CN114841024A - Beam forming method and device based on vector expansion co-prime matrix - Google Patents

Beam forming method and device based on vector expansion co-prime matrix Download PDF

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CN114841024A
CN114841024A CN202210780487.4A CN202210780487A CN114841024A CN 114841024 A CN114841024 A CN 114841024A CN 202210780487 A CN202210780487 A CN 202210780487A CN 114841024 A CN114841024 A CN 114841024A
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array
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matrix
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CN114841024B (en
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吕曜辉
陈晓
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Ocean University of China
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Abstract

The invention discloses a beam forming method and device based on a vector expansion co-prime matrix. The method comprises the following steps: step 1: under the premise of setting the array element number requirement of the vector array, the underwater acoustic vector array of the appointed physical array element is subjected to cross-prime array element number drawing to obtain an initial valueMAndN(ii) a Step 2: according to the characteristics of the output zero point and the grating lobe position of the sub-array wave beam of the co-prime array, an array expansion factor is set, and the number of elements of the initial co-prime array is expanded; and step 3: changing the sub-array data channel combination by using a sound pressure and vibration velocity combined processing method to reduce array beam output grating lobes; and 4, step 4: an array weighting factor based on sound pressure and vibration velocity combined processing is set to further reduce beam output side lobes; and 5: and forming by utilizing a co-prime array beam to obtain the final output space spectrum synthesis of the vector expanded co-prime array beam. The invention can obtain the expanded co-prime vector array beam output with low grating lobe, low side lobe and narrow main lobe.

Description

Beam forming method and device based on vector expansion co-prime matrix
Technical Field
The invention relates to an underwater acoustic signal processing technology, in particular to a beam forming method and device based on a vector expansion co-prime matrix.
Background
In the underwater acoustic vector array signal processing, for a uniform array, the limited array element number limits the array aperture, thereby limiting the array degree of freedom. The sparse array is provided, so that the traditional uniform array obtains larger array aperture and higher degree of freedom, and further obtains higher spectral estimation precision and more advantageous resolution. The co-prime array isA special structure array of the sparse array can be formed by combining two sub-arrays of which the array elements are prime numbers with each other, and the array element spacing of the two sub-arrays is the multiplication of the array element number of the other sub-array by half-wave spacing. Compared with other sparse arrays, the array element position formed by the co-prime array has fixed closed solution, is easier to realize actually, has higher array freedom degree and smaller cross coupling because the array element interval is integral multiple of half wavelength, and when the sub-array elements are respectively the numberMAndNthen, the degree of freedom can reach O: (MN). However, when the co-prime array type and the co-prime array beam forming processing method are applied to the underwater acoustic array, the problems of high grating lobes and high side lobes exist, and the beam forming performance and the accuracy of DOA estimation are further influenced.
Disclosure of Invention
The invention aims to solve the problems that the high sidelobe grating lobe of a co-prime array type is applied to an underwater acoustic vector array, so that the performance of beam forming and target azimuth estimation is influenced, and the complexity of software and hardware is high in engineering implementation.
In order to achieve the purpose, the invention adopts the following technical scheme:
a beam forming method based on a vector-expanded co-prime matrix comprises the following steps:
step 1: constructing a co-prime data pair on the premise of setting the requirement of the array element number of the vector arrayMAndNsetting up the initial value of the number of the underwater acoustic vector array co-prime array elements of the appointed physical array elements;
step 2: based on the characteristics of beam output zero points and grating lobes of the co-prime array subarray, formulating a vector co-prime array expansion scheme, and determining array expansion factors to obtain an expanded vector co-prime array; the vector co-prime matrix expansion scheme adopts a sub-matrix zero grating lobe cross adjustment method, and adopts
Figure 414834DEST_PATH_IMAGE001
：
Figure 892870DEST_PATH_IMAGE002
Figure 204902DEST_PATH_IMAGE003
Wherein
Figure 518072DEST_PATH_IMAGE004
，
Figure 594875DEST_PATH_IMAGE005
Is an integer which is the number of the whole,
Figure 727916DEST_PATH_IMAGE006
，
Figure 843639DEST_PATH_IMAGE007
respectively, the spreading factors of the co-prime submatrices; when in use
Figure 745736DEST_PATH_IMAGE008
，
Figure 52827DEST_PATH_IMAGE009
According to the obtained spreading factor
Figure 407585DEST_PATH_IMAGE006
And
Figure 61420DEST_PATH_IMAGE007
expanding the co-prime subarrays;
and step 3: carrying out sound pressure and vibration velocity combined processing on the extended vector co-prime array obtained in the step 2 to obtain a vector channel data combination;
and 4, step 4: designing a weighting coefficient based on a sound pressure channel combination form of the extended vector co-prime array, and carrying out extended vector co-prime array weighting by adopting a data independent window function;
