Radar communication integrated signal modulation method based on non-uniform finite character optimization

Abstract

The invention discloses a radar communication integrated signal modulation method based on non-uniform finite character optimization. The method comprises the following steps: (1) obtaining input probability distribution of finite character symbols; (2) according to the probability distribution, maximum communication mutual information is used as a target function, and radar four-moment, power and probability constraint conditions are established; (3) designing an algorithm by using an alternative optimization thought, and obtaining a local optimal solution through iteration; on the premise that the communication performance is not obviously reduced, the radar matched filtering performance is effectively improved; and 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] The present invention relates to the technical field of novel signal modulation of the first generation mobile communication (6G), and in particular to a radar communication integrated signal modulation method based on non-uniform finite character optimization. Background Art

[0002] OFDM waveform sharing is a low-cost technical means to achieve integrated radar communication. By collecting the communication echo reflected by the target and using the traditional matched filter to obtain the maximum output signal-to-noise ratio of the radar receiver, the environmental perception capability can be obtained while retaining the original communication function. However, the limited characters modulated by the OFDM communication signal are random (for example, using traditional QAM or PSK modulation), which will also lead to the randomness of the radar perception performance. Specifically, the randomness causes random fluctuations in the matched filter sidelobe level, affecting the radar perception performance. Reducing the sidelobe level is of great significance for weak target detection and preventing ghost target false alarms. Therefore, how to effectively reduce the matched filter sidelobe under the premise of the existing OFDM radar communication integrated waveform sharing has become a key technical difficulty. The existing technology generally adopts uniform character modulation strategy and time sharing strategy to solve the problem, but both methods have great disadvantages: (For uniformly distributed QAM and PSK, there is a "conflict" between radar perception and communication performance. If this traditional solution is adopted, either the best perception performance and the worst communication performance (PSK) are achieved at the same time, or the worst perception performance and the best communication performance (QAM) are achieved. It is difficult to flexibly modulate between radar-communication performance, that is, it is impossible to achieve 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 regarded as the inner bound of the radar-communication performance trade-off, and the performance gain obtained is limited. Summary of the invention

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

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

[0005] (1) Obtaining the input probability distribution of finite character symbols;

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

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

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

[0009] Assume that the communication receiving signal is simplified to:

[0010] y=x+z

[0011] Among them, y represents the receiving model of a single subchannel; x represents the transmitted OFDM communication signal, z represents Gaussian white noise, and for multiple parallel subchannels of OFDM, the mutual information between y and x is directly superimposed.

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

[0013]

[0014] Among them, 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,Y> Seek joint expectations.

[0015] The mutual information is expressed as:

[0016]

[0017] and

[0018]

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

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

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

[0022] (31) For the kth iteration process, given the independent variable p (k) , according to the hidden variable q, the mutual information is maximized, so that q (k) The optimal solution is:

[0023]

[0024] (32) Given q (k) , use the Lagrange multiplier method to solve p to maximize the mutual information, the formula is as follows:

[0025]

[0026] Among them, λ1, λ2, and λ3 represent Lagrange multipliers; ε0 represents a preset value of the fourth-order moment, and P0 represents the transmission signal power.

[0027] Let the partial derivative of the Lagrange multiplier with respect to p(x) be zero, so that p (k+1) The optimal solution is:

[0028]

[0029] Replace p in step (31) (k+1) (x) is brought into the first two constraints of the optimization model in step (2) to obtain the binary 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 between two adjacent iteration results is small enough and the iteration process is completed.

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

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

[0033] Building module: used to establish radar fourth-order moment, power, and probability constraints based on probability distribution and taking maximizing communication mutual information as the objective function;

[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 details are as follows: Assume that the probability distribution vector is: p = [p1, p2, ..., p 16 ] T ; Assume that the communication receiving signal is simplified to:

[0036] y=x+z

[0037] Among them, y represents the receiving model of a single subchannel; x represents the transmitted OFDM communication signal, z represents Gaussian white noise, and for multiple parallel subchannels of OFDM, the mutual information between y and x is directly superimposed.

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

[0039]

[0040] Among them, 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,Y> Seek joint expectations.

