A method and system for designing near-range anti-interference waveform of unmanned aerial vehicle radar

Abstract

The present invention discloses a near-zone anti-interference waveform design method and system for unmanned aerial vehicle-borne radar, and relates to the technical field of radar waveform design. The technical points of the present invention include: for unmanned aerial vehicle-borne radar systems, construct a set of pre-coded waveforms based on orthogonal frequency division multiplexing technology; construct waveform optimization constraints; construct waveform optimization objective functions and reference radar waveforms; use the MM algorithm to transform the waveform optimization objective function, and transform the non-convex constraints in the waveform optimization constraints into convex constraints; use standard numerical tools to iteratively solve the transformed waveform optimization objective function to obtain the optimal waveform sequence. The present invention avoids the problem that the common low peak-to-average ratio constraint fails to fully control the uniformity of the transmitting antenna power, and prevents the situation of high-power dynamic range fluctuations and low transmitting power efficiency. The present invention has significant improvements in symbol error rate and average achievable rate, and improves anti-interception performance, with a lower level of correlated side lobes.

Description

Technical Field

[0001] The present invention relates to the technical field of radar waveform design, and in particular to a method and system for designing a near-range anti-interference waveform of an unmanned aerial vehicle-borne radar. Background Art

[0002] With the increasing complexity of the electromagnetic environment and the demand for ever-increasing radar performance, traditional UAV-mounted radar systems face many challenges, including the increase in interference sources, the complexity of signal reflections, and the need for more powerful multifunctional performance. In addition, they are limited by the form of transmitted signals, have poor anti-interception performance, and have limited ability to suppress shielding interference.

[0003] In order to meet these challenges, the current equipment development trend is to integrate radar and communication equipment to achieve integrated sharing. This integrated design can improve the perception and communication capabilities of radar systems to a certain extent and better adapt to modern complex environments. However, most current research is relatively insufficient in the detection of low RCS non-cooperative targets, and there are deficiencies in the design of multi-functional waveforms that take into account both multi-target detection and communication.

[0004] For the problem of low sidelobe waveform design, the more typical solutions currently studied include the family of cyclic algorithms (such as CAN algorithm), alternating projection algorithm (such as SMIA algorithm), relaxed alternating projection algorithm, alternating direction multiplier algorithm, main optimization algorithm (such as MM algorithm), coordinate descent algorithm (such as PCDM algorithm), etc. In engineering applications, due to the numerous waveform constraints, the mathematical modeling and optimization problems are non-convex, so the robustness of waveform design is crucial. The above iterative algorithms generally have a common problem, that is, the above algorithms take too long, the autocorrelation sidelobe level amplitude is poor, the problem model is not comprehensive, it is difficult to meet the requirements of engineering practice, and none of them consider the situation of multipath fading channels. Summary of the invention

[0005] To this end, the present invention proposes a near-zone anti-interference waveform design method and system for UAV-borne radar, which are used to solve the beam interference problems, poor autocorrelation range sidelobe performance, low communication performance and other problems in multi-UAV collaborative perception scenarios.

[0006] According to one aspect of the present invention, a method for designing a near-range anti-interference waveform for an unmanned aerial vehicle radar is provided, the method comprising the following steps:

[0007] For an unmanned aerial vehicle radar system, a pre-coded waveform set based on orthogonal frequency division multiplexing technology is constructed; the unmanned aerial vehicle radar system is equipped with N t The transmitting antenna array is a uniform linear array and the array element spacing is half a wavelength. The UAV-borne radar system simultaneously serves K downlink single-antenna user equipments and simultaneously senses M far-field targets;

[0008] Construct waveform optimization constraints; construct waveform optimization objective function and reference radar waveform;

[0009] The waveform optimization objective function is transformed by using the MM algorithm, and the non-convex constraint conditions in the waveform optimization constraint conditions are transformed into convex constraint conditions;

[0010] The transformed waveform optimization objective function is iteratively solved using standard numerical tools. When the difference between the sidelobe suppression mean values ​​of the optimal waveform sequences generated by two adjacent iterations is less than the preset error or the number of iterations is greater than the preset total number, the iteration is stopped and the optimal waveform sequence corresponding to the optimal sidelobe suppression mean value is output.

[0011] Furthermore, the precoding waveform set based on orthogonal frequency division multiplexing technology is constructed as follows:

[0012] In the communication time-varying channel of the UAV-borne radar system, each channel is set to have N c -1 time-varying non-zero channel tap, effective data symbol length is N s , then N needs to be modulated during transmission s subcarriers, the symbol data matrix of all user equipment on the subcarrier is expressed as:

[0013]

[0014] In the formula, S n =[s n,1 ,...,s n,K ] T ,n=1,...,N s Represents the matrix of all symbols on the subcarrier, represents the user's specific symbol vector; L represents the length of the radar pulse / communication block, corresponding to the number of OFDM symbols in the time domain;

[0015] The compact precoding matrix for all user equipments on the subcarrier is expressed as:

[0016]

[0017] In the formula, represents the precoding matrix of all user equipments on the subcarrier, represents a specific precoding vector for the user;

[0018] The symbol data matrix S is precoded in the frequency domain using the compact precoding matrix Z:

[0019]

[0020] Where, X srepresents the baseband precoding symbol matrix on all subcarriers, represents the baseband precoding symbol matrix on the nth subcarrier, where N represents the data transmitted at time l t dimensional space domain;

[0021] The baseband precoding symbol matrix X s Perform inverse discrete Fourier transform, and the time domain data signal waveform after inverse discrete Fourier transform is the precoding waveform set, which is expressed as:

[0022]

[0023] In the formula, F s represents the Fourier transform matrix; Indicates size N t The identity matrix of Indicates N on the nth subcarrier t The MIMO-OFDM dual-function radar communication signal transmitted by the antenna, represents the Fourier transform matrix F s The nth column of .