and 5: performing beam forming on the extended vector co-prime array based on the co-prime array beam forming method to obtain the final spatial spectrum output
Figure 83603DEST_PATH_IMAGE010
。
A vector-extended co-prime matrix-based beamforming apparatus, comprising:
a relatively prime array element number construction module for constructing relatively prime data pairs on the premise of setting the vector array element number requirementMAndNsetting up the initial value of the number of the underwater acoustic vector array co-prime array elements of the appointed physical array elements;
the vector co-prime matrix expansion module is used for obtaining an expanded vector co-prime matrix by adopting a sub-matrix zero-point grating lobe cross adjustment method based on the characteristics of the output zero point and the grating lobe of the sub-matrix wave beam of the co-prime matrix; the method for adjusting the zero grating lobe crossing by adopting the subarray comprises the following steps: get
Figure 33367DEST_PATH_IMAGE011
：
Figure 141000DEST_PATH_IMAGE012
Figure 598526DEST_PATH_IMAGE013
Wherein
Figure 209636DEST_PATH_IMAGE004
，
Figure 141687DEST_PATH_IMAGE005
Is an integer which is the number of the whole,
Figure 471037DEST_PATH_IMAGE006
，
Figure 466675DEST_PATH_IMAGE007
respectively, the spreading factors of the co-prime submatrices; when in use
Figure 197871DEST_PATH_IMAGE008
，
Figure 755016DEST_PATH_IMAGE009
According to the obtained spreading factor
Figure 571663DEST_PATH_IMAGE006
And
Figure 636571DEST_PATH_IMAGE007
expanding the co-prime subarrays;
the vector channel data combination module is used for carrying out sound pressure and vibration velocity combined processing on the expanded vector co-prime array obtained by the vector co-prime array expansion module to obtain a vector channel data combination;
the weighting module is used for designing a weighting coefficient based on a sound pressure channel combination form of the extended vector co-prime array, and carrying out extended vector co-prime array weighting by adopting a data independent window function;
a beam forming module for performing beam forming on the extended vector co-prime array based on the co-prime array beam forming method to obtain the final spatial spectrum output
Figure 222273DEST_PATH_IMAGE010
。
A computer device, comprising:
memory storing one or more computer programs that, when executed by one or more processors, cause the one or more processors to perform the steps of the vector extended co-prime matrix based beamforming method as described above.
A computer storage medium, storing one or more computer programs which, when executed by one or more processors, cause the one or more processors to perform the steps of the vector extended co-prime matrix based beamforming method as described above.
Has the advantages that: the invention applies a special sparse array form-co-prime array in a vector hydrophone, carries out array expansion aiming at the problems of the vector co-prime array, adopts the sound pressure and vibration velocity combined processing and the array weighting method to finally improve the beam forming of the expanded vector co-prime array, and finally can obtain the expanded co-prime vector array beam output with low grating lobe, low side lobe and narrow main lobe. Compared with the traditional uniform vector array, under the condition that the array element number is limited and the array element number is the same, the invention can obtain the expanded vector co-prime array, improve the array aperture and further improve the resolution of array beam formation, and simultaneously obtain lower grating lobes and side lobes; under the condition that the array aperture is limited, the invention can realize better beam forming effect under the condition of uniform vector full array by utilizing lower hardware cost, thereby improving the target direction estimation performance. Compared with the traditional sparse vector hydrophone array target direction estimation, the method aims at applying the co-prime array thought to the vector hydrophone array to carry out beam forming, and aims at the characteristics of the vector array, and obtains the additional advantages of the vector co-prime expansion array by utilizing different channel combinations. The array expansion and the array weighting are combined, the problem of main lobe broadening caused by the array weighting is neutralized to a certain extent, and finally the main lobe width is narrowed, so that the beam forming spatial resolution is improved.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic diagram of a co-prime matrix geometry;
FIG. 3 is a schematic diagram of the output characteristics of a co-prime subarray beam;
FIG. 4 is a schematic diagram of a vector hydrophone structure;
FIG. 5 is a comparison graph of different channel data combinations of vectors;
FIG. 6 is a graph comparing the weighting effect of different window function arrays;
FIG. 7 is a graph comparing the effect of different extension of the co-prime submatrix in the simulation experiment;
FIG. 8 is a comparison graph of the vector co-prime matrix and vector uniform matrix beams windowed and un-windowed under the same array elements in a simulation experiment;
fig. 9 is a comparison of the effect of the windowed vector co-prime matrix and the equal aperture vector uniform full matrix beam in the simulation experiment.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
As shown in fig. 1, a beam forming method based on vector-extended co-prime matrix includes the following steps:
step 1: constructing a reciprocal prime number pair on the premise of setting the requirement of the array element number of the vector arrayMAndNfor underwater acoustic vector of specified physical array elementsThe quantity array carries out the drawing up of the initial value of the number of the elements of the relatively prime array.
