Space-frequency joint optimization subarray-level broadband digital array radar waveform design method

Abstract

The invention discloses a space-frequency joint optimization subarray-level broadband digital array radar waveform design method, and the method comprises the steps: generating an array structure matrix according to the division mode of a sub-phased array in a whole array; according to the array structure matrix, constructing a full-array waveform phase matrix represented by an inter-sub-array waveform phase matrix and a phase shifting weight vector of a phase shifter in the full array; constructing a target function which minimizes the directional diagram deviation and the power spectrum deviation; sequentially taking the waveform phase matrix between the sub-arrays and the phase shift weight vector of the phase shifter in the whole array as parameters to be solved, and alternately optimizing and solving the target function by using a conjugate gradient method to obtain an optimal waveform phase matrix between the sub-arrays and a phase shift weight vector of the optimal phase shifter in the whole array; and according to the optimal waveform phase matrix between the sub-arrays and the optimal phase shift weight vector of the phase shifter in the optimal full array, designing and outputting a radar waveform. According to the invention, the radar waveform is designed by using the sub-array, and the array cost is reduced.

Description

Technical Field

[0001] The invention belongs to the field of radar technology, and in particular relates to a space-frequency joint optimization subarray-level broadband digital array radar waveform design method. Background Art

[0002] In the past, radar systems often emitted narrowband signals because of their advantages such as simple design, low data volume, and easy detection. However, with the changes in the electromagnetic environment, narrowband signals can no longer meet the needs. Wideband radar has better distance resolution, can obtain more target information, is conducive to target imaging or target recognition, and is gradually gaining attention.

[0003] In terms of array structure: each array element of phased array radar transmits a coherent waveform, each antenna unit adjusts the phase independently and works synchronously, and the electromagnetic wave signals of each antenna unit are superimposed to form a narrow beam pointing to a predetermined direction. Its structure and working mode are simple; digital array radar has the characteristics of waveform diversity. Due to the diversity of its transmission pattern, the working mode of the digital array radar system is more flexible, and the digital array radar can realize simultaneous multi-beam technology, allocate the required power to the targets pointed by different beams, so as to improve the resource utilization of the radar system. It can also transmit different signals to different targets, so that different beams have different functions. At present, large-scale array radar has become a hot topic of research, while all-digital array radar is too expensive, has many waveform parameters, is highly sensitive, and is not easy to use in large-scale arrays. Subarray-level digital array radar adopts the array mode of phased array within the subarray and digital array between subarrays, so that different waveforms are emitted between subarrays, the same waveform is emitted within the subarray, and the phase is adjusted using a phase shifter. The digital array between subarrays can effectively reduce costs and is suitable for large-scale radar arrays.

[0004] However, there is currently a lack of solutions for effectively utilizing inter-subarray digital arrays to design radar waveforms. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a space-frequency joint optimization subarray-level broadband digital array radar waveform design method. The technical problem to be solved by the present invention is achieved by the following technical solutions:

[0006] The embodiment of the present invention provides a space-frequency joint optimization subarray-level broadband digital array radar waveform design method, the method comprising:

[0007] Generate an array structure matrix according to the division method of sub-phased arrays in the whole array;

[0008] According to the array structure matrix, constructing a full array waveform phase matrix represented by the inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the full array;

[0009] According to the expected directional pattern, the actual directional pattern, and the expected power spectrum and the actual power spectrum at the main beam, an objective function is constructed to minimize the directional pattern deviation and the power spectrum deviation; wherein the directional pattern deviation is calculated according to the expected directional pattern and the actual directional pattern, and the power spectrum deviation is calculated according to the expected power spectrum and the actual power spectrum;

[0010] The inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the entire array are sequentially used as parameters to be determined, and the objective function is alternately optimized and solved using the conjugate gradient method to obtain the optimal inter-subarray waveform phase matrix and the optimal phase shift weight vector of the phase shifter in the entire array;

[0011] The output radar waveform is designed according to the optimal inter-subarray waveform phase matrix and the optimal phase shift weight vector of the optimal full-array intra-phase shifter.

[0012] In one embodiment of the present invention, if the sub-phased arrays in the entire array are divided into uniform divisions, the generated array structure matrix formula is expressed as follows:

[0013]

[0014] Where T represents the array structure matrix, I m represents the identity matrix of dimension m, represents the Kronecker product, 1 (M / m)×1 represents an all-one vector of length M / m, where M represents the total number of array elements in the entire array and m represents the number of sub-phased arrays.

[0015] In one embodiment of the present invention, the constructed full array waveform phase matrix formula is expressed as:

[0016]

[0017] Among them, Φ represents the waveform phase matrix of the entire array, T represents the array structure matrix, Φ′ represents the waveform phase matrix between sub-arrays, represents the phase shift weight vector of the phase shifters in the entire array, represents the phase shift weight of the sth phase shifter in the entire array, E = 1 1×N represents an all-1 vector of length N, M represents the total number of array elements in the array, and N represents the code length of the transmitted signal.

