A spatial two-stage distributed robust beamforming method

Abstract

The application discloses a kind of space two-stage distributed robust beam synthesis methods, comprising: by multiple unmanned aerial vehicle nodes respectively receiving radar signal transmitted by signal source;By phased array, the radar signal received by each unmanned aerial vehicle node is respectively subjected to beam synthesis, and the first beam synthesis signal corresponding to each unmanned aerial vehicle node is obtained;The first-stage beam synthesis signal is subjected to amplitude and phase weighting, and the first beam synthesis is synthesized, and the second beam synthesis signal is obtained.By constructing the two-stage hierarchical new architecture of spatial distributed robust beam synthesis, two-stage joint robust beam synthesis is carried out in node internal phased array and between nodes.Using robust optimization theory, the error distribution is modeled, the problem is converted into a robust optimization problem, a new beam synthesis algorithm robust to model error is designed, efficient solution is carried out, and theoretical analysis is given.The problem of reducing signal-to-noise ratio loss under the condition that the environment information has high uncertainty in traditional radar is solved.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a spatial two-level distributed robust beamforming method. Background Technology

[0002] In practice, the construction of distributed beamforming radar systems is affected by non-ideal factors such as manufacturing errors and limitations in installation techniques. This results in the system failing to achieve ideal coherent accumulation when detecting targets after startup. This is mainly manifested in poor target detection performance and low signal-to-noise ratio during single-node digital receiving beamforming and inter-node beamforming.

[0003] Currently, although some methods employ gradient descent to formulate distributed joint beamforming and null formation problems as unconstrained optimization routines based on common feedback messages broadcast by the receiver, null formation requires precise cancellation of signals from all transmitters at the receiver. This makes null shape highly sensitive to errors. Furthermore, the initial iterations of the gradient descent algorithm must lie in the range space of a matrix containing complex channel gains, requiring well-tuned channel submatrices for each batch of new transmitters. This results in poor algorithm flexibility and an inability to manually control variables for faster convergence and lower power consumption.

[0004] Therefore, how to solve the problem of low signal-to-noise ratio of traditional radar under conditions of high uncertainty in environmental information has become an urgent problem to be solved. Summary of the Invention

[0005] Therefore, it is necessary to provide a space-based two-level distributed robust beamforming method to address the aforementioned technical problems and solve at least one of the problems existing in the prior art.

[0006] This application provides a spatial two-level distributed robust beamforming method, including:

[0007] The system receives radar signals transmitted by a signal source from multiple drone nodes.

[0008] The radar signals received by each UAV node are beamformed by a phased array to obtain the first beamformed signal corresponding to each UAV node.

[0009] The first-stage beamforming signal is weighted by amplitude and phase, and then synthesized to obtain the second beamforming signal.

[0010] In one embodiment, the first beamforming signal is represented as:

[0011]

[0012] in, h is the theoretical upper bound vector of the beamforming performance loss caused by node-level model errors and channel-level model errors. m Represented as a channel, a m The guiding vector τ characterizes array m m Let w represent the delay, n be a random variable representing noise, and w be a variable representing the noise level. m Let Xm represent the weighted vector corresponding to UAV m, Xm represent the intermediate signal variables before the first-stage beamforming, and t represent the time index.

[0013] In one embodiment, the amplitude and phase weighting of the first-level beamforming signal includes:

[0014] Determine the weighting coefficients for each of the first-level beamforming signals;

[0015] The amplitude and phase weights of each first-level beamforming signal are applied according to the weighting coefficients.

[0016] In one embodiment, the second beamforming signal is represented as:

[0017] z(t)=[(β1w1) H a1h1,...,(β M w M ) H a M h M ][s(t-Δτ1), ...,s(t-Δτ) M )] T +(β1w1) H n1(t)+...+(β M w M ) H n M (t)

[0018] in, h is the theoretical upper bound vector of the beamforming performance loss caused by node-level model errors and channel-level model errors. m Represented as a channel, a m The guiding vector τ characterizes array m m Let w represent the delay, n be a random variable representing noise, and w be a variable representing the noise level. m Let [s(t-Δτ1), ..., s(t-Δτ)] represent the weighted vector corresponding to UAV m. M )] T The expression is [s(t-Δτ1),...,s(t-Δτ M The transpose of ], where β represents the weighting coefficient of the synthesized signal of each first beam. mThis represents the weighting coefficient of the first beam synthesized signal corresponding to UAV m. t represents the time index.