In different application scenarios, forMAndNthe choice of (a) is slightly different. Illustratively, when the number of array elements is inDUnder the limitation of (2), can utilizeMAndNconstruct a co-prime array, guaranteeM+N-1=DThe large array aperture under the limited array element number can be achieved; and when the aperture of the array is limited, the hardware load of the array can be saved and the spatial resolution can be improved by utilizing the co-prime array.
Step 2: and formulating a vector co-prime matrix expansion scheme based on the beam output zero point and the grating lobe characteristics of the co-prime matrix sub-array, and determining an array expansion factor to obtain an expanded vector co-prime matrix.
A mathematical model was built according to the geometric relationships shown in figure 2. The sub-array elements of the vector co-prime array are respectivelyMAndNthus the total number of array elements isM+N-1. Consider thatLThe far-field uncorrelated narrowband signals are incident to the vector co-prime matrix, and the received signals of the vector co-prime matrix at the moment t are as follows:
Figure 212969DEST_PATH_IMAGE014
（1）
wherein the variables are defined as follows:
Figure 251332DEST_PATH_IMAGE015
receiving a signal vector for the array;
Figure 182248DEST_PATH_IMAGE016
is a statistically independent gaussian noise component;
Figure 389501DEST_PATH_IMAGE017
is a matrix of the units,
Figure 786984DEST_PATH_IMAGE018
is the noise power;
Figure 578223DEST_PATH_IMAGE019
wherein, in the step (A),
Figure 719354DEST_PATH_IMAGE020
，
Figure 784043DEST_PATH_IMAGE021
，
Figure 352427DEST_PATH_IMAGE022
a pressure component and a vibration velocity channel component representing a noise vector along an x-axis and a y-axis;
'T' is the transpose of a matrix or vector;
Figure 630962DEST_PATH_IMAGE023
is an array flow pattern matrix'
Figure 841363DEST_PATH_IMAGE024
' is the kronecker product, wherein,
Figure 757629DEST_PATH_IMAGE025
（2）
Figure 965757DEST_PATH_IMAGE026
（3）
Figure 731587DEST_PATH_IMAGE027
for array flow pattern vectors targeted in a vector array,
Figure 40952DEST_PATH_IMAGE028
is a vector of the direction of the vector sensor,dthe distance between the array elements is the same as the distance between the array elements,
Figure 575839DEST_PATH_IMAGE029
in order to be the wavelength of the signal,
Figure 158130DEST_PATH_IMAGE030
is the signal incidence orientation.
Suppose that when the target signal is oriented
Figure 145678DEST_PATH_IMAGE031
Then, the co-prime vector array received signal may be written as:
Figure 432302DEST_PATH_IMAGE032
the beamforming output of the array results in:
Figure 323160DEST_PATH_IMAGE033
（4）
'H' is the conjugate transpose of the matrix.
Bringing (2) and (3) into (4) yields:
Figure 669828DEST_PATH_IMAGE034
Figure 144672DEST_PATH_IMAGE035
（5）
wherein the content of the first and second substances,
Figure 969408DEST_PATH_IMAGE036
（6）
Figure 705984DEST_PATH_IMAGE037
（7）
whereinbAndcsatisfies the following conditions:
Figure 223553DEST_PATH_IMAGE038
the Product and Min methods are more classical co-prime array beam forming methods, and because the Min method can obtain lower grating lobes than the Product method, in the present invention, the Min method more suitable for the scene is selected:
first, the beam outputs of the co-prime matrix sub-array are respectively:
Figure 185692DEST_PATH_IMAGE039
Figure 814120DEST_PATH_IMAGE040
（8）
Figure 413991DEST_PATH_IMAGE041
Figure 102461DEST_PATH_IMAGE042
（9）
the beam output based on the Min method is then:
Figure 551897DEST_PATH_IMAGE043
（10）
bringing (8) and (9) into (10) yields:
Figure 718436DEST_PATH_IMAGE044
（11）
wherein the content of the first and second substances,
Figure 435463DEST_PATH_IMAGE045
（12）
Figure 29255DEST_PATH_IMAGE046
（13）
with reference to fig. 3, the specific calculation manner of step 2 is as follows:
first, the beam directivities of the sound pressure co-prime matrix sub-array are respectively
Figure 700408DEST_PATH_IMAGE047
And
Figure 936217DEST_PATH_IMAGE048
it can be expressed as:
Figure 510680DEST_PATH_IMAGE049
（14）
Figure 806533DEST_PATH_IMAGE050
（15）
for the
Figure 699402DEST_PATH_IMAGE047
The positions of some characteristic points of the beam output are represented as follows:
Figure 207744DEST_PATH_IMAGE051
（16）
it can be seen that when
Figure 905222DEST_PATH_IMAGE052
Can obtain its maximum value when
Figure 371976DEST_PATH_IMAGE053
The grating lobe value can be obtained.