[0041] The mutual information is expressed as:

[0042]

[0043] and

[0044]

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

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

[0047] Furthermore, in the optimization module, the details are as follows:

[0048] (31) For the kth iteration process, given the independent variable p (k) , according to the hidden variable q, the mutual information is maximized, so that q (k) The optimal solution is:

[0049]

[0050] (32) Given q (k) , use the Lagrange multiplier method to solve p to maximize the mutual information, the formula is as follows:

[0051]

[0052] Among them, λ1, λ2, and λ3 represent Lagrange multipliers; ε0 represents a preset value of the fourth-order moment, and P0 represents the transmission signal power.

[0053] Let the partial derivative of the Lagrange multiplier with respect to p(x) be zero, so that p (k+1) The optimal solution is:

[0054]

[0055] Replace p in step (31) (k+1) (x) is brought into the first two constraints of the optimization model in step (2) to obtain the binary 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 between two adjacent iteration results is small enough and the iteration process is completed.

[0057] An electronic device described in 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 into the processor, any one of the radar communication integrated signal modulation methods based on non-uniform finite character optimization is implemented.

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

[0059] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: it realizes the dual-function integration of communication and radar perception without significantly changing the existing communication modulation and demodulation module; it effectively improves the radar matched filtering performance without significantly reducing the communication performance; it realizes the dynamic compromise performance of radar and communication, thereby providing guidance for the quantification of modulation parameters under actual system requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is the symbol probability distribution of 16-QAM of the present invention;

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

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

[0063] Figure 4 To build a radar communication integrated principle prototype for the present invention;

[0064] Figure 5 It is the radar perception performance of the present invention. DETAILED DESCRIPTION

[0065] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

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

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

[0068] Assume that the communication receiving signal is simplified to:

[0069] y=x+z

[0070] Among them, y represents the receiving model of a single subchannel; x represents the transmitted OFDM communication signal, z represents Gaussian white noise, and for multiple parallel subchannels of OFDM, the mutual information between y and x is directly superimposed.

[0071] (2) According to the probability distribution, taking maximizing the communication mutual information as the objective function, the radar fourth-order moment, power, and probability constraints are established; step (2) is as follows:

[0072]

[0073] Among them, 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,Y> Seek joint expectations.

[0074] The mutual information is expressed as:

[0075]

[0076] and

[0077]

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

[0079] By introducing hidden variables q, mutual information is expressed as maximizing the joint function Q(p,q);

[0080] Among them, the input probability distribution of limited characters is adjusted by design, that is, E x (|x| 4 ) value, and then get the desired E x,h,n {ε 2}; The specific process is as follows:

[0081] Assuming that the OFDM signal contains M symbols and N subcarriers, the transmission model is expressed as:

[0082]

[0083] The mth transmitted symbol is:

[0084]

[0085] Among them, x n,m Represents the finite character of modulation, T cp represents the cyclic prefix length, T sym represents the symbol length, rect(t) represents the rectangular window within 0≤t<1, and Δft represents the OFDM subcarrier spacing, which is equal to T sym .

[0086] Assume that the single target echo signal is expressed as:

[0087] r(t)=αs(t-t0)e j2pυt +n(t)

[0088] Among them, t0 and υ are the time delay and Doppler frequency corresponding to the target distance, respectively, and α represents the echo attenuation coefficient of the target, which is usually assumed to obey zero mean variance. Gaussian random process; n(t) represents a zero mean with variance σ 2 noise.

[0089] For radar perception, after the OFDM echo signal undergoes fast-time-slow-time sampling, the frequency domain sampling within the mth symbol 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] Assume that the CSI of the radar target channel is expressed as:

[0096] h m =αb(t0)[c * (υ)] m

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

[0098] According to the matched filtering principle, the CSI estimate of the radar target is:

[0099]

[0100] Since the performance of matched filtering depends on the estimation accuracy of the CSI estimator, the expectation of the CSI estimation error is further expressed as:

[0101]

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

[0103] YesE h (h m )=0 and Among them, 0 represents the zero vector. Therefore, the above formula can be further simplified as:

[0104]

[0105] Then the expected CSI estimation error of the mth symbol is obtained. For M OFDM symbols, the cumulative error is:

[0106]

[0107] (3) Design an algorithm using the idea of ​​alternating optimization and obtain the local optimal solution through iteration. The details are as follows:

[0108] (31) For the kth iteration process, given the independent variable p (k) , according to the hidden variable q, the mutual information is maximized, so that q (k) The optimal solution is:

[0109]

[0110] (32) Given q (k) , use the Lagrange multiplier method to solve p to maximize the mutual information, the formula is as follows:

[0111]

[0112] Among them, λ1, λ2, and λ3 represent Lagrange multipliers; ε0 represents a preset value of the fourth-order moment, and P0 represents the transmission signal power.