[0018] In one embodiment of the present invention, the objective function constructed to minimize the pattern deviation and the power spectrum deviation is expressed as follows:

[0019]

[0020] Where Φ represents the phase matrix of the full array waveform, α(Φ) represents the scale factor, L represents the number of sub-band frequency points of the broadband signal, K represents the number of grid points in the azimuth angle, and θ k represents the kth azimuth, w k Indicates that in θ k The pattern matching weight at , I represents the number of main beams, P(θ k ,Φ) indicates that in θ k The actual direction diagram at P d (θ k ) indicates that in θ k The desired directivity pattern at , μ represents the ratio of the directivity pattern error term to the power spectrum error term, represents the i-th main beam pointing angle, Indicated in The weight of the power spectrum at the nth frequency point, Indicated in The actual power spectrum of the nth frequency point at d in Indicated in The expected power spectrum of the nth frequency point at which the scale factor α is solved is updated in real time during the process of using the conjugate gradient method to alternately optimize the objective function.

[0021] In one embodiment of the present invention, when the scale factor α(Φ) is updated in real time, the formula is expressed as:

[0022]

[0023] in, λ1 and λ2 represent balance factors.

[0024] In one embodiment of the present invention, the inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the entire array are respectively used as parameters to be determined, and the conjugate gradient method is used to alternately optimize and solve the objective function to obtain the optimal inter-subarray waveform phase matrix and the optimal phase shift weight vector of the phase shifter in the entire array, including:

[0025] The inter-subarray waveform phase matrix is ​​used as a parameter to be determined, and the execution steps include: initializing the inter-subarray waveform phase matrix, the phase shift weight vector of the phase shifter in the whole array, and initializing the number of iterations; calculating the first gradient value of the objective function with respect to the inter-subarray waveform phase matrix according to the initialized inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the whole array; judging whether it is the first iteration, if so, directly resetting the first search direction according to the first gradient value; if not, calculating the first correction coefficient of the first search direction according to the first gradient value, and resetting the first search direction according to the first gradient value, the first correction coefficient and the first search direction set in the last iteration; using a The method comprises the following steps: determining a first search step length by a dimensional linear search method; updating an inter-subarray waveform phase matrix according to the first search step length and the reset first search direction; judging whether the updated inter-subarray waveform phase matrix satisfies a first iteration stop condition; if so, taking the updated inter-subarray waveform phase matrix as the optimal inter-subarray waveform phase matrix, calculating and recording a first objective function value, and initializing the number of iterations; if not, taking the updated inter-subarray waveform phase matrix as the initialized inter-subarray waveform phase matrix, returning the step of calculating a first gradient value of the objective function according to the initialized inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the entire array until the first iteration stop condition is satisfied;

[0026] The phase shift weight vector of the phase shifter in the whole array is taken as the parameter to be determined, and the execution steps include: calculating the second gradient value of the objective function with respect to the phase shift weight vector of the phase shifter in the whole array according to the optimal inter-subarray waveform phase matrix and the initialized phase shift weight vector of the phase shifter in the whole array; judging whether it is the first iteration, if so, directly resetting the second search direction according to the second gradient value; if not, calculating the second correction coefficient of the second search direction according to the second gradient value, and resetting the second search direction according to the second gradient value, the second correction coefficient and the second search direction set in the last iteration; determining the second search step length by using a one-dimensional linear search method; determining the second search step length according to the second The phase shift weight vector of the phase shifter in the whole array is updated according to the search step size and the reset second search direction; whether the updated phase shift weight vector of the phase shifter in the whole array satisfies the second iteration stop condition is determined; if so, the updated phase shift weight vector of the phase shifter in the whole array is used as the optimal phase shift weight vector of the phase shifter in the whole array, and the second objective function value is calculated and recorded; if not, the updated phase shift weight vector of the phase shifter in the whole array is used as the initialized phase shift weight vector of the phase shifter in the whole array, and the step of calculating the second gradient value of the objective function according to the optimal inter-subarray waveform phase matrix and the initialized phase shift weight vector of the phase shifter in the whole array is returned until the second iteration stop condition is satisfied;

[0027] The difference between the first objective function value and the second objective function value is calculated, and it is determined whether the difference satisfies a third iteration stop condition. If so, the optimal inter-subarray waveform phase matrix and the optimal phase shift weight vector of the phase shifter in the entire array are output; if not, the optimal inter-subarray waveform phase matrix and the optimal phase shift weight vector of the phase shifter in the entire array are used as the initialized inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the entire array, respectively, and the number of iterations is initialized. The step of calculating the first gradient value of the objective function according to the initialized inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the entire array is returned until the third iteration stop condition is satisfied.

[0028] In one embodiment of the present invention, a first correction coefficient of a first search direction is calculated according to the first gradient value, and the formula is expressed as:

[0029]

[0030] Among them, β Φ′ (k) represents the first correction coefficient for the first search direction, represents the first gradient value of the inter-subarray waveform phase matrix at the kth iteration, represents the first gradient value of the phase matrix of the waveform between sub-arrays at the k-1th iteration, Tr represents the tracing operation, Express The transpose operation, Express The transpose operation of

[0031] The first search direction is reset according to the first gradient value, the first correction coefficient and the first search direction set in the last iteration, and the formula is expressed as:

[0032]

[0033] in, represents the first search direction of the kth iteration, β Φ′ (k) represents the first correction coefficient of the kth iteration, represents the first search direction of the k-1th iteration;

[0034] The inter-subarray waveform phase matrix is ​​updated according to the first search step size and the reset first search direction, and the formula is expressed as:

[0035]

[0036] Among them, Φ′ (k+1) represents the inter-subarray waveform phase matrix of the k+1th iteration, Φ′ (k)represents the inter-subarray waveform phase matrix of the kth iteration, represents the first search step size of the kth iteration.