Likewise, for
Figure 17721DEST_PATH_IMAGE054
The distribution characteristics of the extreme points are as follows:
Figure 329753DEST_PATH_IMAGE055
（17）
it can be seen that when
Figure 878809DEST_PATH_IMAGE056
Can obtain its maximum value when
Figure 250884DEST_PATH_IMAGE057
The grating lobe value can be obtained.
And the null values of the output beams of the two sub-arrays are:
Figure 383925DEST_PATH_IMAGE058
（18）
in order to reduce the area of the grating lobe in the cross-prime total array beam output, only the overlapping area of the grating lobe and the overlapping area of the grating lobe and the side lobe need to be reduced as much as possible, and the overlapping area is taken
Figure 234070DEST_PATH_IMAGE059
The invention designs a subarray zero grating lobe cross adjustment method which is expressed as follows:
Figure 900281DEST_PATH_IMAGE060
（19）
Figure 443258DEST_PATH_IMAGE061
（20）
Figure 532436DEST_PATH_IMAGE062
，
Figure 451851DEST_PATH_IMAGE063
is an integer which is the number of the whole,
Figure 709919DEST_PATH_IMAGE064
，
Figure 689376DEST_PATH_IMAGE065
respectively the spreading factors of the two sub-arrays. Find when
Figure 531431DEST_PATH_IMAGE066
，
Figure 988957DEST_PATH_IMAGE067
In time, no extension is obtained for the co-prime subarrays; when in use
Figure 116180DEST_PATH_IMAGE068
，
Figure 266539DEST_PATH_IMAGE069
，
Figure 595889DEST_PATH_IMAGE070
，
Figure 591527DEST_PATH_IMAGE071
Time of flightMThe sub-array is expanded when
Figure 824187DEST_PATH_IMAGE072
，
Figure 145447DEST_PATH_IMAGE073
，
Figure 493252DEST_PATH_IMAGE074
，
Figure 761422DEST_PATH_IMAGE075
Time of flightNExpanding a subarray;
Figure 845659DEST_PATH_IMAGE076
，
Figure 72241DEST_PATH_IMAGE077
both subarrays are expanded. Therefore, when the formula (19) and the formula (20) are satisfied, and
Figure 172921DEST_PATH_IMAGE078
，
Figure 979203DEST_PATH_IMAGE079
then, the expansion factor can be obtained according to the obtained expansion factor
Figure 717614DEST_PATH_IMAGE080
And
Figure 583939DEST_PATH_IMAGE081
the two sub-arrays are expanded.
And step 3: and (3) carrying out sound pressure and vibration velocity combined processing on the extended vector co-prime matrix obtained in the step (2) to obtain a vector channel data combination.
With reference to fig. 4 and 5, the step 3 specifically includes: the received signal for a vector hydrophone can be expressed as:
Figure 906336DEST_PATH_IMAGE082
（21）
Figure 516309DEST_PATH_IMAGE083
is composed of
Figure 580998DEST_PATH_IMAGE084
The sound pressure information received by the vector hydrophone,
Figure 149382DEST_PATH_IMAGE085
and
Figure 427917DEST_PATH_IMAGE086
the vibration velocity component information is orthogonal to each other.
By combining the vector hydrophone channel data, one can obtain:
Figure 372739DEST_PATH_IMAGE087
（22）
Figure 289005DEST_PATH_IMAGE088
and
Figure 28291DEST_PATH_IMAGE089
two kinds of combined vibration velocity are adopted, wherein
Figure 528542DEST_PATH_IMAGE085
And
Figure 73793DEST_PATH_IMAGE086
respectively a target orientation and a guiding orientation.
Several combinations are known to exist:
Figure 44898DEST_PATH_IMAGE090
the processing method of the invention is based on a combination by analysis and comparison
Figure 486244DEST_PATH_IMAGE091
Unfolding; additional directional gain can be obtained using a dataform constructed from channel combinations. The achievable directivity for the combination of channels is:
Figure 473791DEST_PATH_IMAGE092
（23）
and 4, step 4: based on the sound pressure channel combination form of the extended vector co-prime array, a weighting coefficient is designed, and a window function with independent data is adopted to carry out the weighting of the extended vector co-prime array.
