CN109491009B - Optical fiber combined array and grating lobe suppression method based on optical fiber combined array - Google Patents

Optical fiber combined array and grating lobe suppression method based on optical fiber combined array Download PDF

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CN109491009B
CN109491009B CN201811310209.2A CN201811310209A CN109491009B CN 109491009 B CN109491009 B CN 109491009B CN 201811310209 A CN201811310209 A CN 201811310209A CN 109491009 B CN109491009 B CN 109491009B
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王逸林
兰天
邱龙皓
邹男
张光普
付进
王晋晋
王燕
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Harbin Engineering University
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Abstract

The invention provides an optical fiber combined array and a grating lobe suppression method based on the optical fiber combined array. (1) Three sub-arrays of the optical fiber combination array respectively receive incident signals, the optical fiber combination array comprises three sub-arrays 1,2 and 3 which are sequentially arranged, each sub-array is a uniform equal-interval linear array, the intervals of array elements in each sub-array are mutually prime, and the intervals of the three sub-arrays are half wavelengths of the received signals; (2) the incident signals received by each subarray utilize each co-prime subarray to form beams, and beam data output of each scanning azimuth is obtained; (3) and comprehensively processing the information of the three subarray wave beam domains by utilizing the characteristic of the co-prime of the array element intervals among the subarrays to obtain a space spectrum and a target direction estimation result after the grating lobes are suppressed. The method can improve the reliability and accuracy of the spatial target azimuth estimation and obtain higher resolution; compared with the traditional uniform area array, the method can enlarge the equivalent aperture, reduce the number of array elements and has stronger engineering practical value.

Description

Optical fiber combined array and grating lobe suppression method based on optical fiber combined array
Technical Field
The invention relates to an optical fiber combined array. The invention also relates to a grating lobe suppression method based on the optical fiber combined array.
Background
Array signal processing uses an array to spatially and temporally sample a signal, employs appropriate methods for computation, processing and processing, and extracts useful information. Array signal processing has two basic tasks: one is beamforming and the other is spatial spectrum estimation. The array signal processing theory is developed to the present, and algorithms such as CBF, MVDR, MUSIC, ESPRIT, maximum likelihood method, sparse reconstruction and the like appear. For the above algorithms, most of them are based on uniform arrays, the internal array element spacing of the uniform arrays must be smaller than or equal to half wavelength of the incident signal, so that the array aperture is restricted by the number of array elements. For a uniform array, to obtain high resolution, the number of array elements must be increased, which leads to problems of high hardware cost, difficult array design, and the like.
The optical fiber hydrophone has the advantages of high sensitivity, small transmission loss, small signal crosstalk and the like, the volume and the weight of the array are greatly reduced, the array can be carried on various platforms, a large-range, omnibearing and three-dimensional underwater sound sensing network is convenient to establish, and the real-time monitoring capability of an underwater space is improved. However, due to the unique structure of the optical fiber hydrophone, the requirement of array half-wavelength spacing arrangement cannot be met when azimuth estimation of underwater sound high-frequency signals is carried out, and the optical fiber hydrophone is easily affected by the problem of azimuth estimation ambiguity.
Disclosure of Invention
The invention aims to provide a sparse optical fiber combination array capable of inhibiting grating lobe interference. The invention also aims to provide a grating lobe suppression method based on the optical fiber combination array, which can solve the problem of azimuth ambiguity caused by the grating lobe when the optical fiber hydrophone array is used for azimuth estimation.
The optical fiber combined array comprises three sub-arrays 1,2 and 3 which are sequentially arranged, wherein each sub-array is a uniform equal-interval linear array, the intervals of array elements in each sub-array are mutually prime, and the intervals of the three sub-arrays are half-wavelength of a received signal.
