Waveform optimization method for radar communication integration based on detection probability constraints

Abstract

The present invention discloses a radar communication integrated waveform optimization method based on detection probability constraints. The method comprises the following steps: setting the number of antennas equipped in a dual-function radar communication base station at the transmitting end, the number of service users, and the radar detection angle; determining the total transmission rate of the users based on the signal-to-interference-noise ratio (SIN) in the downlink; establishing a maximum likelihood estimation detection equation by making binary assumptions about the echo information received by the base station, and analyzing to obtain radar detection performance indicators, including detection probability and false alarm probability. Using these two as constraints, an optimization equation for radar waveform design is established to obtain the optimal radar communication waveform matrix. The method assumes that the channel state information and the location of the detection target are known, improves the user transmission rate by selecting an appropriate waveform, and employs a semidefinite relaxation technique to solve the non-convex quadratic programming quadratic radar communication waveform matrix. This method improves the transmission rate of users in the downlink while ensuring a high radar detection probability.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a radar communication integrated waveform optimization method based on detection probability constraints. Background Art

[0002] With the increasing number of connected devices and the inefficiency of spectrum allocation, it is necessary to find a suitable additional spectrum resource to meet the basic needs of users, among which the radar band is widely considered to be one of the best candidates.

[0003] There are two common approaches to achieving radar and communication spectrum sharing (RCSS): the first is radar-communication coexistence (RCC), which involves designing effective interference cancellation and management techniques to prevent interference between the two. The second is a dual-functional radar-communication (DFRC) system, in which radar and communication systems share not only the same spectrum but also the same hardware platform, achieving both communication and radar perception capabilities through the design of an integrated signal processing solution.

[0004] The significance and applications of DFRC technology go far beyond improving spectrum utilization. It can be applied to a variety of new civilian and military scenarios, including connected vehicles and indoor positioning and covert communications. Integrated radar and communication waveform design is crucial for DFRC systems. However, existing signal matrix designs suffer from the following issues: radar performance saturation at high signal-to-noise ratios results in unnecessary resource waste; downlink signal interference noise is high, resulting in low downlink communication performance; and high inter-user interference results in low downlink rates. Summary of the Invention

[0005] The purpose of the present invention is to provide a radar communication integrated waveform optimization method based on detection probability constraints. By utilizing the characteristics of dual-function radar and combining detection probability and power constraints, the optimal transmission signal is obtained by establishing a quadratic programming quadratic problem using the CVX toolkit, thereby improving the transmission rate of users in the downlink under the condition of a high radar detection probability.

[0006] The technical solution to achieve the purpose of the present invention is: a radar communication integrated waveform optimization method based on detection probability constraints, the steps are as follows:

[0007] Step 1: Assume that the transmitting end dual-function radar communication base station is equipped with N antennas, the number of service users is K, and the radar detection angle is θ;

[0008] Step 2: Determine the total transmission rate of K users based on the signal-to-interference-plus-noise ratio (SINR) in the downlink;

[0009] Step 3: By making a binary hypothesis on the echo information received by the base station, a maximum likelihood estimation detection equation is established, and the radar detection performance indicators are analyzed to obtain the detection probability and false alarm probability;

[0010] Step 4: Using the radar detection probability and false alarm probability as constraints, establish an optimization equation for radar waveform design, and solve the optimization equation to obtain the optimal radar communication waveform matrix.

[0011] Furthermore, in step 1, the range of the radar detection angle θ is [-2 / π, 2 / π]. While serving K users, the base station detects targets within the angle range by receiving echoes reflected from the target end.

[0012] Furthermore, in step 2, the total transmission rate of K users is determined according to the signal-to-interference-plus-noise ratio (SINR) in the downlink, as follows:

[0013] The base station transmits a radar communication signal, and the signal Y received by the user is expressed as:

[0014] Y=HX+W

[0015] in, represents the channel matrix with K rows and L columns, Represented as a signal matrix with N rows and L columns, the base station's transmission power L is the length of the transmitted signal, It is defined as an additive white Gaussian noise (AWGN) matrix with K rows and L columns;

[0016] The multi-user interference (MUI) power P is obtained from the signal received by the user. ∈

[0017]

[0018] in, represents the F norm, The downlink user has a known constellation symbol matrix, so the signal interference and noise ratio γ of the i-th user is obtained i :

[0019]

[0020] Where N0 represents additive Gaussian white noise, P ∈i represents the MUI power of the i-th user, s j represents the jth column of the modulation symbol matrix, x j is the jth column of the transmitted signal matrix, represents the expectation of the time index;