[0024] Furthermore, the precoding waveform set based on orthogonal frequency division multiplexing technology is constructed as follows:

[0025] In each valid data symbol N s Add a length of N before c The cyclic prefix is ​​added to deal with the inter-symbol interference caused by time variation. Then the baseband precoding symbol matrix on the subcarrier after adding the cyclic prefix is ​​expressed as

[0026]

[0027] In the formula, represents the baseband precoding symbol matrix on the nth subcarrier after adding the cyclic prefix, where each value represents the baseband precoding symbol on the nth subcarrier after adding the cyclic prefix to transmit data at each time N t dimensional space domain;

[0028] The baseband precoding symbol matrix on the subcarrier after adding the cyclic prefix The time domain data signal waveform obtained by performing inverse discrete Fourier transform is the corresponding pre-coded waveform set after adding the cyclic prefix, which is expressed as:

[0029]

[0030] In the formula, represents the Fourier transform matrix corresponding to the addition of the cyclic prefix, in Each value represents the Fourier transform matrix The nth column of .

[0031] Furthermore, the waveform optimization constraint condition is constructed as follows:

[0032] The constraints for constructive interference are as follows:

[0033]

[0034] in, and Respectively represent the rotation signal The real and imaginary parts of h k,n is the kth row of the overall effective downlink channel matrix on the nth symbol subcarrier, i.e., the channel corresponding to the user, Γ k and are amplitude and phase respectively; is the central angle, is the modulation order of the QPSK scheme;

[0035] The peak-to-valley power ratio constraint is constructed as follows:

[0036]

[0037] Where, χ represents the parameter that controls the dynamic range of the waveform modulus, and the symbol represents the Kronecker inner product, Representation Matrix the (i,l)th element of ;

[0038] The overall energy constraint is constructed as follows:

[0039]

[0040] in, vec(·) represents the matrix vectorization operator, τ 2 represents the total energy change;

[0041] The power allocation constraints are constructed as follows:

[0042]

[0043] Among them, P t Indicates the maximum transmit power;

[0044] Construct the tradeoff constraints for radar and communication:

[0045]

[0046] Where G0 represents the reference radar waveform; δ 2A trade-off factor representing the radar communication compromise.

[0047] Furthermore, the waveform optimization objective function WPISL is constructed as follows:

[0048]

[0049] Among them, ω k represents non-negative weights; 2<p<∞, different metrics of interest can be obtained by setting different p values; e k =Tr(U k xx H ), U k is a Toeplitz matrix, the kth diagonal element of which is 1 and the other elements are 0;

[0050] The reference radar waveform is constructed as follows:

[0051]

[0052] Among them, X s,0 Represents the radar waveform before inverse discrete Fourier transform.

[0053] Furthermore, the transforming of the waveform optimization objective function by using the MM algorithm includes:

[0054] The waveform optimization objective function is optimized by a quadratic function to optimize each function, and the conversion process includes:

[0055] For a given qth iteration value |(e k ) (q) |, function|(e k ) (q) | p exist The local optimization function at is:

[0056]

[0057] in,

[0058] definition Using the idea of ​​minimizing the upper bound function, we can further obtain:

[0059]

[0060] in, Representation Matrix The maximum eigenvalue of λ u Represents based on ω k The weight of constant means constant;

[0061] x (q) represents the waveform sequence of the qth iteration;

[0062] The transformed waveform optimization objective function is expressed as:

[0063]

[0064] Furthermore, the conversion of the non-convex constraint condition in the waveform optimization constraint condition into a convex constraint condition includes: the peak-to-valley power ratio constraint is a non-convex constraint condition; a shrinkage factor variable β is introduced into the peak-to-valley power ratio constraint to convert the non-convex constraint condition into a convex constraint condition, and the peak-to-valley power ratio constraint is reconstructed as follows:

[0065]

[0066] According to another aspect of the present invention, a near-range anti-interference waveform design system for unmanned aerial vehicle radar is provided, the system comprising:

[0067] The precoding waveform construction module is configured to construct a precoding waveform set based on orthogonal frequency division multiplexing technology for an unmanned aerial vehicle radar system; the unmanned aerial vehicle radar system is equipped with N t The transmitting antenna array is a uniform linear array and the array element spacing is half a wavelength. The UAV-borne radar system simultaneously serves K downlink single-antenna user equipments and simultaneously senses M far-field targets;

[0068] a constraint construction module configured to construct waveform optimization constraints;

[0069] an objective function construction module configured to construct a waveform optimization objective function and a reference radar waveform;

[0070] An objective function optimization module, configured to transform the waveform optimization objective function using the MM algorithm, and transform the non-convex constraint conditions in the waveform optimization constraint conditions into convex constraint conditions;

[0071] The optimal waveform solving module is configured to use standard numerical tools to iteratively solve the transformed waveform optimization objective function. When the difference between the sidelobe suppression mean values ​​of the optimal waveform sequences generated by two adjacent iterations is less than a preset error or the number of iterations is greater than a preset total number, the iteration is stopped and the optimal waveform sequence corresponding to the optimal sidelobe suppression mean value is output.

[0072] According to another aspect of the present invention, an electronic device is provided, comprising: a memory; a processor; and a computer program; wherein the computer program is stored in the memory and configured to be executed by the processor to implement the method as described above.

[0073] According to another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored; the computer program is executed by a processor to implement the method described above.