[0113] Let the partial derivative of the Lagrange multiplier with respect to p(x) be zero, so that p (k+1) The optimal solution is:

[0114]

[0115] Replace p in step (31) (k+1) (x) is brought into the first two constraints of the optimization model in step (2) to obtain the binary 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 between two adjacent iteration results is small enough and the iteration process is completed.

[0117] Test results:

[0118] like Figure 2 As shown, the symbol distribution of limited characters can be seen. After optimization, improving the perception performance requires that the random symbols have a constant modulus as much as possible. Figure 3 The compromise effect of radar communication performance is shown; in general, after the optimization of the present invention, the performance is significantly improved.

[0119] like Figure 4 As shown in the figure, a radar communication integrated principle prototype was built to perform matched filtering by sending and receiving measured data. The measured results are shown in Figure 5 As shown in the figure, after non-uniform finite symbol optimization, the side lobes of the matched filter range image are significantly reduced compared to the traditional uniform QAM results, and the performance gain is about 5-6dB.

[0120] The present invention can be calculated offline, 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 groups of input probability distribution samples under different radar communication performance are given (Table 2).

[0121] Table 1 Communication performance: symbol error rate measurement results

[0122]

[0123]

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

[0125]

[0126] The embodiment of the present invention further 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 limited character symbols; the details are as follows: Let the probability distribution vector be: p = [p1, p2, ..., p 16 ] T ;

[0128] Assume that the communication receiving signal is simplified to:

[0129] y=x+z

[0130] Among them, y represents the receiving model of a single subchannel; x represents the transmitted OFDM communication signal, z represents Gaussian white noise, and for multiple parallel subchannels of OFDM, the mutual information between y and x is directly superimposed.

[0131] Building module: used to establish radar fourth-order moment, power, and probability constraints based on probability distribution and taking maximizing communication mutual information as the objective function; the details are as follows:

[0132]

[0133] Among them, 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,Y> Seek joint expectations.

[0134] The mutual information is expressed as:

[0135]

[0136] and

[0137]

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

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

[0140] Optimization module: It is used to design algorithms using the idea of ​​alternating optimization and obtain local optimal solutions through iteration. The details are as follows:

[0141] (31) For the kth iteration process, given the independent variable p (k) , according to the hidden variable q, the mutual information is maximized, so that q (k) The optimal solution is:

[0142]

[0143] (32) Given q (k), use the Lagrange multiplier method to solve p to maximize the mutual information, the formula is as follows:

[0144]

[0145] Among them, λ1, λ2, and λ3 represent Lagrange multipliers; ε0 represents a preset value of the fourth-order moment, and P0 represents the transmission signal power.

[0146] Let the partial derivative of the Lagrange multiplier with respect to p(x) be zero, so that p (k+1) The optimal solution is:

[0147]

[0148] Replace p in step (31) (k+1) (x) is brought into the first two constraints of the optimization model in step (2) to obtain the binary 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 between two adjacent iteration results is small enough and the iteration process is completed.

[0150] An embodiment of the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is loaded into the processor, any one of the radar communication integrated signal modulation methods based on non-uniform finite character optimization is implemented.

[0151] An embodiment of the present invention further provides a storage medium storing a computer program, wherein the computer program, when executed by a processor, 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: The following steps are involved: (1) Obtaining the input probability distribution of finite character symbols; (2) Based on the probability distribution, the radar fourth-order moment, power, and probability constraints are established with the objective function of maximizing the communication mutual information; (3) Design an algorithm using the idea of ​​alternating optimization and obtain the local optimal solution through iteration.

