CN111740767A - Side lobe canceller auxiliary channel antenna selection method based on beam pattern - Google Patents

Side lobe canceller auxiliary channel antenna selection method based on beam pattern Download PDF

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CN111740767A
CN111740767A CN202010793123.0A CN202010793123A CN111740767A CN 111740767 A CN111740767 A CN 111740767A CN 202010793123 A CN202010793123 A CN 202010793123A CN 111740767 A CN111740767 A CN 111740767A
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auxiliary channel
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CN111740767B (en
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王向荣
翟唯童
王向华
曹先彬
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Beihang University
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    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0602—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using antenna switching
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Abstract

The invention discloses a method for selecting an auxiliary channel antenna of a side lobe canceller based on a beam directional diagram, which comprises the steps of selecting the position of the auxiliary channel antenna taking a single array element as a unit, firstly forming a main channel directional diagram by a conventional beam, and calculating the height of the main channel directional diagram in an interference direction; designing an auxiliary channel directional diagram according to a minimum power criterion, wherein the auxiliary channel directional diagram is as high as the main channel directional diagram in the interference direction; and calculating the superposition directional diagrams of the two channels, finding the relation between the main lobe distortion of the directional diagram of the main channel caused by the auxiliary channel and the antenna position selected by the auxiliary channel, and selecting the optimal antenna position of the auxiliary channel according to the minimum principle of the main lobe distortion. The method can be used for selecting the antenna of the auxiliary channel of the sidelobe canceller in any array, realizes the cancellation of interference signals from the angle of a directional diagram, simultaneously ensures that expected signals are not weakened due to the introduction of the auxiliary channel, and is a widely applicable antenna selection method for the auxiliary channel of the sidelobe canceller.

Description

Side lobe canceller auxiliary channel antenna selection method based on beam pattern
Technical Field
The invention belongs to the technical field of array signal processing, and particularly relates to a beam pattern-based selection method of an auxiliary channel antenna of a side lobe canceller.
Background
The signals received by the array usually consist of desired signals, interference signals and noise, and how to eliminate interference and noise parts in the received signals and design an optimal beam former is always a hot spot for array signal processing. The traditional methods have a Minimum Variance Distortionless Response (MVDR) beam former, a Minimum Power Distortionless Response (MPDR) beam former and the like, and all the methods need to perform inversion operation on correlation matrixes of all array element received signals, and the operation complexity is high. This may affect the real-time performance in actual use.
In order to reduce the amount of computation, the side lobe canceller is an effective solution. The sidelobe canceller is a common airspace anti-interference means, and the anti-interference principle is that both a main channel antenna and an auxiliary channel antenna receive signals with interference, and the optimal weight is selected to enable the interference output of the auxiliary antenna to be as close to the main channel as possible, so that the interference of the main channel is counteracted. The sidelobe canceller usually selects a part of array elements to form an auxiliary channel, and only the correlation matrix of the array element receiving signals of the auxiliary channel part needs to be inverted in the operation process, so that the operation complexity is greatly reduced compared with the traditional method. Most of the existing side-lobe cancellation methods adopt a method of minimum output power, so that the power of the output difference between a main channel and an auxiliary channel is minimum, and the cancellation of interference signals is realized. In practical application, however, the target signal is also partially cancelled while the interference is eliminated, which affects the performance of the side lobe canceller to some extent. How to reduce the attenuation of the auxiliary channel to the desired signal becomes an important factor affecting the performance of the side lobe canceller.
In a conventional sidelobe canceller, generally, given an auxiliary channel and a main channel, cancellation is achieved by optimizing weights. In practical applications, the effect of different auxiliary channel positions on the performance of the sidelobe canceller is also significant.
Disclosure of Invention
In order to solve the defects of the prior art, based on the requirements of the sidelobe canceller on maximum reservation of an expected signal and optimization of the auxiliary channel position in practice, the invention adopts any linear array or planar array, and provides a method for selecting an auxiliary channel antenna of the sidelobe canceller based on a beam pattern, and the specific technical scheme of the invention is as follows:
a method for selecting an auxiliary channel antenna of a sidelobe canceller based on a beam pattern is characterized by comprising the following steps:
s1: obtaining a main channel beam pattern, and calculating the amplitude of the main channel beam pattern in the interference direction;
s2: calculating the constraint condition of a beam pattern of an auxiliary channel, wherein the amplitude of the auxiliary channel in the interference direction is the same as the amplitude of the auxiliary channel in the corresponding direction of the main channel;
s3: designing an auxiliary channel directional diagram according to the minimum output power criterion and by combining the auxiliary channel beam directional diagram constraint condition of the step S2 to obtain a corresponding weight vector;
s4: calculating the main lobe distortion of the side lobe canceller to obtain the relation between the main lobe distortion and the auxiliary channel antenna position;
s5: and selecting the antenna position which enables the main lobe distortion to be minimum as the optimal auxiliary channel antenna position.
