A port and starboard fuzziness suppressed algorithm based on vector directivity zero

Conventional linear array based on acoustic pressure hydrophone can not distinguish the target signal from the port side, so it can not locate the target accurately. The vector hydrophone has natural directivity and can be resolved from starboard to starboard after being formed. However, in practical engineering, it is necessary to further improve the resolution of starboard to starboard because of noise or interference, etc. A new method of port and starboard suppression based on directivity of vector linear array is proposed. The simulation results show that the starboard suppression ratio of vector beam output is enhanced. Experimental data processing results show that this method can suppress the starboard ambiguity of vector beamforming and improve the starboard resolution of vector linear array. The processing results verify the feasibility of the algorithm, and the algorithm has certain application value.


Principle
Single vector sensor, acoustic pressure hydrophone is non-directional, vibration velocity sensor has dipole directivity, combining the two mutually orthogonal components of vibration velocity v x and v y , the combined vibration velocity v c is v c t =v x t cos φ +v y (t) sin φ 1 In the formula: φ represents the guiding orientation.

Normalized directivity
Let p be the sound pressure part of the received signal, the normalized directivity R(θ)of (p+v c ) 2 is θ is the horizontal azimuth.In the above directivity formula, φ orientation is the main maximum direction of v c . Figure 1 (a) is showing (p+v c ) 2 normalized directivity diagram, Figure 1 (b) is showing (p+v c )v c normalized directivity diagram.It can be seen from the figure, in the two unilateral directivity, the zero of directivity is the reverse of the main maximum direction, that is, the direction of 180° after the main maximum.Because the Angle is the zero of directivity, interference will be suppressed to a certain extent, making the side lobe reduced in this region.

The directivity function of the matrix
The (p+v c ) combination directivity of vibration velocity sensor linear array is In the formula, f is the frequency, θ 0 is the guiding orientation, θ is the azimuth, the end direction of the matrix is 0°, M is the number of matrix elements, d is the interval of matrix elements, and λ is the wavelength.
Using a vector sonar array for beamforming.Simulation: 16-element uniform linear array, half wavelength spacing, simulate 1200Hz single frequency transmission signal, do not set the noise background temporarily, signal direction is 60°.There is starboard blur at -60°.In the opposite direction of the main lobe, which is -120 °, it can be seen that the side lobe is lower, and the background sinks in about -13 decibels in this direction.This is because part of the beamforming in Figure 2(b) is based on the time delay summation of sound pressure data, which is scalar, so there will be ambiguity in the symmetric side of the target signal.In theoretical analysis, starboard and starboard signals can generally be distinguished, but in engineering practice, because of noise or interference, it is often impossible to distinguish starboard signals correctly, so in signal processing, it is necessary to put forward some algorithms to improve the resolution of starboard and starboard signals.

Design of a beamforming algorithm based on vector directivity zero
In engineering practice, it is often necessary to improve the resolution ability of array port and port sides to cope with complex environment and sea conditions.In Figure 1(a), there are different directivity responses in different directions.In order to suppress the other side symmetrical to the target side, it is considered to rotate the directivity diagram and align the zero point of the directivity curve with the side Angle to be suppressed, that is, always align the zero point of the directivity curve with the other side symmetrical to the target side during the pre-beamforming.The point of maximum directivity is aligned with the opposite side of the board, the angle of rotation of the board 180°, the angle complementary to the target angle: (180°-θ).The intention of this method can be seen directly in Figure 3 (a), which is a directivity diagram pointing to 60°, representing the directivity effect of the traditional method.The two dotted lines represent the response of the port and port sides, and the ratio of the length of the two dotted lines is similar to the suppression ratio of the port and port sides.Figure 3 (b) shows that the maximum point is aligned with the complementary direction of 60°, that is, the direction of 120°, which represents the directivity effect of the proposed method.At this time, the response of the target direction of 60° is no longer the largest.It is found in the figure that the other side symmetric to the target side, the direction of 300° is the opposite direction of 120°, therefore, it becomes the zero direction in the whole directivity diagram, and the corresponding azimuthal response becomes 0. In this case, the ratio of dotted line lengths in the 60° and 300° directions is better than that in Figure 3 (a), and the suppression ratio of starboard and starboard sides is improved.Theoretically, the starboard and starboard resolution of the array is enhanced.Let v c ' be the combined vibration velocity after changing the directivity direction.Next, the proposed method is simulated and compared with the traditional method.