[0074] The beneficial technical effects of the present invention are:

[0075] The present invention proposes the "cognition-radar-communication integration concept", which introduces the cognitive anti-interference idea into the balanced waveform design of radar and communication through intelligent agile transmission waveform. This method provides a transmitter-side guarantee for the detection of non-cooperative targets through waveform anti-interference processing; at the same time, the target detection knowledge will in turn provide information assistance to the radar transmitter, reflecting the "intelligent" idea of ​​the new system radar; at the same time, this concept also takes into account the urgent needs of information transmission and information sharing between unmanned aerial vehicles.

[0076] The waveform design method proposed in this invention combines communication and sensing and has the potential to improve the overall energy, cost and frequency efficiency of the system. In order to reduce the interference between antennas and targets for high-quality sensing, tolerable changes are introduced to the data symbols modulated on the MIMO-OFDM subcarriers to enhance the orthogonality of time and space domain signals. The designed waveform comprehensively considers multi-target detection, communication, multipath effects and shielding problems, thereby achieving efficient perception and communication capabilities in complex environments. Its advantages are as follows:

[0077] (1) For the control of waveform dynamic range, the invention shows better effect by introducing peak-to-valley power ratio constraint. Compared with the traditional method that only considers low peak-to-average power ratio constraint, peak-to-valley power ratio constraint helps to improve transmission efficiency. It makes the designed energy-constrained waveform more adaptable under actual hardware conditions and enhances the fidelity of the waveform.

[0078] (2) For radar performance, an optimized weighted peak sidelobe level (WPISL) and phase coded waveform are used to significantly reduce the sidelobe and improve radar performance. For communication performance, a design based on constructive interference constraints is used, combined with waveform similarity error (WSE) constraints, which effectively improves communication capabilities.

[0079] (3) As for the waveform optimization effect, the dual-function radar communication waveform design method proposed in the present invention has achieved significant improvements in sidelobe reduction, symbol error rate (SER) and average achievable sum rate, verifying its superiority in enhancing the dual-function radar communication system. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] The present invention can be better understood by referring to the description given below in conjunction with the accompanying drawings, which together with the following detailed description are included in this specification and form a part of this specification, and are used to further illustrate the preferred embodiments of the present invention and explain the principles and advantages of the present invention.

[0081] Figure 1 The present invention is a flowchart of a method for designing a near-range anti-interference waveform for an unmanned aerial vehicle-borne radar according to an embodiment of the present invention.

[0082] Figure 2 It is a schematic diagram of autocorrelation sidelobe suppression of an integrated signal in a single specific area according to an embodiment of the present invention.

[0083] Figure 3 It is a schematic diagram of autocorrelation sidelobe suppression of an integrated signal in multiple specific areas according to an embodiment of the present invention.

[0084] Figure 4 Schematic diagram of the convergence rate of the integrated signal at different p-values ​​PSL in an embodiment of the present invention.

[0085] Figure 5 Schematic diagram of the effect of constraints of different PVPR values ​​on local correlation suppression of the integrated signal in an embodiment of the present invention.

[0086] Figure 6 It is a schematic diagram of the relationship between the bit error rate and the transmission signal-to-noise ratio of the integrated signal in an embodiment of the present invention. DETAILED DESCRIPTION

[0087] In order to enable those skilled in the art to better understand the scheme of the present invention, exemplary implementations or embodiments of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described implementations or embodiments are only implementations or embodiments of a part of the present invention, not all of them. Based on the implementations or embodiments of the present invention, all other implementations or embodiments obtained by ordinary technicians in the field without creative work should fall within the scope of protection of the present invention.

[0088] The present invention is dedicated to addressing the problems of beam interference, poor autocorrelation range sidelobe performance, and high computational complexity in multi-UAV collaborative sensing scenarios in complex environments. Starting from the idea of ​​the MM algorithm framework, the present invention introduces orthogonal frequency division multiplexing technology to improve the anti-interception performance and robustness of the system, and successfully solves the problems faced by multi-UAV collaborative sensing scenarios in complex environments.

[0089] The embodiment of the present invention provides a method for designing a near-range anti-interference waveform of a UAV-borne radar, such as Figure 1 As shown, the method comprises the following steps:

[0090] Step 1: For an unmanned aerial vehicle radar system, a pre-coded waveform set based on orthogonal frequency division multiplexing technology is constructed; the unmanned aerial vehicle radar system is equipped with N t The transmitting antenna array is a uniform linear array, and the array element spacing is half a wavelength. The UAV-borne radar system simultaneously serves K downlink single-antenna user equipments and simultaneously senses M far-field targets;

[0091] Step 2: For the UAV-mounted radar system, construct waveform optimization constraints;

[0092] Step 3: For the UAV-mounted radar system, construct a waveform optimization objective function and a reference radar waveform;

[0093] Step 4: Use the MM algorithm framework to transform the waveform optimization objective function, and transform the non-convex constraints in the waveform optimization constraints into convex constraints;

[0094] Step 5: Use standard numerical tools to iteratively solve the transformed waveform optimization objective function. When the difference between the sidelobe suppression mean values ​​of the optimal waveform sequences generated by two adjacent iterations is less than a preset error or the number of iterations is greater than a preset total number, stop the iteration and output the optimal waveform sequence corresponding to the optimal sidelobe suppression mean value.

[0095] The method starts from step 1. In step 1, for the unmanned aerial vehicle radar system, a pre-coded waveform set based on orthogonal frequency division multiplexing technology is constructed.

