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CN114444540A - Robust beam former for resisting mismatching of wave arrival angle directions based on MIMO radar - Google Patents

Robust beam former for resisting mismatching of wave arrival angle directions based on MIMO radar Download PDF

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CN114444540A
CN114444540A CN202111642371.6A CN202111642371A CN114444540A CN 114444540 A CN114444540 A CN 114444540A CN 202111642371 A CN202111642371 A CN 202111642371A CN 114444540 A CN114444540 A CN 114444540A
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万环
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Abstract

The invention discloses a MIMO radar-based robust beam former for resisting mismatching of wave arrival angle directions, and belongs to the technical field of radar signal processing and adaptive beam forming. Signal angle and amplitude information, including the angle of arrival of the interference and the response amplitude for the corresponding angular direction, is first obtained by applying a standard Capon beamformer. Thus, if we limit the response levels of these angles to the magnitudes in the Capon beamformer beam pattern, then interference can be suppressed. Furthermore, the response amplitude within the angular range of the target signal is limited to be uniform to keep the target signal uninhibited. Thus, under these response constraints, robust beamforming against angular direction of arrival mismatch can be achieved by maximizing the output signal-to-interference-and-noise ratio. In practical MIMO radar applications, the sample size is limited, so that the accuracy of the sample covariance matrix is limited, resulting in degraded beamformer performance. Since the problem obtained by the present invention can be reconstructed without data-dependent terms (such as the sample covariance matrix), the proposed beamformer is robust against performance degradation caused by the presence of interfering signals in the training samples.

Description

Robust beam former for resisting mismatching of wave arrival angle directions based on MIMO radar
Technical Field
The invention relates to the technical field of signal processing and adaptive beam forming, in particular to a robust beam former for resisting mismatching of wave arrival angle directions based on an MIMO radar.
Background
Adaptive beamforming technology has been widely used in the engineering fields of radar, sonar, wireless communication, etc. as a basic technology for directional signal transmission and reception. The optimal beamforming is designed by maximizing the output signal-to-interference-and-noise ratio. It is known that Capon beamforming can suppress interference better than fixed weight beamforming under the condition that the steering vector corresponding to the target signal is precisely known. However, if the steering vector of the actual target signal deviates from the steering vector estimated by the angle-of-arrival direction estimation technique, Capon beamformer performance is significantly degraded.
The present invention proposes a new adaptive beamforming technique that is very robust against mismatching of the direction of arrival angle estimates with the direction of the target signal and under consideration of the target signal in the training set. To ensure that the proposed robust beamforming technique can effectively suppress interference, we need to first determine the response amplitude of the interference arrival direction using a standard Capon beamformer. And then, the expression of the weight vector is derived by constraining the response amplitude of the direction of the arrival angle of the interference signal and the direction of the maximum possible angle range of the target signal and maximizing the output signal-to-interference-and-noise ratio. And finally, solving the derived non-convex optimization problem approximately by applying a semi-positive definite relaxation technology.
In view of this, the present invention proposes a robust beamformer for combating angular direction of arrival mismatch based on MIMO radar.
Disclosure of Invention
1. Technical problem to be solved
The present invention is directed to a robust beamformer for resisting mismatching of direction of arrival angles based on MIMO radar, so as to solve the above-mentioned problems in the background art.
2. Technical scheme
A robust beamformer for resisting mismatching of direction of arrival (DOA) based on MIMO radar comprises the following steps:
s1: the MIMO radar array unit processes the collected space beam signals, and the processed space beam signals can form a signal covariance matrix;
s2: the obtained signal covariance matrix passes through a standard Capon beam former to obtain a standard Capon beam pattern;
s3: the standard Capon beam pattern is used for detecting nulls and finding out sidelobe nulls, so that a group of estimation values of the arrival angle containing interference and the response amplitude of the corresponding angle direction can be found out;
s4: the estimate is carried into a robust beamformer which suppresses the interfering signal and keeps the target signal from being suppressed. Finding the weight vector of the optimal beam former and identifying the weight vector;
preferably, in step S1, 1 target signal and J interference signals are received. At time K, the array received signal vector X (K) may be expressed as
Figure BDA0003442830400000021
Wherein s is0(k) And
Figure BDA0003442830400000022
waveforms, theta, representing target and interfering signals, respectively0Is the direction of the angle of arrival of the target signal,
Figure BDA0003442830400000023
is the angle of arrival direction of the interference, n (k) is additive Gaussian noise, e.g.