Combined directional of (p+v c )*(p+v c
' ) The (p+v c )*(p+v c ' ) combination directivity of vibration velocity sensor linear array is Simulation: 16-element uniform linear array, half wavelength spacing, simulate 1200Hz single frequency transmission signal, no noise background is set, signal to 60°.Ensure that the maximum point of the preformed beam of (p+v c )*(p+v c ' ) is aligned at all times (180°-θ) and that the preformed beam is aligned at zero time (θ).  ) combined directivity of the 16-element vector linear array.It can be seen that compared with the (p+v c ) array directivity of Figure 2(a), The directivity amplitude of the two methods is their maximum value at 60°from the signal target, which firstly proves the feasibility of this method for azimuth estimation.Furthermore, in the other azimuth symmetrical 0° from the target side, namely 300°, shown in Figure 2(a), Traditional (p+v c ) method is larger, the directivity of amplitude is about 13 decibels, and in Figure 4 ) method can be reduced to about -40 decibels in this azimuth, which indicates that compared with the traditional method, the proposed method can suppress the beam output in the other azimuth, thus enhancing the starboard resolution of array signal processing.

Combined directional of (p+v
The (p+v c +p+v c ' combination directivity of vibration velocity sensor linear array is Simulation: 32-element uniform linear array, half wavelength spacing array, simulate 1200Hz single frequency transmission signal, do not set noise background, signal to 60°.Ensure that the maximum point of the preformed beam of (p+v c +p+v c ' is aligned at all times (180°-θ) and that the preformed beam is aligned at zero time (θ). Figure 5(a) is the (p+v c +p+v c ' ) 2 combined directivity of the 32-element vector linear array , which is similar to the (p+v c )*(p+v c ' ) method mentioned above, it can be seen that compared with the directivity of the array (p+v c ) in Figure 2(a), the directivity amplitude of the two methods is their maximum at 60° to the signal target, which firstly proves the feasibility of this method for azimuth estimation.Furthermore, when the other azimuth is symmetrical at 0° to the target side, In Figure 2(a), the traditional method(p+v c ) has a larger directivity range of about -13 decibels, while in Figure 5 2 method in the location of the output amplitude around -17 decibels, Although the (p+v c )*(p+v c ' ) method is not as effective as the one described above, it can also be shown that this method can suppress the beam output in the other side orientation compared with the traditional method, thus enhancing the starboard resolution of array signal processing.

Beamforming in the background of uniform noise and interference signals 4.2.1. Uniform background noise
Under the background of uniform noise, the beamforming of (p+v c )*(p+v c ' ) , (p+v c +p+v c ' and general methods is investigated and compared below. Simulation: 32-element uniform linear array, half wavelength spacing, simulate 1200Hz single frequency transmission signal, noise background is spatial omnidirectional uniform random noise, signal to noise ratio is set at 10 decibels, signal direction is 30°, beamforming of (p+v c )*(p+v c ' ) and beamforming of p+v c 2 , the former beamforming, promised to advance into the maximum point of the beam moment alignment (180°-θ), Align the preformed beam at zero to (θ).v c ' represents the combined vibration velocity after changing the directional direction to make the starboard contrast diagram of the two beamforming.The simulation results are run under the condition of 10 decibels signal-to-noise ratio.In Figure 6(a) and (b), the solid line is the result of conventional vibration velocity processing, while the dashed line is the result of (p+v c +p+v c ' ) 2 The line marking of the circle data is the processing result of p+v c * p+v c ' method.As you can see, p+v c *(p+v c ' ) , (p+v c +p+v c ' ) 2 , and the traditional method in signal target to 30 °, directivity maximum amplitude is their own, The three methods give the correct estimation results of azimuth.Furthermore, the normalization amplitude of the traditional method is about -3 decibels for the other azimuth symmetrical 0° to the target side, namely -30° azimuth.
(p+v c +p+v c ' ) 2 method has a normalization amplitude of about -5 decibels at -30°, which is 2 decibels lower than that of the traditional method and has improved the starboard resolution of signal processing.p+v c *(p+v c ' )method in 30 ° azimuth of normalized amplitude is about -16 decibels, compared with the traditional method reduces the 13 decibels, port/starboard discrimination ability has been improved significantly.Therefore, in the case of uniform background noise, compared with traditional methods, these two methods can still suppress the beam output in the other side orientation, so as to enhance the starboard resolution of array signal processing.