[0037] In one embodiment of the present invention, a second correction coefficient of the second search direction is calculated according to the second gradient value, and the formula is expressed as:

[0038]

[0039] in, represents the second correction coefficient of the second search direction of the kth iteration, represents the second gradient value of the phase shift weight vector of the phase shifter in the entire array at the kth iteration, represents the second gradient value of the phase shift weight vector of the phase shifter in the entire array at the k-1th iteration, Tr represents the tracking operation, Express The transpose operation, Express The transpose operation of

[0040] The second search direction is reset according to the second gradient value, the second correction coefficient and the second search direction set in the last iteration, and the formula is expressed as:

[0041]

[0042] in, represents the second search direction of the k-th iteration, represents the second correction coefficient of the kth iteration, represents the second search direction of the k-1th iteration;

[0043] The inter-subarray waveform phase matrix is ​​updated according to the second search step size and the reset second search direction, and the formula is expressed as:

[0044]

[0045] in, represents the phase shift weight vector of the phase shifters in the entire array at the k+1th iteration, represents the phase shift weight vector of the phase shifters in the entire array at the kth iteration, represents the second search step size of the kth iteration.

[0046] In one embodiment of the present invention, the radar waveform to be output is designed, and the formula is expressed as follows:

[0047]

[0048] Among them, X optrepresents the radar waveform of the designed output, T represents the array structure matrix, Φ′ opt represents the optimal inter-subarray waveform phase matrix, represents the phase shift weight vector of the optimal phase shifter in the entire array, E = 1 1×N represents a vector of all 1s with a length of N, where N represents the code length of the transmitted signal.

[0049] Beneficial effects of the present invention:

[0050] The space-frequency joint optimization subarray-level broadband digital array radar waveform design method proposed in the present invention innovatively proposes a scheme for designing radar waveforms using digital arrays between subarrays. Specifically: an array structure matrix is ​​generated according to a subarray division method, and a full-array waveform phase matrix represented by a waveform phase matrix between subarrays and a phase shift weight vector of a phase shifter in the entire array is constructed according to the array structure matrix to achieve decomposition of the entire array, and the problem is converted into a solution to the waveform phase matrix between subarrays and the phase shift weight vector of the phase shifter in the entire array. At the same time, an objective function that minimizes the pattern deviation and the power spectrum deviation is constructed by alternately optimizing the solution using the conjugate gradient method, and the pattern and the power spectrum are fitted by optimizing the design of the phase matrix of the transmitted waveform, so as to obtain the optimal waveform phase matrix between subarrays and the optimal phase shift weight vector of the optimal phase shifter in the entire array to design the output radar waveform. It can be seen that the method proposed in the present invention makes full use of the degrees of freedom of the sub-array-level digital array, realizes the matching of the spatial pattern and the frequency domain power spectrum, dynamically plans the distribution form of the transmitted energy from the two aspects of spatial and frequency domains, and manages the distribution of electromagnetic energy of the broadband radar in the spatial and frequency domains, so that it can realize the design of diverse patterns and power spectra like digital array radars, and reduce the array cost.

[0051] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a flow chart of a method for designing a waveform of a wideband digital array radar at a subarray level by joint optimization of space and frequency provided by an embodiment of the present invention;

[0053] Figure 2 It is a schematic diagram of a convergence curve obtained by alternately optimizing and solving an objective function using a conjugate gradient method provided in an embodiment of the present invention;

[0054] Figure 3 is a schematic diagram of comparison between an actual directional pattern after convergence and an expected directional pattern provided by an embodiment of the present invention;

[0055] Figure 4 It is a schematic diagram of comparison between the power spectrum at the actual main beam after convergence and the power spectrum at the expected main beam provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0056] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0057] See also Figure 1 The embodiment of the present invention provides a space-frequency joint optimization subarray-level broadband digital array radar waveform design method, which specifically includes the following steps:

[0058] S10, generating an array structure matrix according to a division method of sub-phased arrays in the entire array.

[0059] In the embodiment of the present invention, the subarray of the subarray-level digital array radar is a phased array inside, emitting coherent waveforms; the subarrays are digital array radars emitting different waveforms. The entire array is divided into a number of sub-phased arrays, and the generated array structure matrix is ​​different according to the different sub-array division methods. If the division method of the sub-phased arrays in the entire array is uniform division, the generated array structure matrix formula is expressed as:

[0060]

[0061] Where T represents the array structure matrix, T is M×m dimensional, I m represents the identity matrix of dimension m, represents the Kronecker product, 1 (M / m)×1 represents an all-one vector of length M / m, where M represents the total number of array elements in the entire array and m represents the number of sub-phased arrays.