[0019] In one embodiment, the signal-to-noise ratio of the first beamforming signal and the second beamforming signal during synthesis is obtained through the following first optimization model:

[0020]

[0021]

[0022] Where, θ m Indicates azimuth, φ m Pitch angle, a m The guiding vector h characterizing array m m Represented as a channel, β m W represents the weighting coefficient of the first beamformed signal corresponding to UAV m. m σ represents the weighted vector corresponding to drone m. m Indicates the standard error.

[0023] In one embodiment, the w m The solution is obtained through the following second optimization model:

[0024]

[0025] subject to||z m (θ m φ m )|-1|+δ m y m (θ m φ m )≤c m ,

[0026]

[0027] ||w m ||2≤y m

[0028]

[0029] The augmented Lagrangian function of the second optimization model is expressed as:

[0030]

[0031] in, θ represents taking all possible cases. m and φ m Summation, L p() represents the Lagrange augmented function, Re[] indicates taking the real part of the complex number within the brackets, η represents efficiency, and λ and ρ are parameters for weight allocation.

[0032] In one embodiment, the augmented Lagrangian function is solved by the following steps:

[0033] Step a: Oriented towards {w m ,y m Minimize the augmented Lagrangian function of}, let:

[0034]

[0035]

[0036]

[0037]

[0038] Therefore, the third optimization model is obtained as follows:

[0039]

[0040] subject to||w m ||2≤y m

[0041] The optimal third optimization model Represented as:

[0042]

[0043] Wherein, the eigenvalue decomposition of A is UAU H ,

[0044] Step b: Oriented towards {y} m (θ m φ m ), z m (θ m φ m Minimize the augmented Lagrangian function of}, let

[0045]

[0046]

[0047] b2(θ m φ m )=-η m (θ m φ m )-ρy m ;

[0048] The fourth optimization model is then obtained as follows:

[0049]

[0050] subject to |z-1|+δ m y≤c.

[0051] Define ψ as a complex number (2a1(θ) m φ m )+b1(θ m φ m The argument of )) is r, where r is a complex number. If the modulus is given, then the optimal solution of the fourth optimization model is expressed as:

[0052]

[0053] z = 1 - ce jψ +e jψ max{cr,δ m y}.

[0054] Where δ and c represent constants of change; e represents exponential operation; j is the imaginary unit; and ψ is the complex number (2a1(θ)). m φ m )+b1(θ m φ m The argument of )) , δ m y represents δ m The product of y and y.

[0055] Step c: Perform dual update using the following formula:

[0056]

[0057] η m (θ m φ m )=η m (θ m φ m )+ρ(y m -y m (θ m φ m ))

[0058] The solution is obtained by iteratively solving steps a-c. When the number of iterations reaches a first preset value, the value of W is output. m .

[0059] In one embodiment, the weighting coefficients are obtained by solving the following fifth optimization model:

[0060]

[0061]

[0062] in, This represents the estimation of the channel intermediate variable q of the first beam synthesized signal corresponding to UAV node m, where Σ represents the diagonal elements, and σ... m δ represents the standard error. m c represents the constant of change.

[0063] In one embodiment, q and Σ are obtained through the following sixth optimization model:

[0064]

[0065] subjectto Q=qq H +∑,

[0066] ∑=Diag([d1,...,d M ])

[0067]

[0068] Where l and u are known constants, det(Q) refers to the determinant of Q, Q represents the covariance matrix variable to be optimized, Ry represents the sample covariance matrix, and dm represents the m-th element of the diagonal component of Q.