[0021] The total transmission rate R of K users in downlink communication is:

[0022]

[0023] Furthermore, in step 3, by making a binary hypothesis on the echo information received by the base station, a maximum likelihood estimation detection equation is established, and the radar detection performance index is obtained by analysis, which is as follows:

[0024] The covariance matrix E of the transmitted signal is

[0025]

[0026] Make a binary assumption about the echo received by the base station:

[0027]

[0028]

[0029] in, represents the null hypothesis that there are no existing targets within the radar's detection range; represents the alternative hypothesis, that is, there is indeed a target within the detection range;

[0030] is the radar cross section RCS factor, is the symbol frame vector of the i-th user in the transmitted signal matrix, z represents the echo vector received by the base station, v represents the Gaussian white noise vector, a t (θ) and a r (θ) represents the signal transmission and reception steering vectors, and θ is the angle information;

[0031] Assuming equal steering vectors:

[0032]

[0033] Using the maximum likelihood ratio estimation detection method, the distribution of radar detection probability β and false alarm probability α is obtained:

[0034]

[0035]

[0036] Where g represents the threshold of radar reception, λ represents the non-central parameter of the non-central chi-square distribution, and χ represents the random variable of the normal distribution. Represents the radar cross section RCS factor.

[0037] Furthermore, in step 4, the radar detection probability and false alarm probability are used as constraints to establish an optimization equation for radar waveform design, as follows:

[0038] Assuming that the false alarm probability is a constant, the optimization equation of the radar waveform is obtained through the known distribution of the detection probability:

[0039]

[0040]

[0041] β≥Γ

[0042] The objective function in the optimization equation is the MUI power of K downlink users served by the base station. The constraints are the power and detection probability limits, where 0≤Γ≤1 represents the size limit of the radar detection probability, P t Expressed as the signal transmission power.

[0043] Furthermore, in step 4, the optimization equation is solved to obtain the optimal radar communication waveform matrix, specifically:

[0044] The optimization equations are solved using MATLAB's CVX toolbox to obtain a waveform matrix that can simultaneously meet the communication needs of radar and users.

[0045] Compared with the prior art, the present invention has the following significant advantages: (1) a convex quadratic programming quadratic form problem is constructed for the radar communication waveform matrix, which is optimized by semidefinite relaxation technology and solved by CVX data packets, thereby obtaining a DFRC system that can simultaneously meet radar and communication performance; (2) by controlling the radar detection performance and reallocating resources, the signal-to-interference-to-noise ratio of the downlink is effectively minimized, so that the communication performance of the downlink reaches a higher level; (3) on the basis of ensuring the radar detection performance, the energy of interference between users is minimized, so that the downlink rate is maximized. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flow chart of the radar communication integrated waveform optimization method based on detection probability constraints of the present invention.

[0047] Figure 2 It is the detection probability β and signal-to-noise ratio η curve, and the signal-to-noise ratio η and rate curve.

[0048] Figure 3 It is the detection probability β rate curve. DETAILED DESCRIPTION

[0049] This paper proposes an integrated radar communication waveform optimization method based on detection probability constraints. Assume that the transmitting end, a dual-function radar communication base station, is equipped with N antennas, serves K users, and the radar detection angle θ ranges from [-2 / π to 2 / π]. While serving K users, the base station also detects targets within this angle range. By minimizing the energy of inter-user interference while ensuring radar detection performance and maximizing the downlink rate, this method can minimize inter-user interference compared to directly designing the signal matrix.

[0050] The Matlab CVX package is increasingly being used in fields such as communications, mathematics, and electronics, where it plays a crucial role. Its semidefinite relaxation techniques also facilitate the solution of wireless communication system optimization problems. This paper constructs a convex quadratic programming quadratic form problem, optimizes it using semidefinite relaxation techniques, and solves it using the CVX package, resulting in a DFRC system that meets both radar and communication performance requirements.

[0051] The present invention is further illustrated below with reference to the accompanying drawings and specific examples. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0052] Example

[0053] Combine Figure 1 The present invention provides a radar communication integrated waveform optimization method based on detection probability constraints, and the specific steps are as follows:

[0054] S1. In the radar communication integrated waveform design, the transmitting dual-function radar communication base station is equipped with N antennas, serving K users, and the radar detection angle θ range is [-2 / π, 2 / π]. While serving K users, the base station also detects targets within the angle range by using the echo reflected from the target end;

[0055] S2. Determine the total transmission rate of K users based on the signal-to-interference-plus-noise ratio (SINR) in the downlink.