Signal interference background
Consider the effect on the beamforming of the presence of other interfering signals in a given direction.
Simulation: 64-element uniform linear array, half wavelength spacing, simulate 1200Hz single frequency transmission signal, signal direction is 60°, in the uniform background noise environment, there is also a 120° to 1200Hz interference, signal-to-noise ratio is 10 decibels, signal-to-dry ratio is 10 decibels.The simulation results are run under the conditions of 10 decibels signal-to-noise ratio and 10 decibels signal-to-dry ratio.In Figure 7(a) and (b), the solid line is the result of conventional vibration velocity processing, while the dashed line is the result of (p+v c +p+v c ' ) 2 The line marking of the circle data is the processing result of p+v c * p+v c ' method.It can be seen that, p+v c * p+v c ' , (p+v c +p+v c ' ) 2 and traditional method in the signal of the target to 60 °, directional maximum amplitude is their own, the three methods give correct azimuth estimation results, and recognize the existence of interference signals in the direction of 120°.At the other broadside bearing symmetrical 0° to the target side, which is -60°, the normalization amplitude of the conventional method is about -12 decibels, and (p+v c +p+v c ' ) 2 the normalization amplitude of the conventional method is about -17 decibels at -30 °, which is 5 decibels lower than that of the conventional method.p+v c * p+v c ' method has a normalization amplitude of about -26 decibels at -60°, which is 14 decibels lower than the traditional method, and the starboard resolution has been significantly improved.Therefore, in the case of uniform background noise, compared with traditional methods, these two methods can still suppress the beam output in the other side orientation, so as to enhance the starboard resolution of array signal processing.It is worth mentioning that the array used in this simulation is a 64-element hydrophone, so the beamforming effect is generally better than the aforementioned simulation of uniform background noise.
In general, even if there is interference in the direction of the maximum value of the combined beam, the two improved methods can still form a certain suppression in the direction of the other side symmetrical to the target side at a signal-to-trunk ratio of 10 decibels.

Experimental data processing
In order to verify the correctness and actual effect of the above-mentioned resolution method of starboard and starboard, some measured signals in a lake test were used for data processing.The matrix is a 16-element linear array with equal spacing and uniform distribution.The signal is directed horizontally at 140° to the broadside of the front of the array.The conventional beam forming method is compared with the algorithm in this paper.In the experiment, there is a signal at 140°, and the other side symmetrical to the target side is near -140°.In Figure 8, the solid line is the result of conventional vibration velocity processing, while the dashed line is the result of (p+v c +p+v c ' ) 2 The line marking of the circle data is the processing result of p+v c * p+v c ' method.It can be seen that the three methods estimate the orientation of the target signal accurately.In the conventional method, the other beam symmetrical on the target side is about -5 decibels.p+v c * p+v c ' method in the side of the beam is about -10 decibels, the method of beam compared with average velocity method of beam decreased about 5 decibels, (p+v c +p+v c ' ) 2 method has a beam of about -8 decibels on the beam, which is about 3 decibels lower than that of the conventional vibration velocity method.By comparing the above two methods, it can be seen that in practical data processing, compared with the traditional method, these two methods can still suppress the beam output in the other side azimuth, so as to strengthen the resolution of the left and right side of the array signal processing in engineering practice, so as to better distinguish the specific target signal, verify the feasibility of the algorithm, and have certain application value.