Combining different window weighting comparisons shown in fig. 6, in order to further reduce the side lobe of the beam output of the co-prime array, the beam output of the sub-array is further optimized, the sub-array is respectively processed according to the side lobe optimization of the uniform linear array, and the side lobe problem existing in the sub-array output is optimized by utilizing the array weighting. Meanwhile, considering the calculation cost and the operation load of array hardware and software, a window function irrelevant to data is selected for array weighting operation, the existing window function array weighting is analyzed and compared, and finally a Hamming window is selected for side lobe optimization of the output of the co-prime subarray wave beam, namely the weight values expressed in the formulas (12) and (13) are respectively changed into
Figure 589777DEST_PATH_IMAGE093
And
Figure 979170DEST_PATH_IMAGE094
the beam outputs of the obtained co-prime subarrays are respectively
Figure 325838DEST_PATH_IMAGE095
And
Figure 535102DEST_PATH_IMAGE096
(ii) a Wherein the content of the first and second substances,
Figure 118094DEST_PATH_IMAGE097
and
Figure 361993DEST_PATH_IMAGE098
the sub-matrix weight values generated after the channel combination windowing is carried out on the expanded vector co-prime matrix,
Figure 145141DEST_PATH_IMAGE099
and
Figure 107281DEST_PATH_IMAGE100
respectively the array output obtained after the extended vector co-prime array is combined by the channels,
Figure 237174DEST_PATH_IMAGE101
the hamming window weight coefficient:
Figure 538842DEST_PATH_IMAGE102
（24）
Figure 24050DEST_PATH_IMAGE103
（25）
and 5: and obtaining improved beam forming of the extended vector co-prime matrix based on the co-prime matrix beam forming method to obtain final spatial spectrum output.
In the invention, the output of the co-prime matrix wave beam obtained in the step 4 is processed by a Min method, and finally an output space power spectrum formed by the extended vector co-prime matrix wave beam is obtained:
Figure 207907DEST_PATH_IMAGE104
（26）
the performance of the method is verified by the following simulation experiment.
Simulation experiments are shown in fig. 7, which is a beam directivity comparison of different spreading cases of the vector co-prime matrix. Conditions are as follows: the elements of the vector co-prime matrix are respectively
Figure 138560DEST_PATH_IMAGE105
，
Figure 357052DEST_PATH_IMAGE106
Signal frequency 500Hz, sampling rate 20k, target orientation 70 °, signal-to-noise ratio 20 dB. Fig. 7 (a) shows the total beam output of the array when the spreading factors are all 1, that is, when both the two subarrays of the co-prime array are not spread, it can be seen that there are higher grating lobes and side lobes in the beam output of the array, fig. 7 (b) and fig. 7 (c) respectively show that one of the two subarrays is spread, and the other is not spread, it can be seen that the grating lobes are reduced when the beam output of the array is output, and fig. 7 (d) shows that the beam output of the array when both the two subarrays are spread, it can be seen that the grating lobes and the side lobes are reduced with respect to the spreading of one of the subarrays, and the problems of the grating lobes and the side lobes are significantly improved with respect to the beam output when not spread.
As shown in fig. 8, the second simulation experiment is to compare the weighted and unweighted vector relatively-prime array arrays and unweighted vector uniform arrays subjected to channel combination preprocessing with the beam output conditions when the arrays are equal in array element. Simulation conditions are as follows: the elements of the vector co-prime matrix are respectively
Figure 216423DEST_PATH_IMAGE105
，
Figure 887576DEST_PATH_IMAGE106
Signal frequency 500Hz, sampling rate 20k, target orientation 30 °, signal-to-noise ratio 20 dB. It can be seen that for a uniform vector array under the same array element, better port and starboard rejection ratio can be obtained by performing channel data combination preprocessing output, and after array weighting is performed on the basis, lower grating lobes and side lobes can be obtained, so that the method has certain significance for subsequent target detection and azimuth estimation.
Fig. 9 shows a comparison between the output of the beam of the vector co-prime matrix and the output of the beam of the same-aperture vector uniform full matrix. Simulation conditions are as follows:
Figure 359271DEST_PATH_IMAGE107
，
Figure 432269DEST_PATH_IMAGE108
，
Figure 462542DEST_PATH_IMAGE109
and the array element number of the vector uniform full array is 59 elements, so that the vector co-prime array saves 16% of hardware load compared with the vector uniform full array. The signal frequency is 500Hz, the sampling rate is 20k, the target orientation is 15 degrees, and the signal-to-noise ratio is 20 dB. It can be seen that after the array hardware burden is saved, the beam main lobe width equivalent to that of a full array can be obtained through the processing method provided by the invention, and better port and starboard inhibition capability and lower side lobes and grating lobes can be obtained.