Figure BDA0003442830400000024
Wherein
Figure BDA0003442830400000025
Is the noise variance, and I is the identity matrix. In this work, the target signal, interference, and noise are assumed to be statistically independent.
Preferably, in step S1, the covariance matrix of the columns can be expressed as
R＝E{(x(k)x(k)}H}＝Rs+Ri+n (4)
Wherein E {. represents a statistical expectation operator, (.)HDenotes Hermite transposition, RsAnd Ri+nRespectively, the signal covariance matrix and the interference-plus-noise covariance matrix, which can be expressed as
Figure BDA0003442830400000026
Figure BDA0003442830400000027
Wherein,
Figure BDA0003442830400000028
is the power of the signal of interest and,
Figure BDA0003442830400000029
is the power of the ith interference. The radar array received signal sample covariance matrix is represented as:
Figure BDA0003442830400000031
where K is the sample size. The signal receiver weight vector is represented as
w＝[w1，w2，…，wM]T (5)
Wherein (·)TRepresenting the transpose operator, given a beamformer weight vector w, the array output is y (k) wHx(k)。
Preferably, in step S2, the weight vector is expressed as
w＝[w1，w2，…，wM]T (4)
Wherein (·)TRepresenting the transpose operator, given a beamformer weight vector w, the array output is y (k) wHx(k)。
Preferably, in step S2, the signal covariance matrix is processed by a standard Capon beam former to obtain a standard Capon beam pattern.
Preferably, in step S3, the angular position of the null (including the direction of arrival of the interference) is detected by the Capon beamformer, and the response level at the notch is recorded.
Preferably, in the step S2, the signal sample is loadedThe weight vector w of the standard Capon beam former can be obtained by a covariance matrix and maximizing the output signal-to-noise ratioSCBSuch as
Figure BDA0003442830400000032
Preferably, in step S4, when suppressing the interference signal, the deep notch will form a target signal angle direction of the main lobe under the condition of mismatching of the interference angle and the arrival angle of the beam pattern side lobe; according to this case, let Θ be the null angle outside the target signal region, i.e.
Θ＝{θ′1，θ′2，…，θ′L} (7)
And let the corresponding response amplitude be pl
Figure BDA0003442830400000041
3. Advantageous effects
Compared with the prior art, the invention has the advantages that:
in this method, a set of angles, including the interference arrival angle direction and the corresponding response level, is first obtained by applying a Capon beamformer. Therefore, if the response levels of these angles are limited to the magnitudes in the Capon beamformer beam pattern, interference can be suppressed. Furthermore, the response amplitude within the angular range of the target signal is constrained to be uniform to keep the target signal uninhibited. Thus, under these response constraints, robust beamforming against angular direction of arrival mismatch can be achieved by maximizing the output signal-to-interference-and-noise ratio. Since the resulting problem can be reconstructed without data-dependent terms (e.g., sample covariance matrix), the proposed beamformer is robust against performance degradation caused by the presence of interfering signals in the training samples.
Drawings
FIG. 1 is a block diagram of a robust beamformer system for resisting mismatching of the DOA of MIMO radar according to the present invention;
fig. 2 is a beam contrast diagram of the present invention, where K is 500, SNR is 10dB, INR is 30 dB;
fig. 3 is a graph of the output SNR versus input SNR of the present invention, where K is 100 and INR is 30 dB;
fig. 4 is a diagram of the relationship between the SNR of the output signal-to-interference-and-noise ratio and the mismatching angle of the target signal arrival angle, where SNR is 10dB and INR is 30 dB.
Detailed Description
In the description of the present invention, it is to be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", and the like, indicate orientations and positional relationships based on those shown in the drawings, and are used only for convenience of description and simplicity of description, and do not indicate or imply that the equipment or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be considered as limiting the present invention.
In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "disposed," "sleeved/connected," "connected," and the like are to be construed broadly, e.g., "connected," which may be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Referring to fig. 1-4, the present invention provides a technical solution:
example 1, consider an array of M antennas receiving 1 target signal and J interfering signals. At time K, the array received signal vector X (K) may be expressed as
Figure BDA0003442830400000051
Wherein s is0(k) And
Figure BDA0003442830400000052
waveforms, theta, representing target and interfering signals, respectively0Is the direction of the angle of arrival of the target signal,
Figure BDA0003442830400000053
is the angle of arrival direction of the interference, n (k) is additive Gaussian noise, e.g.