[0062] If the sub-phased arrays in the whole array are divided in a non-uniform way, the corresponding array structure matrix is ​​generated according to the actual sub-phased array division method. For example, if three sub-phased arrays are divided in an uneven way, and the three sub-phased arrays include 3, 5, and 6 array elements respectively, the array structure matrix generated according to the uneven division method is expressed as:

[0063]

[0064] S20. According to the array structure matrix, construct a full-array waveform phase matrix represented by the inter-sub-array waveform phase matrix and the phase shift weight vector of the phase shifter in the full array.

[0065] When transmitting a sub-array digital array radar waveform, if the total number of array elements is M, it is evenly divided into m sub-phased arrays, and the code length of the transmitted signal is N, let E = 1 1×N , the phase shift weight vector of the phase shifter in the entire array is Then the full array waveform phase matrix represented by the inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the full array is expressed as:

[0066]

[0067] Among them, Φ represents the waveform phase matrix of the entire array, T represents the array structure matrix, Φ′ represents the waveform phase matrix between sub-arrays, represents the phase shift weight vector of the phase shifters in the entire array, represents the phase shift weight of the sth phase shifter in the entire array, E = 1 1×N represents an all-1 vector of length N, M represents the total number of array elements in the array, and N represents the code length of the transmitted signal.

[0068] S30. Construct an objective function that minimizes the pattern deviation and the power spectrum deviation based on the expected pattern, the actual pattern, and the expected power spectrum and the actual power spectrum at the main beam; wherein the pattern deviation is calculated based on the expected pattern and the actual pattern, and the power spectrum deviation is calculated based on the expected power spectrum and the actual power spectrum.

[0069] The embodiment of the present invention selects to construct an objective function that minimizes the pattern deviation and the power spectrum deviation based on the expected pattern, the actual pattern, and the expected power spectrum and the actual power spectrum at the main beam, and the formula is expressed as follows:

[0070]

[0071] Where Φ represents the phase matrix of the full array waveform, α(Φ) represents the scale factor, L represents the number of sub-band frequency points of the broadband signal, K represents the number of grid points in the azimuth angle, and θ k represents the kth azimuth, w k Indicates that in θ k The pattern matching weight at , I represents the number of main beams, P(θ k ,Φ) indicates that in θ k The actual direction diagram at P d (θ k ) indicates that in θ k The expected directivity at , μ represents the ratio of the directivity error term to the power spectrum error term, μ ≥ 0, for example, in the experiment, μ = 1, represents the i-th main beam pointing angle, Indicated in The weight of the power spectrum at the nth frequency point, Indicated in The actual power spectrum of the nth frequency point at d in Indicated in The expected power spectrum at the nth frequency point;

[0072] Among them, the scale factor α(Φ) is updated in real time during the process of using the conjugate gradient method to alternately optimize and solve the objective function, and the formula is expressed as:

[0073]

[0074] in, λ1 and λ2 represent balance factors, and their values ​​are both greater than 0, for example, λ1=1, λ2=1.

[0075] To find the expression for the gradient, make the following substitution:

[0076] f k (Φ) = P(θ k ,Φ)-α(Φ)P d (θ k ) (5);

[0077]

[0078] Then f k (Φ) and h in The gradient of (Φ) can be expressed as:

[0079]

[0080] in,

[0081]

[0082] At this point, the expression for the objective function gradient can be written as:

[0083]

[0084] in,

[0085]

[0086] Among them, a n (θ k ), Respectively represent the nth frequency point θ k and Direction of the steering vector, X = e jΦ represents the transmitted signal matrix, i.e. the output radar waveform to be determined, f n =[1,e -j2πn / N ,…,e -j2πn(N-1) / N ] T , Im represents the operation of taking the imaginary part. At this point, the gradient of the objective function to the phase matrix of the entire array waveform can be obtained, that is, the conjugate gradient method can be used to solve the minimum point of the objective function.

[0087] Furthermore, combined with formula (2), according to the chain derivation rule of matrix functions, it can be seen that the gradient of the objective function with respect to the waveform phase matrix between sub-arrays and the phase shift weight vector of the phase shifter in the entire array can be expressed as:

[0088]

[0089] in, represents the gradient, T T represents the transpose operation of T, E T Represents the transpose operation on E.

[0090] S40, taking the inter-sub-array waveform phase matrix and the phase shift weight vector of the phase shifter in the whole array as parameters to be determined, using the conjugate gradient method to alternately optimize and solve the objective function, so as to obtain the optimal inter-sub-array waveform phase matrix and the optimal phase shift weight vector of the phase shifter in the whole array.