[0069] In one embodiment, the sixth optimization model is solved in the following manner:

[0070] Step d: For Perform eigenvalue decomposition, denoted as W is a unitary matrix composed of eigenvectors, Λ=diag(λ1,...,λ M ) is a diagonal matrix with elements of . The eigenvalues ​​of λ satisfy λ i ≥λ i+1 ;

[0071] Step e:

[0072] Step f: q = Σ 1 / 2 We;

[0073] Step g: Σ=min(max(diag(R) z -qq H ), D l )D u );

[0074] Where min() represents the minimum value, max() represents the maximum value, and diag(R) represents the maximum value. z -qq HThe expression () represents the construction of a square matrix whose non-diagonal elements are all 0.

[0075] Step h: Q = qq H +Σ, iterate through steps e to h, and when the number of iterations reaches the second preset value, output q and Σ.

[0076] The aforementioned two-level distributed robust beamforming method for space includes: receiving radar signals transmitted by a signal source from each UAV node; performing beamforming on the radar signals received by each UAV node using a phased array to obtain a first beamformed signal corresponding to each UAV node; weighting the first beamformed signal by amplitude and phase, and then performing a synthesis process to obtain a second beamformed signal. This application constructs a novel two-level hierarchical architecture for space-distributed robust beamforming, performing two-level joint robust beamforming within the phased array and between nodes. Robust optimization theory is employed to model the error distribution, transforming the problem into a robust optimization problem. A novel beamforming algorithm robust to model errors is designed for efficient solution, and theoretical analysis is provided. This addresses the problem of reducing signal-to-noise ratio loss in traditional radar systems when environmental information has high uncertainty. Attached Figure Description

[0077] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0078] Figure 1 This is a schematic diagram of an application environment for a spatial two-level distributed robust beamforming method according to an embodiment of the present invention;

[0079] Figure 2 This is a schematic flowchart of a spatial two-level distributed robust beamforming method in one embodiment of the present invention. Detailed Implementation

[0080] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0081] This embodiment provides a two-level distributed robust beamforming method for space applications, which can be applied to, for example... Figure 1 In this application environment, the first stage is UAV-level beamforming, involving M UAV systems, each equipped with a linear array of N elements. The second stage is virtual beamforming at the fusion center (FC), which directly communicates with the M UAVs. Each UAV node is equipped with a phased array antenna array, with each array including multiple antennas to receive radar signals from different azimuths. After receiving the radar signals, each antenna on each UAV node performs first-stage beamforming through its internal phased array, adjusting the amplitude and phase. After phased array processing, the first-stage beamforming signal is sent to the fusion center. The fusion center delays the first-stage beamforming signals from each node to align the waveforms in time, and then performs amplitude and phase weighting to achieve second-stage beamforming. By constructing a novel two-level hierarchical architecture for spatially distributed robust beamforming, two-level joint robust beamforming is achieved both within the node's internal phased array and between nodes. This addresses the problem of reducing signal-to-noise ratio loss in traditional radar systems operating under high environmental uncertainty.

[0082] The spatial location of the fusion center is (0,0,0). The spatial location of each UAV is provided with high-precision positioning information by GPS or BeiDou. For the m-th UAV, p... m =(x m ,y m ,z m ) indicates its position in the global coordinate system. p s =(x s ,y s ,z s ) represents the far-field location of the narrowband signal radiation source. The return single-channel signal of T sample points [z(1),z(2),z(3),…z(T)].

[0083] In one embodiment, such as Figure 2 As shown, a two-level distributed robust beamforming method in space is provided, which is then applied to... Figure 1 Taking the server-side as an example, the explanation includes the following steps:

[0084] In step S110, radar signals transmitted by the signal source are received by multiple UAV nodes respectively;

[0085] In this embodiment of the application, the signal source may be a narrowband signal radiation source.

[0086] In this embodiment of the application, multiple UAV nodes can be arranged, and each UAV node can be configured with a phased array antenna. Each phased array antenna can include multiple antennas for receiving radar signals transmitted by the signal source.

