Brief introduction of the first author: Yu Ping, male, senior engineer, 1993 graduated from the Instrument Department of Changchun Institute of Geology, majoring in electronic instrument and measurement technology. Now he is mainly engaged in the application of multi-beam technology and the technical management of marine geological survey.
(Guangzhou Marine Geological Survey Guangzhou 5 10760)
Different arrangements and combinations of transducer elements determine their directivity, and beamforming is the key technology of multi-beam measurement. In this paper, the working principle of beamforming of different transducer arrays is summarized by mathematical calculation, and the general method of frequency domain beamforming using two-dimensional DFT is introduced. Finally, combined with the existing multi-beam sounding system, the beamforming technologies adopted by different systems are briefly explained.
Multi-beam array element; Directional beamforming; sound
1 preface
Since the early 1990s, China has introduced a large number of multi-beam sounding systems from Europe and America (see table 1) to meet the needs of offshore navigation channels, marine surveys, national special economic zones and continental shelf surveys. These multi-beam sounding systems cover different sea areas such as deep water, medium-deep water and shallow water, and the application of multi-beam technology in China has reached its first peak.
After entering the 2 1 century, with the aging of the old multi-beam sounding system and the introduction of new multi-beam technology, the multi-beam sounding system has been upgraded, and the multi-beam system with high precision, high coverage and high beam number has been applied in some special projects. In the practical use of multi-beam sounding system, technicians engaged in multi-beam sounding have done a lot of research work on the problems existing in different multi-beam sounding systems, published multi-beam technical monographs and written a large number of papers. Among these applied research results, the key technology of multi-beam sounding system-beamforming technology is either a simple metaphor or a general description. On the basis of summarizing different beamforming principles, combined with practical application, this paper tries to explain the beamforming methods of different systems in order to further understand the working principle of multi-beam sounding system.
2 beamforming principle
The so-called beamforming refers to the method of forming spatial directivity through processing (such as weighting, delay, summation, etc.). ) the output of each array element of a multivariate array with a certain geometric shape (line, cylinder, arc, etc.). ) (Tian Tan et al, 2000). Beamforming is also an appropriate method to deal with multi-element arrays so that they have the required response to sound waves in some spatial directions. There are many methods of beamforming, especially in practical applications. With the rapid development of microelectronics and computing technology, digital signal processing technology makes the beamforming methods in time domain and frequency domain penetrate each other.
Table 1 Multi-beam Sounding System Installed and Used in China (before 2004) Table 1 Multi-beam Sounding System Installed and Used in China (before 2004)
2. 1 General principle of beamforming
Beamforming technology comes from the principle that the array is directional (Jiang Nanxiang, 2000). Set up a receiving transducer array consisting of n non-directional elements (as shown in figure 1). Each array element is located at a spatial point (xn, yn, zn), and the natural directivity of the array is formed by adding the signals of all the array elements to obtain the output. At this time, if a far-field plane wave is incident on this array, its output amplitude will change with the change of plane incident angle.
When the direction of signal source is different, because the phase difference between the received signal and the reference signal of each array is different, the amplitude of formation and output is different, that is, the response of the array is different.
If the array is an N-element linear array, the distance between elements is d, the receiving sensitivity of each element is the same, and the incident direction of plane wave is θ (as shown in Figure 2). The output signal of each array element is:
F0(t)=Acos(ωt)( 1)
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……
Figure 2 Linear array geometry
Fig. 2 Geometry of linear array transducer
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Where a is the signal amplitude; ω is the angular frequency of the signal; φ is the phase difference of signals received by adjacent array elements, and Re is the real part, including:
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Therefore, 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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Divide both sides of the above formula by NA at the same time for normalization, and get:
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R(θ) indicates that the output amplitude of the multi-cell array varies with the signal incident angle. Generally speaking, for any array, it is impossible to form in-phase addition or get the maximum output no matter which direction the sound wave is incident. Only linear array or spatial plane array will form in-phase addition in the normal direction of the array and get the maximum output. However, as long as it is handled properly, any array can form in-phase addition in the predetermined direction and get the maximum output, which is the general principle of beamforming.
2.2 Linear array phase shift beamforming
On the basis of the previous discussion, the fundamental purpose of linear array phase-shift beamforming is to insert phase shift β between adjacent array elements, then the sum output of linear array is:
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The normalized array output amplitude becomes:
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So the main beam direction satisfies:
φ-β=0
Namely:
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So:
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Or:
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The above formula shows that the main beam can be controlled in different directions by inserting different phase shifts between elements. This method of inserting phase shifts between elements and controlling the main beam direction in different directions is called phase-shifted beamforming. In narrowband (active sonar) applications, phase-shifted beamforming is usually used.
2.3 Linear Array Delay Beamforming
In the discussion of linear array phase shift beamforming, there are:
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Because:
β=2πfτ
So:
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The above formula shows that the main beam can be controlled in different directions by inserting different time delays between elements. This method of inserting time delay between elements to control the main beam direction in different directions is called delayed beamforming. In broadband (passive sonar) applications, the delayed beamforming method is usually used.
2.4 Circular Array Beamforming
The elements of a circular array are usually evenly distributed on the circumference. Because the circular array is geometrically symmetric about the origin, it has no directionality. There is no natural directional beam, so it is necessary to delay or phase shift the unit signal to form directivity, even if it is compensated as an equivalent linear array. The simple realization method is electronic switch beamforming, which uses electronic switch to control and connect a group of delay lines to different array elements to form beams in different directions.