[0091] Based on the construction of the S30 objective function and the theory of finding the gradient of the objective function, the waveform phase matrix between sub-arrays and the phase shift weight vector of the phase shifter in the entire array are taken as the parameters to be determined in turn, and the conjugate gradient method is used to alternately optimize and solve the objective function to obtain the optimal waveform phase matrix between sub-arrays and the optimal phase shift weight vector of the phase shifter in the entire array, including:

[0092] The inter-subarray waveform phase matrix is ​​used as a parameter to be determined, and the execution steps include: initializing the inter-subarray waveform phase matrix, the phase shift weight vector of the phase shifter in the whole array, and initializing the number of iterations; calculating the first gradient value of the objective function with respect to the inter-subarray waveform phase matrix according to the initialized inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the whole array; judging whether it is the first iteration, if so, directly resetting the first search direction according to the first gradient value, if not, calculating the first correction coefficient of the first search direction according to the first gradient value, and resetting the first search direction according to the first gradient value, the first correction coefficient and the first search direction set in the last iteration; using a one-dimensional linear The search method determines a first search step length; updates the inter-subarray waveform phase matrix according to the first search step length and the reset first search direction; determines whether the updated inter-subarray waveform phase matrix satisfies a first iteration stop condition; if so, uses the updated inter-subarray waveform phase matrix as the optimal inter-subarray waveform phase matrix, calculates and records the first objective function value, and initializes the number of iterations; if not, uses the updated inter-subarray waveform phase matrix as the initialized inter-subarray waveform phase matrix, returns the step of calculating the first gradient value of the objective function according to the initialized inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the entire array until the first iteration stop condition is satisfied;

[0093] The phase shift weight vector of the phase shifter in the whole array is taken as the parameter to be determined, and the execution steps include: calculating the second gradient value of the objective function with respect to the phase shift weight vector of the phase shifter in the whole array according to the optimal inter-subarray waveform phase matrix and the initialized phase shift weight vector of the phase shifter in the whole array; judging whether it is the first iteration, if so, directly resetting the second search direction according to the second gradient value; if not, calculating the second correction coefficient of the second search direction according to the second gradient value, and resetting the second search direction according to the second gradient value, the second correction coefficient and the second search direction set in the last iteration; determining the second search step length by using a one-dimensional linear search method; determining the second search step length according to the second search step length and The reset second search direction updates the phase shift weight vector of the phase shifter in the whole array; determines whether the updated phase shift weight vector of the phase shifter in the whole array satisfies the second iteration stop condition; if so, uses the updated phase shift weight vector of the phase shifter in the whole array as the optimal phase shift weight vector of the phase shifter in the whole array, calculates and records the second objective function value; if not, uses the updated phase shift weight vector of the phase shifter in the whole array as the initialized phase shift weight vector of the phase shifter in the whole array, returns to the step of calculating the second gradient value of the objective function according to the optimal inter-subarray waveform phase matrix and the initialized phase shift weight vector of the phase shifter in the whole array until the second iteration stop condition is satisfied;

[0094] Calculate the difference between the first objective function value and the second objective function value, and determine whether the difference satisfies the third iteration stop condition. If so, output the optimal inter-subarray waveform phase matrix and the optimal phase shift weight vector of the phase shifter in the entire array. If not, use the optimal inter-subarray waveform phase matrix and the optimal phase shift weight vector of the phase shifter in the entire array as the initialized inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the entire array, respectively, and initialize the number of iterations. Return to the step of calculating the first gradient value of the objective function according to the initialized inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the entire array until the third iteration stop condition is met. More specifically:

[0095] S401, initialize the phase matrix of the sub-phased array wave to Φ′ (0) , the phase shift weight vector of the phase shifter in the whole array is Initialization can be performed in a random manner, with the initial number of iterations k set to 0;

[0096] S402: If k=0, calculate the first gradient value of the phase matrix of the waveform between sub-arrays. Set the first search direction

[0097] S403: If k≠0, that is, k≥1, calculate the first gradient value of the phase matrix of the waveform between sub-arrays. Calculate the first correction coefficient of the first search direction at the kth iteration: Among them, β Φ′(k) represents the first correction coefficient for the first search direction, represents the first gradient value of the inter-subarray waveform phase matrix at the kth iteration, represents the first gradient value of the phase matrix of the waveform between sub-arrays at the k-1th iteration, Tr represents the trace operation, Express The transpose operation, Express Transpose operation; set the first search direction to in, represents the first search direction of the kth iteration, represents the first search direction of the k-1th iteration;

[0098] S404: Determine the first search step length using a one-dimensional linear search method And update the phase matrix Among them, Φ′ (k+1) represents the inter-subarray waveform phase matrix of the k+1th iteration, Φ′ (k) represents the inter-subarray waveform phase matrix of the kth iteration, represents the first search step size of the kth iteration;

[0099] S405: Determine the iteration stop condition Is it established? Express Find the F norm, ε0 is a small positive number, such as ε0 = 1. If it does not hold, set k = k + 1 and jump to S402. At this time, the sub-array waveform phase matrix updated by the current iteration is used as the initialized sub-array waveform phase matrix, and the phase shift weight vector of the phase shifter in the entire array is initialized. remains unchanged. If it holds, the inter-sub-array waveform phase matrix of the current iteration is taken as the optimal inter-sub-array waveform phase matrix, denoted as Φ′ opt , calculate and record the current first objective function value f1, and set the number of iterations k = 0;

[0100] S406: If k=0, according to the optimal sub-array waveform phase matrix Φ′ opt , the phase shift weight vector of the phase shifters in the entire array initialized Calculate the second gradient value of the phase shift weight vector of the phase shifter in the whole array At this time, set the search direction