The invention provides an improved method for forming beams based on an underwater sound co-prime vector array, which combines the characteristics of a vector array, utilizes the characteristics of beam zero points and grating lobes output by a co-prime vector sub-array, designs a co-prime vector array expansion method, combines vector channel data by a sound pressure and vibration velocity joint processing method after obtaining an expanded vector co-prime array, and finally designs array weighting to finally obtain expanded vector co-prime array beam forming output with suppressed side lobes and grating lobes. The method improves the beam forming performance of the vector co-prime array, obtains high spatial resolution, reduces grating lobes and side lobes, provides possibility for realizing stable beam forming of the vector co-prime array, and greatly saves array hardware burden compared with a uniform vector array with the same aperture.
The invention also provides a beam forming device based on the vector-expanded co-prime matrix, which comprises:
a mutual prime array element number construction module for constructing a mutual prime data pair on the premise of setting the vector array element number requirementMAndNdrawing up the initial value of the number of the underwater acoustic vector array co-prime array elements of the appointed physical array elements;
the vector co-prime matrix expansion module is used for obtaining an expanded vector co-prime matrix by adopting a sub-matrix zero-point grating lobe cross adjustment method based on the characteristics of the output zero point and the grating lobe of the sub-matrix wave beam of the co-prime matrix; the method for adjusting the zero grating lobe crossing by adopting the subarray comprises the following steps: get the
Figure 355412DEST_PATH_IMAGE110
：
Figure 899307DEST_PATH_IMAGE111
（27）
Figure 92390DEST_PATH_IMAGE112
（28）
Wherein
Figure 27985DEST_PATH_IMAGE113
，
Figure 408151DEST_PATH_IMAGE114
Is an integer which is the number of the whole,
Figure 221649DEST_PATH_IMAGE115
，
Figure 862714DEST_PATH_IMAGE116
respectively, the spreading factors of the co-prime submatrices; when the temperature is higher than the set temperature
Figure 438052DEST_PATH_IMAGE117
，
Figure 69629DEST_PATH_IMAGE118
According to the obtained spreading factor
Figure 185352DEST_PATH_IMAGE119
And
Figure 415345DEST_PATH_IMAGE120
expanding the co-prime subarrays;
the vector channel data combination module is used for carrying out sound pressure and vibration velocity combined processing on the expanded vector co-prime array obtained by the vector co-prime array expansion module to obtain a vector channel data combination;
the weighting module is used for designing a weighting coefficient based on a sound pressure channel combination form of the extended vector co-prime array, and carrying out extended vector co-prime array weighting by adopting a data independent window function;
a beam forming module for performing beam forming on the extended vector co-prime array based on the co-prime array beam forming method to obtain the final spatial spectrum output
Figure 725366DEST_PATH_IMAGE121
。
According to the embodiment of the invention, the mutual prime array element number construction module is used for constructing the mutual prime array element number in different application scenesMAndNthe choice of (a) is slightly different. Illustratively, when the number of elements is in the arrayDUnder the limitation of (2), can utilizeMAndNconstruct co-prime arrays, guaranteeM+N-1=DThe large array aperture under the limited array element number can be achieved; and when the aperture of the array is limited, the hardware load of the array can be saved and the spatial resolution can be improved by utilizing the co-prime array.
According to an embodiment of the present invention, the vector channel data combining module combines the vector hydrophone channel data according to the following equation:
Figure 548966DEST_PATH_IMAGE122
（29）
Figure 468380DEST_PATH_IMAGE123
and
Figure 490563DEST_PATH_IMAGE124
the vibration speed is combined into two vibration speeds, wherein,
Figure 48450DEST_PATH_IMAGE125
（30）
Figure 156083DEST_PATH_IMAGE126
for the sound pressure information received by the vector hydrophone,
Figure 613610DEST_PATH_IMAGE127
and
Figure 195026DEST_PATH_IMAGE128
is the information of the vibration velocity components which are orthogonal to each other,
Figure 79805DEST_PATH_IMAGE129
and
Figure 674735DEST_PATH_IMAGE130
respectively a target orientation and a guiding orientation.
The invention is based on combination in the embodiment
Figure 762383DEST_PATH_IMAGE131
And expanding to obtain the directivity of the combined channel as follows:
Figure 759158DEST_PATH_IMAGE132
。
according to the embodiment of the invention, the weighting module adopts a Hamming window to carry out side lobe optimization on the beams of the co-prime subarray, and the beam outputs of the co-prime subarray are respectively obtained
Figure 18101DEST_PATH_IMAGE133
And
Figure 834747DEST_PATH_IMAGE134
(ii) a Wherein, the first and the second end of the pipe are connected with each other,
Figure 666699DEST_PATH_IMAGE135
and
Figure 252401DEST_PATH_IMAGE136
the sub-array weighted values generated after the extended vector co-prime array is subjected to channel combination windowing,
Figure 478983DEST_PATH_IMAGE137
and
Figure 782926DEST_PATH_IMAGE138
respectively the array output obtained after the extended vector co-prime array is combined by the channels,
Figure 890340DEST_PATH_IMAGE139
is the hamming window weight coefficient. The subarray weighted values generated after the channel combination windowing are respectively as follows:
Figure 330548DEST_PATH_IMAGE140
（31）
Figure 993611DEST_PATH_IMAGE141
（32）
wherein the content of the first and second substances,
Figure 519270DEST_PATH_IMAGE142
is composed ofMThe space between the array elements of the subarrays,
Figure 427446DEST_PATH_IMAGE143
is composed ofNThe space between the array elements of the subarrays,
Figure 722161DEST_PATH_IMAGE144
as to the wavelength of the signal, is,
Figure 556125DEST_PATH_IMAGE145
to guide the orientation.
