Researching methods to improve the quality of an underwater sensor array receiving signals in shallow water areas

rritorial waters, so it will be a good basis and orientation when designing sonar systems or underwater positioning devices in Vietnamese. 2 CHAPTER1: UNDERWATER SENSOR ARRAY AND PROBLEM TO IMPROVE QUALITY ARRAY IN THE SHALLOW WATER 1.1 Overview of underwater sensor array 1.1.1 Model of sensor array The sources of interest in sonar and ultrasound are the narrowband and wideband applications that satisfy the wave transmission equation in [31], [37], and their spatial properties can be independently separated. Therefore, the measurement of the 𝑧 𝑟 , 𝑡 is stimulated by negative sources that can determine the time-space response 𝑥 𝑟 , 𝑡 . The vector 𝑟 is the relative position of the sensor and the sound source, t is the time. Figure 1.1 Space-Time Model receiving signal of sensor array Response output 𝑥 𝑟 , 𝑡 is convolution of 𝑧 𝑟 , 𝑡 and response of sensor array ℎ 𝑟 , 𝑡 . 𝑥 𝑟 , 𝑡 = 𝑧 𝑟 , 𝑡 ⊗ ℎ 𝑟 , 𝑡 (1.1) There 𝑧 𝑟 , 𝑡 is defined are input of receiver, and is convolution of acoutic souce parameter 𝑦 𝑟 , 𝑡 with underwater environment Ψ 𝑟 , 𝑡 . 𝑧 𝑟 , 𝑡 = 𝑦 𝑟 , 𝑡 ⊗ Ψ 𝑟 , 𝑡 (1.2) 1.1.2 Sensor array and underwater passive sonar system Model of structure system The sonar system is a system of devices that determine the position of the sound source in the space under the sea surface. Depending on the application and different characteristics, the system 3 has the form: mobile or fixed. The basic structure model of a passive sonar system with M sensors can be described according to the progress of the identification detection information as follows (Figure 1.2): Figure 1.2: Model of underwater passive sonar system The accuracy positioning of sound source 𝜎𝑝 𝐷 = 𝜎đ𝑡 2 𝐷 + 𝜎𝑚𝑡 2 𝐷 + 𝜎𝑡𝑛 2 𝐷 𝜎𝑖 2 𝐷 𝑖 (1.7) 1.2 Shallow water and characteristic 1.2.1 The concept of shallow sea 1.2.2 Multi-path effect in the shallow sea Figure 1.3: Multipath trajectories in an isvelocity shallow water configuration. (A) direct path; (B) Reflection on the surface; (C) Reflection on the bottom and surface 4 For shallow waters the transmission environment is limited by the sea surface and the seabed, the signal propagation is reflected many times before go to the receiver. According to the experimental results of Lurton [37] in Figure 1.3a, the path of the negative rays in shallow water is reflected many times, Figure 1.3b shows the multi-path effect of measuring signals in real time domain. Hình 1.4: Simulate multi-path with 5 acouctic path Figure 1.5: Receiving pulse in the shallow water Figure 1.4 illustrates the sound channel in shallow water affected by the multi-path with 5 rays: sound speed is 1520 m/s, depth of channel is 100m, source with coordinates [0,0, -60], receiver 1 has coordinates [500,0, -40], receiver 2 has coordinates [500, 1000, -70], isotropic sources and direct and reflected sound at the bottom have a loss of 0.5dB. 5 The isotropic source generates a pulse of 13.2ms width into the audio channel with 5 rays received at the receiver. In Figure 1.5, the signal receives multiple echoes generated by reflected sound rays, which interfere with each other. Thus, in the shallow sea, the effect of multi- path effect on signal quality is enormous. To solve this problem, there are several solutions such as: The first is design the geometric structure of the array to increase the gain of the receiving array. The second is beamforming of the sensor array so that the main beam is directed towards the direct beam while the signal coming from the other directions is noise, in order to increase the SNR. Thirdly, solution DSP to recontruct signal. These solutions are discussed in detail in the following sections. 