following steps:

[0025] Step S1: To address the problem of using a unified indicator for integrated waveform design in the ISAC system, a unified performance evaluation framework based on KL divergence is established to implement the use of KL divergence to evaluate the communication and perception performance of the ISAC system. Specifically, a scenario model of the ISAC system is first constructed. The scenario model includes an ISAC base station, a drone target hovering above the base station to be sensed and detected by the ISAC base station, and a communication user not far from the base station. The KL divergence indicator for the unified performance representation of the ISAC system is obtained. The KL divergence indicator is composed of a KL divergence expression for the communication performance of the ISAC system and a KL divergence expression for the perception performance of the ISAC system.

[0026] Among them, the drone is a scatterer sensing target. There are K scattering points on its body. There are K sensing links between it and the ISAC base station. The signal transmitted by the base station is reflected by each reflection point of the drone target, and each echo reaches the base station through the corresponding sensing link. After receiving the echo, the base station analyzes it to obtain the drone sensing parameters (including the distance between the drone and the base station, the drone speed, etc.). There is a direct path (LoS) and P between the communication user and the ISAC base station. l The ISAC base station is equipped with a uniform planar array of transmitting antennas and receiving antennas. The number of antennas is M. The receiving antenna is used to receive the echo of the sensing signal. The status of the communication user and the UAV remains unchanged in a time slot. In this time slot, the signal received by the communication user is The perceived echo is Where ρ0 represents the path loss per unit distance, d c and d t They represent the distances of the communication user and the drone target to be detected by the base station from the ISAC base station, θ c ,θ p and θ k They represent the departure angles of the direct path communication link, the non-direct path communication link and the sensing link corresponding to the kth scattering point, α p represents the small-scale fading coefficient of the pth non-direct path communication link, a(·)=[1,e j2πδsin(·) ,...,e j2π(M-1)δsin(·) ] T Represents the antenna steering vector, reflecting multiple antennas, a * (·) means taking the conjugate of a(·), a H (·) represents the conjugate transpose of a(·), n c Represents the Gaussian white noise of the communication link, which has a mean of zero and a variance of Gaussian distribution, n r Represents the Gaussian white noise of the sensing link, which has a mean of zero and a variance of Gaussian distribution, w represents the signal beamforming vector, and s represents the signal sent by the ISAC base station;

[0027] According to whether there is a sensing target in the echo after the signal transmitted by the ISAC base station is reflected by the UAV target, the sensing echo is expressed as a binary hypothesis problem. in, Indicates that there is no perceived target in the target echo, only noise, and Indicates that the perceived target is successfully detected in the target echo.

[0028] In this embodiment, ρ0=-30dB, P l =4, M=16, K=10, dc =800m,d t =1000m,θ c =0°,θ s =10° or 90°,

[0029] KL divergence is used to evaluate the degree of difference between a pair of probability density functions (PDF), which is defined as Among them, f m (x) and f n (x) represents a pair of PDFs whose differences need to be compared.

[0030] For the Q-order modulated signal transmitted by the ISAC base station, under the Gaussian channel, each constellation point obeys the Gaussian distribution with different means and the same variance, that is, the constellation point c m The PDF representation of Substituting this formula into the definition formula of KL divergence, we can get the KL divergence expression of the ISAC system communication performance: The greater the difference between the PDFs of different constellation points, that is, the greater the KL divergence, the better the demodulation performance of the signal and the better the communication performance of the ISAC system. In this case, m represents the subscript corresponding to the mth constellation point in the Q-order constellation diagram, n represents the subscript corresponding to the nth constellation point in the Q-order constellation diagram, and μ m Represents the intermediate variable corresponding to the mth constellation point, μ n Represents the intermediate variable corresponding to the nth constellation point, c n represents the complex number representation of the nth constellation point in the Qth order constellation diagram;

[0031] Regarding the binary hypothesis problem of sensing echo expression, whether there is a target in the target echo (corresponding to the hypothesis and ) are:

[0032]

[0033]

[0034] Then get and The KL divergence between is expressed as follows, that is, the KL divergence formula of perceptual performance: in, W=ww H ; Q represents the Q-order modulation signal transmitted by the I SAC base station. M represents the identity matrix of order M, P r(·) represents the probability of something happening, c m It represents the complex representation of the mth constellation point in the Q-order constellation diagram, represents the variance of the Gaussian white noise of the sensing link, I represents the unit vector, Represents Σ n The square root of the inverse matrix of , w represents the signal beamforming vector;

[0035] Finally, the KL divergence index KLD of unified performance representation is obtained I =(1-η1)KLD c +η1KLD r , η1 is the weight factor used to balance communication performance and perception performance.

[0036] Step S2: Designing an ISAC system transmit constellation optimization problem based on the KL divergence index of the unified performance representation obtained in step S1, and solving the problem using a neural network to obtain a transmit constellation. The base station uses the constellation to perform integrated waveform mapping to form an integrated waveform.

