CN107544059A - A kind of robust adaptive beamforming method based on diagonal loading technique - Google Patents
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Abstract
The present invention relates to a kind of robust adaptive beamforming method based on diagonal loading technique, comprise the following steps：Calculate the sample covariance matrix R that radar antenna array reception signal is built by the reception signal x (k) of K snap sampling；Using Lagrange operators, the Wave beam forming vector of Capon Beam-formers is tried to achieve；Using diagonal loading technique, the weight vectors w of radar antenna array is calculatedDLI.e. each array element is added with weights；Export the adaptive beam of radar antenna array.
Description
Technical Field
The invention belongs to the field of digital signal processing, and relates to a beam forming technology in the field of array signal processing.
Background
Beamforming is an important research in the field of array signal processing, and is widely applied in the fields of radar, sonar, wireless communication, voice signal processing, medical imaging, seismology, and the like. Among many adaptive beamforming algorithms, Capon beamforming algorithm is popular among researchers because of its advantages of good performance and flexible expression form. However, the standard Capon beamforming algorithm relies on some assumptions about the matrix, signal model, etc., and the performance of the beamformer degrades severely when there is an error in the steering vector. In order to improve the robustness, a plurality of robust adaptive beamforming algorithms based on Capon beamforming algorithms emerge in recent decades.
The diagonal loading beam forming algorithm realizes the correction of the covariance matrix by adding a small loading amount to the sampling covariance matrix, and can achieve the purpose of inhibiting noise beams under the condition of not changing the structure of the characteristic vector of the matrix. The diagonal loading beam forming algorithm is simple, obvious in effect and easy to realize in engineering. The key of the algorithm is the selection of a loading factor, and the loading factor can be usually found by methods such as optimization, iteration and the like. Due to the lack of accurate theoretical guidance, it is difficult to select the optimal loading factor. If the selected loading factor is too small, the norm of the weighting vector will be large, and the noise beam cannot be effectively inhibited; when the weighting factor is too large, the beamformer's ability to suppress interference and reduce noise is impaired, and therefore a compromise is often required in selecting the loading factor.
Disclosure of Invention
The invention aims to provide a beam forming method which can improve the anti-interference performance of the beam forming of an adaptive radar antenna array, resist the mismatching of array steering vectors and has a simple algorithm. The technical scheme of the invention is as follows:
a robust adaptive beam forming method based on a diagonal loading technology comprises the following steps:
the method comprises the following steps: and calculating a sampling covariance matrix R of the receiving signals of the radar antenna array constructed by the receiving signals x (K) sampled by K times of snapshots.
Step two: using Lagrange operator, find the beamforming vector of Capon beamformer as:
wherein,estimated steering vector, R, representing the desired signali+nFor the interference-plus-noise covariance matrix, R is replaced by the sampled covariance matrix R of the received signali+n。
Step three: calculating the weighting vector w of the radar antenna array by adopting a diagonal loading technologyDLNamely, the complex weight of each array element:
wherein the factor is loaded Is the average noise energy.
Step four: and outputting the adaptive beam of the radar antenna array.
The invention has the beneficial effects that:
the invention enhances the robustness of the radar antenna array when the received signal guide vector has errors by carrying out diagonal loading on the covariance matrix of the signals received by the radar antenna array. Meanwhile, the diagonal loading matrix G is set in a specific mode based on the covariance matrix R of the signals received by the radar antenna array, and the loading factor gamma is further avoided from being subjected to complex calculation such as optimization and iteration. The invention can better overcome the performance loss caused by the mismatching of the observation direction and the existence of local coherent scattering to the radar antenna array, and has better robustness.
Drawings
Fig. 1 is a graph of the variation of the signal-to-interference-and-noise ratio output by the radar antenna array with the sampling fast-beat number K in different methods under the observation direction mismatch.
Fig. 2 is a graph of the variation of the output signal-to-interference-and-noise ratio of the radar antenna array with the sampling fast-beat number K in the presence of locally coherent scattering by different methods.