[0096] According to the embodiment of the present invention, in order to improve the performance of OFDM (Orthogonal Frequency Division Multiplexing) technology and reduce the impact of inter-symbol interference caused by multipath channels, the traditional OFDM technology is adopted and a cyclic prefix is ​​added. For the convenience of theoretical analysis, it is assumed that the cyclic prefix length is not less than the maximum delay of the channel. The drone-mounted radar system is equipped with N t The transmitting antenna array is a uniform linear array with a half-wavelength array element spacing. Its main goal is to simultaneously serve K downlink single-antenna user devices and simultaneously sense M far-field targets. In a time-varying channel, each channel has N c -1 time-varying non-zero channel tap, effective data symbol length is N s , N needs to be modulated during transmission s subcarriers, then N s The symbol data matrix of all user equipment on subcarriers is expressed as:

[0097]

[0098] In the formula, S n =[s n,1 ,...,s n,K ] T ,n=1,...,Ns Represents the matrix of all symbols on the subcarrier, represents the user's specific symbol vector; L represents the length of the radar pulse / communication block, which corresponds to the number of OFDM symbols in the time domain.

[0099] The compact precoding matrix for all user equipment on the subcarrier is expressed as:

[0100]

[0101] In the above formula, represents the precoding matrix of all user equipments on the subcarrier, represents the user's specific precoding vector.

[0102] The symbol data matrix S is first precoded by Z in the frequency domain and then converted to the time domain by an IDFT operation (Inverse Discrete Fourier Transform) before subcarrier modulation.

[0103]

[0104] Where, X s represents the baseband precoding symbol matrix on all subcarriers before IDFT processing, represents the baseband precoding symbol matrix on the nth subcarrier, where N represents the data transmitted at time l t dimensional space domain.

[0105] Normalized DFT matrix for data transmission It is expressed as:

[0106]

[0107] Indicates F s The time domain data signal waveform after IDFT can be further expressed as:

[0108]

[0109] In the above formula, F s represents the DFT matrix, Indicates size N t The identity matrix of Denotes the DFT matrix F s The nth column of Indicates the number of subcarriers N on the nth subcarrier t Antenna transmit MIMO-OFDM dual-function radar communication.

[0110] Furthermore, in each data symbol N s Add a length of N before cThe cyclic prefix of the extended OFDM symbol is used to deal with the inter-symbol interference caused by time variation. The design of the MIMO-OFDM dual-function radar communication waveform with a cyclic prefix is ​​crucial to mitigate the inter-symbol interference caused by multipath frequency selective fading. The period of the extended OFDM symbol becomes N = N s +N c .

[0111] The baseband precoding symbol matrix on the subcarrier with the cyclic prefix added is expressed as:

[0112]

[0113]

[0114] In the formula, represents the baseband precoding symbol matrix on the nth subcarrier after adding the cyclic prefix, where each value represents the baseband precoding symbol on the nth subcarrier after adding the cyclic prefix to transmit data at each time N t dimensional space domain.

[0115] The baseband precoding symbol matrix on the subcarrier after adding the cyclic prefix After the IDFT operation is performed, the waveform of the time domain data signal after the IDFT operation is the corresponding pre-coded waveform set after the cyclic prefix is ​​added, which is expressed as:

[0116]

[0117] In the formula, It represents the DFT matrix corresponding to the addition of the cyclic prefix. in Each value in this matrix represents the DFT matrix. The nth column of .

[0118] After applying the cyclic prefix, the signal is modulated onto subcarriers and converted to the RF domain. It is then connected to the N t Antenna N t The transmission is carried out on the RF link. Assume that the wireless channel from the base station to the user equipment is a broadband frequency selective fading channel. The discrete time impulse response of the channel from the base station to the user is expressed as follows:

[0119]

[0120] in is a time-invariant channel vector, and δ represents the Dirac function. The channel from the base station to K downlink users is expressed as:

[0121]

[0122] The overall effective downlink channel matrix of the MIMO-OFDM dual-function radar communication system on the nth symbol subcarrier can be expressed in the frequency domain as:

[0123]

[0124] in is the channel corresponding to the user. The received signal of the symbol data sequence can be expressed as:

[0125] Y s =S+(H s X s -S)+Z s

[0126] in It is in N s The subcarriers have independent and identically distributed Gaussian white noise, and their random variables follow

[0127] Then, step 2 is performed. In step 2, for the UAV-mounted radar system, waveform optimization constraints are constructed.

[0128] According to an embodiment of the present invention, in the communication model, the multi-user interference (MUI) signal caused by multi-user transmission can be represented by H s X s -S indicates that the traditional waveform design method aims to achieve effective communication by reducing the MUI energy of the user. However, it should be noted that not all interference is harmful. Therefore, it is not necessary to minimize all types of interference. Interference can be divided into destructive interference and constructive interference. The latter pushes the received signal into the correct decision area, called the constructive area. In order to derive the mathematical formula of the constructive interference constraint, the concept of phase rotation is considered to be introduced, rotating the QPSK constellation point 45° clockwise, focusing on a quarter of the nominal QPSK constellation diagram without losing generality, and expressing the rotated signal as in and represents the interference signal required to ensure that the received signal remains within the built area, Γ k and are amplitude and phase respectively.

[0129] 1) The constraints for constructive interference can be expressed as follows:

[0130]

[0131] in is the central angle, and Expressed as The real and imaginary parts of is the modulation order of the QPSK scheme.

[0132] OFDM systems have a high peak-to-average ratio, which not only reduces the efficiency of the power amplifier in the transmitter, but also reduces the quantization signal-to-noise ratio of the analog-to-digital converter and the digital-to-analog converter. As we all know, the low peak-to-average ratio is defined as the ratio between the maximum power of the passband signal and its average power, which only limits the upper limit of the waveform amplitude but not its lower limit. In this case, the waveform may exhibit a larger modulus dynamic range.

[0133] 2) In order to compensate for the disadvantage of low peak-to-average ratio constraint, the peak-to-valley power ratio (PVPR) constraint of the controllable waveform dynamic range of the precoded waveform based on OFDM technology is defined as:

[0134]

[0135] Where χ is the parameter that controls the dynamic range of the waveform modulus, and the symbol represents the Kronecker inner product.