[0056] S3. In terms of radar function, by making binary assumptions about the base station received information and establishing the maximum likelihood estimation detection equation, the radar detection performance indicators are obtained from the analysis, including the detection probability and the false alarm probability.

[0057] S4. Using the radar detection probability and false alarm probability as constraints, an optimization equation for radar waveform design is established, and the optimal radar communication waveform matrix is ​​obtained by solving the optimization equation.

[0058] The method proposed in this invention can quickly solve this optimization problem under the radar detection probability constraint condition through the CVX toolbox of MATLAB, and finally obtain a waveform matrix that can simultaneously meet the communication requirements of radar and user. The detailed process is as follows:

[0059] The present invention assumes that the transmitting end (DFRC BS) is equipped with antennas, the expected number of users is K, and the range of radar detection angle θ is [-2 / π, 2 / π]. When the base station transmits the radar communication signal, the signal received by the user end can be expressed as

[0060] Y=HX+W (1)

[0061] in, represents the channel matrix with K rows and L columns, Represented as a signal matrix with N rows and L columns, the base station's transmission power L is the length of the transmitted signal, It is defined as an additive white Gaussian noise (AWGN) matrix with K rows and L columns.

[0062] The multi-user interference (MUI) power P is obtained from the signal received by the user. ∈

[0063]

[0064] in, represents the F norm, The downlink user has a known constellation symbol matrix, so the signal interference and noise ratio γ of the i-th user is obtained i :

[0065]

[0066] Where N0 represents additive Gaussian white noise, P ∈i represents the MUI power of the i-th user, s j represents the jth column of the modulation symbol matrix, x j is the jth column of the transmitted signal matrix, represents the expectation of the time index;

[0067] Then, the total rate R achievable in downlink communication for K users is

[0068]

[0069] For the radar part, the covariance matrix E of the transmitted signal will be the key to controlling the radar performance. The covariance matrix E of the transmitted signal is:

[0070]

[0071] Make a binary assumption about the echo received by the base station:

[0072]

[0073] in represents the null hypothesis that there are no existing targets within the radar's detection range, represents the alternative hypothesis, that is, there is indeed a target within the detection range;

[0074] is the radar cross section RCS factor, is the symbol frame vector of the i-th user in the transmitted signal matrix, z represents the echo vector received by the base station, v represents the Gaussian white noise vector, a t (θ) and a r (θ) represents the signal transmission and reception steering vectors, and θ is the angle information;

[0075] Assuming equal steering vectors:

[0076]

[0077] Using the maximum likelihood ratio estimation detection method, the distribution of radar detection probability β and false alarm probability α is obtained:

[0078]

[0079]

[0080] Where g represents the threshold of radar reception, λ represents the non-central parameter of the non-central chi-square distribution, and χ represents the random variable of the normal distribution. Represents the radar cross section RCS factor.

[0081] Assuming that the false alarm probability is a constant, the optimization equation for radar waveform design is expressed as follows based on the known distribution of detection probability:

[0082]

[0083] The objective function in the optimization equation is the power of K served by the BS and the MUI of the downlink user. The constraint distribution is the power and detection probability limit, where 0≤Γ≤1 represents the size limit of the radar detection probability, P t Expressed as the signal transmission power.

[0084] The method proposed in the present invention can quickly solve this optimization problem under the radar detection probability constraint condition through the CVX toolbox of MATLAB, and finally obtain a waveform matrix that can simultaneously meet the communication needs of radar and user.

[0085] The present invention avoids unnecessary resource waste caused by radar performance saturation under high signal-to-noise ratio conditions. By controlling radar detection performance and reallocating resources, the signal-to-interference-noise ratio of the downlink is effectively minimized, thereby achieving a higher level of downlink communication performance.

[0086] Additional aspects and advantages of the present invention will be set forth in part in the following description, will be obvious from the following description, or may be learned by practice of the present invention.

[0087] from Figure 2 Given K = 4 users, N = 8 base station antennas, and power P t = 1 demonstrates that the radar communication waveform under PTP (power and probability constraints) can better control the detection probability of the DFRC waveform to a fixed value. The average achievable sum rate of this method is higher than that of existing methods. In particular, the PTP of the proposed method is lower than the average achievable sum rate of ZF (zero inter-user interference), but outperforms the other two methods.

[0088] from Figure 3 In this paper, K = 6, the number of base station antennas is N = 8, and the SNR is 8dB. Three different false alarm probabilities α = [10^{-2}, 10^{-4}, 10^{-6}] are given. Simulation results show that when α is constant, the average achievable sum rate decreases as α increases. When β is a constant, the lower α, the higher the average achievable sum rate.