Further, for the auxiliary channel antenna position selection in units of single array element, the specific process of step S1 is:
the receiving signal of the sidelobe canceller consists of an expected signal, K interferences and noises, the noises are zero mean Gaussian white noises, the receiving antenna array has M array elements in total, N array elements are selected to form an auxiliary channel,
output of the main channel
Figure 818937DEST_PATH_IMAGE001
Wherein
Figure 302264DEST_PATH_IMAGE002
an array steering vector that points the main channel to the desired signal,
Figure 841830DEST_PATH_IMAGE003
noise vectors received for main channel array elements;
Figure 691974DEST_PATH_IMAGE004
a matrix of array steering vectors that point the main channel to K interferers,
Figure 266175DEST_PATH_IMAGE005
steering the vector for the array pointing to the ith interferer, i =1,2, …, K;
Figure 418939DEST_PATH_IMAGE006
a column vector consisting of K interference signals received at the time t;
output of auxiliary channel
Figure 711380DEST_PATH_IMAGE007
Wherein
Figure 99636DEST_PATH_IMAGE008
each element represents a signal received by the auxiliary channel array element at the corresponding position respectively;
Figure 466026DEST_PATH_IMAGE009
for the noise vectors received by the auxiliary channel array elements,
Figure 852008DEST_PATH_IMAGE010
a matrix of array steering vectors pointing to K interferers for the auxiliary channel,
Figure 428483DEST_PATH_IMAGE011
steering the vector for the array pointing to the ith interferer, i =1,2, …, K;
the main channel beam pattern is obtained by the conventional beam forming of all array elements of the main channel and is recorded as
Figure 558113DEST_PATH_IMAGE012
，
Figure 44589DEST_PATH_IMAGE013
Is the angle between the incident direction and the XOY plane，
Figure 601473DEST_PATH_IMAGE014
Is the angle between the projection of the incident direction on the XOY plane and the X-axis,
Figure 665244DEST_PATH_IMAGE015
the height in the K interference directions is respectively
Figure 598565DEST_PATH_IMAGE016
Wherein
Figure 438082DEST_PATH_IMAGE017
respectively, the spatial incident angles under the ith interference sphere coordinate.
Further, for the auxiliary channel antenna position selection in units of single array element, the specific process of step S2 is:
auxiliary channel beam pattern
Figure 165867DEST_PATH_IMAGE018
Wherein
Figure 716934DEST_PATH_IMAGE019
in the form of a vector of weights,
Figure 453946DEST_PATH_IMAGE020
is composed of
Figure 383856DEST_PATH_IMAGE021
The conjugate transpose of (a) is performed,
Figure 344859DEST_PATH_IMAGE022
for assisting the channel array to guide the vector, for achieving interference cancellation, it is necessary to
Figure 320905DEST_PATH_IMAGE023
Obtaining K constraint conditions of K interferences, writing the constraint conditions into a matrix form to obtain a total constraint condition
Figure 533711DEST_PATH_IMAGE024
Memory for recording
Figure 646024DEST_PATH_IMAGE025
Then the constraint is written as
Figure 43507DEST_PATH_IMAGE026
。
Further, for the auxiliary channel antenna position selection in units of single array element, the specific process of step S3 is:
combining the constraint conditions obtained in the step S2, designing an auxiliary channel directional diagram according to the minimum output power criterion, and obtaining the optimal weight corresponding to the antenna position of the auxiliary channel at the moment;
the output power of the auxiliary channel is
Figure 241270DEST_PATH_IMAGE027
Wherein
Figure 257768DEST_PATH_IMAGE028
the autocorrelation matrix of the received signal for the auxiliary channel, E represents the desired operation,
Figure 224587DEST_PATH_IMAGE029
in order to be able to measure the power of the noise,
Figure 792971DEST_PATH_IMAGE030
is composed of
Figure 478031DEST_PATH_IMAGE031
The unit array is formed by a plurality of unit arrays,
Figure 268526DEST_PATH_IMAGE032
forming a diagonal matrix by the power of K interferences; the process of finding the optimal weight of the auxiliary channel is written as an optimization problem:
Figure 621010DEST_PATH_IMAGE033
expression for obtaining optimal weight by Lagrange multiplier method
Figure 360295DEST_PATH_IMAGE034
Obtained by applying matrix inversion lemma
Figure 532651DEST_PATH_IMAGE035
Wherein, define
Figure 890951DEST_PATH_IMAGE036
Again using matrix inversion theorem to solve
Figure 832362DEST_PATH_IMAGE037
Obtaining the optimal weight and a steering vector matrix determined by the position of the auxiliary channel antenna
Figure 476970DEST_PATH_IMAGE038
In the context of (a) or (b),
Figure 74305DEST_PATH_IMAGE039
。
further, for the auxiliary channel antenna position selection in units of single array element, the specific process of step S4 is:
defining the main lobe distortion as the distortion of the auxiliary channel, which causes the total directional diagram of the side lobe canceller to generate in the direction of the desired signal, the amplitude of the total directional diagram at the desired signal is as the main lobe distortionD，
Figure 33033DEST_PATH_IMAGE040
The signal direction magnitude is desired for the main channel pattern,
Figure 156847DEST_PATH_IMAGE041
for the auxiliary channel desired signal direction amplitude, for maximum retention of the desired signal, minimum main lobe distortion is required, i.e. minimum main lobe distortion is requiredDIs the maximum value, is obtained from the optimal weight vector obtained in step S3
Figure 910040DEST_PATH_IMAGE042
。
Further, for the auxiliary channel antenna position selection in units of single array element, the specific process of step S5 is:
as is known from step S4, the requirement for minimum distortion of the main lobe is equivalent to the requirement for minimum distortion of the main lobe
Figure 994670DEST_PATH_IMAGE043
Minimum value of (d);
defining an antenna selection vector
Figure 757090DEST_PATH_IMAGE044
，
Figure 735410DEST_PATH_IMAGE045
Is one
Figure 925083DEST_PATH_IMAGE046
The vector of the dimension respectively represents the selection condition of the auxiliary channel to all M array elements, all elements are composed of 0 and 1, 0 represents that the auxiliary channel does not select the array element, and 1 represents that the auxiliary channel selects the position array element; two matrices are defined which are,
Figure 729966DEST_PATH_IMAGE047
a matrix formed by guiding vectors in K interference directions for all M array elements;
Figure 30497DEST_PATH_IMAGE048
steering vectors of all M array elements in the direction of the expected signal; matrix determined by auxiliary channel antenna position
Figure 128903DEST_PATH_IMAGE049
The relationship between them is:
Figure 489477DEST_PATH_IMAGE050
then, the antenna position which makes the main lobe distortion minimum is selected as the optimal auxiliary channel antenna position to describe as an optimization problem:
Figure 283121DEST_PATH_IMAGE051
and solving the optimization problem to obtain the antenna position which is the auxiliary channel antenna position which enables the main lobe distortion of the total direction diagram of the side lobe canceller to be minimum.
