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A modulation method of parametric array for underwater acoustic communication
Applied Acoustics 145 (2019) 305–313
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Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
A modulation method of parametric array for underwater acoustic communication Shengyu Tang a,b, Guangping Zhu a,b, Jingwei Yin a,b,⇑, Xiao Zhang c, Xiao Han a,b a
Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China c College of Computer Science and Technology, Jilin University, Changchun 130000, China b
a r t i c l e
i n f o
Article history: Received 9 October 2017 Received in revised form 13 June 2018 Accepted 25 July 2018
Keywords: Underwater acoustic communication Parametric array Covert communication
a b s t r a c t Focusing on the potential value of narrow directivity of parametric sonar in underwater acoustic communication, a broadband recursive filtering modulation method is proposed in this paper to generate parametric array excitation signal. The idea is to design the transient waveform by reversing the relationship between the envelope of original wave and difference frequency wave with the recursive filter. The method could process broadband and unknown arbitrary waveform signal (such as voice, image and video signal) in real time to get almost undistorted packets with low computation complexity. The feasibility and efficiency of the proposed method are verified by pool and trial experiments. The single carrier underwater acoustic communication system based on parametric array is applied to test the method in a distributed network. Performance of the system is improved effectively since the approximately distortion-free and narrow directivity compared with the conventional broadcast underwater acoustic communication system in Dalian sea trial. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction With the continuous exploration of the ocean, unmanned and intelligent vehicles were developed rapidly which result in the demand growth for acoustic devices, especially in Arctic Ocean [1]. Efficient, convenient and high-speed underwater information transmission greatly accelerated the understanding and utilization of marine science. Considering the complex variability of underwater acoustic channels (especially Chinese shallow waters) and the complexity of the underwater acoustic equipment implementation, directional communication implementations are an urgent issue in many applications such as secure communications and multi-user underwater acoustic communications (UAC) in a hot spot. Since oriented communication can not only increase channel capacity by spatial reuse, but also suppress multipath diffusion, and also has unique advantages in secure communication and network communication of multi-user groups. The parametric array utilizes the non-linear effect of the medium to produce the desired sound wave. In other words, the excitation signal of the parametric array is self-demodulated in water, resulting in the secondary wave field [2]. In general, the
⇑ Corresponding author. E-mail address: [email protected] (J. Yin). https://doi.org/10.1016/j.apacoust.2018.07.032 0003-682X/Ó 2018 Elsevier Ltd. All rights reserved.
structure and auxiliary equipment of the parametric array are not very complicated. The produced difference frequency component with narrow directivity in the secondary field is the desired signal in most underwater acoustic applications. This unique feature has been applied to UAC successfully [3–5]. However, few engineering applications are reported because the energy conversion of the parametric array is ineffective and difficult to align with receiver. In recent years, with the diversity of UAC nodes and the increasing use of large unmanned equipment, the energy supply and forwarding positioning issues are being addressed [6,7] or can be ignored. Therefore, parametric array for UAC is gradually coming back to our attention. For example, in a UAC network, which consists of fixed nodes (anchored platforms, shore-based underwater platforms or large surface vessels) with positioning function and mobile nodes (autonomous underwater vehicles, manned submarines, moving ships). The parametric array embedded in a fixed platform provides two important benefits based on the energy supply and source positioning of the system. Firstly, directional communication can improve the information capacity of a network. Secondly, one can send messages to the intended nodes without being intercepted. In this case, the energy consumption is even an acceptable overhead. As mentioned above, energy efficiency is an inevitable flaw of the parametric array. Besides, its excellent directionality, is like a
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double-edged sword that is hard to apply in practice, though appealing. Motivatived by solving these two disadvantages of parametric array in UAC practical application, this paper is committed to improve the gain loss caused by difference frequency signal distortion and the processing ability of parametric by innovativing modulation method, so as to better coordinate with the platform’s positioning and energy system. The earlier modulation methods of parametric array are conducting double-sideband modulation [8] and single side-band modulation [9] between carrier and data flow. Then the synthesized signal is sent as the excitation signal. These two methods are simple to realize, but distortion is observed in the received broadband communication signal after the nonlinear effect of aqueous medium. Square root modulation method [10] reduces the distortion of difference frequency wave by preprocessing the data flow. If 12 dB/oct compensation filter can be conducted before amplitude modulation, this method can achieve no distortion. However, the implementation of compensation filter with 12 dB/oct is not flexible enough for transient broadband signal (particularly when the signal’s parameters are unknown), which limits the application of this method. Double integral presquare rooting method [11,12] is in conformity with undistorted conditions in far field derived by Berktay [13]. However, integration results often lead to divergence when the method is used to design the excitation signal in practical application, due to the initial value and some factors. Other modulation methods [14–17] obtain the communication signal at the receiver without distortion approximately through the iterative calculation, but the large computations are not conducive to real-time processing. Motivated by the modulation distortions and engineering restrictions of above methods, this article presents an excitation signal modulation method of parametric array according to Berktay’s far field solution, which called the recursive filter to support the application of parametric array in UAC network. It is designed with the time series relationship between the envelopes of original frequency wave and difference frequency wave to obtain approximate undistorted communication signal. Meanwhile, its calculation effort is relatively less, which shows a potential value in real-time signal processing of transient, broadband, unknown arbitrary waveform signal. It is very conducive to the practical engineering application. Single carrier system combining equalizer with phase locked loop technology at the receiver, has been widely used in UAC network to achieve high-speed stable information transmission [18– 21] due to its trade-off between communication rate and robustness compared with Orthogonal Frequency Division Multiplexing (OFDM) and Direct Sequence Spread Spectrum (DSSS). In the application of UAC network and directional secure communication, single carrier may be a better choice with the parameter array. In this paper, we use single carrier system based on parametric array that works in moderate condition to transmit a large amount of data. The energy distribution of single carrier system depends on the constellation points and the roll-off factor of shaping filter. Its peak to average power ratio is lower and the equipment performance requirement is less than that of OFDM technique. In addition, the single-carrier avoids the issues caused by orthogonal mismatch of carriers. Its tolerance to synchronization error and Doppler shift is better [22]. The proposed modulation method is tested on a single carrier system based on parametric array for secure communication. The paper is organized as follows: In Section 2, the principle of the recursive filter modulation is introduced. Scheme of the single carrier parametric array UAC system is illustrated in Section 3, and we present the result of pool experiment to verify the effectiveness. In Section 4, the proposed system is verified by trial experiment. Finally, Section 5 concludes our work.