Detailed Description
The method comprises the following steps: calculating a sampling covariance matrix R of a radar antenna array receiving signal:
according to the structural model of the radar antenna array received signals, defining the snapshot model of the radar antenna array received signals with the array element number of N as follows: x (k) ═ s (k) + i (k) + n (k), where s (k) denotes the desired signal, i (k) denotes the interference signal, and n (k) denotes the noise signal. Constructing a covariance matrix of the receiving signals of the sensor array from the receiving signals x (K) sampled by the K times of snapshots:k is the number of sampling snapshots, x (K) is the kth sampling snapshot, (. C)HIs Hermitian (Hermitian) transpose.
Step two: finding the weighting vector w of a Capon beamformerc：
A typical Capon beamformer can be represented as an optimization problem as follows:
using Lagrange operator, the weighting vector of Capon beamformer can be obtained as:
wherein,estimated steering vector, R, representing the desired signali+nIs an interference plus noise covariance matrix. True Ri+nIs known only in simulations, and it is therefore common practice to replace R with a covariance matrix R of K samples of the received signali+n。
Step three: weight vector (i.e. arrangement of complex weights for each array element) w for constructing radar antenna arrayDLExpression (c):
applying diagonal loading techniques to the weighting vector w of a radar antenna arrayDLIn the calculation of (a), further:wherein gamma is a loading factor and G is a diagonal loading matrix.
Step four: constructing a diagonal loading matrix G:
the diagonal loading matrix G constructed in the invention is based on a sampling covariance matrix R, and the specific form is as follows: g ═ R-0.5。
Step five: determining a loading factor gamma:
the loading factor gamma value of the invention adopts a specific mode, is the average noise energy.
Step six: calculating a weighted vector w for a radar antenna arrayDL：
Utilizing the fourth step and the fifth step to obtain the weighting vector w of the radar antenna arrayDLThe specific calculation formula is as follows:
step seven: and finally, carrying out weighted summation on the sampled signal data by using the obtained weighted vector of the radar antenna array to obtain the self-adaptive beam of the radar antenna array as follows:
y(k)＝wDL Hx(k)
the effects of the present invention can be further illustrated by the following simulation experiments.
1. Simulation conditions are as follows:
the radar antenna array model is a uniform linear array with the spacing of half wavelength, the array element number is 10, the number of expected signals is 1, the number of interference signals is 2, the signal-to-noise ratio SNR is-10 dB, the dry-to-noise ratio is 30dB, the two interference signals are respectively incident from 30 degrees and 50 degrees, and the predicted value of the incident angle of the expected signals is 0 degree. The method compares the performance of the output signal-to-interference-and-noise ratio with the following three algorithms which are respectively (1) the traditional diagonal loading algorithmFor convenience, the TDL algorithm is abbreviated; (2) based on the worst case optimized robust adaptive beamforming algorithm (the value of epsilon is 0.3N), which is abbreviated as WCB algorithm; (4) robust adaptive beamforming algorithm based on less prior information (spatial azimuth range of useful signal is [ -5 °,5 ° ])]) Abbreviated here as API algorithm. For reference, the optimal output signal-to-interference-and-noise ratio is also indicated in the simulation plot. Each point in the simulated plot was averaged from the results of 200 monte carlo experiments.
2. Simulation content:
simulation 1: in this experiment, the actual incident angle of the desired signal is 3 ° (i.e., there is an error of 3 ° in the observation direction), and the sampling fast beat number K varies from 10 to 100. Fig. 1 shows the curves of the different methods for the variation of the output signal-to-interference-and-noise ratio of the radar antenna array with the sampling fast beat number K. Wherein, the horizontal axis represents the sampling fast beat number of the received signal of the radar antenna array, and the vertical axis represents the signal-to-interference-and-noise ratio of the output signal of the radar antenna array.