Further, for the selection of the auxiliary channel antenna position using the sub-array as a unit, in step S1, first, beam forming is performed on each sub-array, and then, uniform weighted beam forming is performed on the output of each sub-array to obtain a main channel beam pattern, which specifically includes:
the receiving signal of the sidelobe canceller consists of an expected signal, K interferences and noises, the noises are zero mean Gaussian white noises, and the receiving antenna array consists ofNA plurality of sub-arrays, each sub-array havingCThe array elements and receiving antennas are sharedMArray element
Figure 184081DEST_PATH_IMAGE052
Selecting L sub-arrays to form an auxiliary channel;
first, each subarray is conventionally beamformed to weight the received signal, and the output of the p-th subarray is
Figure 74676DEST_PATH_IMAGE053
Wherein
Figure 543835DEST_PATH_IMAGE054
is the array steering vector for the p-th sub-array to the desired signal,
Figure 887092DEST_PATH_IMAGE055
the noise vectors received for the array elements of the p-th sub-array,
Figure 591743DEST_PATH_IMAGE056
the matrix is formed by leading vectors of the p-th sub-matrix to K interferences;
Figure 336845DEST_PATH_IMAGE057
respectively the steering vector of the p-th sub-array in each interference direction,
Figure 976905DEST_PATH_IMAGE058
a column vector consisting of K interference signals received at the time t;
output of the main channel
Figure 807457DEST_PATH_IMAGE059
The output of the auxiliary channel is:
Figure 315799DEST_PATH_IMAGE060
Figure 915408DEST_PATH_IMAGE061
wherein,
Figure 227834DEST_PATH_IMAGE062
is as follows
Figure 545682DEST_PATH_IMAGE063
The individual sub-arrays point to an array steering vector of the desired signal,
Figure 592136DEST_PATH_IMAGE064
is as follows
Figure 983934DEST_PATH_IMAGE065
The noise vectors received by the array elements of the individual sub-arrays,
Figure 28113DEST_PATH_IMAGE066
is as follows
Figure 895575DEST_PATH_IMAGE067
The direction of each sub-array in the corresponding interference direction is proper,
Figure 683403DEST_PATH_IMAGE068
Figure 195287DEST_PATH_IMAGE069
definition of
Figure 410367DEST_PATH_IMAGE070
The position of the selected subarray is determined by the position of the selected subarray of the auxiliary channel, and the main channel beam pattern is formed by the conventional beams of all the array elements of the main channel and is recorded as
Figure 765125DEST_PATH_IMAGE071
，
Figure 763168DEST_PATH_IMAGE072
The height in the K interference directions is respectively
Figure 191876DEST_PATH_IMAGE073
，
Figure 905754DEST_PATH_IMAGE074
Wherein
Figure 419912DEST_PATH_IMAGE075
respectively, the spatial incident angles under the ith interference sphere coordinate.
Further, in step S1, the array is a linear array or a planar array, and the antenna position is half of the source wavelength, that is, the antenna position is the wavelength of the source
Figure 985760DEST_PATH_IMAGE076
In the unit of the number of the units,
Figure 534553DEST_PATH_IMAGE077
is the source wavelength.
The invention has the beneficial effects that:
1. the invention can realize the interference cancellation of any linear array or planar array from the angle of a beam directional diagram, and simultaneously greatly reduces the weakening of an expected signal, so that the total directional diagram of the canceller has excellent directivity in the direction of the expected signal.
2. The invention breaks through the thinking of fixing the auxiliary channel, designs an algorithm for selecting the optimal auxiliary channel position, can select the optimal condition from a plurality of auxiliary channel position selections, and optimizes the position, so that the side lobe canceller can maximally reserve the expected signal.