According to the embodiment of the invention, the beam forming module carries out Min method processing on the obtained co-prime subarray beam output, and finally obtains an output space power spectrum formed by the extended vector co-prime subarray beam:
Figure 569080DEST_PATH_IMAGE146
（33）
as will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (10)

1. A beam forming method based on a vector-expanded co-prime matrix is characterized by comprising the following steps:
step 1: on the premise of setting the element number requirement of the vector array, constructing a relatively prime data pairMAndNsetting up the initial value of the number of the underwater acoustic vector array co-prime array elements of the appointed physical array elements;
and 2, step: based on the characteristics of beam output zero points and grating lobes of the co-prime array subarray, formulating a vector co-prime array expansion scheme, and determining array expansion factors to obtain an expanded vector co-prime array; the vector co-prime matrix expansion scheme adopts a sub-matrix zero grating lobe cross adjustment method, and adopts
Figure 829754DEST_PATH_IMAGE001
：
Figure 169731DEST_PATH_IMAGE002
Figure 808523DEST_PATH_IMAGE003
Wherein
Figure 47741DEST_PATH_IMAGE004
Is an integer which is the number of the whole,
Figure 127693DEST_PATH_IMAGE005
respectively, the spreading factors of the co-prime submatrices; when in use
Figure 12472DEST_PATH_IMAGE006
According to the obtained spreading factor
Figure 702342DEST_PATH_IMAGE007
Expanding the co-prime subarrays;
and step 3: carrying out sound pressure and vibration velocity combined processing on the extended vector co-prime array obtained in the step 2 to obtain a vector channel data combination;
and 4, step 4: designing a weighting coefficient based on a sound pressure channel combination form of the extended vector co-prime array, and carrying out extended vector co-prime array weighting by adopting a data independent window function;
and 5: performing beam forming on the extended vector co-prime array based on the co-prime array beam forming method to obtain the final spatial spectrum output
Figure 760296DEST_PATH_IMAGE008
。
2. The method according to claim 1, wherein the step 3 of jointly processing the sound pressure and the vibration velocity comprises:
the two vibration rates were combined as follows:
Figure 225913DEST_PATH_IMAGE009
Figure 576866DEST_PATH_IMAGE010
and
Figure 986988DEST_PATH_IMAGE011
the vibration speed is combined into two vibration speeds, wherein,
Figure 84519DEST_PATH_IMAGE012
Figure 299250DEST_PATH_IMAGE013
for the sound pressure information received by the vector hydrophone,
Figure 588148DEST_PATH_IMAGE014
and
Figure 783769DEST_PATH_IMAGE015
as information of vibration velocity components orthogonal to each other,
Figure 714684DEST_PATH_IMAGE016
and
Figure 122270DEST_PATH_IMAGE017
respectively a target orientation and a guiding orientation.
3. The method as claimed in claim 2, wherein the step 3 is based on the vector-extended co-prime matrix
Figure 519753DEST_PATH_IMAGE018
The combination form is expanded to obtain the directivity of a combined channel
Figure 576571DEST_PATH_IMAGE019
。
4. The method according to claim 1, wherein the step 4 adopts a Hamming window to perform the sidelobe optimization of the co-prime subarray beam, and the beam outputs of the co-prime subarray are obtained as
Figure 547063DEST_PATH_IMAGE020
And
Figure 169674DEST_PATH_IMAGE021
(ii) a Wherein the content of the first and second substances,
Figure 3638DEST_PATH_IMAGE022
and
Figure 688697DEST_PATH_IMAGE023
for expanding vector co-prime matrix passesThe sub-array weights generated after windowing the channel combinations,
Figure 860616DEST_PATH_IMAGE024
and
Figure 868892DEST_PATH_IMAGE025
respectively the array output obtained after the extended vector co-prime array is combined by the channels,
Figure 342599DEST_PATH_IMAGE026
is the hamming window weight coefficient.