[0087] In step S120, the radar signals received by each UAV node are beamformed by a phased array to obtain the first beamformed signal corresponding to each UAV node.

[0088] In this embodiment of the application, the received radar signal is appropriately delayed by the phased array antenna set in the UAV node to obtain the array beam deflection, and delay compensation is performed simultaneously in different azimuths, and beam synthesis is performed to output the first beam synthesis signal.

[0089] In this embodiment of the application, the first beamforming signal is represented as:

[0090]

[0091] in, h is the theoretical upper bound vector of the beamforming performance loss caused by node-level model errors and channel-level model errors. m Represented as a channel, a m The guiding vector τ characterizes array m m W represents the delay, where n is a random variable representing noise. m Let Xm represent the weighted vector corresponding to UAV m, Xm represent the intermediate signal variables before the first-stage beamforming, and t represent the time index.

[0092] In step S130, the first-level beamforming signal is weighted by amplitude and phase, and the first beamforming signal is processed to obtain the second beamforming signal.

[0093] In one embodiment, the amplitude and phase weighting of the first-level beamforming signal includes:

[0094] Determine the weighting coefficients for each of the first-level beamforming signals;

[0095] The amplitude and phase weights of each first-level beamforming signal are applied according to the weighting coefficients.

[0096] Specifically, after receiving the first beamforming signal output by multiple UAV nodes, the fusion center can perform a delay processing on the first beamforming signal to align it with the waveform in time. After accommodating it, the amplitude and phase weights can be applied to perform beamforming processing on the first beamforming signal to output the second beamforming signal.

[0097] The second beamforming signal is represented as follows:

[0098] z(t)=[(β1w1) H a1h1,...,(β M w M )H a M h M ][s(t-Δτ1), ...,s(t-Δτ) M )] T +(β1w1) H n1(t)+...+(β M w M ) H n M (t)

[0099] in, h is the theoretical upper bound vector of the beamforming performance loss caused by node-level model errors and channel-level model errors. m Represented as a channel, a m The guiding vector τ characterizes array m m Let w represent the delay, n be a random variable representing noise, and w be a variable representing the noise level. m Let [s(t-Δτ1), ..., s(t-Δτ)] represent the weighted vector corresponding to UAV m. M )] T The expression is [s(t-Δτ1),...,s(t-Δτ M The transpose of ], where β represents the weighting coefficient of the synthesized signal of the first beam of each channel, and t represents the time index.

[0100] Further, define but:

[0101]

[0102] Where u represents the noise after passing through the two-stage system. The representation is defined as follows: () H W[|u|] represents the transpose and conjugate of a matrix, where n represents a noisy random variable. 2 ] represents the expression for |u| 2 The mathematical expectation, This indicates the following after the operator This indicates that after the operation |(β) m w m ) H n m | 2 The formula sums all results from m=1 to m=M, Tr() represents the sum of all elements in the same row and column of the matrix, and σ m Denotes the standard error, ||β m w m ||For β m w m The norm of .

[0103] Further, define

[0104]

[0105] as well as but:

[0106]

[0107] Where r is the signal after passing through the two-stage system, s(t) is the transmitted narrowband signal, and h M τ represents the direct path channel coefficient from the radiating source M (lowercase) to the reference element m in the array. m For the time delay, s * Let be the conjugate matrix of s, [s(t-Δτ1), ..., s(t-Δτ)] M )] T is s(t-Δτ1),...,s(t-Δτ M The transpose of ), v represents the beamforming equivalent weight coefficients, and R is the autocorrelation matrix of the time-delay compensated signal s(t-Δτ), R = 11. T

[0108] The signal-to-noise ratio of this two-stage system can be expressed as:

[0109]

[0110] Where, vector a m The steering vector representing array m, without affecting the signal-to-noise ratio (SNR) value, can be equivalent to solving the following first optimization model:

[0111]

[0112]

[0113] Where, θ m Indicates azimuth. This represents the pitch angle, due to the optimal β m and w m Since the product invariance is satisfied, it can be set. To ensure the uniqueness of the solution:

[0114]

[0115]

[0116]

[0117] The optimal β can be obtained through the following process. m and w m To solve the above optimization problem:

[0118] Step 1: Solve for the optimal w m ;

[0119] Solve the following optimization problem:

[0120]

[0121]

[0122] Due to the uncertainty of location, there are in, The specific form is:

[0123]

[0124] exp() represents an exponential function with base e of the natural law. It is a m The estimated value of θ is given by σ, which represents the error vector. Since the steering vector is not precise, we need to ensure that for any m, θ... m φ m , Both have ||Δa m ||2≤δ m ,or, and |α m (θ m φ m If |=1, then ||Δa m ||2≤δ m If let Then all the original constraints can be satisfied.

[0125] Therefore, for each drone, for w m Enforce robust constraints, and in (θ) m φ m Minimize ||w within the uncertain region of ) m || 2 ,Right now:

[0126]

[0127]

[0128] |α m (θ m φ m )|=1,

[0129]

[0130] Where, θ m and φ m They are all discrete and uniformly rasterized, θ m，lower θm，upper They represent θ m Similarly, φ's lower and upper bounds are also related. m，lower φ m，upper Represents φ m The upper and lower bounds.

[0131] To obtain θ m，lower θ m，upper and φ m，lower φ m，upper Due to the uncertainty of the location, the measurement angle is also uncertain. The measured and true values ​​of the azimuth and elevation angles are as follows:

[0132]

[0133]

[0134]

[0135]

[0136] Because of the uncertainty of location, θ m There is an upper boundary and a lower boundary:

[0137] θ m，lower ≤θ m ≤θ m，upper

[0138]

[0139] θ m，lower =minθ

[0140] θ m，upper =maxθ

[0141] Similarly, φ m There is also an upper boundary and a lower boundary:

[0142] φ m，lower ≤φ m ≤φ m，upper

[0143]

[0144] φ m，lower =minΦ,

[0145] φ m，upper =maxΦ.

[0146] Where ε is the error constant, Let xs, ys, and zs represent the estimated three-dimensional coordinates of the m-th UAV, where xs, ys, and zs represent the three-dimensional coordinates of the signal source location. Here, ε = 0.15, and arctan refers to calculating the arctangent function, which is then expressed in the formula. This symbolizes the positional error from GPS or BeiDou. A typical example. The value is 10 meters.

[0147] Therefore, the original problem can be restated as:

[0148]

[0149] subject to|z m (θ m φ m )-α m (θ m φ m )|+δ m y m (θ m φ m )≤ m

[0150] |α m (θ m φ m )|=1,

[0151]

[0152] ||W m ||2≤y m

[0153]

[0154] Among them, c m This represents a constant of change.

[0155] Based on the optimization problem described above, we can directly conclude that:

[0156]

[0157] arg() represents the argument of the complex number inside the parentheses.

[0158] Therefore, it can be concluded that:

[0159]

[0160] Therefore, a second optimization model can be obtained. By solving this second optimization model, the value of w can be obtained. m The details are as follows:

[0161]

[0162] subject to||z m (θ m φ m |-1|+δ m y m (θ m φ m )≤c m ,

[0163]

[0164] ||w m ||2≤y m

[0165]

[0166] The augmented Lagrangian function of the second optimization model is expressed as:

[0167]

[0168] in, θ represents taking all possible cases. m and φ m Summation, L p () represents the augmented Lagrange function, Re[] indicates taking the real part of the complex number within the brackets, η represents efficiency, and λ and ρ are parameters that assign weights in the augmented Lagrange function.

[0169]

[0170] subject to||z m (θ m φ m )|-1|+δ m y m (θ m φ m )≤c m ,

[0171]

[0172] ||w m ||2≤y m

[0173]

[0174] The specific solution steps are as follows: A preset number of iterations is required. Let the number of iterations be defined as S and initialized to 1. Then, increment it by 1 for each iteration until the first preset value, such as 100, is reached. At this point, the optimal value w can be output. m .