2. According to claim 1, a radar communication integrated signal modulation method based on non-uniform finite character optimization is characterized in that: Step (1) is as follows: Assume that the probability distribution vector is: p = [p1, p2, ..., p 16 ] T ; Assume that the communication receiving signal is simplified to: y=x+z Among them, y represents the receiving model of a single subchannel; x represents the transmitted OFDM communication signal, z represents Gaussian white noise, and for multiple parallel subchannels of OFDM, the mutual information between y and x is directly superimposed.

3. The radar communication integrated signal modulation method based on non-uniform finite character optimization according to claim 1 is characterized in that: Step (2) is as follows: Among them, 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,Y> Seek joint expectations. The mutual information is expressed as: and Among them, the p vector represents the vector composed of discrete values ​​corresponding to p(x), and the q vector represents the vector composed of discrete values ​​of q(x|y); By introducing the hidden variable q, the mutual information is expressed as maximizing the joint function Q(p,q).

4. The radar communication integrated signal modulation method based on non-uniform finite character optimization according to claim 1 is characterized in that: Step (3) is as follows: (31) For the kth iteration process, given the independent variable p (k) , according to the hidden variable q, the mutual information is maximized, so that q (k) The optimal solution is: (32) Given q (k) , use the Lagrange multiplier method to solve p to maximize the mutual information, the formula is as follows: Among them, λ1, λ2, and λ3 represent Lagrange multipliers; ε0 represents a preset value of the fourth-order moment, and P0 represents the transmission signal power. Let the partial derivative of the Lagrange multiplier with respect to p(x) be zero, so that p (k+1) The optimal solution is: Replace p in step (31) (k+1) (x) is brought into the first two constraints of the optimization model in step (2) to obtain the binary 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 between two adjacent iteration results is small enough and the iteration process is completed.

5. 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 limited character symbols; Building module: used to establish radar fourth-order moment, power, and probability constraints based on probability distribution and taking maximizing communication mutual information as the objective function; Optimization module: used to design algorithms using the idea of ​​alternating optimization and obtain local optimal solutions through iteration.

6. The radar communication integrated signal modulation system based on non-uniform finite character optimization according to claim 5 is characterized in that: In the probability distribution module, the details are as follows: Let the probability distribution vector be: p = [p1, p2, ..., p 16 ] T ; Assume that the communication receiving signal is simplified to: y=x+z Among them, y represents the receiving model of a single subchannel; x represents the transmitted OFDM communication signal, z represents Gaussian white noise, and for multiple parallel subchannels of OFDM, the mutual information between y and x is directly superimposed.

7. The radar communication integrated signal modulation system based on non-uniform finite character optimization according to claim 5 is characterized in that: In the construction module, the details are as follows: Among them, 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,Y> Seek joint expectations. The mutual information is expressed as: and Among them, the p vector represents the vector composed of discrete values ​​corresponding to p(x), and the q vector represents the vector composed of discrete values ​​of q(x|y); By introducing the hidden variable q, the mutual information is expressed as maximizing the joint function Q(p,q).

8. The radar communication integrated signal modulation system based on non-uniform finite character optimization according to claim 1 is characterized in that: In the optimization module, the details are as follows: (31) For the kth iteration process, given the independent variable p (k) , according to the hidden variable q, the mutual information is maximized, so that q (k) The optimal solution is: (32) Given q (k) , use the Lagrange multiplier method to solve p to maximize the mutual information, the formula is as follows: Among them, λ1, λ2, and λ3 represent Lagrange multipliers; ε0 represents a preset value of the fourth-order moment, and P0 represents the transmission signal power. Let the partial derivative of the Lagrange multiplier with respect to p(x) be zero, so that p (k+1) The optimal solution is: Replace p in step (31) (k+1) (x) is brought into the first two constraints of the optimization model in step (2) to obtain the binary 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 between two adjacent iteration results is small enough and the iteration process is completed.

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 computer program is loaded into the processor, the radar communication integrated signal modulation method based on non-uniform finite character optimization according to any one of claims 1 to 4 is implemented.

10. A storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, a radar communication integrated signal modulation method based on non-uniform finite character optimization according to any one of claims 1 to 4 is implemented.

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