1.2.3 Parametric effect of shallow sea on the quality of passive sonar system 1.3 Solutions to improve the quality of sensor array. 1.3.1 Optimize the geometric structure of the array 1.3.2 Beamforming sensor array 1.3.3 Signal processing array sensors Figure 1.7: Block diagram of sensor signal processing array system Signal processing underwater sensor array is an extended concept including processing sonar sensor, underwater communication network ... including functional blocks such as ADC conversion, FIR filtering, Adaptive LMS filter, Kalman, adaptive noise suppression, linear adaptive enhancement, DEMON / LOFAR analysis, FFT / MUSIC spectrum analysis, target detection (torpedoes, submarines, strange ships, clones, fish stocks, etc.), target identification, of SNR of the array, recording, tracking, etc. (Figure 1.7). 1.4 The problem of improving the quality of the underwater sensor array and the research direction of the thesis 1.4.1 Related studies have been published Researches in our country, International pulication 1.4.2 Requirements and research directions of the thesis 6 From scientific requirements and practical requirements on the quality of sensor arrays, based on the theory of electronic and engineering, the thesis aims at the following tasks: - Develop solutions to improve the quality of the underwater sensor array by the method of customized beamforming; - Develop a solution to improve the receiving signal quality of the underwater sensor array using a customized complex signal processing method (Figure 1.9). Figure 1.9: Proccesing signal model to impove quality of sensor array 1.4.3 Researching of the thesis The research problem was raised to propose a solution to improve the quality when working in shallow sea environment, characterized by the multi-path effect and high noise. In order to solve the above, it is necessary to fix the following issues: The first is to study a customized beamforming, combining conventional and adaptive control mail lobe in order to improve the SNR ratio of the sensor array. The second is to research a solution processing suitable to the structure of the underwater sensor array based on the combination of ICA technology and the solution of multi-channel blind deconvolution by neural network into processing sensor signal array to restore original signal. 2 CHAPTER 2: SOLUTION TO IMPROVING SIGNAL QUALITY BASED ON CUSTOMIZE BEAMFORMING ARRAY 2.1 Beamforming sensor array 2.1.1 Linear beamforming Considering the array of sensors (Figure 2.2), there are N sensors placed along the z axis with equal spacing and d (ULA - Uniform Linear Arrays). Put array in the center of the coordinate system; sensor positions 𝐩𝑧𝑛 = 𝑛 − 𝑁−1 2 𝑑 𝑛 = 0, 1, 2, , 𝑁 − 1 (2.8) 7 𝐩𝑥𝑛 = 𝐩𝑦𝑛 = 0 (2.9) Figure 2.2: Linear array along z-axis Where: ϒ 𝜔, 𝑘𝑧 = 𝐰 𝐻𝐯𝐤 𝑘𝑧 = 𝐰𝑛 ∗ 𝑁−1 𝑛=0 𝑒−𝑗 𝑛− 𝑁−1 2 𝑘𝑧𝑑 (2.13) 𝐵𝜓 𝜓 = 𝐰 𝐻𝐯𝜓 𝜓 = 𝑒 −𝑗 𝑁−1 2 𝜓 𝑤𝑛 ∗𝑒𝑗𝑛𝜓 , 𝑁−1 𝑛=0 − 2𝜋𝑑 𝜆 ≤ 𝜓 ≤ 2𝜋𝑑 𝜆 (2.26) We now restrict our attention to the uniform weighting case, 𝑤𝑛 = 1 𝑁 , 𝑛 = 0, 1, , 𝑁 − 1 (2.29) We can also write (2.29) as 𝐰 = 1 𝑁 𝟏 (2.30) where 1 is the Nx1 unity vector. Thus, the frequency-wavenumber function can be written in ψ –space. ϒ.