[0175] Step a: Oriented towards {w m y m To minimize the augmented Lagrange function, we can let

[0176]

[0177]

[0178]

[0179]

[0180] Therefore, the following third optimization model can be obtained:

[0181]

[0182] subiect to||w m ||2≤y m

[0183] The optimal third optimization model Represented as:

[0184]

[0185] Wherein, the eigenvalue decomposition of A is UΛU H , Furthermore, f(y) is a strictly monotonically decreasing function, and even further, the unique solution to f(y) = 1 can be obtained by applying... Obtained by binary search.

[0186] Step b: Oriented towards {y} m (θ m φ m ), z m (θ m φ m Minimize the augmented Lagrangian function of}, let

[0187]

[0188]

[0189] b2(θ m φ m )=-η m (θ m φ m )-ρym,;;

[0190] This leads to the following subproblems:

[0191]

[0192] subject to||z m (θ m φ m )|-1|+δ m y m (θ m φ m )≤c m

[0193] It can be seen that,

[0194] Therefore, the following fourth optimization model can be obtained:

[0195]

[0196] subject to |z-1|+δ m y≤c.

[0197] Define ψ as a complex number (2a1(θ) m ,φ m )+b1(θ m ,φ m The argument of )) is r, where r is a complex number. If the modulus is given, then the optimal solution of the fourth optimization model is expressed as:

[0198]

[0199] z = 1 - ce jψ +e jψ max{cr,δ m y}.

[0200] Where δ and c represent constants of change, e represents exponential operation, j is the imaginary unit, and ψ is the complex number (2a1(θ)). m ,φ m )+b1(θ m ,φ m The argument of )) , δ m y represents δ m The product of y and y.

[0201] Step c: Perform dual update using the following formula:

[0202]

[0203] η m (θ m φ m )=η m (θ m φ m )+ρ(y m -ym (θ m φ m ))

[0204] The solution is obtained by iteratively solving steps a-c. When the number of iterations reaches a first preset value, the value w is output. m .

[0205] The first preset value can be 100. Through steps f-h above, the calculation is performed cyclically starting from s=1. In each cycle, s=s+1 until s=100, at which point w is output. m .

[0206] Step 2: Δa m It remains constant over a period of time, so intermediate output can be estimated using statistical methods. The fusion center collects the synchronization signal sequence z(t) = [z(1), z(2), z(3), ... z(T)] from the m-th UAV and calculates the sequence with all... The sample mean covariance matrix R z In covariance, q is estimated from z(t). m .

[0207] The covariance formula can be expressed as:

[0208]

[0209] in, Indicates all The sample matrix Let q represent the covariance of the vectors in the vectors. m Including additive noise, therefore, R z It has a rank-1 plus diagonal structure. Therefore, q can be obtained through maximum likelihood estimation. m The value of .

[0210] The estimation is solved using the following sixth optimization model.

[0211] subject to Q=qq H +∑,

[0212] ∑=Diag([d1,...,d M ])

[0213]

[0214] Where l and u are known constants, det(Q) refers to the determinant of Q, Q represents the covariance matrix variable to be optimized, Ry represents the sample covariance matrix, and dm represents the m-th element of the diagonal component of Q.

[0215] This algorithm is an iterative algorithm. First, define the number of iterations S, which is the second preset value, and initialize it to 1. Then, increment it by 1 for each iteration. Then define the following variables:

[0216]

[0217]

[0218] The sixth optimization model can be solved iteratively through the following steps, each iteration including the following steps:

[0219] Step d: For Perform eigenvalue decomposition, denoted as W is a unitary matrix composed of eigenvectors, Λ=diag(λ1,...,λ M ) is a diagonal matrix with elements of . The eigenvalues ​​of λ satisfy λ i ≥λ i+1 ;

[0220] Step e: e=[ξ1 1 / 2 [0, ..., 0] T ξ1=max(λ1-1,0);

[0221] Step f: q = ∑ 1 / 2 We;

[0222] Step g: ∑=min(max(diag(R) z -qq H ), D l ), D u );

[0223] Where min() represents the minimum value, max() represents the maximum value, and diag(R) represents the maximum value. z -qq H The expression () represents the construction of a square matrix whose non-diagonal elements are all 0.