Drawings
In order to illustrate embodiments of the present invention or technical solutions in the prior art more clearly, the drawings which are needed in the embodiments will be briefly described below, so that the features and advantages of the present invention can be understood more clearly by referring to the drawings, which are schematic and should not be construed as limiting the present invention in any way, and for a person skilled in the art, other drawings can be obtained on the basis of these drawings without any inventive effort. Wherein:
FIG. 1 is a flow chart of a method for selecting the position of an array element of an auxiliary channel of a side lobe canceller in a unit of a single array element, which is applicable to any antenna array based on a directional diagram;
FIG. 2 is a flow chart of a method for selecting a position of a subarray of an auxiliary channel of a side lobe canceller in subarray units according to the present invention, which is applicable to any antenna array based on directional diagrams;
FIG. 3 is a schematic diagram of an optimal position of a 16-array element linear array auxiliary channel;
fig. 4(a) is a schematic diagram of a main channel, an auxiliary channel and a general direction of a 16 antenna linear array two-interference side lobe canceller;
FIG. 4(b) is a beam pattern of a main channel of a sidelobe canceller in two interference of a linear array of 16 antennas;
FIG. 4(c) is a beam pattern of an auxiliary channel of a sidelobe canceller under two-interference of a linear array of 16 antennas;
FIG. 4(d) is a synthesized directional diagram of a 16-antenna linear array side lobe canceller under two-interference;
FIG. 5 is a schematic diagram of an optimal position of a 16-array element linear array auxiliary channel;
fig. 6(a) is a schematic diagram of a main channel, an auxiliary channel and a general direction of a 16-antenna linear array three-interference side lobe canceller;
FIG. 6(b) is a beam pattern of a main channel of the sidelobe canceller under three-interference of the 16 antenna linear array;
FIG. 6(c) is a beam pattern of an auxiliary channel of a sidelobe canceller under three-interference of a linear array of 16 antennas;
FIG. 6(d) is the combined directional diagram of the sidelobe canceller under three-interference of the 16 antenna linear array;
fig. 7 is a schematic diagram of 8 sub-arrays, each of which is a 3-element linear array auxiliary channel sub-array selection diagram;
fig. 8(a) is a schematic diagram of a main channel, an auxiliary channel and a general direction of a sidelobe canceller under 8 sub-array linear arrays three-interference;
FIG. 8(b) is a beam pattern of a main channel of the sidelobe canceller under 8 subarray linear arrays three-interference;
FIG. 8(c) is a beam pattern of an auxiliary channel of a sidelobe canceller under 8 subarray linear arrays three-interference;
FIG. 8(d) is the synthetic directional diagram of the sidelobe canceller under three interferences of the 8 subarray linear arrays;
fig. 9 is a graph showing the relationship between the input signal-to-noise ratio and the output signal-to-interference-and-noise ratio between the optimal position and the other three random positions when the array elements are selected in units of two interferences of the 16-array element linear array;
fig. 10 is a graph showing the relationship between the input snr and the output snr at the optimal position and the other three random positions when the sub-array is selected in units of two sub-arrays under 8 sub-arrays.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments of the present invention and features of the embodiments may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore the scope of the present invention is not limited by the specific embodiments disclosed below.
According to the invention, the auxiliary channel is designed based on the beam pattern, and the weakening of the auxiliary channel to the expected signal is greatly reduced on the premise of realizing interference signal cancellation; meanwhile, a set of auxiliary channel antenna selection algorithm is designed, and the optimal auxiliary channel antenna position can be selected, so that not only is the performance optimized, but also the position is optimized.
As shown in fig. 1-2, a method for selecting an auxiliary channel antenna of a side lobe canceller based on a beam pattern, for auxiliary channel antenna position selection in units of subarrays,
in step S1, first, beam forming is performed on each subarray, and then, uniform weighted beam forming is performed on the output of each subarray to obtain a main channel beam pattern, which specifically includes the following steps:
the receiving signal of the sidelobe canceller consists of an expected signal, K interferences and noises, the noises are zero mean Gaussian white noises, and the receiving antenna array consists ofNA plurality of sub-arrays, each sub-array havingCThe array elements and receiving antennas are sharedMArray element
Figure 153753DEST_PATH_IMAGE078
Selecting L sub-arrays to form an auxiliary channel;
first, each subarray is conventionally beamformed to weight the received signal, and the output of the p-th subarray is
Figure 155207DEST_PATH_IMAGE079
Wherein
Figure 760632DEST_PATH_IMAGE080
is the array steering vector for the p-th sub-array to the desired signal,
Figure 226248DEST_PATH_IMAGE081
the noise vectors received for the array elements of the p-th sub-array,
Figure 954033DEST_PATH_IMAGE082
the matrix is formed by leading vectors of the p-th sub-matrix to K interferences;
Figure 380466DEST_PATH_IMAGE083
respectively the steering vector of the p-th sub-array in each interference direction,
Figure 851899DEST_PATH_IMAGE084
a column vector consisting of K interference signals received at the time t;
main channelOutput of (2)
Figure 172022DEST_PATH_IMAGE085
The output of the auxiliary channel is:
Figure 336287DEST_PATH_IMAGE086
Figure 250016DEST_PATH_IMAGE087
，
wherein,
Figure 259561DEST_PATH_IMAGE088
Figure 434190DEST_PATH_IMAGE089
Figure 954644DEST_PATH_IMAGE090
is as follows
Figure 417986DEST_PATH_IMAGE091
The individual sub-arrays point to an array steering vector of the desired signal,
Figure 293538DEST_PATH_IMAGE092
the noise vectors received for the array elements of the p-th sub-array,
Figure 525937DEST_PATH_IMAGE093
the p-th sub-array is guided in the corresponding interference direction by a proper amount,
Figure 969687DEST_PATH_IMAGE094
representing the order of the p-th subarray of the auxiliary channel in the total N subarrays;
definition of
Figure 654747DEST_PATH_IMAGE095
The position of the sub-array selected by the auxiliary channel determines the main channel beam pattern from the main channelIs a key matrix used for selecting the antenna position and is recorded as
Figure 333990DEST_PATH_IMAGE096
，
Figure 420894DEST_PATH_IMAGE097
Is the angle between the incident direction and the XOY plane,
Figure 35546DEST_PATH_IMAGE098
is the angle between the projection of the incident direction on the XOY plane and the X-axis,
Figure 207902DEST_PATH_IMAGE099
the height in the K interference directions is respectively
Figure 425256DEST_PATH_IMAGE100
，
Figure 632247DEST_PATH_IMAGE101
Wherein
Figure 417800DEST_PATH_IMAGE102
respectively, the spatial incident angles under the ith interference sphere coordinate.