𝜓 𝜓 = 1 𝑁 𝑒 𝑗 𝑛− 𝑁−1 2 𝜓𝑁−1 𝑛=0 = 1 𝑁 e −j 𝑁−1 2 𝜓 𝑒𝑗𝑛𝜓𝑁−1𝑛=0 = 1 𝑁 e −j 𝑁−1 2 𝜓 1−𝑒 𝑗𝑁𝜓 1−𝑒 𝑗𝜓 (2.31) as 8 𝑥𝑛 = 1 − 𝑥𝑛 1 − 𝑥 𝑁−1 𝑛=0 or ϒ .𝜓 𝜓 = 1 𝑁 𝑠𝑖𝑛 𝑁 𝜓 2 𝑠𝑖𝑛 𝜓 2 , −∞ ≤ 𝜓 ≤ +∞ (2.32) We observe that ϒ.𝜓 𝜓 is periodic with period 2π for N odd. If N is even, the lobes at ±2π, ±6π are negative and period is 4π. The period of |ϒ.𝜓 𝜓 | is 2π for any value of N. ϒ 𝑤: 𝑘𝑧 = 1 𝑁 𝑠𝑖𝑛 𝑁𝑘𝑧 𝑑 2 𝑠𝑖𝑛 𝑘𝑧 𝑑 2 , −∞ ≤ 𝜓 ≤ +∞ (2.34) ϒ 𝑤: 𝑘𝑧 is periodic with period 2π/d. Note that the response function depends only upon the wavenumber component kz and is periodic with respect to kz at intervals of 2π/d. So that beam lobe in ψ space is: 𝐵𝜓 𝜓 = 1 𝑁 𝑠𝑖𝑛 𝑁 𝜓 2 𝑠𝑖𝑛 𝜓 2 , − 2𝜋𝑑 𝜆 ≤ 𝑢 ≤ 2𝜋𝑑 𝜆 (2.37) Simulate uniform linear array beamforming in polar and 3D. Figure 2.6: ULA beamforming ϒ(ψ) in polar (dB) 9 Figure 2.7: ULA beamforming ϒ(ψ) in 3D space 2.1.2 Beamforming sensor array with different geometry 2.2 Adaptive Beamforming sensor array 2.2.1 Model and method adaptive beamforming 2.2.2 Frost adaptive beamforming 2.3 A solution to solve multi-path based on a customized array of beams 2.3.1 Rectangular customized beamforming On the basis of rectangular array of NxM hydrophone, building calculation models and designing beam for arrays based on manifold vectors and weighted arrays [17]. The beam of a rectagular array with a source at position p(r,θ,ϕ) is calculated as follows: 𝐵 𝜓𝑥 , 𝜓𝑦 = 𝑒 −𝑗 𝑁−1 2 𝜓𝑥 + 𝑀−1 2 𝜓𝑦 𝒘𝑛𝑚 ∗ 𝑀−1 𝑚=0 𝑒𝑗 𝑛𝜓𝑥 +𝑚𝜓𝑦 𝑁−1 𝑛=0 (2.49) Where: 𝜓𝑥 = 2𝜋 𝜆 𝑑𝑥𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙, 𝜓𝑦 = 2𝜋 𝜆 𝑑𝑦𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜙 If array is uniform with dx = dy = λ/2 và N x M = 5 x 7 the beam with is lobe Figure 2.20. The manifold vectors is m th row along the y-axis of the retangular array is calculated: 𝒗𝑚 (𝜓) = 𝑒𝑗 (𝑚𝜓𝑦 ) 𝑒𝑗 (𝜓𝑥 +𝑚𝜓𝑦 ) ⋯ 𝑒𝑗 ((𝑁−1)𝜓𝑥 +𝑚𝜓𝑦 ) (2.50) 10 Figure 2.20: Geometry and5x7 rectangular array beamforming thus, for the all array, we have a manifold matrix with NxM hydrophone as follows: 𝑽𝜓 𝜓 = 𝒗0 𝜓 ⋮ ⋯ ⋮ 𝒗𝑀−1 𝜓 T, véc tơ 𝝍 = 𝜓𝑥 𝜓𝑦 (2.51) from this, it is possible to define a generalized vector by folding in turn to have a vector NM x 1 value. 𝑣𝑒𝑐 𝑽𝝍 𝜓 = 𝒗0(𝜓) ⋯ 𝒗𝑀−1(𝜓) (2.52) The same is true for the matrix of weights of a rectangular array we have 𝑾 = 𝒘0 ⋯ 𝒘𝑚 ⋯ 𝒘𝑀−1 , with m^th row 𝒘𝑚 = 𝑤0,𝑚 𝑤1,𝑚 ⋯ 𝑤𝑁−1,𝑚 (2.53) and 𝑣𝑒𝑐[𝑾] = 𝒘0 ⋯ 𝒘𝑚 ⋯ 𝒘𝑀−1 (2.54) Thus: 𝐵 𝜓 = 𝐵 𝜓𝑥 , 𝜓𝑦 = 𝑣𝑒𝑐 H[𝑾]𝑣𝑒𝑐 𝑽𝜓 𝜓 (2.55) is an overview format to design an NxM hydrophone all planar array. 2.3.2 Calculate and customize arrays to reduce multi-path effect - Calculating arrays to enhance signals when the target is approaching Consider the ULA of 30 hydrophones to observe the target from afar into the array, the array can be customized as follows: + A ULA of 30 hydrophone: Array gain GA = 30dBi, The figure shows that the main-lobe is very narrow and pointed, the side-lobe are suppressed, when looking at the distant target, it is good (Fig.2.25). 