A Radar-Communication Integrated Signal Modulation Method Based on Non-Uniform Finite Character Optimization

Abstract

This invention discloses a radar-communication integrated signal modulation method based on non-uniform finite character optimization, comprising the following steps: (1) obtaining the input probability distribution of finite character symbols; (2) establishing radar fourth-order moment, power, and probability constraints based on the probability distribution and with maximizing communication mutual information as the objective function; (3) designing an algorithm using the idea of ​​alternating optimization and obtaining a local optimal solution through iteration; this invention effectively improves radar matched filtering performance without significantly reducing communication performance; and achieves a dynamic trade-off between radar and communication performance, thereby providing guidance for the quantification of modulation parameters under actual system requirements.

Description

Technical Field

[0001] This invention relates to a novel signal modulation technology field for next-generation mobile communication (6G), specifically to an integrated radar communication signal modulation method based on non-uniform finite character optimization. Background Technology

[0002] OFDM waveform sharing is a low-cost technique for achieving radar-communication integration. By collecting communication echoes reflected from targets and utilizing traditional matched filters, the radar receiver's output signal-to-noise ratio is maximized, thus acquiring environmental awareness while retaining the original communication functionality. However, the finite number of characters modulated by OFDM communication signals is random (e.g., using traditional QAM or PSK modulation), which leads to randomness in radar perception performance. Specifically, this randomness causes random fluctuations in the matched filter sidelobe level, affecting radar perception performance. Reducing sidelobe levels is crucial for weak target detection and preventing false alarms from ghost targets. Therefore, effectively reducing matched filter sidelobes while maintaining existing OFDM radar-communication integration waveform sharing capabilities has become a key technical challenge. Existing technologies generally employ uniform character modulation (QAM) and time-sharing strategies to address this issue. However, both approaches have significant drawbacks: (For uniformly distributed QAM and PSK, there is a "conflict" between radar sensing and communication performance. Using this traditional approach, one must simultaneously achieve either optimal sensing performance and worst-case communication performance (PSK), or worst-case sensing performance and optimal communication performance (QAM), making flexible modulation between radar and communication performance difficult, thus failing to achieve a performance trade-off. For the time-sharing strategy, this method can only achieve a linear trade-off between radar and communication performance, which can be seen as the inner bound of the radar-communication performance trade-off, resulting in limited performance gains.) Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a radar-communication integrated signal modulation method based on non-uniform finite character optimization, which achieves a tighter radar-communication performance outer boundary through offline processing, thereby obtaining greater gain compared to time-sharing strategies.

[0004] Technical solution: The radar communication integrated signal modulation method based on non-uniform finite character optimization described in this invention includes the following steps:

[0005] (1) Obtain the input probability distribution of a finite number of character symbols;

[0006] (2) Based on the probability distribution, with the objective function of maximizing communication mutual information, establish the fourth-order moment, power, and probability constraints of the radar;

[0007] (3) Design an algorithm using the idea of ​​alternating optimization and obtain a local optimal solution through iteration.

[0008] Furthermore, step (1) is as follows: Let the probability distribution vector be: p = [p1, p2, ..., p 16 ] T ;

[0009] Suppose the received communication signal is simplified as follows:

[0010] y = x + z

[0011] Where y represents the receiving model of a single sub-channel; x represents the transmitted OFDM communication signal; and z represents Gaussian white noise. For multiple parallel sub-channels of OFDM, the mutual information between y and x is directly superimposed.

[0012] Furthermore, step (2) is as follows:

[0013]

[0014] Where P(y|x) represents the conditional probability density function of the received communication signal y given x, p(y) represents the probability density function of y, and similarly, p(x) is the probability density function of x; E_{X,Y} represents the probability density function of x.<X,Y> Seek joint expectations.

[0015] Mutual information is represented as:

[0016]

[0017] and

[0018]

[0019] Wherein, vector p represents the vector composed of discrete values ​​corresponding to p(x), and vector q represents the vector composed of discrete values ​​of q(x|y);

[0020] By introducing a latent variable q, mutual information is represented as maximizing the joint function Q(p,q).

[0021] Furthermore, step (3) is as follows:

[0022] (31) For the k-th iteration, given the independent variable p (k) Based on maximizing mutual information according to the latent variable q, we can obtain q. (k) The optimal solution is:

[0023]

[0024] (32) Given q (k) The method of Lagrange multipliers is used to solve for p to maximize mutual information, and the formula is as follows:

[0025]

[0026] Where λ1, λ2, and λ3 represent Lagrange multipliers; ε0 represents the preset value of the fourth moment; and P0 represents the transmitted signal power.