Figure BDA0003442830400000054
Wherein
Figure BDA0003442830400000055
Is the noise variance, and I is the identity matrix. In this work, the target signal, interference, and noise are assumed to be statistically independent. The covariance matrix of the array may be expressed as
R＝E{(x(k)x(k))H}＝Rs+Ri+n (6)
Wherein E {. represents a statistical expectation operator, (. C)HDenotes Hermite transposition, RsAnd Ri+nRespectively, the signal covariance matrix and the interference-plus-noise covariance matrix, which can be expressed as
Figure BDA0003442830400000056
Figure BDA0003442830400000057
Wherein,
Figure BDA0003442830400000061
is the power of the signal of interest，
Figure BDA0003442830400000062
Is the power of the ith interference. The radar array received signal sample covariance matrix is represented as:
Figure BDA0003442830400000063
where K is the sample size.
Example 2 adaptive beamforming is performed by designing an appropriate beamformer weight vector, denoted as
w＝[w1，w2，…，wM]T (5)
Wherein (.)TRepresenting the transpose operator, given a beamformer weight vector w, the array output is y (k) wHx (k), the output signal-to-interference-and-noise ratio can be written as
Figure BDA0003442830400000064
It is well known that maximizing the output signal-to-noise ratio yields an optimal beamformer weight vector wopt. Thus, the following unconstrained optimization problem is expressed as
Figure BDA0003442830400000065
It can be equivalently expressed as
Figure BDA0003442830400000066
Solving (8) by Lagrange multiplier method, we can obtain
Figure BDA0003442830400000067
When unifying constraints wHa(θ0) When 1, can derive
Figure BDA0003442830400000068
Therefore, the formula (6) can be equivalently expressed as
Figure BDA0003442830400000071
Example 3 in practical cases, an estimate of the array covariance matrix is available, which can be obtained from sample data
Figure BDA0003442830400000072
Where K is the sample size. The weight vector can be expressed as in a standard Capon beamformer
Figure BDA0003442830400000073
Given K snapshots, a sample covariance matrix
Figure BDA0003442830400000074
And the weight vector w of the standard Capon beamformeroptCan be obtained by the formulae (11) and (12), respectively. Thus, the beam pattern is given by:
Figure BDA0003442830400000075
example 4, in general, deep notch nulls will form the target signal angular direction of the main lobe at the interference angle of the beam pattern side lobes and with the angle of arrival mismatch. According to this case, let Θ be the null angle outside the target signal region, i.e.
Θ＝{θ′1，θ′2，…，θ′L} (14)
And let the corresponding response amplitude be
Figure BDA0003442830400000076
Note that, in general, we have
Figure BDA0003442830400000077
However, when the interfering signal is strong enough, there is a deeper null at the angle of arrival of the interfering signal. In this common case, the angle of arrival side of the interference can be more easily determined, so we have L ═ J and Θ ═ θ1，θ2，…，θL}。
Embodiment 5, to design a robust beamformer weight vector w to combat angle-of-arrival mismatch to suppress interfering signals while maintaining the target signal, θ 'is preferably set'1，θ′2，…，θ′LThe magnitude of the response at (1) is shown as equation (15), i.e. | wHa(θ′l)|＝ρl，θ′lE.g. theta. Furthermore, the response amplitude of the target signal region should be uniform, i.e. uniform
Figure BDA0003442830400000081
In fact, Ω should discretize it into N points, e.g.
Figure BDA0003442830400000082
And for
Figure BDA0003442830400000083
When the discretization is good enough, we have θ0∈Ωd. Thus, this weight vector can be determined by minimizing the output power and limiting these constraints, i.e.
Figure BDA0003442830400000084
As previously mentioned, the beamformer thus obtained is due to limited accuracy
Figure BDA0003442830400000085
And the presence of the target signal in the training samples fails to achieve good enough performance. Therefore, we further suggest obtaining the beamformer weight vector by maximizing the signal to interference plus noise ratio
Figure BDA0003442830400000086
Obviously, since the precise theta cannot be obtained0And R is not obtained in practicei+nThe above problems cannot be directly solved. To this end, we rewrite the objective function signal-to-interference-and-noise ratio to
Figure BDA0003442830400000087
Example 6, under the conditions given in (16), θ0E.g. omega x and
Figure BDA0003442830400000088
we can further simplify the signal to interference and noise ratio to
Figure BDA0003442830400000089
Therefore, the problem in the formula (17) can be rewritten as
Figure BDA0003442830400000091
Wherein | · | purple2Representing a 2 norm.