[0101] S407: If k≠0, that is, k≥1, calculate the second gradient value of the phase shift weight vector of the phase shifters in the entire array. Calculate the second correction coefficient for the kth second search direction: in, represents the second correction coefficient of the second search direction of the kth iteration, represents the second gradient value of the phase shift weight vector of the phase shifter in the entire array at the kth iteration, represents the second gradient value of the phase shift weight vector of the phase shifter in the entire array at the k-1th iteration, Tr represents the tracking operation, Express The transpose operation, Express Transpose operation; set the second search direction to: represents the second search direction of the k-th iteration, represents the second search direction of the k-1th iteration;

[0102] S408: Determine the second search step length using a one-dimensional linear search method And update the phase matrix in, represents the phase shift weight vector of the phase shifters in the entire array at the k+1th iteration, represents the phase shift weight vector of the phase shifters in the entire array at the kth iteration, represents the second search step length of the kth iteration;

[0103] S409: Determine the second iteration stop condition Is it established? Express Calculate the F norm. If it does not hold, set k = k + 1 and jump to S406. At this time, the optimal phase shift weight vector of the phase shifter in the entire array updated by the current iteration is used as the optimal phase shift weight vector of the phase shifter in the entire array to be initialized. The waveform phase matrix Φ′ between sub-arrays opt remains unchanged. If it holds, the optimal phase shift weight vector of the phase shifter in the entire array updated by the current iteration is taken as the optimal phase shift weight vector of the optimal phase shifter in the entire array, recorded as Calculate and record the current second objective function value f2;

[0104] S410, determine whether the third iteration stop condition |f1-f2|≤ε1 is established, ε1 is a small positive number, such as ε1=1, if established, then end, output the optimal sub-array waveform phase matrix Φ′ opt , the optimal phase shift weight vector of the optimal phase shifter in the entire array If not, set k = 0 and jump to S402, at which time the optimal sub-array waveform phase matrix Φ′ is opt , the optimal phase shift weight vector of the optimal phase shifter in the entire array They are used as the initialization parameters for the waveform phase matrix between sub-arrays and the phase shift weight vector of the phase shifter in the entire array, respectively. A new round of optimization is carried out with the waveform phase matrix between sub-arrays and the phase shift weight vector of the phase shifter in the entire array as the parameters to be determined, and the conjugate gradient method is used to alternately optimize and solve the objective function until |f1-f2|≤ε1 is satisfied.

[0105] S50, designing an output radar waveform according to an optimal inter-subarray waveform phase matrix and an optimal phase shift weight vector of an optimal phase shifter within the entire array.

[0106] The optimal inter-subarray waveform phase matrix Φ′ obtained based on S40 opt , the optimal phase shift weight vector of the optimal phase shifter in the entire array The radar waveform finally designed and output by the embodiment of the present invention is expressed as follows:

[0107]

[0108] Among them, X opt represents the radar waveform of the designed output, T represents the array structure matrix, Φ′ opt represents the optimal inter-subarray waveform phase matrix, represents the phase shift weight vector of the optimal phase shifter in the entire array, E = 1 1×N represents a vector of all 1s with a length of N, where N represents the code length of the transmitted signal and j represents the imaginary unit.

[0109] In order to verify the effectiveness of the space-frequency joint optimization subarray-level wideband digital array radar waveform design method provided in the embodiment of the present invention, the following experiment is performed for verification.

[0110] The array element parameters and beam settings during the experiment are shown in Table 1.

[0111] Table 1 Array element parameters and beam settings

[0112] Number of array elements 48 Number of subarrays 6 Carrier frequency 10GHz bandwidth 500MHz Quick sort number 200 Beam 1 pointing / power spectrum range constraints -40° / -80MHz~80MHz Beam 2 pointing / power spectrum range constraints 0° / -250MHz~90MHz Beam 3 pointing / power spectrum range constraints 40° / 90MHz 250MHz

[0113] The experimental results are as follows Figure 2 , Figure 3 , Figure 4 As shown. Figure 2 It can be seen that: using the method proposed in the present invention, the objective function value decreases from 86091.6 to 6052.43 with iteration, and converges after 220 iterations. Figure 3 It can be seen that after convergence, the actual directional pattern designed by the method proposed in the present invention achieves a good match with the expected directional pattern. Figure 4 It can be seen that after convergence, the designed power spectrum at the actual main beam (-40°, 0°, 40°) using the method proposed in the present invention achieves a good fit with the power spectrum at the expected main beam.

[0114] In summary, the space-frequency joint optimization subarray-level broadband digital array radar waveform design method proposed in the embodiment of the present invention innovatively proposes a scheme for designing radar waveforms using inter-subarray digital arrays. Specifically, an array structure matrix is ​​generated according to the subarray division method, and a full-array waveform phase matrix represented by an inter-subarray waveform phase matrix and a phase shift weight vector of a phase shifter in the entire array is constructed according to the array structure matrix to achieve decomposition of the entire array, and the problem is converted into a solution for the inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the entire array. At the same time, it is proposed to use the conjugate gradient method to alternately optimize and solve the objective function that minimizes the pattern deviation and the power spectrum deviation, and the pattern and power spectrum are fitted by optimizing the design of the phase matrix of the transmitted waveform, so as to solve the optimal inter-subarray waveform phase matrix and the optimal phase shift weight vector of the optimal phase shifter in the entire array to design the output radar waveform. It can be seen that the method proposed in the present invention makes full use of the degrees of freedom of the sub-array-level digital array, realizes the matching of the spatial pattern and the frequency domain power spectrum, dynamically plans the distribution form of the transmitted energy from the two aspects of spatial and frequency domains, and manages the distribution of electromagnetic energy of the broadband radar in the spatial and frequency domains, so that it can realize the design of diverse patterns and power spectra like digital array radars, and reduce the array cost.