[0027] Setting the partial derivatives of the Lagrange multipliers with respect to p(x) to zero, we obtain p (k+1) The optimal solution is:

[0028]

[0029] In step (31), p (k+1) Substituting (x) into the first two constraints of the optimization model in step (2), we obtain the set of two nonlinear equations that λ1 and λ2 need to satisfy. The final results of λ1 and λ2 can be solved by classical numerical algorithms.

[0030] (33) Repeat steps (31)-(32) until the mean square error of the results of two adjacent iterations is small enough, and the iteration process is complete.

[0031] The radar-communication integrated signal modulation system based on non-uniform finite character optimization described in this invention includes:

[0032] Probability distribution module: used to obtain the input probability distribution of a finite number of character symbols;

[0033] The building module is used to establish the radar's fourth-order moment, power, and probability constraints based on the probability distribution, with the objective function of maximizing communication mutual information.

[0034] Optimization module: Used to design algorithms using the idea of ​​alternating optimization, and obtain local optimal solutions through iteration.

[0035] Furthermore, in the probability distribution module, the specifics are as follows: Let the probability distribution vector be: p = [p1, p2, ..., p 16 ] T Suppose the communication received signal is simplified as follows:

[0036] y = x + z

[0037] Where y represents the receiving model of a single sub-channel; x represents the transmitted OFDM communication signal; and z represents Gaussian white noise. For multiple parallel sub-channels of OFDM, the mutual information between y and x is directly superimposed.

[0038] Furthermore, in the construction module, the specifics are as follows:

[0039]

[0040] Where P(y|x) represents the conditional probability density function of the received communication signal y given x, p(y) represents the probability density function of y, and similarly, p(x) is the probability density function of x; E_{X,Y} represents the probability density function of x.<X,Y> Seek joint expectations.

[0041] Mutual information is represented as:

[0042]

[0043] and

[0044]

[0045] Wherein, vector p represents the vector composed of discrete values ​​corresponding to p(x), and vector q represents the vector composed of discrete values ​​of q(x|y);

[0046] By introducing a latent variable q, mutual information is represented as maximizing the joint function Q(p,q).

[0047] Furthermore, the optimization module specifically includes the following:

[0048] (31) For the k-th iteration, given the independent variable p (k) Based on maximizing mutual information according to the latent variable q, we can obtain q. (k) The optimal solution is:

[0049]

[0050] (32) Given q (k) The method of Lagrange multipliers is used to solve for p to maximize mutual information, and the formula is as follows:

[0051]

[0052] Where λ1, λ2, and λ3 represent Lagrange multipliers; ε0 represents the preset value of the fourth moment; and P0 represents the transmitted signal power.

[0053] Setting the partial derivatives of the Lagrange multipliers with respect to p(x) to zero, we obtain p (k+1) The optimal solution is:

[0054]

[0055] In step (31), p (k+1) Substituting (x) into the first two constraints of the optimization model in step (2), we obtain the set of two nonlinear equations that λ1 and λ2 need to satisfy. The final results of λ1 and λ2 can be solved by classical numerical algorithms.

[0056] (33) Repeat steps (31)-(32) until the mean square error of the results of two adjacent iterations is small enough, and the iteration process is complete.

[0057] 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. When the computer program is loaded onto the processor, it implements any of the radar communication integrated signal modulation methods based on non-uniform finite character optimization.

[0058] The present invention provides a storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, it implements any one of the radar communication integrated signal modulation methods based on non-uniform finite character optimization.

[0059] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: it realizes the integration of dual functions of communication and radar sensing without significantly changing the existing communication modulation and demodulation module; it effectively improves the radar matched filtering performance without significantly reducing the communication performance; and it achieves a dynamic trade-off between radar and communication performance, thereby providing guidance for the quantification of modulation parameters under actual system requirements. Attached Figure Description

[0060] Figure 1 The symbol probability distribution of the 16-QAM of this invention;

[0061] Figure 2 This is a diagram showing the optimization results of the non-uniform finite character representation of the present invention; wherein, Figure 2 In (a) ε0 = 1.25; (b) ε0 = 1.0; (c) is a uniform 64-QAM;

[0062] Figure 3 This is the radar communication performance trade-off curve of the present invention;

[0063] Figure 4 To build a prototype of the integrated radar and communication principle of this invention;

[0064] Figure 5 This refers to the radar sensing performance of the present invention. Detailed Implementation

[0065] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0066] like Figure 1 As shown, this embodiment of the invention provides a radar-communication integrated signal modulation method based on non-uniform finite character optimization, characterized by the following steps:

[0067] (1) Obtain the input probability distribution of a finite number of character symbols; specifically as follows: Figure 1 As shown, taking 16-QAM as an example, let the probability distribution vector be: p=[p1,p2,…,p 16 ] T ;

[0068] Suppose the received communication signal is simplified as follows:

[0069] y = x + z

[0070] Where y represents the receiving model of a single sub-channel; x represents the transmitted OFDM communication signal; and z represents Gaussian white noise. For multiple parallel sub-channels of OFDM, the mutual information between y and x is directly superimposed.

