CN113656747B - Array self-adaptive wave beam forming method under multiple expected signals based on branch delimitation - Google Patents
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Abstract
The invention discloses an array self-adaptive wave beam forming method under a plurality of expected signals based on branch delimitation, which comprises the following steps: maximizing the output signal-to-interference-and-noise ratio, and simultaneously adopting a linear division type semi-positive fixed relaxation method to reduce the side lobe level of the array beam; introducing a complex auxiliary variable, optimizing the phase of response under the condition of keeping the amplitude of the array response of the expected signals unchanged, and solving the planning problem of the full array by using a branch-and-bound algorithm to realize the full array self-adaptive beam forming under the multiple expected signals; and (3) introducing iterative re-weighting l 1 norm to punish the weight vector of the array, and solving the planning problem of the sparse array by using a branch-and-bound algorithm to realize the sparse array self-adaptive beam forming under multiple expected signals. The invention improves the pattern performance of full array and sparse array under multiple expected signals, reduces the side lobe level, improves the output signal-to-interference-and-noise ratio of the array, and reduces the pattern amplitude error of the multiple expected signals.
Description
Technical Field
The invention belongs to the field of modern electronic system design, and particularly relates to an array self-adaptive beam forming method under multiple expected signals based on branch delimitation.
Background
In radar and communication electronic systems, in order to make the antenna beam have strong directivity, low side lobe and easy to realize electric scanning and beam forming, array antennas have been widely used, so the optimal design of the array antennas is also an important link in the design of modern electronic systems. However, the development cost of the large two-dimensional solid-state active phased array radar is high, the cost of the antenna array is approximately proportional to the total number of array elements, in a uniform structure, the total number of array elements N is proportional to the caliber length L of the array, and the main lobe width HP=51° lambda/L (lambda represents the wavelength) of the antenna array. When the antenna is required to have high angular resolution, the array caliber length L is relatively large, so that the number N of array elements required for uniform array is relatively large, which greatly increases the design cost and the manufacturing cost of the array antenna system. Meanwhile, in order to avoid grating lobes in a visible area of the directional diagram, the interval d of adjacent elements of the uniform line array is required to be less than or equal to lambda/(1+|sin theta|) (d is less than or equal to lambda/2 in end shooting), and the defects caused by the method are that: the mutual coupling between adjacent elements is strong. The coupling between two identical array elements is defined as C mn＝sin(kdmn)/(kdmn), where d mn is the distance between array elements m and n and k is a constant. From this, it can be seen that the coupling coefficient fluctuates with the size of the interval d mn between the array elements, and the envelope of the coupling coefficient decreases directly with the increase of the distance. In practical engineering, the antenna structure is fixed, when the array works at low frequency, the radiation wavelength is relatively large, so that a large mutual coupling effect exists between array elements due to a small electric length, the gain, the beam width and other electric parameters of the antenna array are influenced to a certain extent, and the amplitude and the phase of the antenna array signals are changed, so that the signal processing performance of the antenna array is seriously influenced. Thus, sparse arrays have evolved.
The sparse array antenna is widely applied to military fields such as missile guidance, airborne early warning, precise tracking measurement, high-frequency ground radars, anti-interference satellite receiving antennas and the like, and civil fields such as air traffic control, airport foreign matter detection, weather forecast, radio astronomy and the like. Compared with the traditional uniformly-arranged array, the array can realize narrow wave beams and high resolution by using as few array elements as possible, thereby reducing the production cost and daily maintenance cost of the array antenna and reducing the complexity and failure rate of a feed system. In the field of mobile communication, by using a sparse algorithm, under the condition of not losing the performance of a target pattern, some array elements which are not used for synthesizing the target pattern are closed, so that the aim of saving precious resources (power supply) in mobile communication is fulfilled, and a good compromise can be reached between the performance of the target pattern and the number of the used array elements (power supply), which has important value for mobile communication. Meanwhile, as the array element distance of the sparse array is increased, the coupling between adjacent elements is smaller, the performance reduction caused by mutual coupling can be effectively reduced, and each performance index of the array is close to an ideal value to the greatest extent.
Although the gain of a sparse array may be reduced compared to a homogeneous array, in many practical engineering applications, only a narrow scanned beam is required for the antenna, no corresponding gain is required, and when multiple desired signals are present in the environment, the beams of the full and sparse arrays have amplitude errors in the desired signal direction, and the side lobe level is higher.