[0136] 3) The overall energy constraint is also considered as follows:

[0137]

[0138] in, vec(·) represents the matrix vectorization operator, τ 2 represents the total energy change.

[0139] 4) In practical scenarios, radars often need to transmit at the maximum available power, imposing the following power allocation constraints:

[0140]

[0141] Where P t represents the maximum transmit power. The equality constraint ensures that its transmit power is P t , which is also because radar usually needs to operate at maximum transmit power.

[0142] 5) Considering the better trade-off performance between radar and communication, a tolerable square norm threshold δ is introduced 2 , the trade-off constraints for constructing radar and communication are as follows:

[0143]

[0144] Where G0 represents the reference radar waveform; δ 2 A trade-off factor representing the radar communication compromise.

[0145] Then, step three is executed, in which a waveform optimization objective function and a reference radar waveform are constructed.

[0146] According to an embodiment of the present invention, in order to achieve a lower sidelobe level in the designed waveform, clutter from adjacent range units must be suppressed to avoid the masking effect of strong targets on weak targets. In order to effectively minimize the sidelobes, the minimum norm (p ≥ 2) as a design metric, which provides great flexibility to radar designers in various scenarios. For example, the choice of p helps to achieve diverse waveform characteristics, including integrated sidelobe level (ISL), peak sidelobe level (PSL). A more general p-norm-based metric is considered to optimize the autocorrelation sidelobe. Define e k =Tr(U k xx H ),in

[0147]

[0148] The waveform optimization objective function is constructed as follows:

[0149]

[0150] where ω k Denotes non-negative weights. This metric easily includes the integrated sidelobe level ISL (or weighted integrated sidelobe level WISL) and the peak sidelobe level PSL as special cases: Let p = 2, and we get the WISL metric; further let Get the ISL metric; let p→+∞ and get That is the PSL metric.

[0151] Since the radar beam pattern has a high correlation with the covariance matrix R of its transmitted waveform, the design of the MIMO radar beam pattern can be equivalently transformed into the design of the radar detection waveform. In order to design the MIMO-OFDM waveform, an ideal reference MIMO-OFDM radar waveform is used, which is expressed as Where X s,0 represents the radar waveform before the IDFT operation, which can achieve an ideal recognition probability. And assuming that R is the Hermitian semi-positive covariance matrix corresponding to the designed MIMO radar beam pattern, considering the directional beamforming design, the radar detection waveform can be obtained by solving the following multi-user interference minimization problem

[0152]

[0153]

[0154] The problem in the above formula can be described as an orthogonal Procrustes problem with a closed-form solution in represents the Cholesky decomposition, and represents the singular value decomposition. Therefore, the reference radar waveform X s,0 It is independent of the power of the desired constellation S.

[0155] Then, step 4 is executed. In step 4, the waveform optimization objective function is transformed using the MM algorithm, and the non-convex constraints in the waveform optimization constraints are transformed into convex constraints.

[0156] According to an embodiment of the present invention, firstly, it can be seen from the peak-to-valley power ratio PVPR constraint expression that the constraint is nonlinear, non-convex, and extremely challenging, so a shrinkage factor variable β is introduced to restate the peak-to-valley power ratio PVPR constraint as follows:

[0157]

[0158] The above formula transforms the original non-smooth and difficult-to-solve constraint problem into a serially differentiable constraint problem.

[0159] Then, in order to effectively solve the non-convex waveform design problem, the idea of ​​the MM algorithm framework is used to transform the original problem into a more tractable optimization problem. An upper bound surrogate function is sought, which locally approximates the objective function in each iteration, and the surrogate function is minimized. The idea is to optimize each function through a quadratic function. Given the value of |(e k ) (q) |, function|(e k ) (q) | p exist The local optimization function at is:

[0160]

[0161] in

[0162] For convenience, define And by using the idea of ​​minimizing the upper bound function, we can further obtain:

[0163]

[0164] Next, observe and

[0165] |e k ||(e -k ) (q) |≥Re[e k ·(e -k ) (q) ]

[0166] Then we get:

[0167]

[0168] in constant is a constant, λ u Based on ω k The weight and

[0169]

[0170]

[0171] where x (q) represents the waveform sequence of the qth iteration;

[0172] Note that there is a total energy constraint, namely This means

[0173]

[0174] From this, the described problem is converted into its equivalent vector form as follows:

[0175]

[0176]

[0177]

[0178]

[0179]

[0180]

[0181] Finally, step five is executed. In step five, the transformed waveform optimization objective function is iteratively solved using standard numerical tools. When the difference between the sidelobe suppression mean values ​​of the optimal waveform sequences generated by two adjacent iterations is less than a preset error or the number of iterations is greater than a preset total number, the iteration is stopped and the optimal waveform sequence corresponding to the optimal sidelobe suppression mean value is output.

[0182] According to an embodiment of the present invention, the problem in the above formula is convex and can be solved by some standard numerical tools, such as the CVX toolbox.

[0183] The technical effect of the present invention is further verified through experiments.

[0184] In order to evaluate the performance of the designed waveform, it is assumed that the strong scatterer is located in the single sidelobe interference interval and the multi-sidelobe interference interval. The number of transmitting antennas is N t =8, the sequence code length is L=256, P t=1, cyclic prefix length N c =3, a total of N s = 16 available subcarriers, there are K = 2 user devices and M = 3 designated targets. The constellation selected for the communicating users is the unit power QPSK alphabet. The autocorrelation amplitude level (ACL) is defined as follows:

[0185]

[0186] In order to comprehensively evaluate the performance of the algorithm, 100 independent repeated experiments were carried out, and the average time consumption and the average autocorrelation amplitude in the suppression interval were defined as: Aver-time and Aver-ACL.