[0071] (2) Based on the probability distribution, with maximizing communication mutual information as the objective function, establish the radar fourth-order moment, power, and probability constraints; step (2) is as follows:

[0072]

[0073] Where P(y|x) represents the conditional probability density function of the received communication signal y given x, p(y) represents the probability density function of y, and similarly, p(x) is the probability density function of x; E_{X,Y} represents the probability density function of x.<X,Y> Seek joint expectations.

[0074] Mutual information is represented as:

[0075]

[0076] and

[0077]

[0078] Wherein, vector p represents the vector composed of discrete values ​​corresponding to p(x), and vector q represents the vector composed of discrete values ​​of q(x|y);

[0079] By introducing a latent variable q, mutual information is represented as maximizing the joint function Q(p,q);

[0080] This involves designing and adjusting the input probability distribution of a finite number of characters, i.e., E. x (|x| 4 The value of ) is then used to obtain the expected value E. x,h,n {ε 2 The specific process is as follows:

[0081] If an OFDM signal contains M symbols and N subcarriers, then the transmission model is represented as:

[0082]

[0083] The m-th transmitted symbol is:

[0084]

[0085] Among them, x n,m T represents a finite number of characters used for modulation. cp T represents the length of the cyclic prefix. sym The symbol length is represented by rect(t), the rectangular window is represented by 0 ≤ t < 1, and Δft represents the OFDM subcarrier spacing, which is equal to T. sym .

[0086] Let the single-target echo signal be represented as:

[0087] r(t)=αs(t-t0)e j2pυt +n(t)

[0088] Where t0 and υ represent the time delay and Doppler frequency corresponding to the target distance, respectively, and α represents the target's echo attenuation coefficient, which is usually assumed to follow a zero mean and variance. A Gaussian random process; n(t) represents a process with zero mean and variance σ. 2 The noise.

[0089] For radar sensing, the frequency domain sampling within the m-th symbol of the OFDM echo signal after fast-time-slow-time sampling can be expressed as:

[0090] r m =diag(x m )h m +n m

[0091] in,

[0092] r m =[r[0 / B],r[1 / B],…,r[(N-1) / B]] T

[0093] x m =[x[0 / B],x[1 / B],…,x[(N-1) / B]] T

[0094] n m =[n[0 / B],n[1 / B],…,n[(N-1) / B]] T

[0095] Let the CSI of the radar target channel be represented as:

[0096] h m =αb(t0)[c * (υ)] m

[0097] Where b(t) = [1, e -j2p△ft ,…,e -j2p(N-1)△ft ] T and Δf represents the steering vectors for time delay and Doppler, respectively, and Δf represents the subcarrier frequency spacing.

[0098] Based on the principle of matched filtering, the CSI estimate of a radar target is:

[0099]

[0100] Since the performance of matched filtering depends on the estimation accuracy of the CSI estimator, the expected value of the CSI estimation error can be further expressed as:

[0101]

[0102] Where A = diag(x) m ), and D=A H AI. I represents the identity matrix.

[0103] There is E h (h m ) = 0 and Where 0 represents the zero vector. Therefore, the above equation can be further simplified to:

[0104]

[0105] Then the expected CSI estimation error for the m-th symbol is obtained. For M OFDM symbols, the cumulative error is:

[0106]

[0107] (3) An algorithm is designed using the idea of ​​alternating optimization to obtain a local optimum through iteration. Specifically:

[0108] (31) For the k-th iteration, given the independent variable p (k) Based on maximizing mutual information according to the latent variable q, we can obtain q. (k) The optimal solution is:

[0109]

[0110] (32) Given q (k) The method of Lagrange multipliers is used to solve for p to maximize mutual information, and the formula is as follows:

[0111]

[0112] Where λ1, λ2, and λ3 represent Lagrange multipliers; ε0 represents the preset value of the fourth moment; and P0 represents the transmitted signal power.