5. The method as claimed in claim 4, wherein the sub-array weights generated after the windowing of the channel combination are respectively:
Figure 609895DEST_PATH_IMAGE027
Figure 420725DEST_PATH_IMAGE028
wherein the content of the first and second substances,
Figure 627715DEST_PATH_IMAGE029
is the distance between the array elements of the M subarrays,
Figure 803481DEST_PATH_IMAGE030
the distance between the array elements of the N sub-arrays,
Figure 23985DEST_PATH_IMAGE031
in order to be the wavelength of the signal,
Figure 310610DEST_PATH_IMAGE032
to guide the orientation.
6. The method according to claim 1, wherein in step 5, the output of the co-prime subarray beam of the extended vector co-prime matrix obtained in step 4 is processed by Min.
7. A beam forming apparatus based on a vector-extended co-prime matrix, comprising:
a mutual prime array element number construction module for constructing a mutual prime data pair on the premise of setting the vector array element number requirementMAndNsetting up the initial value of the number of the underwater acoustic vector array co-prime array elements of the appointed physical array elements;
the vector co-prime matrix expansion module is used for obtaining an expanded vector co-prime matrix by adopting a sub-matrix zero-point grating lobe cross adjustment method based on the characteristics of the output zero point and the grating lobe of the sub-matrix wave beam of the co-prime matrix; the method for adjusting the zero grating lobe crossing by adopting the subarray comprises the following steps: get
Figure 231161DEST_PATH_IMAGE033
：
Figure 577829DEST_PATH_IMAGE034
Figure 554138DEST_PATH_IMAGE035
Wherein
Figure 847716DEST_PATH_IMAGE036
，
Figure 91615DEST_PATH_IMAGE037
Is an integer which is a function of the number of the atoms,
Figure 343605DEST_PATH_IMAGE038
，
Figure 810139DEST_PATH_IMAGE039
respectively, the spreading factors of the co-prime submatrices; when in use
Figure 438567DEST_PATH_IMAGE040
，
Figure 802552DEST_PATH_IMAGE041
According to the obtained spreading factor
Figure 225443DEST_PATH_IMAGE038
And
Figure 176344DEST_PATH_IMAGE039
expanding the co-prime subarrays;
the vector channel data combination module is used for carrying out sound pressure and vibration velocity combined processing on the expanded vector co-prime array obtained by the vector co-prime array expansion module to obtain a vector channel data combination;
the weighting module is used for designing a weighting coefficient based on a sound pressure vibration velocity channel combination form of the extended vector co-prime array, and carrying out extended vector co-prime array weighting by adopting a data independent window function;
a beam forming module for performing beam forming on the extended vector co-prime array based on the co-prime array beam forming method to obtain the final spatial spectrum output
Figure 608462DEST_PATH_IMAGE042
。
8. The vector-extended co-prime matrix-based beam forming device of claim 7, wherein the vector channel data combining module performs joint processing on the sound pressure vibration velocity according to the following formula:
Figure 561375DEST_PATH_IMAGE043
Figure 420746DEST_PATH_IMAGE010
and
Figure 590434DEST_PATH_IMAGE011
the vibration speed is combined into two vibration speeds, wherein,
Figure 91823DEST_PATH_IMAGE044
Figure 164821DEST_PATH_IMAGE045
for the sound pressure information received by the vector hydrophone,
Figure 195094DEST_PATH_IMAGE046
and
Figure 589428DEST_PATH_IMAGE047
as information of vibration velocity components orthogonal to each other,
Figure 628928DEST_PATH_IMAGE048
and
Figure 556433DEST_PATH_IMAGE017
respectively a target orientation and a guiding orientation.
9. A computer device, comprising:
memory storing one or more computer programs that, when executed by one or more processors, cause the one or more processors to perform the steps of the vector extended co-prime matrix based beamforming method according to any of claims 1-6.
10. A computer storage medium, having one or more computer programs stored thereon that, when executed by one or more processors, cause the one or more processors to perform the steps of the vector extended co-prime matrix based beamforming method according to any of claims 1-6.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6501747B1 (en) * 1998-08-20 2002-12-31 Metawave Communications Corporation Manifold assisted channel estimation and demodulation for CDMA systems in fast fading environments
CN109075427A (en) * 2016-05-04 2018-12-21 瑞典爱立信有限公司 Use the beam forming of antenna assembly
CN113325385A (en) * 2021-07-15 2021-08-31 中国人民解放军火箭军工程大学 Anti-interference method for phased array-MIMO radar mode transmit-receive beam forming

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6501747B1 (en) * 1998-08-20 2002-12-31 Metawave Communications Corporation Manifold assisted channel estimation and demodulation for CDMA systems in fast fading environments
CN109075427A (en) * 2016-05-04 2018-12-21 瑞典爱立信有限公司 Use the beam forming of antenna assembly
CN113325385A (en) * 2021-07-15 2021-08-31 中国人民解放军火箭军工程大学 Anti-interference method for phased array-MIMO radar mode transmit-receive beam forming

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