11 Figure 2.25: Linear beamforming 30 hydrophones + Three independent linear arrays each with 10 hydrophone arrays: GA = G1 + G2 + G3 = 30 dBi. The simulation shows that the main-lobe are larger, the side-lobe also increase, but ensuring the gain (Figure 2.6). Figure 2.26: Linear beamforming 3 arrays each 10 hydrophone + one vertical array in the middle and two customizable segments independently rotated by 10 degrees (Figure 2.27): Hình 2.27: Beamforming one vertical and two rotated by 10o When observing a distant target, the signal field to the array is parallel, the first two cases are well observed. When the target comes near, both of the above arrays are much worse. To calculate the attenuation, consider the magnitude of the main beam at 3dB (the half- power beamwidth, HPBW). According to [17] the half-power beamwidth main-lobe: 12 𝐻𝑃𝐵𝑊 = 𝛥𝑢1 = 0.886𝜆 𝑁𝑑 𝑟𝑎𝑑 ≈ 50 𝜆 𝑁𝑑 (𝑑𝑒𝑔𝑟𝑒𝑒) (2.56) With 3 arrays, each designed 10 hydrophone 50m distance (d = 50m) observed frequency f = 15Hz (λ = 100m), assuming the sound velocity in water c = 1500 m/s. We have HPBW ≈ 10O. So the distance R = 550/sin10 O = 3167 m. Thus, when the target near the array to a distance of 3167m, in the case of 2 the gain will decrease and GA = G1 /2 + G2 + G3 /2 dB, the further the gain decreases. In the case of 3 custom arrays that have been rotated to 10 O , when the target is close, the gain is still constant. - Customized array to optimize reception of the desired signal Consider the rectangular array of 10x10 hydrphone which assumes that the desired signal comes from the direction of 28 O , the noise signal comes from the direction of 62 O and the noise comes from the direction of 75 O . Customizing the planar array into 3 parallel arrays and determining the gain with the 3 main beams turning in the direction of 28 O . Simulate 3 different linear arrays of configurations to calculate the 62 O and 75 O directional gain of the array in the cases to determine Gmin, GA(θ o )= G1(θ o )+ G2(θ o )+ G3(θ o ) gain regulation = 10 dBi for each array. Table 2.4: Array gain GA at the direction of the customized planar array Num- ber Geometry of 3 ULA Direction of main-lobe GA(28 o ) dBi GA(62 o ) dBi GA(75 o ) dBi 1 2:26:2 28 o :28 o :28 o 30 1.2459 2.4640 2 3:24:3 28 o :28 o :28 o 30 2.9497 0.9837 3 4:22:4 28 o :28 o :28 o 30 1.5707 2.7985 4 5:20:5 28 o :28 o :28 o 30 2.8708 1.9806 5 6:18:6 28 o :28 o :28 o 30 1.8016 2.3296 6 7:16:7 28 o :28 o :28 o 30 2.6718 2.1814 7 8:14:8 28 o :28 o :28 o 30 1.9362 0.8144 8 9:12:9 28 o :28 o :28 o 30 2.3617 3.0255 9 10:10:10 28 o :28 o :28 o 30 1.9791 2.4735 10 11:8:11 28 o :28 o :28 o 30 1.9562 0.7255 11 12:6:12 28 o :28 o :28 o 30 1.9407 2.8942 12 13:4:13 28 o :28 o :28 o 30 1.4770 2.1124 13 14:2:14 28 o :28 o :28 o 30 1.8366 2.1415 14 15:0:15 28 o :0 o :28 o 30 0.9500 2.0887 The simulation data from Table 2.4 shows that with the direction of 62 O Gmin = 0.95 in the case of Num-14 customized in to 2 linear of 15 13 hydrophones, with the direction of 75 O Gmin = 0.7255, in the case of Num -10, arrays customized into 3 arrays 11: 8: 11. So to minimize the effects of inference and noise, the optimal configuration can be completely determined. 