[0113] Setting the partial derivatives of the Lagrange multipliers with respect to p(x) to zero, we obtain p (k+1) The optimal solution is:

[0114]

[0115] In step (31), p (k+1) Substituting (x) into the first two constraints of the optimization model in step (2), we obtain the set of two nonlinear equations that λ1 and λ2 need to satisfy. The final results of λ1 and λ2 can be solved by classical numerical algorithms.

[0116] (33) Repeat steps (31)-(32) until the mean square error of the results of two adjacent iterations is small enough, and the iteration process is complete.

[0117] Experimental results:

[0118] like Figure 2 As shown, the symbol distribution of a finite number of characters is visible. After optimization, to improve perception performance, random symbols are required to maintain constant modulus in the region as much as possible. Figure 3 This demonstrates a trade-off in radar communication performance; overall, the performance is significantly improved after optimization by this invention.

[0119] like Figure 4 As shown, a prototype radar-communication integrated system was built, and matched filtering was performed by transmitting and receiving measured data. The measured results are as follows. Figure 5 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 performance gain of approximately 5-6 dB.

[0120] This invention can perform offline calculations, which means that for a specific radar and communication performance index, the probability distribution is uniquely determined. Taking Table 1 16-QAM as an example, three sets of input probability distribution examples under different radar and communication performance are given (Table 2).

[0121] Table 1 Communication Performance: Actual Symbol Error Rate Results

[0122]

[0123]

[0124] Table 2. Finite character input probability distribution under different ε0 constraints (taking 16-QAM as an example)

[0125]

[0126] This invention also provides a radar-communication integrated signal modulation system based on non-uniform finite character optimization, comprising:

[0127] Probability Distribution Module: Used to obtain the input probability distribution of a finite number of character symbols; specifically as follows: Let the probability distribution vector be: p = [p1, p2, ..., p 16 ] T ;

[0128] Suppose the received communication signal is simplified as follows:

[0129] y = x + z

[0130] Where y represents the receiving model of a single sub-channel; x represents the transmitted OFDM communication signal; and z represents Gaussian white noise. For multiple parallel sub-channels of OFDM, the mutual information between y and x is directly superimposed.

[0131] The building module is used to establish the radar's fourth-order moment, power, and probabilistic constraints based on the probability distribution, with the objective function of maximizing communication mutual information; specifically as follows:

[0132]

[0133] Where P(y|x) represents the conditional probability density function of the received communication signal y given x, p(y) represents the probability density function of y, and similarly, p(x) is the probability density function of x; E_{X,Y} represents the probability density function of x.<X,Y> Seek joint expectations.

[0134] Mutual information is represented as:

[0135]

[0136] and

[0137]

[0138] Wherein, vector p represents the vector composed of discrete values ​​corresponding to p(x), and vector q represents the vector composed of discrete values ​​of q(x|y);

[0139] By introducing a latent variable q, mutual information is represented as maximizing the joint function Q(p,q).

[0140] The optimization module is used to design algorithms based on the idea of ​​alternating optimization, and obtains local optima through iteration. Specifically:

[0141] (31) For the k-th iteration, given the independent variable p (k) Based on maximizing mutual information according to the latent variable q, we can obtain q. (k) The optimal solution is:

[0142]

[0143] (32) Given q (k)The method of Lagrange multipliers is used to solve for p to maximize mutual information, and the formula is as follows:

[0144]

[0145] Where λ1, λ2, and λ3 represent Lagrange multipliers; ε0 represents the preset value of the fourth moment; and P0 represents the transmitted signal power.

[0146] Setting the partial derivatives of the Lagrange multipliers with respect to p(x) to zero, we obtain p (k+1) The optimal solution is:

[0147]

[0148] In step (31), p (k+1) Substituting (x) into the first two constraints of the optimization model in step (2), we obtain the set of two nonlinear equations that λ1 and λ2 need to satisfy. The final results of λ1 and λ2 can be solved by classical numerical algorithms.

[0149] (33) Repeat steps (31)-(32) until the mean square error of the results of two adjacent iterations is small enough, and the iteration process is complete.

[0150] This invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements any of the radar communication integrated signal modulation methods based on non-uniform finite character optimization.

[0151] This invention also provides a storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, it implements any one of the radar-communication integrated signal modulation methods based on non-uniform finite character optimization.

