Multibeam Key Technology--Beam Formation Principle

Yu Ping, Liu Fanglan, Xiao Bo

First author's introduction: Yu Ping, male, senior engineer, graduated from Changchun Institute of Geology, Department of Instrumentation, majoring in electronic instrumentation and measurement technology in 1993, is now mainly engaged in the application of multibeam technology and the technical management of marine geological survey.

(Guangzhou Marine Geological Survey Guangzhou 510760)

Abstract Different combinations of transducer arrays determine their directivity, and beam formation is the key technology of multibeam measurement. In the paper, the working principle of beam formation with different transducer arrays is summarized through mathematical calculations, and the general method of frequency domain beam formation using two-dimensional DFT is introduced. Finally, the beam formation techniques adopted by different systems are briefly explained in relation to the in-service multibeam bathymetry system.

Keywords: multibeam, array element, directivity, beam formation, bathymetry

1 Preface

China has introduced a large number of multibeam bathymetry systems from Europe and the United States since the beginning of the 1990s in order to satisfy the needs of the offshore waterways, oceanic surveys, and surveys of the National Economic Specialized Areas (NESAs) and continental shelves (see Table 1), which cover different sea areas, such as deep, medium and shallow waters. These multibeam bathymetric systems cover different sea areas such as deep water, medium depth water and shallow water, and the application of multibeam technology in China has ushered in the first peak period.

After entering the 21st century, with the aging of the old multibeam bathymetric systems and the introduction of new multibeam technologies, the renewal of multibeam bathymetric systems has been carried out, and the multibeam systems with high precision, high coverage, and high number of beams have begun to be applied in some special projects. In the practical use of multibeam bathymetric systems, technicians engaged in multibeam surveying have carried out a lot of research work on the problems existing in different multibeam bathymetric systems, and published monographs on multibeam technology and written a large number of papers. In these application-oriented research results, the key technology about the working principle of multibeam bathymetry system - beam formation technology - is either a simple analogy or a generalized and approximate description. This paper attempts to further understand the working principle of multibeam bathymetry system by describing the patterns of beam formation of different systems based on summarizing the principles of beam formation in different forms and combining them with practical applications.

2 Principle of beam formation

The so-called beam formation refers to the method of forming spatial directivity by processing (e.g., weighting, time-delay, summation, etc.) the outputs of each array element of a multivariate base array arranged in a certain geometric shape (straight line, cylindrical, curved, etc.) (Tian Tan et al., 2000). Beam formation is also a method in which a multivariate array is appropriately processed to give a desired response to acoustic waves in certain spatial directions. There are many methods of beam formation, especially in practical applications, with the rapid development of microelectronics technology, computing technology, digital signal processing technology so that the time domain, frequency domain under the beam formation methods through each other.

Table1 Multibeam sounding system has been installed and used in China (Before 2004)

2.1 General principle of beam formation

Beam The formation technique comes from the principle that the base array has directionality (Jiang Nanxiang, 2000). Let's set up a receiving transducer array consisting of N non-directional array elements (Figure 1). Each array element is located at the spatial point (xn, yn, zn), and the signals of all the array elements are summed to obtain the output, which forms the natural directivity of the base array. At this time, if there is a far-field plane wave incident on this base array, its output amplitude will change with the change of plane incident angle.

When the signal source in different directions, due to the different phase difference between the array received signal and the base signal, and thus the formation and output amplitude is different, that is, the array response is different.

If the above array is an N-element line array, the spacing of the array elements is d, the reception sensitivity of each array element is the same, and the plane wave incidence direction is θ (Figure 2). The output signal of each array element is:

F0(t)=Acos(ωt)(1)

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......

Fig. 2 Geometry shape of line array

Fig.2 Geometry shape of line array transducer

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Where A is the signal amplitude; ω is the signal angular frequency; φ is the phase difference between the received signals of neighboring array elements, and Re is the real part of the fetch, there are:

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So, the output of the array is:

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Because:

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Then:

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So:

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The two sides of the above formula are divided by NA at the same time for normalization, which gives:

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R(θ) shows that the magnitude of output amplitude of a multivariate array varies with the angle of incidence of the signal. Generally speaking, for an arbitrary array, no matter from which direction the sound wave is incident, it is impossible to form a homogeneous summation or get the maximum output, and only a linear array or a spatial plane array will form a homogeneous summation in the normal direction of the array and get the maximum output. However, any formation of the array after appropriate processing, can be formed in a predetermined direction of the same phase addition, get the maximum output, which is the general principle of beam formation.