[0115] In the description of the present invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0116] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art may understand and implement other variations of the disclosed embodiments by viewing the specification and its drawings. In the specification, the word "comprising" does not exclude other components or steps, and "a" or "one" does not exclude multiple situations. Certain measures are recorded in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0117] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A space-frequency joint optimization subarray-level broadband digital array radar waveform design method, characterized in that: The method comprises: Generate an array structure matrix according to the division method of sub-phased arrays in the whole array; According to the array structure matrix, constructing a full array waveform phase matrix represented by the inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the full array; According to the expected directional pattern, the actual directional pattern, and the expected power spectrum and the actual power spectrum at the main beam, an objective function is constructed to minimize the directional pattern deviation and the power spectrum deviation; wherein the directional pattern deviation is calculated according to the expected directional pattern and the actual directional pattern, and the power spectrum deviation is calculated according to the expected power spectrum and the actual power spectrum; The inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the entire array are sequentially used as parameters to be determined, and the objective function is alternately optimized and solved using the conjugate gradient method to obtain the optimal inter-subarray waveform phase matrix and the optimal phase shift weight vector of the phase shifter in the entire array; The output radar waveform is designed according to the optimal inter-subarray waveform phase matrix and the optimal phase shift weight vector of the optimal full-array intra-phase shifter.

2. The space-frequency joint optimization subarray-level broadband digital array radar waveform design method according to claim 1 is characterized in that: If the sub-phased arrays in the entire array are divided evenly, the generated array structure matrix formula is expressed as: Where T represents the array structure matrix, I m represents the identity matrix of dimension m, represents the Kronecker product, 1 (M / m)×1 represents an all-one vector of length M / m, where M represents the total number of array elements in the entire array and m represents the number of sub-phased arrays.

3. The space-frequency joint optimization subarray-level broadband digital array radar waveform design method according to claim 1 is characterized in that: The constructed full array waveform phase matrix formula is expressed as: Among them, Φ represents the waveform phase matrix of the entire array, T represents the array structure matrix, Φ′ represents the waveform phase matrix between sub-arrays, represents the phase shift weight vector of the phase shifters in the entire array, represents the phase shift weight of the sth phase shifter in the entire array, E = 1 1×N represents an all-1 vector of length N, M represents the total number of array elements in the array, and N represents the code length of the transmitted signal.

4. The space-frequency joint optimization subarray-level broadband digital array radar waveform design method according to claim 1 is characterized in that: The objective function constructed to minimize the pattern deviation and power spectrum deviation is expressed as follows: Where Φ represents the phase matrix of the full array waveform, α(Φ) represents the scale factor, L represents the number of sub-band frequency points of the broadband signal, K represents the number of grid points in the azimuth angle, and θ k represents the kth azimuth, w k Indicates that in θ k The pattern matching weight at , I represents the number of main beams, P(θ k ,Φ) indicates that in θ k The actual direction diagram at P d (θ k ) indicates that in θ k The desired directivity pattern at , μ represents the ratio of the directivity pattern error term to the power spectrum error term, represents the i-th main beam pointing angle, Indicated in The weight of the power spectrum at the nth frequency point, Indicated in The actual power spectrum of the nth frequency point at d in Indicated in The expected power spectrum of the nth frequency point at which the scale factor α is solved is updated in real time during the process of using the conjugate gradient method to alternately optimize the objective function.

5. The space-frequency joint optimization subarray-level broadband digital array radar waveform design method according to claim 4 is characterized in that: When the scale factor α(Φ) is updated in real time, the formula is expressed as: in, λ1 and λ2 represent balance factors.