[0224] Step h: Q = qq H +Σ, iterate through steps e to h, and when the number of iterations reaches the second preset value, output q and Σ.

[0225] The second preset value can be 100. Through steps d-h above, the calculation is performed iteratively starting with s=1. In each cycle, s=s+1 until s=100, at which point q and Σ are output. Here, q represents the intermediate channel variable, and Σ represents the diagonal element.

[0226] Step 3: Calculate the optimal β.

[0227] Assign any m-th diagonal element of Σ to The estimated value of q is expressed as It should be pointed out that It is inaccurate; its uncertainty stems from... therefore, and Similarly, to ensure Under any conditions, ||Δa m ||≤δ m Therefore, this constraint can be tightened in the following way:

[0228]

[0229] If The original constraints will be satisfied naturally, so we can obtain the optimal β by solving the relevant optimization problem.

[0230] Based on estimation The optimization β is obtained by solving the diagonal element Σ using the following fifth optimization model:

[0231]

[0232]

[0233] Where, σ m δ represents the standard error. m c represents the constant of change.

[0234] Since this problem is convex, an existing solver can be used to obtain β, and the algorithm can ultimately output the optimal w. m And β, through this w m And β can be used to obtain the maximum signal-to-noise ratio. Since there are model errors in the phased array elements and model errors between nodes, robust optimization theory is used to model the error distribution and transform the problem into a robust optimization problem. A new beamforming algorithm that is robust to model errors is designed for efficient solution. Theoretical analysis is given. By synthesizing beams through a two-level hierarchical architecture, the signal-to-noise ratio loss can be effectively reduced.

[0235] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0236] This application provides a two-level distributed robust beamforming method for space, which can be widely applied in fields such as enemy reconnaissance, radar signal processing, and target detection. The method includes: receiving radar signals transmitted by a signal source from each UAV node; performing beamforming on the radar signals received by each UAV node using a phased array to obtain a first beamformed signal for each UAV node; weighting the first beamformed signal by amplitude and phase, and then performing a synthesis process to obtain a second beamformed signal. This application constructs a novel two-level hierarchical architecture for space-distributed robust beamforming, performing two-level joint robust beamforming within the node phased array and between nodes. Robust optimization theory is employed to model the error distribution, transforming the problem into a robust optimization problem. A novel beamforming algorithm robust to model errors is designed for efficient solution, and theoretical analysis is provided. This addresses the problem of reducing signal-to-noise ratio loss in traditional radar systems when environmental information has high uncertainty. Furthermore, this application, through physical mechanism analysis of model errors between nodes and model errors between array elements within nodes, adopts a different approach from conventional methods that simply increase the number of array elements in a radar phased array, overcoming the degradation of radiation pattern performance caused by model errors. A novel two-level hierarchical architecture for space-distributed robust beamforming is constructed, a new beamforming algorithm robust to model errors is designed, and simulation verification experiments are conducted, achieving robustness against large model errors. The feasibility of integrating and applying related technologies is preliminarily verified, improving the radiation pattern performance and collaborative detection capabilities of radar equipment.

[0237] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by instructing related hardware through computer-readable instructions. These computer-readable instructions can be stored in a non-volatile readable storage medium or a volatile readable storage medium. When executed, these computer-readable instructions can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), direct memory bus dynamic RAM (DRDRAM), etc.

[0238] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is used as an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above.