2.2 Linear array phase-shifted beam formation

Based on the previous discussion, the fundamental purpose of the linear array phase-shifted beam formation is: inserting the phase-shifted β between neighboring array elements, then the summation output of the linear array is:

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The output amplitude of the normalized array becomes:

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So the main beam direction satisfies:

φ-β=0

i.e.

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So:

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Or:

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The above equation shows that: inserting the array elements between the Different phase shift β, can control the main beam is located in different directions, this insertion of phase shift between the array elements to make the main beam direction control in different orientations is called phase shift beam formation. In narrow-band (active sonar) applications, generally commonly used phase-shifted beam formation method.

2.3 Linear array time-delayed beam formation

In the discussion of linear array phase-shifted beam formation, there are:

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Because:

β=2πfτ

So:

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The above formula shows that: inserting the array elements with Different time delay τ, can control the main beam is located in different directions, this insertion of time delay between the array elements so that the main beam direction control in different directions is called time-delay beam formation. In broadband (passive sonar) applications, generally commonly used time-delayed beam formation method.

2.4 Circular array beam formation

The array elements of a circular array are generally uniformly distributed on the circumference. Since the circular array is geometrically symmetric about the origin, it has no directionality. Without a natural directional beam, the array element signals must be delayed or phase-shifted to develop directionality, even if they are compensated into an equivalent line array. A simple implementation is the electronically switched beam-forming method, which utilizes electronic switches for control and a set of delay lines into different array elements to form beams with different orientations.

The 16-element circular array is illustrated as an example. Assuming that only seven array elements on the circular arc are used to form the beam (Figure 3), if the target signal comes from directly in front, in order to form an in-phase summation, it is necessary to compensate for the delay of the signals of the various array elements to the straight line (blue) shown in the figure. Let the angle of the center of the arc where the two neighboring array elements are located be α0, then the corresponding delay required by each array element is:

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τ1=τ7=0(15)

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2.5 Arc Array Beam Formation

Arc Array Beam Formation is a kind of special case of the Circular Array beam formation, which is distributed in the arc array. case, where the array elements distributed on the arc array must eventually be projected into an equivalent line array. If the directivity control is accomplished with time delays, the time delay algorithm for each element is the same as in the "circular array beamforming" example.

2.6 Frequency-domain beamforming

From the previous discussion, it is clear that a beamformer can respond to signals in one part of space while suppressing signals in other parts of space, so beamforming is actually a spatial filtering process. According to the theory of linear systems, beam formation is also a convolution operation, and thus can be realized by multiplication in the frequency domain. So the beam can also be formed in the frequency domain, which is the frequency domain beam formation. Frequency domain beam formation often uses discrete Fourier transform (DFT), which can be realized by fast Fourier transform (FFT) in digital signal processing, so the frequency domain beam formation is less arithmetic than the time domain beam formation (Cao Hongze et al., 2002).

Set a uniformly spaced linear array with N array elements and a spacing of d. Sample the output signal xi(t) of array element i and take the L point for the DFT operation, i.e.

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Where i is the number of the array element, k is the number of the spectral line, and l is the number of the time sequence. Therefore Xi (k) denotes the spectrum of the time sequence received by the ith array element.

Secondly, a spatial Fourier transform is applied to the spectral line of the same sequence number k, and Xi (k) is rearranged to Xk (i), which performs the following operation:

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Where m is the beam number; wi is the amplitude weight of the array element; and Yk (m) represents the output of the mth beam of the kth frequency component. This is how frequency domain beam formation is realized using a two-dimensional DFT.

3 Conclusion

In summary, the directivity of the transducer is the basis of the beam forming principle. At present, China's active multibeam bathymetric systems mainly include SeaBea m series, Elac Botto mChart series, EM series, SeaBat series and Atlas DS series, etc. [4], due to the different manufacturers of each system and the working water depth range, the multibeam system adopts different transducers and transmitting frequencies, so the beam formation methods adopted by different systems are also are not the same.