Step S2 is to calculate the constraint condition of the auxiliary channel beam pattern, and the amplitude of the auxiliary channel in the interference direction is the same as the amplitude of the auxiliary channel in the direction corresponding to the main channel, and the specific process is as follows:
auxiliary channel beam pattern
Figure 77452DEST_PATH_IMAGE103
Wherein
Figure 98497DEST_PATH_IMAGE104
in the form of a vector of weights,
Figure 894415DEST_PATH_IMAGE105
is composed of
Figure 349405DEST_PATH_IMAGE106
The conjugate transpose of (2) weighting the outputs of the L sub-arrays of the auxiliary channel,
Figure 496352DEST_PATH_IMAGE107
and guiding vectors for the arrays of all array elements in the L sub-arrays of the auxiliary channel.
To eliminate interference, the main channel directional diagram and the auxiliary channel directional diagram need to have the same amplitude in the interference direction, that is, the amplitude is equal
Figure 321089DEST_PATH_IMAGE108
Obtaining K constraint conditions of K interferences, writing the constraint conditions into a matrix form to obtain a total constraint condition
Figure 237092DEST_PATH_IMAGE109
Memory for recording
Figure 98869DEST_PATH_IMAGE110
Then the constraint is written as
Figure 529851DEST_PATH_IMAGE111
。
Step S3 is to design an auxiliary channel directional diagram according to the minimum output power criterion and in combination with the constraint condition, and obtain a weight vector corresponding to each subarray of the auxiliary channel, which includes the following specific processes:
combining the constraint conditions obtained in the step S2, designing an auxiliary channel directional diagram according to the criterion of minimum output power, and obtaining the optimal weight corresponding to each subarray of the auxiliary channel at the moment;
the output power of the auxiliary channel is
Figure 830382DEST_PATH_IMAGE112
Wherein
Figure 804154DEST_PATH_IMAGE113
an autocorrelation matrix of the output signal for each sub-array of auxiliary channels,
Figure 899149DEST_PATH_IMAGE114
for the number of array elements contained in each sub-array,
Figure 83006DEST_PATH_IMAGE115
an identity matrix of dimensions; the process of finding the optimal weight of the auxiliary channel is written as an optimization problem:
Figure 187228DEST_PATH_IMAGE116
expression for obtaining optimal weight by Lagrange multiplier method
Figure 749927DEST_PATH_IMAGE117
Obtained by applying matrix inversion lemma
Figure 281403DEST_PATH_IMAGE118
Wherein, define
Figure 686976DEST_PATH_IMAGE119
And solving again by matrix inversion theorem
Figure 594890DEST_PATH_IMAGE120
Obtaining the optimal weight and the matrix determined by the position of the auxiliary channel subarray
Figure 779140DEST_PATH_IMAGE121
In the context of (a) or (b),
Figure 481516DEST_PATH_IMAGE122
。
step S4 is to calculate the main lobe distortion of the side lobe canceller, and obtain the relationship between the main lobe distortion and the position of the auxiliary channel subarray, and the specific process is as follows:
defining the main lobe distortion as the distortion of the auxiliary channel, which causes the total directional diagram of the side lobe canceller to generate in the direction of the desired signal, the amplitude of the total directional diagram at the desired signal is as the main lobe distortionD，
Figure 374386DEST_PATH_IMAGE123
，
Figure 820411DEST_PATH_IMAGE124
The signal direction magnitude is desired for the main channel pattern,
Figure 357703DEST_PATH_IMAGE125
for the auxiliary channel to expect the signal direction amplitude, and for the expected signal to be maximally preserved, the main lobe distortion is required to be minimum, i.e. the value of D is maximum, which is obtained from the optimal weight vector obtained in step S3
Figure 230981DEST_PATH_IMAGE126
。
Step S5 is to select the subarray position that minimizes the main lobe distortion as the optimal auxiliary channel subarray position, and the specific process is as follows:
as is known from step S4, the requirement for minimum distortion of the main lobe is equivalent to the requirement for minimum distortion of the main lobe
Figure 611147DEST_PATH_IMAGE127
Minimum value of (d);
defining a sub-array selection vector
Figure 595283DEST_PATH_IMAGE128
，
Figure 252660DEST_PATH_IMAGE129
Is one
Figure 296840DEST_PATH_IMAGE130
The vector of the dimension respectively represents the selection condition of the auxiliary channel to all N sub-arrays, elements are all composed of 0 and 1, 0 represents that the auxiliary channel does not select the sub-array, and 1 represents that the auxiliary channel selects the position sub-array; defining a matrix
Figure 164302DEST_PATH_IMAGE131
A matrix formed by multiplying a proper amount of steering vectors in the expected signal direction and K steering vectors in the interference direction is guided to all N sub-arrays; matrix determined by position of auxiliary channel subarrays
Figure 952129DEST_PATH_IMAGE132
And
Figure 464013DEST_PATH_IMAGE133
the relationship between them is:
Figure 679094DEST_PATH_IMAGE134
then, selecting the position of the subarray which causes the minimum main lobe distortion as the optimal position of the subarray of the auxiliary channel to describe as an optimization problem:
Figure 768272DEST_PATH_IMAGE135
the antenna position obtained by solving the optimization problem is the antenna position to be selected by the auxiliary channel which enables the main lobe distortion of the total direction diagram of the side lobe canceller to be minimum.
For the convenience of understanding the above technical aspects of the present invention, the following detailed description will be given of the above technical aspects of the present invention by way of specific examples.