[0187] The proposed method (Proposed in the table and figure) is simulated and compared with the weighted CAN algorithm (WeCAN) in document 1, the alternating projection algorithm (SMIA) in document 2, the main optimization algorithm (MM) in document 3, and the coordinate descent algorithm (PCDM) in document 4. All algorithms use the same iteration threshold of 10 -10 The method of the present invention has achieved significant optimization effects in both single sidelobe interval and multi-sidelobe interval, reaching -288dB and -279dB respectively. Its good interference interval sidelobe suppression effect performance is shown in Table 1, Table 2, Figure 2 and Figure 3 shown.

[0188] Table 1 Performance comparison of different algorithms in single sidelobe suppression

[0189]

[0190]

[0191] Table 2 Performance comparison of different algorithms in multi-sidelobe suppression

[0192]

[0193] Figure 2 For a single specific sidelobe suppression area p = 2, ω k =1, k∈{1,2,...,50} Schematic diagram of autocorrelation sidelobe suppression. It can be seen from the results of multiple simulation tests that the method of the present invention achieves the best effect in sidelobe suppression in the interference interval, which is consistent with the performance difference in Table 1.

[0194] Figure 3 For multiple specific sidelobe suppression areas p = 2, ω k=1, k∈{1,2,...,30}∪{100,101,...,130} schematic diagram of autocorrelation sidelobe suppression. It can be observed from the multiple simulation test results in Table 2 that the method of the present invention still performs well in interference interval sidelobe suppression. It is worth noting that for the suppression of multiple sidelobe intervals, the algorithm of the method of the present invention still has the same advantages as that of a single interval, which is not available in other algorithms.

[0195] Figure 4 The convergence rate of PSL for different p values ​​is shown in Figure 2. Specifically, p = 10, 10 2 ,10 3 ,10 4 Schematic diagram of PSL convergence rate. The maximum number of iterations is set to 4×10 4 It is obvious that smaller p values ​​usually lead to faster convergence. However, if p is too small, PSL will not continue to decrease but stop at a higher value, which also shows that the larger the p value, The closer the norm is norm. Therefore, in practical cases, gradually increasing the value of p will achieve a more efficient method.

[0196] Figure 5 Schematic diagram of the effect of constraints of different PVPR values ​​on local correlation suppression, and set p = 2, ω k =1, k∈{1,2,...,50}. Obviously, when transitioning from the constant modulus constraint (PVPR=1) to the slightly loose PVPR≤2 constraint, the ACL decreases from about -150 dB to nearly -300 dB. Subsequently, as the PVPR constraint is gradually relaxed from PVPR≤2 to PVPR≤6, it is observed that the ACL changes very little, hovering around -300 dB, which confirms that the method of the present invention is capable of designing nearly orthogonal local low-correlation transmission waveforms.

[0197] Figure 6 Schematic diagram of the relationship between bit error rate (SER) and transmission signal-to-noise ratio (SNR), assuming K = 4, SNR = P t / σ 2 It varies from 0dB to 25dB. The results show that by sacrificing radar performance, better communication performance can be achieved as the square root value of the WSE norm increases. In addition, due to the use of constructive interference (CI) as a green energy source, the CI-based method of the present invention is superior to the existing least squares (LS) method [Reference 5].

[0198] The present invention proposes the MM algorithm framework concept to design dual-function radar communication waveforms. Compared with the existing waveform design method, the present invention has better waveform fidelity and adaptability to power control under actual hardware conditions. The CI-based method is superior to the LS-based method in terms of SER and average achievable sum rate, and can reduce the computational complexity and have lower correlation sidelobes. The low-sidelobe anti-interference multifunctional waveform design method based on the MM algorithm framework concept of the present invention can enable unmanned aerial vehicle radars to more effectively cope with interference in complex environments.

[0199] Another embodiment of the present invention provides a near-range anti-interference waveform design system for an unmanned aerial vehicle-borne radar, the system comprising:

[0200] The precoding waveform construction module is configured to construct a precoding waveform set based on orthogonal frequency division multiplexing technology for an unmanned aerial vehicle radar system; the unmanned aerial vehicle radar system is equipped with N t The transmitting antenna array is a uniform linear array and the array element spacing is half a wavelength. The UAV-borne radar system simultaneously serves K downlink single-antenna user equipments and simultaneously senses M far-field targets;

[0201] a constraint construction module configured to construct waveform optimization constraints;

[0202] an objective function construction module configured to construct a waveform optimization objective function and a reference radar waveform;

[0203] An objective function optimization module, configured to transform the waveform optimization objective function using the MM algorithm, and transform the non-convex constraint conditions in the waveform optimization constraint conditions into convex constraint conditions;

[0204] The optimal waveform solving module is configured to use standard numerical tools to iteratively solve the transformed waveform optimization objective function. When the difference between the sidelobe suppression mean values ​​of the optimal waveform sequences generated by two adjacent iterations is less than a preset error or the number of iterations is greater than a preset total number, the iteration is stopped and the optimal waveform sequence corresponding to the optimal sidelobe suppression mean value is output.

[0205] For the undetailed parts of the near-zone anti-interference waveform design system for an unmanned aerial vehicle radar according to an embodiment of the present invention, please refer to the above specific description of the method embodiment.

[0206] Another embodiment of the present invention provides an electronic device, comprising: a memory; a processor; and a computer program; wherein the computer program is stored in the memory and is configured to be executed by the processor to implement the UAV-borne radar near-zone anti-interference waveform design method as described above.

[0207] Another embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon; the computer program is executed by a processor to implement the method for designing a near-range anti-interference waveform for an unmanned aerial vehicle-borne radar as described above.