Disclosure of Invention
The invention aims to provide an adaptive beam forming method for reducing the amplitude error and side lobe level of multiple expected signals of an array radiation pattern based on a branch-and-bound algorithm.
The technical solution for realizing the purpose of the invention is as follows: an array adaptive beamforming technique under multiple desired signals, comprising the steps of:
step 1, maximizing output signal-to-interference-and-noise ratio, and simultaneously adopting a linear division type semi-normal relaxation method to reduce the side lobe level of an array beam;
Step 2, introducing complex auxiliary variables, optimizing the phase of response under the condition of keeping the amplitude of the array response of the expected signals unchanged, and solving the planning problem of the full array by using a branch-and-bound algorithm to realize the full array self-adaptive beam forming under the condition of multiple expected signals;
And 3, introducing iteration re-weighting l 1 norm to punish the weight vector of the array, and solving the planning problem of the sparse array by using a branch-and-bound algorithm to realize the sparse array self-adaptive beam forming under multiple expected signals.
Compared with the prior art, the invention has the remarkable advantages that: (1) The linear partial semi-positive relaxation method and the introduced auxiliary variable are utilized to optimize the phase of the array response of the expected signal, so that the signal-to-interference-plus-noise ratio of the array output is larger, and the side lobe level of the directional diagram is lower; (2) When there are a plurality of desired signals and a plurality of interference signals in the environment, the directional deviation of the desired signals is reduced.
Drawings
Fig. 1 is a flow chart of the present invention for solving the problem of full array adaptive beamforming using a branch-and-bound algorithm.
Fig. 2 is a full array radiation pattern for multiple desired signals in an embodiment of the invention.
Fig. 3 is a sparse array radiation pattern for multiple desired signals in an embodiment of the invention.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples.
The method comprises the steps of firstly, forming deep nulls in the interference direction by beams of a full array through maximizing output signal-to-interference-and-noise ratio, enabling the expected direction to have high gain, and reducing the side lobe level of the beams of the array by adopting a linear division type semi-positive relaxation method; then introducing complex auxiliary variables, keeping the amplitude of the array response of the expected signals unchanged, and optimizing the phase of the array response; finally, the planning problem is solved by using a branch-and-bound algorithm. On the basis, the modified heavy weighting l 1 norm is introduced to punish the weight vector of the array, so that the sparseness of the array is realized. The invention improves the pattern performance of full array and sparse array under multiple expected signals, reduces the side lobe level, improves the output signal-to-interference-and-noise ratio of the array, and reduces the pattern pointing error of the multiple expected signals.
Referring to fig. 1 to 3, the array adaptive beamforming method under multiple expected signals based on branch-and-bound according to the present invention comprises the following steps:
step 1, maximizing output signal-to-interference-and-noise ratio, and simultaneously adopting a linear division type semi-normal relaxation method to reduce the side lobe level of an array beam;
Step 2, introducing complex auxiliary variables, optimizing the phase of response under the condition of keeping the amplitude of the array response of the expected signals unchanged, and solving the planning problem of the full array by using a branch-and-bound algorithm to realize the full array self-adaptive beam forming under the condition of multiple expected signals;
And 3, introducing iteration re-weighting l 1 norm to punish the weight vector of the array, and solving the planning problem of the sparse array by using a branch-and-bound algorithm to realize the sparse array self-adaptive beam forming under multiple expected signals.
Further, the maximizing of the output signal-to-interference-and-noise ratio in step 1 enables the full array beam to form deep nulls in the interference direction and have high gain in the expected direction, and meanwhile adopts the linear division type semi-positive relaxation method to reduce the side lobe level of the array beam, which is as follows:
step 1.1, converting a Capon algorithm based on a maximum signal-to-interference-and-noise ratio (MSINR) criterion into a convex optimization problem;
MSINR aims to maximize the output signal-to-interference-and-noise ratio of the system, i.e
Wherein W is a weight, and R S and R i+n respectively represent a signal covariance matrix and an interference noise covariance matrix;
converting the formula (1) into a convex optimization problem, as shown in the formula (2),
Wherein,The covariance matrix of the Q-th desired signal is represented, Q represents the number of the desired signal, and Q represents the total amount of the desired signal.