Example 1
The method for selecting the auxiliary channel antenna of the side lobe canceller based on the directional diagram by using the single array element as the unit is proved to be correct.
A uniform linear array adopting 16 antennas is shown in figure 3, and the positions of the array elements are half of the wavelength of the information source
Figure 359791DEST_PATH_IMAGE136
The unit is that the incident angle of the expected signal is 0 degrees, two interferences exist, the incident angle is respectively 30 degrees and 60 degrees, and 4 array elements are selected to form an auxiliary channel for side lobe cancellation.
According to the method of the present invention, the positions of the selected auxiliary channels, i.e. positions 0, 1, 10, 11, are obtained, and the four position antennas are selected to make the main channel, the auxiliary channel, and the sidelobe canceller directional diagrams for the auxiliary channels, respectively, as shown in fig. 4(a) -4 (d). As seen from fig. 4(a) to 4(d), the main channel and the auxiliary channel directional patterns are equal in height in the interference direction, and the auxiliary channel directional pattern is extremely low in the desired signal direction. Therefore, nulls are generated in the total direction diagram in the synthesis direction diagram of the sidelobe canceller at 30 degrees and 60 degrees in the interference direction, and the cancellation of interference signals is realized; the height of 0 degrees in the direction of the expected signal is basically consistent with that of the main channel, the main lobe distortion is basically not generated, and the maximum retention of the expected signal is realized.
In summary, the position of the auxiliary channel selected by the invention in this embodiment has good performance.
Example 2
The method for selecting the auxiliary channel antenna of the side lobe canceller based on the directional diagram by using the single array element as the unit is additionally verified.
As shown in FIG. 5, the position of the array element is half of the wavelength of the source
Figure 959137DEST_PATH_IMAGE137
The unit is that the incidence angle of the expected signal is 0 degrees, three interferences exist, the incidence angles are respectively-60 degrees, 30 degrees and 60 degrees, and 6 array elements are selected to form an auxiliary channel for side lobe cancellation.
According to the method of the present invention, the positions of the selected auxiliary channels, i.e. positions 2, 4, 5, 10, 11, 12, are obtained, and the six position antennas are selected to make the main channel, the auxiliary channel, and the side lobe canceller directional diagrams for the auxiliary channels respectively as shown in fig. 6(a) -6 (d). It can be seen from the figure that the main channel and auxiliary channel directional diagrams are equal in height in the interference direction, and the auxiliary channel directional diagrams are extremely low in the desired signal direction. Therefore, nulls are generated in the total direction diagram in the synthesized directional diagram of the side lobe canceller at-60 degrees, 30 degrees and 60 degrees of the interference direction, and the cancellation of the interference signals is realized; the height of 0 degrees in the direction of the expected signal is basically consistent with that of the main channel, the main lobe distortion is basically not generated, and the maximum retention of the expected signal is realized.
In summary, the position of the auxiliary channel selected by the invention in this embodiment has good performance.
Example 3
The method verifies the correctness of the method for selecting the auxiliary channel subarrays of the side lobe canceller based on the directional diagram by taking the subarrays as units.
8 sub-arrays are adopted, each sub-array is a uniform linear array consisting of three array elements, as shown in figure 7, the position of the array elements is half of the wavelength of the information source
Figure 407436DEST_PATH_IMAGE137
The unit is that the incident angle of the expected signal is 0 degrees, two interferences exist, the incident angles are respectively 30 degrees and 60 degrees, and 3 sub-arrays are selected to form an auxiliary channel for side lobe cancellation.
According to the method of the present invention, the positions of the selected auxiliary channel subarrays, i.e., positions 0, 5, and 7, are obtained, and the three position subarrays are selected as the auxiliary channels to respectively make the directional diagrams of the main channel, the auxiliary channel, and the sidelobe canceller as shown in fig. 8(a) -8 (d). It can be seen from the figure that the main channel and auxiliary channel directional diagrams are equal in height in the interference direction, and the auxiliary channel directional diagrams are extremely low in the desired signal direction. Therefore, nulls are generated in the total direction diagram in the synthesis direction diagram of the sidelobe canceller at 30 degrees and 60 degrees in the interference direction, and the cancellation of interference signals is realized; the height of 0 degrees in the direction of the expected signal is basically consistent with that of the main channel, the main lobe distortion is basically not generated, and the maximum retention of the expected signal is realized.
In summary, the position of the auxiliary channel subarray selected by the present invention in this embodiment has a good performance.
Through the three embodiments, the optimal auxiliary channel array element position or the optimal auxiliary channel sub-array position has good performance, and the cancellation of interference signals and the maximum reservation of expected signals are realized.
After the graphs of the three embodiments are verified, the output performance of the side lobe canceller is further verified. The selected index is the relation between the input signal-to-noise ratio and the output signal-to-interference-and-noise ratio, as shown in fig. 9 and 10, two graphs respectively represent two situations of antenna selection by taking an array element as a unit and subarray selection by taking a subarray as a unit, in the graphs, the topmost curve reflects the performance of the optimal position auxiliary channel side lobe canceller, and the other three curves represent the performance of randomly selecting three auxiliary channel side lobe cancellers. It can be seen from the figure that the optimal auxiliary channel selected according to the method of the present invention has an output signal-to-noise ratio better than that in other cases, which can be higher than that in some poor cases by more than 10dB, and has an obvious performance improvement.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (8)

1. A method for selecting an auxiliary channel antenna of a sidelobe canceller based on a beam pattern is characterized by comprising the following steps:
s1: obtaining a main channel beam pattern, and calculating the amplitude of the main channel beam pattern in the interference direction;
s2: calculating the constraint condition of a beam pattern of an auxiliary channel, wherein the amplitude of the auxiliary channel in the interference direction is the same as the amplitude of the auxiliary channel in the corresponding direction of the main channel;
s3: designing an auxiliary channel directional diagram according to the minimum output power criterion and by combining the auxiliary channel beam directional diagram constraint condition of the step S2 to obtain a corresponding weight vector;
s4: calculating the main lobe distortion of the side lobe canceller to obtain the relation between the main lobe distortion and the auxiliary channel antenna position;
s5: and selecting the antenna position which enables the main lobe distortion to be minimum as the optimal auxiliary channel antenna position.