6. The space-frequency joint optimization subarray-level broadband digital array radar waveform design method according to claim 1 is characterized in that: The inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the entire array are respectively taken as parameters to be determined, and the objective function is solved by alternate optimization using the conjugate gradient method to obtain the optimal inter-subarray waveform phase matrix and the optimal phase shift weight vector of the phase shifter in the entire array, including: The inter-subarray waveform phase matrix is ​​used as a parameter to be determined, and the execution steps include: initializing the inter-subarray waveform phase matrix, the phase shift weight vector of the phase shifter in the whole array, and initializing the number of iterations; calculating the first gradient value of the objective function with respect to the inter-subarray waveform phase matrix according to the initialized inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the whole array; judging whether it is the first iteration, if so, directly resetting the first search direction according to the first gradient value; if not, calculating the first correction coefficient of the first search direction according to the first gradient value, and resetting the first search direction according to the first gradient value, the first correction coefficient and the first search direction set in the last iteration; using a The method comprises the following steps: determining a first search step length by a dimensional linear search method; updating an inter-subarray waveform phase matrix according to the first search step length and the reset first search direction; judging whether the updated inter-subarray waveform phase matrix satisfies a first iteration stop condition; if so, taking the updated inter-subarray waveform phase matrix as the optimal inter-subarray waveform phase matrix, calculating and recording a first objective function value, and initializing the number of iterations; if not, taking the updated inter-subarray waveform phase matrix as the initialized inter-subarray waveform phase matrix, returning the step of calculating a first gradient value of the objective function according to the initialized inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the entire array until the first iteration stop condition is satisfied; The phase shift weight vector of the phase shifter in the whole array is taken as the parameter to be determined, and the execution steps include: calculating the second gradient value of the objective function with respect to the phase shift weight vector of the phase shifter in the whole array according to the optimal inter-subarray waveform phase matrix and the initialized phase shift weight vector of the phase shifter in the whole array; judging whether it is the first iteration, if so, directly resetting the second search direction according to the second gradient value; if not, calculating the second correction coefficient of the second search direction according to the second gradient value, and resetting the second search direction according to the second gradient value, the second correction coefficient and the second search direction set in the last iteration; determining the second search step length by using a one-dimensional linear search method; determining the second search step length according to the second The phase shift weight vector of the phase shifter in the whole array is updated according to the search step size and the reset second search direction; whether the updated phase shift weight vector of the phase shifter in the whole array satisfies the second iteration stop condition is determined; if so, the updated phase shift weight vector of the phase shifter in the whole array is used as the optimal phase shift weight vector of the phase shifter in the whole array, and the second objective function value is calculated and recorded; if not, the updated phase shift weight vector of the phase shifter in the whole array is used as the initialized phase shift weight vector of the phase shifter in the whole array, and the step of calculating the second gradient value of the objective function according to the optimal inter-subarray waveform phase matrix and the initialized phase shift weight vector of the phase shifter in the whole array is returned until the second iteration stop condition is satisfied; The difference between the first objective function value and the second objective function value is calculated, and it is determined whether the difference satisfies a third iteration stop condition. If so, the optimal inter-subarray waveform phase matrix and the optimal phase shift weight vector of the phase shifter in the entire array are output; if not, the optimal inter-subarray waveform phase matrix and the optimal phase shift weight vector of the phase shifter in the entire array are used as the initialized inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the entire array, respectively, and the number of iterations is initialized. The step of calculating the first gradient value of the objective function according to the initialized inter-subarray waveform phase matrix and the phase shift weight vector of the phase shifter in the entire array is returned until the third iteration stop condition is satisfied.

7. The space-frequency joint optimization subarray-level broadband digital array radar waveform design method according to claim 6 is characterized in that: The first correction coefficient of the first search direction is calculated according to the first gradient value, and the formula is expressed as: Among them, β Φ′ (k) represents the first correction coefficient for the first search direction, represents the first gradient value of the inter-subarray waveform phase matrix at the kth iteration, represents the first gradient value of the phase matrix of the waveform between sub-arrays at the k-1th iteration, Tr represents the tracing operation, Express The transpose operation, Express The transpose operation of The first search direction is reset according to the first gradient value, the first correction coefficient and the first search direction set in the last iteration, and the formula is expressed as: in, represents the first search direction of the kth iteration, β Φ′ (k) represents the first correction coefficient of the kth iteration, represents the first search direction of the k-1th iteration; The inter-subarray waveform phase matrix is ​​updated according to the first search step size and the reset first search direction, and the formula is expressed as: Among them, Φ′ (k+1) represents the inter-subarray waveform phase matrix of the k+1th iteration, Φ′ (k) represents the inter-subarray waveform phase matrix of the kth iteration, represents the first search step size of the kth iteration.

8. The space-frequency joint optimization subarray-level broadband digital array radar waveform design method according to claim 6 is characterized in that: The second correction coefficient of the second search direction is calculated according to the second gradient value, and the formula is expressed as: in, represents the second correction coefficient of the second search direction of the kth iteration, represents the second gradient value of the phase shift weight vector of the phase shifter in the entire array at the kth iteration, represents the second gradient value of the phase shift weight vector of the phase shifter in the entire array at the k-1th iteration, Tr represents the tracking operation, Express The transpose operation, Express The transpose operation of The second search direction is reset according to the second gradient value, the second correction coefficient and the second search direction set in the last iteration, and the formula is expressed as: in, represents the second search direction of the k-th iteration, represents the second correction coefficient of the kth iteration, represents the second search direction of the k-1th iteration; The inter-subarray waveform phase matrix is ​​updated according to the second search step size and the reset second search direction, and the formula is expressed as: in, represents the phase shift weight vector of the phase shifters in the entire array at the k+1th iteration, represents the phase shift weight vector of the phase shifters in the entire array at the kth iteration, represents the second search step size of the kth iteration.

9. The space-frequency joint optimization subarray-level broadband digital array radar waveform design method according to claim 1 is characterized in that: The radar waveform of the designed output is expressed as follows: Among them, X opt represents the radar waveform of the designed output, T represents the array structure matrix, Φ′ opt represents the optimal inter-subarray waveform phase matrix, represents the phase shift weight vector of the optimal phase shifter in the entire array, E = 1 1×N represents a vector of all 1s with a length of N, where N represents the code length of the transmitted signal.

Images