It should be mentioned that one might point out that the actual angle of arrival direction of the target signal might be at ΩdMedium off-grid, and the angle of arrival Θ may not completely contain the interfering signal. This is, of course, present in practice. However, when several are applied to the target signal regionWith uniform constraint, the corresponding beam pattern will be (approximately) flat, so we have
Figure BDA0003442830400000092
Moreover, even if there is a bias, we usually have | w between the actual and estimated interference arrival anglesHa(θi)|2≈ρii is 1, …, J. Therefore, the identity in (19) can still be well approximated. This will be verified by the following simulation results.
Example 6, it can be seen that the problem in (20) is non-convex. Therefore, it cannot be directly solved by the convex optimization method, and further processing is required. To solve this problem, the following equation will be used:
Figure BDA0003442830400000093
and | wHa(θ)|2＝trace{wHa(θ)a(θ)Hw}＝trace{a(θ)a(θ)HwwHRepresents the trace of the matrix. We define
Figure BDA0003442830400000094
And
Figure BDA0003442830400000095
can be rewritten as in formula (20)
Figure BDA0003442830400000096
Where rank {. cndot } represents the rank of the matrix and 0 represents the matrix to the left of the inequality is semi-positive.
By discarding the constraint of rank 1, i.e., rank { W } ═ 1, the above problem can be relaxed to the following SDP problem:
Figure BDA0003442830400000101
this problem can be addressed by an efficient convex optimization solverFor example CVX. Assuming that the solution of solution (22) is WproIt should be mentioned that, due to the relaxation, WproMay not be a matrix of rank 1. In case of a matrix of rank 1, the proposed robust beamformer weight vector wproCan be directly from WproIs extracted by feature decomposition, e.g.
Figure BDA0003442830400000102
Wherein λmaxRepresents WproMaximum eigenvalue of, VmaxIs the corresponding feature vector.
Example 7 if WproInstead of a matrix of rank 1, the resulting beamformer weight vector in equation (23) is an approximate solution. To obtain a better solution in this case, a plurality of W-based renderings may be made using a random methodproAnd selects the best solution among them. In this work, we use the solution of equation (23) as the beamformer weight, and it can be seen that the final beamformer design is data independent. The proposed beamformer is therefore able to overcome the performance degradation problem due to the presence of the target signal in the training samples and achieve relatively better performance, especially in high SNR situations. This will be verified by several examples in the next section.
Example 8, assuming an input signal-to-noise ratio (SNR) of 10dB, the sample size K is 500. The beam pattern for each method is shown in fig. 2. It can be seen that the Capon beamformer method forms nulls in both the angle of arrival directions of the interfering signal (2 °) and the interference (20 °, 60 °). Although the diagonally loaded Capon beamformer does not force a null in the direction of the angle of arrival of the interfering signal, it does not provide sufficient robustness. On the other hand, the main beam of the RCB and the proposed robust beamformer is enlarged to preserve the interfering signals. Furthermore, the proposed beamformer has lower sidelobes. This means that noise can be better suppressed and a higher output signal-to-noise ratio can be obtained, which can be observed from the following experimental results. In this section, two experiments will be completed. In the first experiment, the sample size was fixed at K100, and the input SNR was between-20 dB and 20dB with a step size of 5 dB. In a second experiment, we fixed the signal-to-noise ratio to 10dB, while the sample size K was between 10 and 100, with a step size of 10. The output signal-to-noise ratio of the proposed method was compared with the output signal-to-noise ratio of the conventional method (Capon beamformer, diagonally loaded Capon beamformer) by two experiments. It is clear from fig. 3 and 4 that the proposed robust beamformer is superior to the existing methods we tested. This is because the proposed method not only suppresses interference as in the prior art, but also overcomes the problem of signal self-suppression due to the presence of interfering signals in the training samples. In addition, the proposed method has better noise suppression capability by forcibly reducing side lobes.