2.4 Effective method of customized beamforming 2.4.1 Cancellation noise and interference Simulation of conventional beamforming (Delay and Time) and Frost adaptive beamforming [15] for regular and customized arrays. The signal used to simulate is the signal emitted from the underwater target with a length of 10 seconds (Fig.2.30). Figure 2.30: Some of the underwater signals used for simulation Figure 2.35 shows that the signal has been significantly improved in terms of noise and no secondary signal has been seen. Thus, the Frost adaptive algorithm can significantly improve the quality with the conventional waveform algorithm. However, with the number of sensors being constant, the signal quality can be even better when applied with a 4x3 triangular flat array (Fig. 2.36), the simulation clearly shows the effect of the waveform shaping solution. Customization has reduced noise coming from uninteresting directions. 14 Figure 2.35: Frost beamforming with ULA S1 [-30 O , 0 O ] Figure 2.36: Frost beamforming with customize array S1 [-30 O , 0 O ] 2.4.2 Improve signal gain with customize array. To see an improvement in the quality of array gain by the following formula [40]: 𝐺𝐴 = 𝑆𝑁𝑅0(𝜔) 𝑆𝑁𝑅𝑖𝑛 (𝜔) = 1 𝑤𝑛 2 𝑁−1 𝑛=0 (2.57) Or 𝐺𝐴 = 𝑤𝑛 2 𝑁−1 𝑛=0 −1 = 𝑤 2 (2.58) 15 Table 2.5: Gain of ULA with 3 directions arrived of signal N U M Linear (ULA) Delay and Time beamforming Frost beamforming Direction S1[-30,0] Direction S2[-10,10] Direction S3[20,0] Direction S1[-30,0] Direction S2[-10,10] Direction S3[20,0] 1 Linear 12 com- ponents (ULA) 0.8645 0.2235 0.4764 10.9068 1.6913 3.6562 Table 2.6: Gain of customized array with 3 directions arrived of signal N U M Rectagular customized array with diff. geometry Delay and Time beamforming Frost beamforming Direction S1[-30,0] Direction S2[-10,10] Direction S3[20,0] Direction S1[-30,0] Direction S2[-10,10] Direction S3[20,0] 1 Customized planar 3x4 type Rectagular 2.1456 0.4610 0.5727 11.5240 1.6544 3.6667 2 Customized planar 4x3 type Rectagular 1.3982 0.3187 0.6418 11.7307 1.6818 3.6482 3 Customized planar 2x6 type Triangular 4.1100 0.6899 1.01621 11.7816 1.6808 3.6731 4 Customized planar 6x2 type Triangular 1.0032 0.2318 0.7527 11.8109 1.6709 3.6541 5 Customized planar 3x4 type Triangular 2.2093 0.4603 0.6143 11.6094 1.6602 3.6669 6 Customized planar 4x3 type Triangular 1.3950 0.3459 0.6981 11.8155 1.6806 3.6538 The results of Table 2.5 show that the gain when convensional array beamfoming in different directions, in fact the array can sweep in any direction, the thesis only simulates some typical direction to find the solution has the greatest benefit. Table 2.6 is beamforming with a customized plane array activated different geometry, the simulation results show that the gain of the customized plane array has improved, but the disadvantage of that solution is that it takes a lot of the time to calculate the optimal geometric geometry to give the best structure and not all directions of the customized flat array have greater profit than the regular array, this is also consistent with reality. 16 3 CHAPTER 3: SOLUTIONS TO PROCCESING SIGNALS OF SENSOR ARRAY IN THE SHALLOW SEA 3.1 Develop solutions 3.1.1 Model signal proccessing Hình 3.1: Model signal proccessing of array 3.1.2 Proposing signal processing solutions The solution used in Figure 3.2 is that after initializing the array of signals to coventional beamforming and control the main-lobe on the principle of "Delay and Time" horizontal to detect the target. When the power level is higher than the detection threshold, the system will alert the target to appear and based on the energy level, spectral density, array frequency will customize a number of different geometric structures and settings Frost beamforming to find the array configuration for the best signal (Figure 3.3). 