[0208] Although the present invention has been described according to a limited number of embodiments, it will be apparent to those skilled in the art, with the benefit of the above description, that other embodiments are contemplated within the scope of the invention thus described. The disclosure of the present invention is intended to be illustrative rather than restrictive of the scope of the invention, which is defined by the appended claims.

[0209] The documents cited in the present invention are as follows:

[0210] [1]He H, Li J, Stoica P. Waveform Design for Active Sensing Systems: A Computational Approach [M]. Cambridge: Cambridge University Press, 2012.

[0211] [2]Hou M, Xie W, Xiong Y, et al. Optimizing an Algorithm Designed forSparse-Frequency Waveforms for Use in Airborne Radars[J].Remote Sensing,2023,15(17):4322.

[0212] [3]Song J,Babu P,Palomar D P.Optimization Methods for DesigningSequences With Low Autocorrelation Sidelobes[J].IEEE Transactions on SignalProcessing,2015,63(15):3998-4009.

[0213] [4] Wang Xinhai, Wang Chaoyu, Zhang Ning, et al. A phase domain low-integral sidelobe radar waveform optimization method[J]. Journal of Radars, 2022, 11(2): 255-263.

[0214] [5]Liu F,Zhou L,Masouros C,et al.Toward Dual-functional Radar-Communication Systems:Optimal Waveform Design[J].IEEE Transactions on SignalProcessing,2018,66(16):4264-4279.

Claims

1. A method for designing near-range anti-interference waveform of unmanned aerial vehicle radar, characterized in that: The following steps are involved: For an unmanned aerial vehicle radar system, a pre-coded waveform set based on orthogonal frequency division multiplexing technology is constructed; the unmanned aerial vehicle radar system is equipped with N t The transmitting antenna array is a uniform linear array and the array element spacing is half a wavelength. The UAV-borne radar system simultaneously serves K downlink single-antenna user equipments and simultaneously senses M far-field targets. The precoding waveform set based on orthogonal frequency division multiplexing technology is constructed as follows: In the communication time-varying channel of the UAV-borne radar system, each channel is set to have N c -1 time-varying non-zero channel tap, effective data symbol length is N s , then N needs to be modulated during transmission s subcarriers, the symbol data matrix of all user equipment on the subcarrier is expressed as: In the formula, S n =[s n,1 ,...,s n,K ] T ,n=1,...,N s Represents the matrix of all symbols on the subcarrier, k=1,...,K represents the user's specific symbol vector; L represents the length of the radar pulse / communication block, corresponding to the number of OFDM symbols in the time domain; The compact precoding matrix for all user equipments on the subcarrier is expressed as: In the formula, represents the precoding matrix of all user equipments on the subcarrier, represents a specific precoding vector for the user; The symbol data matrix S is precoded in the frequency domain using the compact precoding matrix Z: Where, X s represents the baseband precoding symbol matrix on all subcarriers, represents the baseband precoding symbol matrix on the nth subcarrier, where l=1,...,L represents the N number of data transmitted at the lth moment t dimensional space domain; The baseband precoding symbol matrix X s Perform inverse discrete Fourier transform, and the time domain data signal waveform after inverse discrete Fourier transform is the precoding waveform set, which is expressed as: In the formula, F s represents the Fourier transform matrix; Indicates size N t The identity matrix of Indicates N on the nth subcarrier t The MIMO-OFDM dual-function radar communication signal transmitted by the antenna, represents the Fourier transform matrix F s The nth column of In each valid data symbol N s Add a length of N before c The cyclic prefix is ​​added to deal with the inter-symbol interference caused by time variation. Then the baseband precoding symbol matrix on the subcarrier after adding the cyclic prefix is ​​expressed as In the formula, represents the baseband precoding symbol matrix on the nth subcarrier after adding the cyclic prefix, where each value represents the number of baseband precoding symbols on the nth subcarrier after adding the cyclic prefix that transmit data at each time. t dimensional space domain; N = N s +N c ; The baseband precoding symbol matrix on the subcarrier after adding the cyclic prefix The time domain data signal waveform obtained by performing inverse discrete Fourier transform is the corresponding pre-coded waveform set after adding the cyclic prefix, which is expressed as: In the formula, represents the Fourier transform matrix corresponding to the addition of the cyclic prefix, in Each value represents the Fourier transform matrix The nth column of Construct waveform optimization constraints; Construct waveform optimization objective function and reference radar waveform; The waveform optimization objective function is transformed by using the MM algorithm, and the non-convex constraint conditions in the waveform optimization constraint conditions are transformed into convex constraint conditions; The transformed waveform optimization objective function is iteratively solved using standard numerical tools. When the difference between the sidelobe suppression mean values ​​of the optimal waveform sequences generated by two adjacent iterations is less than the preset error or the number of iterations is greater than the preset total number, the iteration is stopped and the optimal waveform sequence corresponding to the optimal sidelobe suppression mean value is output.

2. The method for designing a near-range anti-interference waveform for a UAV-borne radar according to claim 1 is characterized in that: The waveform optimization constraint condition is constructed as follows: The constraints for constructive interference are as follows: in, and Respectively represent the rotation signal The real and imaginary parts of h k,n is the kth row of the overall effective downlink channel matrix on the nth symbol subcarrier, i.e., the channel corresponding to the user, Γ k and are amplitude and phase respectively; is the central angle, is the modulation order of the QPSK scheme; The peak-to-valley power ratio constraint is constructed as follows: Where, χ represents the parameter that controls the dynamic range of the waveform modulus, and the symbol represents the Kronecker inner product, Representation Matrix the (i,l)th element of ; The overall energy constraint is constructed as follows: in, vec(·) represents the matrix vectorization operator, τ 2 represents the total energy change; The power allocation constraints are constructed as follows: Among them, P t Indicates the maximum transmit power; Construct the trade-off constraints for radar and communication: Where G0 represents the reference radar waveform; δ 2 A trade-off factor representing the radar communication compromise.