[0239] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A spatial two-level distributed robust beamforming method, characterized in that, The method includes: The system receives radar signals transmitted by a signal source from multiple drone nodes. The radar signals received by each UAV node are beamformed by a phased array to obtain the first beamformed signal corresponding to each UAV node. The first beamforming signal is weighted by amplitude and phase, and then synthesized to obtain the second beamforming signal. The signal-to-noise ratio of the first beamforming signal and the second beamforming signal during synthesis is obtained through the following first optimization model: in, Indicates azimuth, indicates Pitch angle, Characterization array The guide vector, Represented as a channel, This represents the weighting coefficients of the first beam synthesized signal corresponding to UAV m. Indicates drone The corresponding weighted vector, Indicates standard error; The The solution is obtained through the following second optimization model: The augmented Lagrangian function of the second optimization model is expressed as: in, This means taking all existing cases. and Summation, That is, the Lagrange augmented function. This indicates taking the real part of the complex number within the parentheses. Indicates efficiency. and These are the parameters for assigning weights.

2. The space-based two-level distributed robust beamforming method as described in claim 1, characterized in that, The first beamforming signal is represented as: in, It is the theoretical upper bound vector of the beamforming performance loss caused by node-level model errors and channel-level model errors. Represented as a channel, Characterizing drones The guide vector, Represents delay, It is a random variable representing noise. Indicates drone The corresponding weighted vector, This represents the intermediate signal variables before the first-stage beamforming, and t represents the time index.

3. The space-based two-level distributed robust beamforming method as described in claim 1, characterized in that, The amplitude and phase weighting of the first beamformed signal includes: Determine the weighting coefficients for each of the first beam synthesized signals; The amplitude and phase weights of each of the first beam synthesized signals are applied according to the weighting coefficients.

4. The space-based two-level distributed robust beamforming method as described in claim 1, characterized in that, The second beamforming signal is represented as: in, It is the theoretical upper bound vector of the beamforming performance loss caused by node-level model errors and channel-level model errors. Represented as a channel, Characterizing drones The guide vector, Represents delay, It is a random variable representing noise. Indicates drone The corresponding weighted vector, It means yes The transpose of , where β represents the weighting coefficients of the synthesized signal of each first beam. denoted by , where represents the weighting coefficient of the first beam synthesized signal corresponding to UAV m, and t represents the time index.

5. The space-based two-level distributed robust beamforming method as described in claim 1, characterized in that, The augmented Lagrange function is solved using the following steps: Step a: Oriented To minimize the augmented Lagrange function, let: Therefore, the third optimization model is obtained as follows: The optimal third optimization model , represented as: in, eigenvalue decomposition into , ; Step b: Oriented Minimize the augmented Lagrangian function, let ； The fourth optimization model is then obtained as follows: definition It is a complex number The argument of r, where r is a complex number. If the modulus is given, then the optimal solution of the fourth optimization model is expressed as: Where δ and c represent constants of change; e represents exponential operation; and j is the imaginary unit. It is a complex number The angle of the argument, express and The product; Step c: Perform dual update using the following formula: The solution is obtained by iteratively solving steps a-c. When the number of iterations reaches the first preset value, the solution is output. .

6. The space-based two-level distributed robust beamforming method as described in any one of claims 2 or 4, characterized in that, The weighting coefficients are obtained by solving the following fifth optimization model: in, express The estimate, Represents diagonal elements. Indicates standard error, c represents the constant of change.

7. The space-based two-level distributed robust beamforming method as described in claim 6, characterized in that, The as well as Obtained through the following sixth optimization model: in, and Given constants, It refers to The determinant of Q is given by , where Q represents the covariance matrix variable to be optimized, Ry represents the sample covariance matrix, and dm represents the m-th element of the diagonal component of Q.

8. The space-based two-level distributed robust beamforming method as described in claim 7, characterized in that, The sixth optimization model is solved in the following way: Step d: For Perform eigenvalue decomposition, denoted as , The unitary matrix formed by the eigenvectors. It is a diagonal matrix, and its elements are The eigenvalues ​​of , and satisfy . Step e: Step f: Step g: in, This indicates taking the minimum value. This indicates taking the maximum value. This indicates the construction of a square matrix where all elements not on the diagonal are 0. , ; Step h: The solution is iteratively solved according to steps e-h. When the number of iterations reaches the second preset value, the solution is output. as well as .

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