The cross prime factors of three sub-arrays in the optical fiber combined array are respectively C1、C2、C3Are positive integers which are mutually prime, and C1,C2,C3Not less than 2, the sub-array spacing is lambda/2, wherein lambda is the wavelength of the received signal, the number of array elements of sub-array 1 is M1＝C2*C3At a pitch of C1λ/2; the number of the sub-array 2 array elements is M2＝C1*C3At a pitch of C2λ/2; the number of 3 array elements of the subarray is M3＝C1*C2At a pitch of C3*λ/2。
The grating lobe suppression method based on the optical fiber combined array comprises the following steps:
(1) three sub-arrays of the optical fiber combination array respectively receive incident signals, the optical fiber combination array comprises three sub-arrays 1,2 and 3 which are sequentially arranged, each sub-array is a uniform equal-interval linear array, the intervals of array elements in each sub-array are mutually prime, and the intervals of the three sub-arrays are half wavelengths of the received signals;
(2) the incident signals received by each subarray utilize each co-prime subarray to form beams, and beam data output of each scanning azimuth is obtained;
(3) and comprehensively processing the information of the three subarray wave beam domains by utilizing the characteristic of the co-prime of the array element intervals among the subarrays to obtain a space spectrum and a target direction estimation result after the grating lobes are suppressed.
The grating lobe suppression method based on the optical fiber combined array can further comprise the following steps:
1. the step (2) specifically includes that the scanning range of the beam forming is: azimuth angle: theta epsilon (0 DEG, 180 DEG); pitch angle:
Figure BDA0001854727060000021
the target position is
Figure BDA0001854727060000022
For each subarray i equal to 1,2,3, the signal received by the subarray i at time t
Figure BDA0001854727060000023
Expressed as a column vector:
Figure BDA0001854727060000024
where N is the number of incident signals, ω0For receiving the signal frequency, si(1～N)(t) represents the complex envelope of the received signal at time t for sub-array i,
Figure BDA0001854727060000025
representing the noise of each array element of the sub-array i at the time t,
Figure BDA0001854727060000026
representing the time delay of the Nth signal reaching each array element of the subarray i relative to the reference array element;
the received signal column vector is expressed in vector form as follows:
Xi(t)＝AiSi(t)+Ni(t),i＝1,2,3
in the formula (I), the compound is shown in the specification,
Figure BDA0001854727060000027
Si(t)＝[si1(t),si2(t),...,siN(t)]T，Aim as subarrays iiXN dimensional flow pattern matrix, expressed as:
Ai＝[ai1(ω0) ai2(ω0) … aiN(ω0)],i＝1,2,3
wherein the guide vector ai(ω0) Comprises the following steps:
Figure BDA0001854727060000028
defining the first array element of the subarray 2 as a reference array element, locating at the origin of coordinates (0,0,0), and the position of any array element in space is (x, y, z), and deducing the time delay difference between two array elements in space from the geometrical relationship as follows:
Figure BDA0001854727060000031
the above formula is expressed by
Figure BDA0001854727060000032
Showing that the weight of the subarray i is set as wiThen the beam output of the sub-array i is:
Figure BDA0001854727060000033
conventional beamforming acquisition
Figure BDA0001854727060000034
Searching in a scanning range to obtain a spatial power spectrum, namely:
Figure BDA0001854727060000035
wherein R isxiFor the data covariance matrix, the array with finite fast beat number is used to receive the signal versus data covariance matrix RxiThe estimation is carried out, namely:
Figure BDA0001854727060000036
wherein p is the fast beat number, according to the space spectrum result of the subarray i
Figure BDA0001854727060000037
And
Figure BDA0001854727060000038
orientation information about the target is obtained.