3. The method for designing a near-range anti-interference waveform for an unmanned aerial vehicle radar according to claim 2 is characterized in that: The waveform optimization objective function WPISL is constructed as follows: Among them, ω k represents non-negative weights; 2<p<∞, different metrics of interest can be obtained by setting different p values; e k =Tr(U k xx H ), U k is a Toeplitz matrix, the kth diagonal element of which is 1 and the other elements are 0; The reference radar waveform is constructed as follows: Among them, X s,0 Represents the radar waveform before inverse discrete Fourier transform.

4. The method for designing a near-range anti-interference waveform for an unmanned aerial vehicle radar according to claim 3 is characterized in that: The transforming of the waveform optimization objective function by using the MM algorithm includes: The waveform optimization objective function is optimized by a quadratic function to optimize each function, and the conversion process includes: For a given qth iteration value |(e k ) (q) |, function|(e k ) (q) | p exist The local optimization function at is: in, definition Using the idea of ​​minimizing the upper bound function, we can further obtain: in, Representation Matrix The maximum eigenvalue of λ u Represents based on ω k The weight of constant means constant; x (q) represents the waveform sequence of the qth iteration; The transformed waveform optimization objective function is expressed as:

5. The method for designing a near-range anti-interference waveform of an unmanned aerial vehicle radar according to claim 4 is characterized in that: The converting of the non-convex constraint condition in the waveform optimization constraint condition into a convex constraint condition includes: the peak-to-valley power ratio constraint is a non-convex constraint condition; a shrinkage factor variable β is introduced into the peak-to-valley power ratio constraint to convert the non-convex constraint condition into a convex constraint condition, and the peak-to-valley power ratio constraint is reconstructed as follows:

6. A near-range anti-interference waveform design system for unmanned aerial vehicle radar, characterized in that: include: A precoding waveform construction module configured to construct a precoding waveform set based on orthogonal frequency division multiplexing technology for the unmanned aerial vehicle radar system; The UAV-borne radar system is equipped with N t The transmitting antenna array is a uniform linear array and the array element spacing is half a wavelength. The UAV-borne radar system simultaneously serves K downlink single-antenna user equipments and simultaneously senses M far-field targets. The precoding waveform set based on orthogonal frequency division multiplexing technology is constructed as follows: In the communication time-varying channel of the UAV-borne radar system, each channel is set to have N c -1 time-varying non-zero channel tap, effective data symbol length is N s , then N needs to be modulated during transmission s subcarriers, the symbol data matrix of all user equipment on the subcarrier is expressed as: In the formula, S n =[s n,1 ,...,s n,K ] T ,n=1,...,N s Represents the matrix of all symbols on the subcarrier, k=1,...,K represents the user's specific symbol vector; L represents the length of the radar pulse / communication block, corresponding to the number of OFDM symbols in the time domain; The compact precoding matrix for all user equipments on the subcarrier is expressed as: In the formula, represents the precoding matrix of all user equipments on the subcarrier, represents a specific precoding vector for the user; The symbol data matrix S is precoded in the frequency domain using the compact precoding matrix Z: Where, X s represents the baseband precoding symbol matrix on all subcarriers, represents the baseband precoding symbol matrix on the nth subcarrier, where l=1,...,L represents the N number of data transmitted at the lth moment t dimensional space domain; The baseband precoding symbol matrix X s Perform inverse discrete Fourier transform, and the time domain data signal waveform after inverse discrete Fourier transform is the precoding waveform set, which is expressed as: In the formula, F s represents the Fourier transform matrix; Indicates size N t The identity matrix of Indicates N on the nth subcarrier t The MIMO-OFDM dual-function radar communication signal transmitted by the antenna, represents the Fourier transform matrix F s The nth column of In each valid data symbol N s Add a length of N before c The cyclic prefix is ​​added to deal with the inter-symbol interference caused by time variation. Then the baseband precoding symbol matrix on the subcarrier after adding the cyclic prefix is ​​expressed as In the formula, represents the baseband precoding symbol matrix on the nth subcarrier after adding the cyclic prefix, where each value represents the number of baseband precoding symbols on the nth subcarrier after adding the cyclic prefix that transmit data at each time. t dimensional space domain; N = N s +N c ; The baseband precoding symbol matrix on the subcarrier after adding the cyclic prefix The time domain data signal waveform obtained by performing inverse discrete Fourier transform is the corresponding pre-coded waveform set after adding the cyclic prefix, which is expressed as: In the formula, represents the Fourier transform matrix corresponding to the addition of the cyclic prefix, in Each value represents the Fourier transform matrix The nth column of a constraint construction module configured to construct waveform optimization constraints; an objective function construction module configured to construct a waveform optimization objective function and a reference radar waveform; An objective function optimization module, configured to transform the waveform optimization objective function using the MM algorithm, and transform the non-convex constraint conditions in the waveform optimization constraint conditions into convex constraint conditions; The optimal waveform solving module is configured to use standard numerical tools to iteratively solve the transformed waveform optimization objective function. When the difference between the sidelobe suppression mean values ​​of the optimal waveform sequences generated by two adjacent iterations is less than a preset error or the number of iterations is greater than a preset total number, the iteration is stopped and the optimal waveform sequence corresponding to the optimal sidelobe suppression mean value is output.

7. An electronic device, characterized in that: include: Memory; processor; and a computer program; wherein the computer program is stored in the memory and is configured to be executed by the processor to implement the method according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that A computer program is stored thereon; the computer program is executed by a processor to implement the method according to any one of claims 1 to 5.

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