3.2 ICA with customized array 3.2.1 Independent Component Analysis - ICA 3.2.2 ICA signal processing enhances target positioning quality a) Structure and model of target position sensor array b) Improve the quality of multi-target positioning with ICA - Develop an ICA pre-proceesing model to track multi-tagets: For positioning follow to (3.23) (3.24), the number of hydro- phone is 4, according to the ICA model above, the number of hydro- phones needed is equal to the number of targets to be monitored. Thus, to monitor 2 targets at the same time, the configuration for 8 hydrophone works, 3 targets need 12 units .., in addition to setting the structure (changing the depth of the sensor as well as the geometric layout of network) easily implemented for monitoring and observation for various purposes (Figure 3.7). 17 Figure 3.2: Flowchart of signal processing algorithms 18 Figure 3.3: Flowchart of the algorithm to beam customized array 19 Figure 3.7: ICA model for multi-target positioning 3.3 Multi-channel blind deconvolution 3.3.1 Model of MBD 3.3.2 MBD condition for the sensor array 3.3.3 Application of Feed-Forward neural network to MBD Feed Forwardward Neural Networks (FFNWs) is a popular used multilayer network with back-propagation algorithm (feedback transmission). This algorithm allows the use of a training signal to train a neural network that splits a mixture of multi-path signals at the input so that it is most similar to the desired signal. Figure 3.11: Structure of Feed-Forward neural network 20 To MBD using FFNWs, consider the advance model Figure 3.10b [11] that have: 𝑦(𝑘) = 𝑦𝑖 𝑘 , 𝑚 𝑖=1 (3.44) With 𝑦𝑖 𝑘 = 𝑤𝑖𝑝 𝑘 𝑥𝑖 𝑘 − 𝑝 = 𝒘𝑖 𝑇𝒙𝑖 𝑘 , 𝐿 𝑝=0 (𝑖 = 1,2, , 𝑚) (3.45) Learning algorithm (3.48) can be rewritten ∆𝒘𝑖 𝑘 = 𝜂 𝑘 𝚲𝑖 𝑘 − 𝐑𝐲𝑖 𝐠 𝑘 𝒘𝑖 𝑘 , (𝑖 = 1,2, 𝑚) (3.49) In that: 𝚲𝑖 𝑘 = 1 − 𝜂0 𝚲𝑖 𝑘−1 + 𝜂0𝑑𝑖𝑎𝑔 𝐲𝑖 𝑘 𝐠 𝑇(𝐲(𝑘)) , (3.50) 𝐑𝐲𝑖 𝐠 𝑘 = 1 − 𝜂0 𝐑𝐲𝑖 𝐠 𝑘−1 + 𝜂0𝐲𝑖 𝑘 𝐠 𝑇 𝐲 𝑘 . (3.51) The above algorithm has the same as the natural gradient algorithm. To MBD with many different algorithms, the thesis uses FFNWs advanced neural network model with back-propagation algorithm to analyze MBD. Extract original signal from the mixed signal obtained through a training signal. 3.3.4 Train FFNNs network to separate the desired signal 3.3.5 Simulate multi-path signal processing with FFNNs Simulation of sound channel in shallow water affected by multi- path effect with 10 sound rays (1 direct and 9 reflections): Assuming the sound speed in water is constant c = 1520m/s . Depth of sound channel h = 100m. - Setting environmental parameters: The simulated multi-path signal is square pulse with a width of t = 13.2ms, input impedance of 50Ω, a amplitude of 1V, equivalent to 13dBm, the signal generator is set to a depth of z = -60m (coordinates [0,0, - 60]), hydrophone H1 set at a depth of -40m with coordinates [500,0, -40], hydrophone H2 at a depth of -70m with coordinates [500, 900, -70], with isotropic sources with rays straight and reflected sound at the bottom have attenuation level of 0.5dB. - Parameters of device transceiver: Hydrophone has sensitivity is - 140dBV re 1μPa, scalar receiver in the range below 30kHz, pre- amplification is 20dB and noise is 10dB. 21 Figure 3.14: Multi-path signal with 10 rays in the underwater channel - Setting up FFNNs: So when the signal passing through the environment of the shallow water is reduced to 1.6x10 -7 (V), equivalent to -123dBm, get 300 typical samples for the multi-path signal obtained. (Figure 3.17b) and get 300 training signal samples that are equivalent to the source signal, with a equivalent to the receiver level. The training purpose for the network to split the desired signal pulse in the set of received signals (Figure 3.17a). Setting up neural network with forward path of 10 input layer cells, 1 output layer, sigmod neuron activation function, transmission algorithm with wji weight and feedback according to LMS principle (least square) . Figure 3.17: Training and signal samples to input the neural network Applying two signal samples in Figure 3.17 to the neural network for processing, the mixture of received multi-signal signals has reconstructed the signal form similar to the training signal (Figure 3.18), the signal form after processing The theorem has not mixed the reflected pulses, the effect of the multi-path effect on the receiver signal has 22 decreased. Target detection will become more reliable, negative hydrographic positioning calculation will be more accurate. Figure 3.18: After process by neural network; a) multi-path suppression signals, b) multi-path suppression signals taken at absolute values 3.4 Effective of complex signal processing solutions 3.4.1 Improve SNR and gain after ICA The multi-component mixed signal receive by hydrophone 1 after spectral analysis showed that many frequency and harmonic components appeared (Figure 3.19.a), calculating the SNR ratio of this signal with the addition white noise SNR0 = 6.8282 (Table 3.5). After ICA process, the submarine's Ping sound is separated from the mixture with noise and harmonics, which is significantly reduced (Figure 3.19.b), SNR1 = 20.0226. Thus, the gain increased to 13.1944 dB. Similarly for the floating diesel engine and whale sound (Figure 3.9.5,8,6,9) both increased the SNR to 14 dB. Calculate the ratio of SNR of the mixed signal collected at 3 hydrophone (Figure 3.9.4,5,6) = SNR0 and SNR of the signal after separation (Figure 3.9.7,8,9) = SNR1. Assuming noise is white noise plus constant energy, the simulation for the signals in Figure 3.9 gives: Table 3.5: Calculating SNR to determine the gain after ICA process Tỷ số SNR (SNR= Ptín hiệu / Ptạp) Tín hiệu 1 (Tiếng Ping của tàu ngầm) Tín hiệu 2 (Tiếng động cơ Diezen tàu mặt nước) Tín hiệu 3 (Âm thanh của cá voi) SNR0 (hỗn hợp trộn) 6.8282 5.8788 5.8438 SNR1 (sau khi tách) 20.0226 19.9942 19.9834 Độ lợi theo công thức (3.63) = SNR1/SNR0 13.1944 14.1154 14.1396 23 Figure 3.19: Frequency domain signal; a) mixed signal received at hydrophone, b) ping sound of submarine after ICA 3.4.2 Improve SNR and gain after process with FFNNs To better see the improvement of signal after processing, simulate calculating SNR ratio of multi-path signal before putting into neural network = SNR0 (Figure 3.17 b), and SNR after processing = SNR1 (Fig. 3.18 b) consider the background noise to be a white noise plus a small and fixed amplitude,