Take 16 yuan cyclic array as an example to illustrate. Assuming that only seven elements on an arc form a beam (as shown in Figure 3), if the target signal comes from the front, in order to form in-phase addition, the signal delay of each element must be compensated to the straight line (blue) shown in the figure. Let the central angle of the arc where two adjacent array elements are located be α0, then the corresponding delay required by each array element is:
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τ 1=τ7=0( 15)
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2.5 Arc Array Beamforming
Beamforming of arc array is a special case of circular array beamforming, and the elements distributed in arc array must be projected into an equivalent linear array eventually. If the directivity is controlled by time delay, the time delay algorithm of each array element is the same as the example of "circular array beamforming"
2.6 frequency domain beamforming
As can be seen from the previous discussion, the beamformer can respond to signals in one direction and suppress signals in other directions. Therefore, beamforming is actually a spatial filtering process. According to the linear system theory, beamforming is also a convolution operation, so it can be realized by the product of frequency domain. So the beam can also be formed in the frequency domain, which is frequency domain beamforming. Frequency domain beamforming often adopts discrete Fourier transform, which can be realized by fast Fourier transform in digital signal processing, so the computational complexity of frequency domain beamforming is less than that of time domain beamforming (Cao Hongze et al., 2002).
Let a linear array with uniform spacing have n elements, and the spacing is d. Sample the output signal xi(t) of array I, and take point L for DFT operation, that is:
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Where I is the array element number, K is the spectral line number and L is the time sequence number. Therefore, Xi(k) represents the frequency spectrum of the time series received by the i-th array element.
Secondly, the spectral lines with the same serial number k are subjected to spatial Fourier transform, and Xi(k) is rearranged into Xk(i), and the following operations are performed:
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Where m is the beam number; Wi is the amplitude weight of the array element; Yk(m) represents the m-th beam output of the k-th frequency component. This is the method of realizing frequency domain beamforming by using two-dimensional DFT.
3 Conclusion
To sum up, the directivity of transducer is the basis of beamforming principle. At present, the active multi-beam sounding systems in China mainly include SeaBea m series, Elac Botto mChart series, EM series, SeaBat series and Atlas DS series [4]. Because the manufacturer and working water depth range of each system are different, the transducer and transmitting frequency used in multi-beam system are also different, so the beamforming methods used in different systems are different.
The transmitting frequency of Sea Bea m 2 1 12 deep-water multi-beam sounding system is 12 KHz, and the transmitter and hydrophone are installed independently, including transmitter 14 module and hydrophone ***80 channel 8 module. The hydrophone is a group of four modules * * * two groups are installed in a "V" shape, and the transducer is installed in a typical "Mill s Cr oss" mode. Even so, the beamforming principle conforms to the linear phase-shifting beamforming principle. 1In August, 1998, the manufacturer upgraded the system according to the contract. Only by replacing the DSP board, the beam number of the system was upgraded from 12 1 to 15 1. It should be the digital interpolation beamforming technology (shifted sideband beamforming) under linear phase-shifting beamforming completed by advanced digital signal processor. The transmitter and receiver of EM 120 deep-water multi-beam sounding system are also independently installed, belonging to the linear "Miller cross" structure array, and its basic beamforming principle also conforms to the linear phase-shifted beamforming principle. Because the number of beams has been greatly improved, frequency domain beamforming technology should be integrated.
The emission frequency of EM950 (or EM 1002) is 95kHz. The transmitter and hydrophone are installed together, and the number of beams is 120. The transducer is a semi-circular array with a radius of 45 cm. As an active sonar system with high transmission frequency, it adopts the synthesis of arc array time delay and phase shift beamforming technology. EM3000 shallow water multi-beam sounding system has a transmitting frequency of 300kHz and a beam number of 120. The transducer is a circular array (Li Jiabiao et al., Zhou Xinghua et al., 1999), and the technology adopted is similar to EM950.
SeaBat series multi-beam system is mainly shallow water multi-beam sounding system in China, and the transducer of shallow water multi-beam system is generally installed by combining transmitter and hydrophone. The frequency of SeaBat8 10 1 multibeam sounding system is 240kHz, and the number of beams is10/. The transducer is a circular array with a diameter of 32cm, and the beam forming method is similar to EM series.
Atlas Fansweep series is a multi-beam sounding system, which uses side-scan sonar technology to calculate multiple water depth data. Compared with the real multi-beam sounding system, its technical index is relatively backward. Due to the change of the manufacturer's product development strategy, the deepwater multi-beam system was launched only in the last two years. Atlas DS series multi-beam system has no users in China. It is said that its new generation multi-beam system adopts Chirp technology, and the number of received beams will exceed 300, so its beamforming technology should be mainly frequency domain beamforming technology.
refer to
Cao Hongze, Li Lei, et al. 2002. Analysis of BDI algorithm based on FFT beamforming. Marine science and technology, 2 1(2), 55 ~ 59.
Jiang Nanxiang. 2000. Sensors and arrays. Harbin: Harbin Engineering University Press, 50 ~ 75.
Li Jiabiao et al. 1999. Principle, technology and method of multi-beam measurement. 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 Mingzuo, et al. Technical specification for multibeam seabed topographic survey. 8 ~ 14.
Key Technology of Multi-beam —— Beamforming
Liu Yuping Lanfang Xiao Bo
(Guangzhou Marine Geological Survey, Guangzhou, 5 10760)
A general frequency domain beamforming method is introduced for different types of transducers. Dimension DFT. Finally, the author briefly explains the different beamforming techniques used in multi-beam applications. Abstract: Different arrangements of transducers determine the directivity of transducer array. The foundation of multi-beam formation-the key technology of multi-beam is how to control the directivity of transducer. In this paper, the theory of multi-beam formation is summarized by mathematical operation.
Keywords: directional beamforming sound of multi-beam transducer