2. The step (3) specifically comprises the following steps:
firstly, the beam output of each subarray i is multiplied, the beam output of different subarrays is subjected to cross-correlation operation in each scanning direction, and the beam output is used as the spatial spectrum output of the direction, namely:
Figure BDA0001854727060000039
wherein the content of the first and second substances,
Figure BDA00018547270600000310
the beam outputs for sub-arrays i, j,
Figure BDA00018547270600000311
the spatial spectrum is processed for the purpose of product processing,
after product processing, the cross-correlation output among the subarrays is subjected to minimum processing, namely, the minimum value in each direction is selected as the spatial spectrum result of the direction:
Figure BDA00018547270600000312
and (3) then, performing beam forming on the half-wavelength uniform linear array consisting of two pairs of sub-array end array elements in the step (2) to obtain a spatial power spectrum of the uniform linear array, wherein the spatial power spectrum is represented as Pula(ii) a To Pmin1,2,3And PulaThen performing one-step minimum treatment to obtain a comprehensive treatment result expressed as PComNamely:
PCom＝min(Pmin1,2,3,Pula)。
aiming at the problems in the prior art, the invention provides a novel sparse array structure and a signal processing method capable of inhibiting grating lobe interference. Unlike a uniform array, the array element spacing can break the half-wavelength limit. Compared with a uniform array under the condition that the aperture of the array elements is equal, the sparse array can reduce the number of the array elements and reduce the hardware cost. The comprehensive processing method not only can accurately estimate the direction of the incident signal, but also can inhibit grating lobe interference, and the spectral peak is sharper. Therefore, when the optical fiber hydrophone is used for azimuth estimation, the method has higher practical significance, can effectively promote the application of the related array signal processing algorithm in reality, saves the cost and is easy to realize.
Compared with a uniform array with half-wavelength spacing arrangement, the method has the advantages that the array element number is less, a sharper spectral peak is obtained, and the azimuth ambiguity caused by grating lobe interference on target azimuth estimation can be eliminated. The grating lobe suppression method based on the fiber combination array has very high practical significance in the aspect of adopting the fiber array to carry out azimuth estimation or in a high-frequency background.
Drawings
FIG. 1 is a schematic diagram of a fiber array module;
FIG. 2 is a geometric relationship diagram of two arbitrary array elements in space;
FIG. 3 is a diagram of a product processor architecture;
FIG. 4 is a diagram of a minimum processor architecture;
FIG. 5 is a block diagram of an integrated processor with grating lobe interference suppression capability;
6 a-6 b are conventional beam forming azimuth spectra of half-wavelength spaced uniform planar arrays;
7 a-7 b are entire array conventional beamforming azimuth spectra;
8 a-8 b are the grating lobe suppression comprehensive processing azimuth spectrum based on the fiber combination array.
Detailed Description
The invention is described in more detail below by way of example.
The invention designs an optical fiber sensor array arrangement structure which comprises three sub-arrays 1,2 and 3 which are sequentially arranged, wherein the sub-arrays are uniform linear arrays with equal intervals, and the intervals of array elements in each sub-array are mutually prime. The distance between the three sub-arrays is half wavelength of the received signal, and the three sub-arrays respectively receive the incident signal. According to incident signals received by each subarray, each co-prime subarray is utilized to carry out beam forming (including CBF, MVDR algorithm and the like). According to the designed array structure, comprehensive processing is carried out on the information of the three sub-array wave beam domains by utilizing the characteristic that the array element intervals among the sub-arrays are relatively prime, and a space spectrum and a target direction estimation result after grating lobes are suppressed are obtained.