[0089] In summary, the present invention's method for integrating radar communication waveforms under detection probability constraints improves the transmission rate of users in the downlink while ensuring a high radar detection probability. The overall transmission rate is related to the inter-user interference (MUI). Obviously, minimizing inter-user interference while ensuring radar performance is extremely important. The present invention assumes that the channel state information H and the location of the detection target are known. For users, selecting an appropriate waveform matrix X to increase their achievable transmission rate and improve system performance is meaningful. After designing the optimization equation, the present invention uses semidefinite relaxation techniques to solve the non-convex quadratic programming quadratic form problem, thereby obtaining the optimal radar communication waveform matrix X.

Claims

1. A radar communication integrated waveform optimization method based on detection probability constraints, characterized in that: Here are the steps: Step 1: Assume that the transmitting end dual-function radar communication base station is equipped with N antennas, the number of service users is K, and the radar detection angle is θ; Step 2: Determine the total transmission rate of K users based on the signal-to-interference-plus-noise ratio (SINR) in the downlink; Step 3: By making a binary hypothesis on the echo information received by the base station, a maximum likelihood estimation detection equation is established, and the radar detection performance indicators are analyzed to obtain the detection probability and false alarm probability; Step 4: Using the radar detection probability and false alarm probability as constraints, an optimization equation for radar waveform design is established, and the optimal radar communication waveform matrix is ​​obtained by solving the optimization equation; In step 1, the radar detection angle θ ranges from [-2 / π, 2 / π]. While serving K users, the base station detects targets within the angle range by receiving echoes reflected from the target end. In step 2, the total transmission rate of K users is determined based on the signal-to-interference-plus-noise ratio (SINR) in the downlink, as follows: The base station transmits a radar communication signal, and the signal Y received by the user is expressed as: Y=HX+W in, represents the channel matrix with K rows and N columns, Represented as a signal matrix with N rows and L columns, the base station's transmission power is L is the length of the transmitted signal, It is defined as an additive white Gaussian noise (AWGN) matrix with K rows and L columns; The multi-user interference (MUI) power P is obtained from the signal received by the user. ∈ in, represents the F norm, is a known constellation symbol matrix for the downlink user, so the signal-to-interference-noise ratio γ of the i-th user is obtained i : Where N0 represents additive Gaussian white noise, P ∈i represents the MUI power of the i-th user, S j represents the jth column of the constellation symbol matrix, x j is the jth column of the transmitted signal matrix, represents the expectation of the time index; The total transmission rate R of K users in downlink communication is: In step 3, by making a binary hypothesis on the echo information received by the base station, a maximum likelihood estimation detection equation is established, and the radar detection performance indicators are analyzed and obtained, as follows: The covariance matrix E of the transmitted signal is Make a binary assumption about the echo received by the base station: in, represents the null hypothesis that there are no existing targets within the radar's detection range; represents the alternative hypothesis, that is, there is indeed a target within the detection range; is the radar cross section RCS factor, is the symbol frame vector of the i-th user in the transmitted signal matrix, z represents the echo vector received by the base station, v represents the Gaussian white noise vector, a t (θ) and a r (θ) represents the signal transmission and reception steering vectors, and θ is the angle information; Assuming equal steering vectors: Using the maximum likelihood ratio estimation detection method, the distribution of radar detection probability β and false alarm probability α is obtained: Where g represents the threshold of radar reception, λ represents the non-central parameter of the non-central chi-square distribution, and χ represents the random variable of the normal distribution. Represents the radar cross section RCS factor.

2. The radar communication integrated waveform optimization method based on detection probability constraint according to claim 1 is characterized in that: In step 4, the radar detection probability and false alarm probability are used as constraints to establish an optimization equation for radar waveform design, as follows: Assuming that the false alarm probability is a constant, the optimization equation of the radar waveform is obtained through the known distribution of the detection probability: The objective function in the optimization equation is the MUI power of K downlink users served by the base station. The constraints are the power and detection probability limits, where 0≤Γ≤1 represents the size limit of the radar detection probability, P t Expressed as the transmitted power of the signal.

3. The radar communication integrated waveform optimization method based on detection probability constraint according to claim 2 is characterized in that: In step 4, the optimization equation is solved to obtain the optimal radar communication waveform matrix, specifically: The optimization equations are solved using MATLAB's CVX toolbox to obtain a waveform matrix that can simultaneously meet the communication needs of radar and users.

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