Sea Bea m 2112 deepwater multibeam bathymetric system transmitting frequency 12 KHz, the transmitter and hydrophone are installed independently, of which the transmitter is 14 modules, hydrophone 8 modules **** 80 channels. Hydrophone is a group of 4 modules *** two groups in a "V" type installation, the transducer is a typical "Miller Criss Cross" (Mill s Cr oss) installation pattern. Even so, the beam formation principle is in line with the linear array phase-shift beam formation principle. in August 1998, the manufacturer upgraded the system according to the contract, and the number of beams of the system was upgraded from 121 to 151 by replacing only the DSP board, which is supposed to utilize the digital interpolated beam formation technology (shifted sideband beam formation) under the linear array phase-shift beam formation accomplished by the advanced digital signal processor. EM120 deep-water multibeam bathymetric system transmitter-receiver is also independently installed, belonging to the linear "Miller's cross" structural array, its basic beam formation principle is also consistent with the principle of linear phase-shifted beam formation, due to the number of beams has been greatly improved, should also be integrated with the frequency domain beam formation technology.

EM950 (or EM1002) in the deep-water multibeam bathymetric system transmitting frequency of 95kHz, transmitter and hydrophone two-in-one installation, the number of beams 120. The transducer is a semi-circular arc array with a radius of 45cm, and as a high transmitting frequency active sonar system, it adopts the synthesis of arc array time delay and phase shift beam forming technology.EM3000 shallow water multibeam bathymetric system transmits at 300kHz, with a number of 120 beams, and the transducer is a circular array (Li Jiabiao et al. and Zhou Xinghua et al. 1999), and adopts the technology with EM950 similar.

SeaBat series of multibeam system in China is mainly shallow water multibeam bathymetry system, shallow water multibeam system of the transducer is generally used in the transmitter and hydrophone two-in-one installation.SeaBat8101 multibeam bathymetry system of the frequency of 240kHz, the number of beams 101. The transducer is a circular array with a diameter of 32cm, using a beam forming method similar to that of the EM series.

The Atlas Fansweep series is a multibeam bathymetric system that utilizes side-scan sonar technology to calculate multiple bathymetric data, which is relatively backward in terms of technical specifications when compared to true multibeam bathymetric systems. Due to the change of product development strategy of manufacturers, the deep water multibeam system has been launched only in the past two years. there is no user of Atlas DS series multibeam system in China, and it is said that its new generation of multibeam system adopts the Chirp technology, and the number of receiving beams will be more than 300, so its beam forming technology should be mainly based on the frequency domain beam forming technology.

References

Cao Hongze, Li Lei et al.2002.An analytical study of a BDI algorithm based on FFT beam formation. Marine Technology, 21(2), 55-59

Nanxiang Jiang.2000.Transducer and base array. Harbin: Harbin Engineering University Press, 50～75

Li Jiabiao et al. 1999. Multi-beam Survey Principles, Techniques and Methods. Beijing: Ocean Press, 6～9

Tian Tan, Liu Guozhi, Sun Dajun.2000.Sonar Technology. Harbin: Harbin Engineering University Press, 63～120

Zhou Xinghua, Liu Zhongchen, Fu Lianzuo et al. 1999. Multibeam Seafloor Topographic Survey Technical Regulations. 8～14

Multibeam Pivotal Technology--Beam Forming

Yu Ping Liu Fanglan Xiao Bo

(Guangzhou Marine Geological Survey, Guangzhou, 510760)

for different type of transducer. and introduces a universal way of frequency domain beam forming by using 2?dimension DFT.Finally, the author simply explains the different beam forming technology which the multibeam have in use.Abstract: Different arranged transducer deter mines the directional property of a transducer array. Multibeampivotal technology-the basis of Beamformingis howto control the directional property of transducer.This article summarizes the theory of beamfor ming with mathematics operation

Key words：Multibeam Transducer Directional Property Beam Forming Sound

Key words：Multibeam Transducer Directional Property Beam Forming