Simulation 2: the actual desired signal steering vector in this experiment consists of 5 coherent signal paths, i.e.Wherein theta is00 ° being the direct path of the desired signal, θiCorresponding to the ith coherent path. Parameter phiiRepresents the phase of the path, which is independent of each other at each simulation run, and is at 0,2 π]The uniform distribution is satisfied in the interval. { theta ]iThe simulation modules are also independent of each other in each simulation operation and are at the angles of-5 degrees and 5 degrees]The uniform distribution is satisfied in the interval. { phii}、{θiAlthough they are different in each simulation, they are not changed with the variation of the number of snapshots. The number of sampled fast beats K also ranges from 10 to 100. Fig. 2 shows the curves of the different methods for the variation of the output signal-to-interference-and-noise ratio of the radar antenna array with the sampling fast beat number K. Wherein, the horizontal axis represents the sampling fast beat number of the received signal of the radar antenna array, and the vertical axis represents the signal-to-interference-and-noise ratio of the output signal of the radar antenna array.
As can be seen from fig. 1 and fig. 2, the signal to interference plus noise ratio output by the conventional diagonal loading algorithm (TDL), the robust adaptive beamforming algorithm (WCB) based on worst-case optimization, and the robust adaptive beamforming Algorithm (API) based on less prior information for the radar antenna array is relatively small. Under the same simulation condition, the invention maximizes the signal-to-interference-and-noise ratio output by the radar antenna array, thereby improving the interference suppression and noise reduction capability of the radar antenna array.
Claims (1)
1. A robust adaptive beam forming method based on a diagonal loading technology comprises the following steps:
the method comprises the following steps: calculating a sampling covariance matrix R of a receiving signal of the radar antenna array constructed by the receiving signals x (K) sampled by K times of snapshots;
step two: using Lagrange operator, find the beamforming vector of Capon beamformer as:
<mrow> <msub> <mi>w</mi> <mi>c</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>R</mi> <mrow> <mi>i</mi> <mo>+</mo> <mi>n</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mover> <mi>a</mi> <mo>&OverBar;</mo> </mover> </mrow> <mrow> <msup> <mover> <mi>a</mi> <mo>&OverBar;</mo> </mover> <mi>H</mi> </msup> <msubsup> <mi>R</mi> <mrow> <mi>i</mi> <mo>+</mo> <mi>n</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mover> <mi>a</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> </mrow>
wherein,estimated steering vector, R, representing the desired signali+nFor the interference-plus-noise covariance matrix, R is replaced by the sampled covariance matrix R of the received signali+n；
Step three: calculating the weighting vector w of the radar antenna array by adopting a diagonal loading technologyDLNamely, the complex weight of each array element:
<mrow> <msub> <mi>w</mi> <mrow> <mi>D</mi> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mo>(</mo> <mi>R</mi> <mo>+</mo> <msup> <mi>&gamma;R</mi> <mrow> <mo>-</mo> <mn>0.5</mn> </mrow> </msup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mover> <mi>a</mi> <mo>&OverBar;</mo> </mover> </mrow> <mrow> <msup> <mover> <mi>a</mi> <mo>&OverBar;</mo> </mover> <mi>H</mi> </msup> <msup> <mrow> <mo>(</mo> <mi>R</mi> <mo>+</mo> <msup> <mi>&gamma;R</mi> <mrow> <mo>-</mo> <mn>0.5</mn> </mrow> </msup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mover> <mi>a</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> </mrow>
wherein the factor is loaded Is the average noise energy;
step four: and outputting the adaptive beam of the radar antenna array.
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| CN110865342A (en) * | 2019-11-12 | 2020-03-06 | 天津大学 | Beam forming method based on combination of guide vector estimation and covariance matrix reconstruction |
| CN111830495A (en) * | 2020-07-08 | 2020-10-27 | 中国人民解放军空军工程大学 | Airborne radar self-adaptive beam forming algorithm based on convex optimization learning |
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| CN110865342A (en) * | 2019-11-12 | 2020-03-06 | 天津大学 | Beam forming method based on combination of guide vector estimation and covariance matrix reconstruction |
| CN111830495A (en) * | 2020-07-08 | 2020-10-27 | 中国人民解放军空军工程大学 | Airborne radar self-adaptive beam forming algorithm based on convex optimization learning |
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