[0037] For a single-antenna ISAC system, the KL divergence metric for unified performance characterization can be simplified to: Where P is the transmit power,

[0038] Then the transmit constellation optimization problem of the ISAC system is expressed as: KLD in its objective function r Follow Monotonically increasing, it can be transformed into the following form In this embodiment, when Q=16, the corresponding η1=0, 0.18, 0.3, 0.33, 0.4; when Q=32, the corresponding η1=0, 0.1, 0.2, 0.25, 0.3, 0.4;

[0039] For the above-mentioned transmit constellation optimization problem, a neural network is used to solve the problem. For this complex optimization problem, the neural network includes two multi-layer perceptron networks. The two multi-layer perceptron (MLP) networks optimize the complex c respectively. m The real part c m,r and the imaginary part c m,i , both multilayer perceptrons use ReLU function as activation function, for the complex number c composed of real and imaginary parts generated by the two multilayer perceptrons m , in order to satisfy The constraints in are modified by the normalization layer, and the corresponding modification function is tanh(·) is used to map complex magnitudes to an interval.

[0040] Will As the loss function of the neural network, the back propagation algorithm is used to train the neural network to obtain the required constellation diagram. The base station uses the constellation diagram to perform integrated waveform mapping, and finally forms an integrated waveform. The balance between communication performance and perception performance in the ISAC system is achieved by weighing the parameter η1, where Represents the average energy of the Q-order constellation point.

[0041] Step S3: Using the KL divergence index of the unified performance representation obtained in step S1, beamforming design is performed for the integrated waveform in step S2 to achieve reasonable allocation of system resources.

[0042] Specifically include:

[0043] Step S31: The KL divergence expression KLD of the perceptual performance r Simplified to in,

[0044] use The strictly monotonically decreasing property of r The problem is expressed as Based on the conclusion of the maximum value of the quadratic form under the constraint conditions, the maximum KLD r The optimal solution to the problem is Among them, v max It's AA H The eigenvector corresponding to the largest eigenvalue;

[0045] Similarly, we get KLD c The optimal beam vector is expressed as in,

[0046] Then the KL divergence expression of perceptual performance KLD r And the KL divergence expression of communication performance KLD c The Pareto frontier problem between in, express When KLD c The value of η2 is used for KLD r With KLD c The performance distribution between them is shown in Figure 2. P = 30dBm represents the transmission power.

[0047] use The strictly monotonically decreasing property of Pareto frontier problem is transformed into Finally, the semi-positive programming method is used to solve the transformed problem and obtain the optimal beamforming vector based on the KL divergence unified performance characterization, where Dr =AA H , h c Represents the steering vector for the communication user.

[0048] Figure 2 In the figure, the x-axis is the real part of the constellation point, and the y-axis is the imaginary axis of the constellation point. The different results of the neural network optimization constellation diagram under different constellation point numbers Q and parameters η1 are compared. Figure 4 It can be seen that as the parameter value increases, the number of constellation points within the unit circle decreases, the number of constellation points on the unit circle increases, the average power of the constellation diagram increases, and the minimum distance between the constellation points decreases. This indicates that the perception performance of the signal waveform increases as the parameter value increases, while the communication performance decreases as the parameter value increases, reflecting the trade-off between the communication and perception performance of the ISAC system.

[0049] Figure 3 In the figure, the x-axis is the KL divergence value of perception, and the y-axis is the KL divergence value of communication. The simulation experiment compares and analyzes the KL divergence values ​​of the waveforms with Q=16 constellation points and Q=32 constellation points, as well as the situations with different angles φ between the communication user and the drone target to be detected. Figure 3 As can be seen, the 16-point constellation performs better than the 32-point constellation because the minimum distance between the 16-point constellation points is greater, resulting in a wider noise tolerance. Perception performance is also better when the angle φ between the communication user and the target drone is smaller. This is because the beam pattern's energy is more concentrated, resulting in a higher signal-to-noise ratio for the echo signal and easier detection of the target. This demonstrates that the present invention effectively achieves its intended objectives and reveals the Pareto frontier for the communication and perception performance of the ISAC system.

[0050] Figure 4 In the simulation, the horizontal axis is the detection probability, which ranges from 0 to 100%, and the vertical axis is the bit error rate. The simulation experiment compares and analyzes the relevant indicators of the 16-constellation point and 32-constellation point waveforms and the situations when the communication user and the unmanned aerial vehicle target have different angles φ. Figure 4 It can be seen that the communication bit error rate of the 16-point constellation diagram is lower, which is consistent with Figure 3 When the angle φ between the communication user and the target UAV is smaller, the probability of detection is higher, which is also consistent with Figure 3 The results in the present invention are consistent with those in the previous communication and perception indicators, and have theoretical guiding significance.

[0051] The above description is merely a preferred embodiment of the present invention and therefore cannot be used to limit the scope of the present invention. In other words, equivalent changes and modifications made according to the scope of the patent application and the contents of the specification should still fall within the scope of the patent of the present invention.