In summary, the following steps: in this method, we first obtain a set of angles, including the interference arrival angle direction and the corresponding response level, by applying a Capon beamformer. Thus, if we limit the response levels of these angles to the magnitudes in the Capon beamformer beam pattern, then interference can be suppressed. Furthermore, the response amplitude within the angular range of the target signal is constrained to be uniform to keep the target signal uninhibited. Thus, under these response constraints, robust beamforming against angular direction of arrival mismatch can be achieved by maximizing the output signal-to-interference-and-noise ratio. Since the resulting problem can be reconstructed without data-dependent terms (e.g., sample covariance matrix), the proposed beamformer is robust against performance degradation caused by the presence of interfering signals in the training samples.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and the preferred embodiments of the present invention are described in the above embodiments and the description, and are not intended to limit the present invention. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (7)

1. Robust beam former based on MIMO radar against mismatching of direction of arrival angles, characterized by: the method comprises the following steps:
s1: the MIMO radar array unit processes the collected space beam signals, and the processed space beam signals can form a signal covariance matrix;
s2: the obtained signal covariance matrix passes through a standard Capon beam former to obtain a standard Capon beam pattern;
s3: the standard Capon beam pattern is used for detecting nulls and finding out sidelobe nulls, so that a group of estimation values of the arrival angle containing interference and the response amplitude of the corresponding angle direction can be found out;
s4: and bringing the estimated value into a steady beam former, suppressing the interference signal, keeping the target signal from being suppressed, searching the optimal beam former weight vector, and identifying the optimal beam former weight vector.
2. The MIMO radar-based robust beamformer for combating angular-of-arrival directional mismatch according to claim 1, wherein: in step S1, 1 target signal and J interference signals are received. At time K, the array received signal vector X (K) may be expressed as
Figure RE-FDA0003570860200000011
Wherein s is0(k) And
Figure RE-FDA0003570860200000012
waveforms, theta, representing target and interfering signals, respectively0Is the direction of the angle of arrival of the target signal,
Figure RE-FDA0003570860200000013
is the angle of arrival direction of the interference, n (k) is additive Gaussian noise, e.g.
Figure RE-FDA0003570860200000014
Wherein
Figure RE-FDA0003570860200000015
Is the noise variance, and I is the identity matrix. In this work, the target signal, interference, and noise are assumed to be statistically independent.
3. The MIMO radar-based robust beamformer for combating angular-of-arrival directional mismatch according to claim 1, wherein: in step S1, the covariance matrix of the signal can be expressed as
R＝E{(x(k)x(k))H}＝Rs+Ri+n (2)
Wherein E {. represents a statistical expectation operator, (. C)HDenotes Hermite transposition, RsAnd Ri+nRespectively, the signal covariance matrix and the interference-plus-noise covariance matrix, which can be expressed as
Figure RE-FDA0003570860200000021
Figure RE-FDA0003570860200000022
Wherein,
Figure RE-FDA0003570860200000023
is the power of the signal of interest and,
Figure RE-FDA0003570860200000024
is the power of the ith interference. The radar array received signal sample covariance matrix is represented as:
Figure RE-FDA0003570860200000025
where K is the sample size. The signal receiver weight vector is represented as
w＝[w1，w2，…，wM]T (5)
Wherein (·)TRepresenting the transpose operator, given a beamformer weight vector w, the array output is y (k) wHx(k)。
4. The MIMO radar-based robust beamformer for combating angular-of-arrival directional mismatch according to claim 1, wherein: in step S2, the signal covariance matrix is passed through a standard Capon beam former to obtain a standard Capon beam pattern.
5. The MIMO radar-based robust beamformer for combating angular-of-arrival directional mismatch according to claim 1, wherein: in said step S3, the angular position for detecting the null (including the direction of arrival angle of the interference) and the response level at the notch are recorded by the Capon beamformer.
6. The MIMO radar-based robust beamformer for combating angular-of-arrival directional mismatch according to claim 1, wherein: in step S2, the signal sample covariance matrix is loaded, and the weight vector w of the standard Capon beamformer can be obtained by maximizing the output signal-to-noise ratioSCBSuch as
Figure RE-FDA0003570860200000031
。
7. The MIMO radar-based robust beamformer for combating angular-of-arrival directional mismatch according to claim 1, wherein: in step S4, when suppressing the interference signal, the deep notch null will form a target signal angle direction of the main lobe at the interference angle of the beam pattern side lobe and under the condition of mismatching of the arrival angle; according to this case, let Θ be the null angle outside the target signal region, i.e.
Θ＝{θ′1，θ′2，…，θ′L} (7)
And let the corresponding response amplitude be pl
Figure RE-FDA0003570860200000032
。
CN202111642371.6A 2021-12-29 2021-12-29 Robust beam former for resisting mismatching of wave arrival angle directions based on MIMO radar Pending CN114444540A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116430347A (en) * 2023-06-13 2023-07-14 成都实时技术股份有限公司 Radar data acquisition and storage method

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116430347A (en) * 2023-06-13 2023-07-14 成都实时技术股份有限公司 Radar data acquisition and storage method
CN116430347B (en) * 2023-06-13 2023-08-22 成都实时技术股份有限公司 Radar data acquisition and storage method

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