(1) As shown in FIG. 1, the co-prime factors of the three sub-arrays are respectively C1、C2、C3Are positive integers which are mutually prime, and C1,C2,C3And the sub-array spacing is lambda/2, wherein lambda is the wavelength of the received signal. The number of the sub-array 1 array elements is M1＝C2*C3At a pitch of C1λ/2; the number of the sub-array 2 array elements is M2＝C1*C3At a pitch of C2λ/2; the number of 3 array elements of the subarray is M3＝C1*C2At a pitch of C3*λ/2。
(2) With reference to fig. 1 and fig. 2, the conventional beamforming scanning range is: azimuth angle: theta epsilon (0 DEG, 180 DEG); pitch angle:
Figure BDA0001854727060000051
the target position is
Figure BDA0001854727060000052
For each subarray i equal to 1,2,3, the signal received by the subarray i at time t
Figure BDA0001854727060000053
Can be expressed as a column vector:
Figure BDA0001854727060000054
where N is the number of incident signals, ω0For receiving the signal frequency, si(1～N)(t) represents the complex envelope of the received signal at time t for sub-array i,
Figure BDA0001854727060000055
representing the noise of each array element of the sub-array i at the time t,
Figure BDA0001854727060000056
and the time delay of the Nth signal arriving at each array element of the subarray i relative to the reference array element is shown.
The received signal column vector is expressed in vector form as follows:
Xi(t)＝AiSi(t)+Ni(t),i＝1,2,3
in the formula (I), the compound is shown in the specification,
Figure BDA0001854727060000057
Si(t)＝[si1(t),si2(t),...,siN(t)]T，Aim as subarrays iiXN dimensional flow pattern matrix, expressed as:
Ai＝[ai1(ω0) ai2(ω0) … aiN(ω0)],i＝1,2,3
wherein the guide vector ai(ω0) Comprises the following steps:
Figure BDA0001854727060000058
defining the first array element of the subarray 2 as a reference array element, locating at the origin of coordinates (0,0,0), and the position of any array element in space is (x, y, z), and deducing the time delay difference between two array elements in space from the geometrical relationship as follows:
Figure BDA0001854727060000059
the above formula is expressed by
Figure BDA00018547270600000510
Showing that the weight of the subarray i is set as wiThen the beam output of the sub-array i is:
Figure BDA00018547270600000511
conventional Beamforming (CBF) acquisition
Figure BDA00018547270600000512
Searching in a scanning range to obtain a spatial power spectrum, namely:
Figure BDA0001854727060000061
wherein R isxiIs a data covariance matrix. In practical application, the array with finite fast beat number is generally adopted to receive the signal-to-data covariance matrix RxiThe estimation is carried out, namely:
Figure BDA0001854727060000062
where p is the number of fast beats. Can be based on the spatial spectrum result of the sub-array i
Figure BDA0001854727060000063
And
Figure BDA0001854727060000064
orientation information about the target is obtained.
(3) With reference to fig. 1,2,3, 4, and 5, due to spatial undersampling, the spatial spectrum obtained by each sub-array in step (2) through conventional beamforming scanning is affected by grating lobe interference, which seriously affects the signal direction estimation effect. And (3) comprehensively processing the target azimuth information acquired by the three sub-arrays by utilizing the characteristic of relatively prime array element intervals among the sub-arrays. And comprehensively processing the target azimuth information acquired by the three sub-arrays by utilizing the characteristic of relatively prime array element intervals among the sub-arrays.
Firstly, the beam output of each subarray i is multiplied, the beam output of different subarrays is subjected to cross-correlation operation in each scanning direction, and the beam output is used as the spatial spectrum output of the direction, namely:
Figure BDA0001854727060000065
wherein the content of the first and second substances,
Figure BDA0001854727060000066
the beam outputs for sub-arrays i, j,
Figure BDA0001854727060000067
the spatial spectrum is processed for the product. Certain suppression capacity is formed at the position of the grating lobe through product processing, but compared with a uniform array of a half-wavelength spacing array, the obtained space spectrum still has larger fluctuation at a non-target direction.