Claims

1. A communication-aware integrated waveform design method based on KL divergence, characterized by: The steps include: Step S1: Construct a scenario model of the ISAC system, which includes an ISAC base station, a drone to be sensed and detected by the ISAC base station, and a communication user, and obtain a KL divergence index for the unified performance representation of the ISAC system. The KL divergence index is composed of a KL divergence expression of the ISAC system's communication performance and a KL divergence expression of the ISAC system's perception performance. Step S2: Designing an ISAC system transmit constellation optimization problem based on the KL divergence index of the unified performance representation obtained in step S1, and solving the problem using a neural network to obtain a transmit constellation. The base station uses the constellation to perform integrated waveform mapping to form an integrated waveform. Step S3: Using the KL divergence index of the unified performance representation obtained in step S1, beamforming design is performed to achieve reasonable allocation of system resources; In step S1, the KL divergence index of the unified performance characterization is KLD I =(1-η1)KLD c +η1KLD r , where η1 is a weight factor used to balance communication performance and perception performance, is the KL divergence expression of perceptual performance, ρ0 represents the path loss per unit distance, d t Indicates the distance between the drone and the ISAC base station. θ j represents the departure angle of the sensing link corresponding to the jth scattering point, J represents the number of scattering points, a(·) represents the antenna steering vector, reflecting multiple antennas, a * (·) means taking the conjugate of a(·), a H (·) represents the conjugate transpose of a(·), W = ww H , Q means that the ISAC base station transmits a Q-order modulated signal, I M represents the identity matrix of order M, P r (·) represents probability, c m represents the complex number representation of the mth constellation point in the Q-order constellation diagram, represents the variance of the Gaussian white noise of the communication link in the signal received by the communication user, Represents Σ n The square root of the inverse matrix of is the KL divergence expression of communication performance, m represents the subscript corresponding to the m-th constellation point in the Q-order constellation diagram, n represents the subscript corresponding to the n-th constellation point in the Q-order constellation diagram, represents the variance of the Gaussian white noise of the sensing link in the sensing echo, μ m represents the intermediate variable corresponding to the mth constellation point, d c represents the distance between the communication user and the ISAC base station, θ c represents the departure angle of the non-direct path communication link, μ n represents the intermediate variable corresponding to the nth constellation point, w represents the signal beamforming vector, c n represents the complex number representation of the nth constellation point in the Qth order constellation diagram; In step S2, the transmit constellation optimization problem is: In step S3, the KL divergence expression KLD of the perceptual performance is firstly r And the KL divergence expression of communication performance KLD c The Pareto frontier problem between Then transform the problem into Finally, the semi-positive programming method is used to solve the transformed problem and obtain the optimal beamforming vector based on the KL divergence unified performance characterization, where D r =AA H , express When KLD c The value of h c represents the steering vector for the communication user, P represents the transmission power, and η2 is used for KLD r With KLD c Distribution of performance between.

2. The communication-awareness integrated waveform design method based on KL divergence according to claim 1, characterized in that: In step S1, there are K scattering points on the fuselage of the UAV, and there are K sensing links between the UAV and the ISAC base station. There is a direct path and P between the communication user and the ISAC base station. l The states of the communication user and the UAV remain unchanged within a time slot. During this time slot, the signal received by the communication user is The perceived echo is Where ρ0 represents the path loss per unit distance, d c and d t are the distances of the communication user and the UAV from the ISAC base station, θ c ,θ p and θ k They represent the departure angles of the direct path communication link, the non-direct path communication link and the sensing link corresponding to the kth scattering point, α p represents the small-scale fading coefficient of the pth non-direct path communication link, n c Represents the Gaussian white noise of the communication link, which has a mean of zero and a variance of Gaussian distribution, n r Represents the Gaussian white noise of the sensing link, which has a mean of zero and a variance of Gaussian distribution, w represents the signal beamforming vector, s represents the signal sent by the ISAC base station, a(·) represents the antenna steering vector, reflecting multiple antennas, a * (·) means taking the conjugate of a(·), a H (·) represents the conjugate transpose of a(·).

3. The communication-awareness integrated waveform design method based on KL divergence according to claim 2, characterized in that: According to whether there is a sensing target in the echo after the signal transmitted by the ISAC base station is reflected by the UAV target, the sensing echo is expressed as a binary hypothesis problem. in, Indicates that there is no perceived target in the target echo, only noise, and Indicates that the perceived target is successfully detected in the target echo.

4. The communication-awareness integrated waveform design method based on KL divergence according to claim 3 is characterized by: In step S2, the neural network includes two multi-layer perceptron networks, which respectively optimize the complex number c m The real part c m,r and the imaginary part c m,i , both multilayer perceptrons use ReLU function as activation function, for the complex number c composed of real and imaginary parts generated by the two multilayer perceptrons m , modified using the normalization layer, the corresponding modification function is tanh(·) is used to map complex magnitudes to an interval.

5. The communication-awareness integrated waveform design method based on KL divergence according to claim 2, characterized in that: In step S2, for the transmit constellation optimization problem, the KL divergence expression KLD of the perceptual performance r Follow Monotonically increasing, the transmit constellation optimization problem is transformed into This formula is used as the loss function of the neural network, and the neural network is trained by the back propagation algorithm to obtain the required constellation diagram, where c n Represents the nth constellation point in the Q-order constellation diagram, Represents the average energy of the Q-order constellation point.

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