Step 1.2, uniformly sampling the side lobe area, wherein H sampling angles are provided, and setting an expected side lobe level delta;
Array gain obtained after uniformly sampling side lobes As shown in the formula (3),
Wherein (-) H represents a conjugate transpose,For array response of side lobe region, f=w H a is array response, a is array manifold vector of each angle of space,/>A S is the array manifold vector of the side lobes and the desired signal, respectively;
the convex optimization problem expression for adding the side lobe constraint condition is shown in (4),
Because ofWherein/>And/>The power and array manifold vector of the q-th desired signal, respectively, so equation (4) is converted to equation (5)
Further, under the condition that the amplitude of the array response of the expected signals is kept unchanged, the phase of the response is optimized, and the planning problem of the full array is solved by using a branch-and-bound algorithm, so that the full array adaptive beam forming under the multi-expected signals is realized, wherein the method comprises the following steps of:
Step 2.1, introducing a complex auxiliary variable v q (q=1, 2, …, Q), the definition of which is shown in formula (6)
Where Θ q is the argument set of the auxiliary variable v q.
Thus, the planning problem (5) can be described as equation (7)
Because problem (6) is a non-convex constraint, it is replaced by its convex hull conv (Θ q) and letThen equation (7) becomes a planning problem (9) that contains only convex constraints, where the convex hull conv (Θ q) is defined as shown in equation (8).
In the method, in the process of the invention,Representing real and imaginary parts.
When (when)When the convex hull coefficients are defined as/>
Wherein,
Step 2.2, combining with fig. 1, solving a problem (9) by using a branch-and-bound algorithm;
the algorithm is as follows:
Input: the calculation of problem (9), error bound ε > 0 and initial argument set
1: Let k=1, solve problem (9), obtain optimal solution v 1 and objective function value L 1, generate feasibility solution
2: Will beSubstituting the problem (9) of removing the convex envelope constraint condition to obtain an objective function value U= (w 1)HRi+nw1 and an optimal weight w) 1
3: Constructing an active node set D, and connecting nodesInsertion D
4：while(1)
5: Selecting an active node in DWherein L K is the smallest term in the K-th node of D
6: Deleting the selected node from D
7: If U-L K < ε, then
Return toAnd w K, algorithm termination
end if
8: Update k=k+1
9: Calculation ofAnd adopt the radial angle segmentation strategy to carry out/>Equally divided into two subintervals/>AndObtain subset/>And/>
10: Solution (9)Obtain the optimal solution/>And objective function value/>Generating a feasibility solution ]And will beSubstituting the problem (9) of removing the convex envelope constraint condition to obtain the objective function value/>Sum weight/>
11：Then
Return to
end if
12：Then
Node is connected withInsertion D
end if
13: Solution (9)Obtain the optimal solution/>And objective function value/>Generating a feasibility solution ]And will/>Substituting the problem (9) of removing the convex envelope constraint condition to obtain the objective function value/>Sum weight/>
14：Then
Return to
end if
15：Then
Node is connected withInsertion D
end if
16：end while
Further, in the step 3, an iterative re-weighting l 1 norm is introduced to punish the weight vector of the array, and a branch-and-bound algorithm is used to solve the planning problem of the sparse array, so as to realize the adaptive beamforming of the sparse array under multiple expected signals, which is specifically as follows:
and 3.1, modifying the weighted l 1 norm and punishing the array weight vector, wherein the expression (9) can be changed into the expression (10).
Wherein μ is a sparse coefficient, and Z is a weighting factor, defined as formula (11). ζ is a minimum value to avoid dividing by zero and trapping in the partial solution.
Step 3.2, in connection with fig. 1, the problem (10) is solved by means of a branch-and-bound algorithm.
Example 1
The embodiment provides an array adaptive beam forming technology under multiple expected signals based on a branch-and-bound algorithm, which firstly assumes that a 16-element uniform linear array exists, and the unit interval is half wavelength. Three expected signals exist in the space, two interference signals are respectively in the directions ofAnd/>The signal to noise ratio is set to 0dB and the interference to noise ratio is set to 20dB. The desired side lobe levels are set to-10 dB and-20 dB, respectively.
The simulation results are shown in fig. 2. As can be seen from the result of fig. 2, compared with the direct iteration rank (DIRR) algorithm, the side lobe level of the radiation pattern calculated by the method of the present invention is lower, and the output signal-to-interference-and-noise ratio is higher.
Example 2
The embodiment provides an array self-adaptive beam forming technology under multiple expected signals based on a branch-and-bound algorithm, which firstly assumes that a 16-element uniform linear array exists, the unit spacing is half wavelength, and 8 excitation is selected from 16 array elements. Three expected signals and three interference signals are arranged in the space, the directions are respectively And/>The signal to noise ratio is set to 0dB and the interference to noise ratio is set to 30dB. The desired side lobe level is set to-3.7 dB.