After product processing, the cross-correlation output among the subarrays is subjected to minimum processing, namely, the minimum value in each direction is selected as the spatial spectrum result of the direction:
Figure BDA0001854727060000068
after the minimum processing, the interference suppression capability at the grating lobe position is further reduced. Then, the half-wavelength uniform linear array composed of two pairs of sub-array end array elements is subjected to conventional beam forming to obtain the space power of the half-wavelength uniform linear arraySpectrum, denoted Pula. To Pmin1,2,3And PulaThen performing one-step minimum treatment to obtain a comprehensive treatment result expressed as PComNamely:
PCom＝min(Pmin1,2,3,Pula)
the comprehensive processing has the advantages of product processing and minimum processing, successfully eliminates the azimuth ambiguity caused by the grating lobe on the target azimuth estimation, and can accurately estimate the azimuth of the target.
The grating lobe suppression method based on the optical fiber combined array mainly comprises the following implementation steps:
(1) an optical fiber sensor array arrangement structure is designed, and comprises three sub-arrays 1,2 and 3 which are sequentially arranged, wherein the sub-arrays are uniform linear arrays with equal intervals, and the intervals of array elements in each sub-array are mutually prime. The distance between the three sub-arrays is half wavelength of the received signal, and the three sub-arrays respectively receive the incident signal.
(2) According to incident signals received by each subarray, each co-prime subarray is utilized to carry out beam forming (including CBF, MVDR algorithm and the like).
(3) According to the designed array structure, comprehensive processing is carried out on the information of the three sub-array wave beam domains by utilizing the characteristic that the array element intervals among the sub-arrays are relatively prime, and a space spectrum and a target direction estimation result after grating lobes are suppressed are obtained.
The effect of the present invention is verified by simulation as follows. The simulation conditions and results are as follows:
referring to fig. 1, the number of array elements of the 3 uniform sparse co-prime linear arrays constituting the optical fiber combined array is 12, 15, and 20, the center frequency of the target signal is 1500Hz, the sound velocity is 1500m/s, the corresponding array element pitches are 2.5m (5-half wavelength), 2.0m (4-half wavelength), and 1.5m (3-half wavelength), respectively, and the SNR is 0 dB. By adopting a conventional beam forming method, the scanning angle range is theta epsilon (0 degree, 180 degrees),
Figure BDA0001854727060000071
target azimuth is set to
Figure BDA0001854727060000072
Referring to fig. 6a, 6b, 7a, 7b, 8a, and 8b, a two-dimensional azimuth spectrum obtained by DOA estimation of a uniform half-wavelength interval area array having the same aperture as the fiber array, a two-dimensional azimuth spectrum obtained by DOA estimation of the entire fiber array, and a two-dimensional azimuth spectrum obtained by a grating lobe suppression method based on the fiber array are shown. Compared with an area array with the same aperture and uniform half-wavelength spacing, the target azimuth spectrum peak estimated by the method is narrower, and a better target azimuth estimation effect can be achieved; compared with the integral DOA estimation of the optical fiber combined array, the method has obvious inhibition effect on grating lobe interference, successfully eliminates the azimuth ambiguity caused by the grating lobe on the target azimuth estimation, and can accurately estimate the real azimuth of the target.