2. The method as claimed in claim 1, wherein for the selection of the auxiliary channel antenna position in unit of single array element, the specific process of step S1 is as follows:
the receiving signal of the sidelobe canceller consists of an expected signal, K interferences and noises, the noises are zero mean Gaussian white noises, the receiving antenna array has M array elements in total, N array elements are selected to form an auxiliary channel,
output of the main channel
Figure 903236DEST_PATH_IMAGE001
Wherein
Figure 434712DEST_PATH_IMAGE002
an array steering vector that points the main channel to the desired signal,
Figure 574706DEST_PATH_IMAGE003
noise vectors received for main channel array elements;
Figure 921767DEST_PATH_IMAGE004
a matrix of array steering vectors that point the main channel to K interferers,
Figure 666869DEST_PATH_IMAGE005
steering the vector for the array pointing to the ith interferer, i =1,2, …, K;
Figure 431563DEST_PATH_IMAGE006
a column vector consisting of K interference signals received at the time t;
output of auxiliary channel
Figure 262116DEST_PATH_IMAGE007
Wherein
Figure 380244DEST_PATH_IMAGE008
each element represents a signal received by the auxiliary channel array element at the corresponding position respectively;
Figure 245432DEST_PATH_IMAGE009
for the noise vectors received by the auxiliary channel array elements,
Figure 915448DEST_PATH_IMAGE010
a matrix of array steering vectors pointing to K interferers for the auxiliary channel,
Figure 170980DEST_PATH_IMAGE011
steering the vector for the array pointing to the ith interferer, i =1,2, …, K;
the main channel beam pattern is obtained by the conventional beam forming of all array elements of the main channel and is recorded as
Figure 155117DEST_PATH_IMAGE012
，
Figure 937128DEST_PATH_IMAGE013
Is the angle between the incident direction and the XOY plane,
Figure 981307DEST_PATH_IMAGE014
is the angle between the projection of the incident direction on the XOY plane and the X-axis,
Figure 724135DEST_PATH_IMAGE015
the height in the K interference directions is respectively
Figure 511963DEST_PATH_IMAGE016
Wherein
Figure 148480DEST_PATH_IMAGE017
respectively, the spatial incident angles under the ith interference sphere coordinate.
3. The method as claimed in claim 1 or 2, wherein for the selection of the auxiliary channel antenna position in unit of single array element, the specific process of step S2 is as follows:
auxiliary channel beam pattern
Figure 363561DEST_PATH_IMAGE018
Wherein
Figure 826641DEST_PATH_IMAGE019
in the form of a vector of weights,
Figure 418159DEST_PATH_IMAGE020
is composed of
Figure 909184DEST_PATH_IMAGE021
The conjugate transpose of (a) is performed,
Figure 967270DEST_PATH_IMAGE022
for assisting the channel array to guide the vector, for achieving interference cancellation, it is necessary to
Figure 747007DEST_PATH_IMAGE023
Obtaining K constraint conditions of K interferences, writing the constraint conditions into a matrix form to obtain a total constraint condition
Figure 673374DEST_PATH_IMAGE024
Memory for recording
Figure 894271DEST_PATH_IMAGE025
Then the constraint is written as
Figure 716734DEST_PATH_IMAGE026
。
4. The method as claimed in claim 1 or 2, wherein for the selection of the auxiliary channel antenna position in unit of single array element, the specific process of step S3 is as follows:
combining the constraint conditions obtained in the step S2, designing an auxiliary channel directional diagram according to the minimum output power criterion, and obtaining the optimal weight corresponding to the antenna position of the auxiliary channel at the moment;
the output power of the auxiliary channel is
Figure 983767DEST_PATH_IMAGE027
Wherein
Figure 713826DEST_PATH_IMAGE028
the autocorrelation matrix of the received signal for the auxiliary channel, E represents the desired operation,
Figure 117125DEST_PATH_IMAGE029
in order to be able to measure the power of the noise,
Figure 782593DEST_PATH_IMAGE030
is composed of
Figure 68081DEST_PATH_IMAGE031
The unit array is formed by a plurality of unit arrays,
Figure 805093DEST_PATH_IMAGE032
forming a diagonal matrix by the power of K interferences; the process of finding the optimal weight of the auxiliary channel is written as an optimization problem:
Figure 513765DEST_PATH_IMAGE033
expression for obtaining optimal weight by Lagrange multiplier method
Figure 412451DEST_PATH_IMAGE034
Obtained by applying matrix inversion lemma
Figure 450814DEST_PATH_IMAGE035
Wherein, define
Figure 725938DEST_PATH_IMAGE036
Again using matrix inversion theorem to solve
Figure 775933DEST_PATH_IMAGE037
Obtaining the optimal weight and a steering vector matrix determined by the position of the auxiliary channel antenna
Figure 111100DEST_PATH_IMAGE038
In the context of (a) or (b),
Figure 371180DEST_PATH_IMAGE039
。
5. the method as claimed in claim 1 or 2, wherein for the selection of the auxiliary channel antenna position in unit of single array element, the specific process of step S4 is as follows:
defining the main lobe distortion as the distortion of the auxiliary channel, which causes the total directional diagram of the side lobe canceller to generate in the direction of the desired signal, the amplitude of the total directional diagram at the desired signal is as the main lobe distortionD，