Table 1 levels of desired signals under different methods
As shown in fig. 3, the simulation results of fig. 3 and table 1 show that, compared with other sparse array adaptive beam forming algorithms implemented in complex domain, the side lobe level of the radiation pattern calculated by the method of the present invention is lower, and the amplitude pointing error of the multiple desired signals is smaller.
Claims (3)
1. An array adaptive beamforming method under multiple expected signals based on branch-and-bound, comprising the steps of:
step 1, maximizing output signal-to-interference-and-noise ratio, and simultaneously adopting a linear division type semi-normal relaxation method to reduce the side lobe level of an array beam;
Step 2, introducing complex auxiliary variables, optimizing the phase of response under the condition of keeping the amplitude of the array response of the expected signals unchanged, and solving the planning problem of the full array by using a branch-and-bound algorithm to realize the full array self-adaptive beam forming under the condition of multiple expected signals;
Step 3, introducing iteration re-weighting l 1 norm to punish the weight vector of the array, and solving the planning problem of the sparse array by using a branch-and-bound algorithm to realize the sparse array self-adaptive beam forming under multiple expected signals;
And (2) maximizing the output signal-to-interference-and-noise ratio, and simultaneously reducing the side lobe level of the array beam by adopting a linear division type semi-positive fixed relaxation method, wherein the method comprises the following steps of:
Step 1.1, converting a Capon algorithm based on a maximum signal-to-interference-and-noise ratio MSINR criterion into a convex optimization problem;
MSINR aims to maximize the output signal-to-interference-plus-noise ratio, SINR, of the system, i.e
Wherein W is a weight, and R S and R i+n respectively represent a signal covariance matrix and an interference noise covariance matrix;
converting the formula (1) into a convex optimization problem, as shown in the formula (2),
Wherein,A covariance matrix representing the Q-th desired signal, Q representing the number of the desired signal, and Q representing the total amount of the desired signal;
step 1.2, uniformly sampling the side lobe area, wherein H sampling angles are provided, and setting an expected side lobe level delta;
Array gain obtained after uniformly sampling side lobes As shown in the formula (3),
Wherein (-) H represents a conjugate transpose,For array response of side lobe region, f=w H a is array response, a is array manifold vector of each angle of space,/>A S is the array manifold vector of the side lobes and the desired signal, respectively;
the convex optimization problem expression for adding the side lobe constraint condition is shown in the formula (4),
Because ofWhere q=1, 2, …, Q,/>And/>The power and array manifold vector of the q-th desired signal, respectively, so equation (4) is converted to equation (5)
In the middle ofIndicating the desired signal power.
2. The method for forming an array adaptive beam under multiple expected signals based on branch-and-bound as set forth in claim 1, wherein the complex auxiliary variables introduced in step 2 optimize the phase of the response while maintaining the amplitude of the array response of the expected signals, and solve the problem of planning a full array with a branch-and-bound algorithm to implement full array adaptive beam forming under multiple expected signals, specifically as follows:
Step 2.1, the definition of introducing complex auxiliary variable v q,q＝1,2,…,Q,vq is shown in formula (6):
Wherein Θ q is the argument set of the auxiliary variable v q;
the planning problem formula (5) is described as formula (7):
Formula (6) is a non-convex constraint, and is replaced by its convex envelope conv (Θ q) and let Then equation (7) becomes a programming problem (9) that contains only convex constraints, where the convex hull conv (Θ q) is defined as shown in equation (8):
In the method, in the process of the invention, Representing real and imaginary parts;
When (when) When the convex hull coefficients are defined as/>
Wherein,
And 2.2, solving the planning problem of the formula (9) by utilizing a branch-and-bound algorithm.
3. The method for forming an array adaptive beam under multiple expected signals based on branch-and-bound as set forth in claim 2, wherein the introducing of the iterative re-weighting l 1 norm in step 3 penalizes the weight vector of the array, and solves the planning problem of the sparse array with a branch-and-bound algorithm to realize the sparse array adaptive beam forming under multiple expected signals, specifically as follows:
Step 3.1, modifying the weighted l 1 norm while penalizing the array weight vector, then equation (9) becomes equation (10):
Wherein μ is a sparse coefficient;
z is a weighting factor, defined as formula (11):
Wherein x is a minimum value for avoiding division by zero and trapping in a local solution;
And 3.2, solving the planning problem of the formula (10) by utilizing a branch-and-bound algorithm.
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