Claims (3)

1. A grating lobe suppression method based on an optical fiber combined array comprises the following steps:
(1) three sub-arrays of the optical fiber combination array respectively receive incident signals, the optical fiber combination array comprises three sub-arrays 1,2 and 3 which are sequentially arranged, each sub-array is a uniform equal-interval linear array, the intervals of array elements in each sub-array are mutually prime, and the intervals of the three sub-arrays are half wavelengths of the received signals;
(2) the incident signals received by each subarray utilize each co-prime subarray to form beams, and beam data output of each scanning azimuth is obtained;
(3) comprehensively processing the information of the three subarray wave beam domains by utilizing the characteristic of the array element spacing between the subarrays which is relatively prime, and obtaining a space spectrum and a target direction estimation result after the grating lobes are suppressed;
the method is characterized in that the step (2) specifically comprises the following steps:
the scanning range of the beam forming is as follows: azimuth angle: theta epsilon (0 DEG, 180 DEG); pitch angle:
Figure FDA0002353520440000011
the target position is
Figure FDA0002353520440000012
For each subarray i equal to 1,2,3, the signal received by the subarray i at time t
Figure FDA0002353520440000013
Expressed as a column vector:
Figure FDA0002353520440000014
where N is the number of incident signals, ω0For receiving the signal frequency, si(1～N)(t) represents the complex envelope of the received signal at time t for sub-array i,
Figure FDA0002353520440000015
representing the noise of each array element of the sub-array i at the time t,
Figure FDA0002353520440000016
representing the time delay of the Nth signal reaching each array element of the subarray i relative to the reference array element;
the received signal column vector is expressed in vector form as follows:
Xi(t)＝AiSi(t)+Ni(t),i＝1,2,3
in the formula (I), the compound is shown in the specification,
Figure FDA0002353520440000017
Si(t)＝[si1(t),si2(t),...,siN(t)]T，Aim as subarrays iiXN dimensional flow pattern matrix, expressed as:
Ai＝[ai1(ω0) ai2(ω0) … aiN(ω0)],i＝1,2,3
wherein the guide vector ai(ω0) Comprises the following steps:
Figure FDA0002353520440000021
defining the first array element of the subarray 2 as a reference array element, locating at the origin of coordinates (0,0,0), and the position of any array element in space is (x, y, z), and deducing the time delay difference between two array elements in space from the geometrical relationship as follows:
Figure FDA0002353520440000022
the above formula is expressed by
Figure FDA0002353520440000023
Showing that the weight of the subarray i is set as wiThen the beam output of the sub-array i is:
Figure FDA0002353520440000024
conventional beamforming acquisition
Figure FDA0002353520440000025
Searching in a scanning range to obtain a spatial power spectrum, namely:
Figure FDA0002353520440000026
wherein R isxiFor the data covariance matrix, the array with finite fast beat number is used to receive the signal versus data covariance matrix RxiThe estimation is carried out, namely:
Figure FDA0002353520440000027
wherein p is the fast beat number, according to the space spectrum result of the subarray i
Figure FDA0002353520440000028
And
Figure FDA0002353520440000029
orientation information about the target is obtained.
2. The grating lobe suppression method based on the optical fiber combined array as claimed in claim 1, wherein the step (3) specifically comprises:
firstly, the beam output of each subarray i is multiplied, the beam output of different subarrays is subjected to cross-correlation operation in each scanning direction, and the beam output is used as the spatial spectrum output of the direction, namely:
Figure FDA00023535204400000210
wherein the content of the first and second substances,
Figure FDA00023535204400000211
the beam outputs for sub-arrays i, j,
Figure FDA00023535204400000212
the spatial spectrum is processed for the purpose of product processing,
after product processing, the cross-correlation output among the subarrays is subjected to minimum processing, namely, the minimum value in each direction is selected as the spatial spectrum result of the direction:
Figure FDA00023535204400000213
and (3) then, performing beam forming on the half-wavelength uniform linear array consisting of two pairs of sub-array end array elements in the step (2) to obtain a spatial power spectrum of the uniform linear array, wherein the spatial power spectrum is represented as Pula(ii) a To Pmin1,2,3And PulaThen performing one-step minimum treatment to obtain a comprehensive treatment result expressed as PComNamely:
PCom＝min(Pmin1,2,3,Pula)。
3. the grating lobe suppression method based on the optical fiber combined array according to claim 1 or 2, wherein in the step (1): the co-prime factors of the three sub-arrays are respectively C1、C2、C3Are positive integers which are mutually prime, and C1,C2,C3Not less than 2, the sub-array spacing is lambda/2, wherein lambda is the wavelength of the received signal, the number of array elements of sub-array 1 is M1＝C2*C3At a pitch of C1λ/2; the number of the sub-array 2 array elements is M2＝C1*C3At a pitch of C2λ/2; the number of 3 array elements of the subarray is M3＝C1*C2At a pitch of C3*λ/2。
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