Claims

1. A radar-communication integrated signal modulation method based on non-uniform finite character optimization, characterized in that, Includes the following steps: (1) Obtain the input probability distribution of a finite number of character symbols; specifically as follows: Let the probability distribution vector be: p = [p1, p2, ..., p 16 ] T ; Suppose the received communication signal is simplified as follows: y = x + z Where y represents the receiving model of a single sub-channel; x represents the transmitted OFDM communication signal; and z represents Gaussian white noise. For multiple parallel sub-channels of OFDM, the mutual information between y and x is directly superimposed. (2) Based on the probability distribution, with the objective function of maximizing communication mutual information, establish the fourth-order moment, power, and probability constraints of the radar; (3) An algorithm is designed using the idea of ​​alternating optimization, and the local optimum is obtained through iteration; the details are as follows: (31) For the k-th iteration, given the independent variable p (k) Based on maximizing mutual information according to the latent variable q, we can obtain q. (k) The optimal solution is: (32) Given q (k) The method of Lagrange multipliers is used to solve for p to maximize mutual information, and the formula is as follows: Where λ1, λ2, and λ3 represent Lagrange multipliers; ε0 represents the preset value of the fourth moment; and P0 represents the transmitted signal power. Setting the partial derivatives of the Lagrange multipliers with respect to p(x) to zero, we obtain p (k+1) The optimal solution is: In step (31), p (k+1) Substituting (x) into the first two constraints of the optimization model in step (2), we obtain the set of two nonlinear equations that λ1 and λ2 need to satisfy. The final results of λ1 and λ2 can be solved by classical numerical algorithms. (33) Repeat steps (31)-(32) until the mean square error of the results of two adjacent iterations is small enough, and the iteration process is complete.

2. The radar-communication integrated signal modulation method based on non-uniform finite character optimization according to claim 1, characterized in that, Step (2) is as follows: Where P(y|x) represents the conditional probability density function of the received communication signal y given x, p(y) represents the probability density function of y, and similarly, p(x) is the probability density function of x; E_{X,Y} represents the probability density function of x.<X,Y> Seek joint expectations; Mutual information is represented as: and Wherein, vector p represents the vector composed of discrete values ​​corresponding to p(x), and vector q represents the vector composed of discrete values ​​of q(x|y); By introducing a latent variable q, mutual information is represented as maximizing the joint function Q(p,q).

3. A radar-communication integrated signal modulation system based on non-uniform finite character optimization, characterized in that, include: Probability Distribution Module: Used to obtain the input probability distribution of a finite number of character symbols; specifically as follows: Let the probability distribution vector be: p = [p1, p2, ..., p 16 ] T ; Suppose the received communication signal is simplified as follows: y = x + z Where y represents the receiving model of a single sub-channel; x represents the transmitted OFDM communication signal; and z represents Gaussian white noise. For multiple parallel sub-channels of OFDM, the mutual information between y and x is directly superimposed. The building module is used to establish the radar's fourth-order moment, power, and probability constraints based on the probability distribution, with the objective function of maximizing communication mutual information. Optimization module: Used to design algorithms using the alternating optimization approach, obtaining local optima through iteration; details are as follows: For the k-th iteration, given the independent variable p (k) Based on maximizing mutual information according to the latent variable q, we can obtain q. (k) The optimal solution is: Given q (k) The method of Lagrange multipliers is used to solve for p to maximize mutual information, and the formula is as follows: Where λ1, λ2, and λ3 represent Lagrange multipliers; ε0 represents the preset value of the fourth moment; and P0 represents the transmitted signal power. Setting the partial derivatives of the Lagrange multipliers with respect to p(x) to zero, we obtain p (k+1) The optimal solution is: p (k+1) Substituting (x) into the first two constraints of the optimization model, we obtain the system of two nonlinear equations that λ1 and λ2 need to satisfy. The final results of λ1 and λ2 can be solved by classical numerical algorithms. Repeat until the mean square error of two consecutive iterations is sufficiently small, at which point the iteration process is complete.

4. The radar-communication integrated signal modulation system based on non-uniform finite character optimization according to claim 3, characterized in that, In the construction module, the specifics are as follows: Where P(y|x) represents the conditional probability density function of the received communication signal y given x, p(y) represents the probability density function of y, and similarly, p(x) is the probability density function of x; E_{X,Y} represents the probability density function of x.<X,Y> Seek joint expectations; Mutual information is represented as: and Wherein, vector p represents the vector composed of discrete values ​​corresponding to p(x), and vector q represents the vector composed of discrete values ​​of q(x|y); By introducing a latent variable q, mutual information is represented as maximizing the joint function Q(p,q).

5. 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 computer program is loaded into the processor, it implements a radar-communication integrated signal modulation method based on non-uniform finite character optimization according to any one of claims 1-2.

6. A storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements a radar-communication integrated signal modulation method based on non-uniform finite character optimization according to any one of claims 1-2.

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