Conclusion
This paper introduces a beamforming algorithm to enhance the resolution of starboard and starboard sides.Different from the general vector beamforming algorithm, this method adjusts the direction of the main beam, alters it to the zero of directivity, and supposes the azimuth of the other side symmetrical to the target side.After simulation of single vector hydrophone and hydrophone linear array, the suppression effect is better than that of conventional vector beamforming.In this paper, the proposed method is also verified by actual data, and the results show that the proposed method can significantly improve the starboard resolution of the array.This method is suitable for the starboard fuzziness suppression of vector beamforming, so as to better distinguish the specific target signal, and it has certain application value.

Figure 2 (
Figure 2(a) shows the (p+v c ) combined directivity of the 16-element vector linear array.Figure 2 (b) is the (p+v c ) beamforming result of the vector linear array.The main lobe is visible at 60°.There is starboard blur at -60°.In the opposite direction of the main lobe, which is -120 °, it can be seen that the side lobe is lower, and the background sinks in about -13 decibels in this direction.This is because part of the beamforming in Figure2(b) is based on the time delay summation of sound pressure data, which is scalar, so there will be ambiguity in the symmetric side of the target signal.In theoretical analysis, starboard and starboard signals can generally be distinguished, but in engineering practice, because of noise or interference, it is often impossible to distinguish starboard signals correctly, so in signal processing, it is necessary to put forward some algorithms to improve the resolution of starboard and starboard signals.

Figure 4 (
Figure 4(a) shows the (p+v c )*(p+v c ') combined directivity of the 16-element vector linear array.It can be seen that compared with the (p+v c ) array directivity of Figure2(a), The directivity amplitude of the two methods is their maximum value at 60°from the signal target, which firstly proves the feasibility of this method for azimuth estimation.Furthermore, in the other azimuth symmetrical 0° from the target side, namely 300°, shown in Figure2(a), Traditional (p+v c ) method is larger, the directivity of amplitude is about 13 decibels, and in Figure4(a), (p+v c )*(p+v c ' ) method in the 300 ° azimuth directional modestly, From the perspective of beamforming, Figure 4(b) compares the beamforming effects of the two methods, where the dotted line represents the traditional (p+v c ) method, Solid lines represent the article (p+v c )*(p+v c ' ) method, can be seen in the figure, (p+v c ) methods of normalized amplitude reached around 13 decibels, The output amplitude of (p+v c )*(p+v c ') method can be reduced to about -40 decibels in this azimuth, which indicates that compared with the traditional method, the proposed method can suppress the beam output in the other azimuth, thus enhancing the starboard resolution of array signal processing.
Figure 4(a) shows the (p+v c )*(p+v c ') combined directivity of the 16-element vector linear array.It can be seen that compared with the (p+v c ) array directivity of Figure2(a), The directivity amplitude of the two methods is their maximum value at 60°from the signal target, which firstly proves the feasibility of this method for azimuth estimation.Furthermore, in the other azimuth symmetrical 0° from the target side, namely 300°, shown in Figure2(a), Traditional (p+v c ) method is larger, the directivity of amplitude is about 13 decibels, and in Figure4(a), (p+v c )*(p+v c ' ) method in the 300 ° azimuth directional modestly, From the perspective of beamforming, Figure 4(b) compares the beamforming effects of the two methods, where the dotted line represents the traditional (p+v c ) method, Solid lines represent the article (p+v c )*(p+v c ' ) method, can be seen in the figure, (p+v c ) methods of normalized amplitude reached around 13 decibels, The output amplitude of (p+v c )*(p+v c ') method can be reduced to about -40 decibels in this azimuth, which indicates that compared with the traditional method, the proposed method can suppress the beam output in the other azimuth, thus enhancing the starboard resolution of array signal processing.

Figure 7 .
Figure 7. Beamforming contrast in the background of interfered signals (a) Beamforming of (p+v c )*(p+v c ' ) , (p+v c +p+v c ' ) 2 and (p+v c ) 2 ; (b) Enlarged view of local data points.