Figure 449994DEST_PATH_IMAGE040
The signal direction magnitude is desired for the main channel pattern,
Figure 620076DEST_PATH_IMAGE041
for the auxiliary channel desired signal direction amplitude, for maximum retention of the desired signal, minimum main lobe distortion is required, i.e. minimum main lobe distortion is requiredDIs the maximum value, is obtained from the optimal weight vector obtained in step S3
Figure 860564DEST_PATH_IMAGE042
。
6. The method as claimed in claim 1 or 2, wherein for the selection of the auxiliary channel antenna position in unit of single array element, the specific process of step S5 is as follows:
as is known from step S4, the requirement for minimum distortion of the main lobe is equivalent to the requirement for minimum distortion of the main lobe
Figure 873519DEST_PATH_IMAGE043
Minimum value of (d);
defining an antenna selection vector
Figure 490446DEST_PATH_IMAGE044
，
Figure 515033DEST_PATH_IMAGE045
Is one
Figure 926423DEST_PATH_IMAGE046
The vector of the dimension respectively represents the selection condition of the auxiliary channel to all M array elements, all elements are composed of 0 and 1, 0 represents that the auxiliary channel does not select the array element, and 1 represents that the auxiliary channel selects the position array element; two matrices are defined which are,
Figure 161095DEST_PATH_IMAGE047
a matrix formed by guiding vectors in K interference directions for all M array elements;
Figure 581712DEST_PATH_IMAGE048
steering vectors of all M array elements in the direction of the expected signal; matrix determined by auxiliary channel antenna position
Figure 693763DEST_PATH_IMAGE049
The relationship between them is:
Figure 603950DEST_PATH_IMAGE050
then, the antenna position which makes the main lobe distortion minimum is selected as the optimal auxiliary channel antenna position to describe as an optimization problem:
Figure 263601DEST_PATH_IMAGE051
and solving the optimization problem to obtain the antenna position which is the auxiliary channel antenna position which enables the main lobe distortion of the total direction diagram of the side lobe canceller to be minimum.
7. The method as claimed in claim 1, wherein for the selection of the auxiliary channel antenna position using the subarray as a unit, in step S1, the beamforming is performed on each subarray first, and then the uniformly weighted beamforming is performed on the output of each subarray to obtain the main channel beam pattern, and the specific process is as follows:
the receiving signal of the sidelobe canceller consists of an expected signal, K interferences and noises, the noises are zero mean Gaussian white noises, and the receiving antenna array consists ofNA plurality of sub-arrays, each sub-array havingCThe array elements and receiving antennas are sharedMArray element
Figure 160013DEST_PATH_IMAGE052
Selecting L sub-arrays to form an auxiliary channel;
first, each subarray is conventionally beamformed to weight the received signal, and the output of the p-th subarray is
Figure 221510DEST_PATH_IMAGE053
Wherein
Figure 302599DEST_PATH_IMAGE054
is the array steering vector for the p-th sub-array to the desired signal,
Figure 183967DEST_PATH_IMAGE055
the noise vectors received for the array elements of the p-th sub-array,
Figure 884070DEST_PATH_IMAGE056
the matrix is formed by leading vectors of the p-th sub-matrix to K interferences;
Figure 800073DEST_PATH_IMAGE057
respectively the steering vector of the p-th sub-array in each interference direction,
Figure 52063DEST_PATH_IMAGE058
a column vector consisting of K interference signals received at the time t;
main channel inputGo out
Figure 686307DEST_PATH_IMAGE059
The output of the auxiliary channel is:
Figure 924521DEST_PATH_IMAGE060
Figure 491769DEST_PATH_IMAGE061
，
wherein,
Figure 852343DEST_PATH_IMAGE062
an array steering vector for the p-th sub-array to the desired signal,
Figure 147451DEST_PATH_IMAGE063
is as follows
Figure 251673DEST_PATH_IMAGE064
The noise vectors received by the array elements of the individual sub-arrays,
Figure 204586DEST_PATH_IMAGE065
is as follows
Figure 736061DEST_PATH_IMAGE066
The direction of each sub-array in the corresponding interference direction is proper,
Figure 17001DEST_PATH_IMAGE067
Figure 924914DEST_PATH_IMAGE068
，
definition of
Figure 670016DEST_PATH_IMAGE069
Is selected by the auxiliary channelThe position of the selected subarray is determined, and the main channel beam pattern is obtained by the conventional beam forming of all array elements of the main channel and is recorded as
Figure 434710DEST_PATH_IMAGE070
，
Figure 937367DEST_PATH_IMAGE071
The height in the K interference directions is respectively
Figure 383392DEST_PATH_IMAGE072
，
Figure 310896DEST_PATH_IMAGE073
Wherein
Figure 449754DEST_PATH_IMAGE074
respectively, the spatial incident angles under the ith interference sphere coordinate.
8. The method as claimed in claim 1, wherein the array is linear or planar in step S1, and the antenna position is half of the source wavelength
Figure 174127DEST_PATH_IMAGE075
In the unit of the number of the units,
Figure 423843DEST_PATH_IMAGE076
is the source wavelength.
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