2. Modulation method In 1965, Berktay derived broadband signal emission theory of parametric array [13] and supposed that acoustic signal is spread in plane waves. The sound pressure far away the equivalent sound center of parametric array is expressed as
h r r i pðt; rÞ ¼ Peap r f t cos xp t c c
ð1Þ
where t is the time, r is distance, c is the sound speed in the water, P is the amplitude of sound pressure, ap is the absorption coefficient of a signal with angular frequency xp . f t cr represents the envelope of the original frequency wave and its maximum frequency component is far less than the frequency of high-frequency carrier, which is the center frequency of original frequency wave. Berktay derived self-demodulation effect of plane waves. The axial sound pressure in the distance R is defined as
ps ðR; tÞ ¼
bP 2 Seas R @ 2 2 R f t 2 4 c 8pqc RaT @t
ð2Þ
where q is the density of water, b is the non-linear parameter of water, S is the beam cross-sectional area, as is the absorption coefficient of the center frequency of the difference frequency wave (assume that the bandwidth of the signal is smaller than the center frequency of the original frequency wave), and aT ¼ 2ap as . 2
as R
Regard A ¼ 8bPpqSec4 Ra as the amplitude factor. The expression for T
axial sound pressure of parametric array is
ps ðR; tÞ ¼ A
@2 2 R f t c @t 2
ð3Þ
Eq. (3) shows that the sound pressure of the receiver is only related to the envelope of the original frequency wave when communication distance is determined. The amplitude of sound pressure of difference frequency wave is a constant. When focusing on the signal envelope form caused by non-linear self-demodulation effect of water, the sound pressure at a fixed distance from the source could be expressed as 2
ps ðtÞ ¼ A
d
dt
2
xðtÞ
ð4Þ
2 where ps ðtÞ is the communication signal, and xðtÞ ¼ f t Rc . f ðtÞ is the envelope of original frequency wave. Eq. (4) is a second order differential equation with constant coefficients, where A can be taken as a constant for simplicity that does not influence the result. In order to obtain the communication signal at the receiving end, the communication signal is usually taken as f ðtÞ [4,8,9]. However, the wide-band difference frequency received by this method has obvious distortion, resulting in a decrease of processing gain. We hope to improve this shortcoming so that the parametric array can be better applied in UAC. we define Dt ¼ 1=f s as the sampling interval and discrete equation with central differencing scheme, then Eq. (4) is converted to
ps ðnÞ ¼ xðn þ 1Þ 2xðnÞ þ xðn 1Þ
ð5Þ
After that, we can design the recursive filter as the preprocessor of parametric array modulator, which is the most critical part of the parametric array in UAC. According to Eq. (5), its transfer function is
HðzÞ ¼
XðzÞ z ¼ P s ðzÞ ð1 zÞ2
ð6Þ
We observed that the system is unstable when its poles are on the unit circle. Therefore, in practical applications, the form of recursive filter is designed as
S. Tang et al. / Applied Acoustics 145 (2019) 305–313
xðn þ 1Þ ¼ ps ðnÞ þ axðnÞ bxðn 1Þ
ð7Þ
where a and b are the weighting coefficients of the filter. Considering the stability, transient characteristics and undistorted requirement of the equation, a and b can be chosen in range of 1:80 6 a 6 1:94 and 0:81 6 b 6 0:94 in practical applications. Fig. 1 shows the diagram of the recursive filter modulation of transient broadband exciting signal of parametric array, which consists of three parts, recursive filter, envelope calculating and side-band modulation, respectively. The recursive filter processing only needs two multiplications, two additions and one root operation for a symbol to be received by the hydrophone without distorted in the far field. Compared with the methods in literature [14–17], this method has lower algorithm complexity and higher computational efficiency. Register only needs to store the amplitude of current input signal and the output signal of filter, which reduces the cost of hardware, and it is conducive to real-time implementation. In the recursive filter, xðn þ 1Þ is the output alternating current (AC) signal, which is necessary to be carried a direct current (DC) bias to ensure that there is no imaginary root in the following modulation process. After the envelope calculating process, the envelope of original frequency wave is
f ðn þ 1Þ ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m þ xðn þ 1Þ
ð8Þ
where the constant m is DC bias. Its value is related to the amplitude dynamic range of the desired signal. After being sampled by interpolation filter, envelope f ðn þ 1Þ will be double-side-band modulated with digital carrier, then it is converted to analogy signals by digital-to-analogy (D/A) converter. Envelope f ðn þ 1Þ can also be converted to the analogy signals by D/A firstly, after that it is double-side-band modulated with analogy carrier to obtain excitation signals of parametric array transmission system. In the implementation of parametric array modulators, we find that the recursive filter is more simple and flexible than the compensating filter mentioned in literature [10], which compensates amplitude after the pretreatment of the square root. It is conducive to process unknown signal, which earn the valuable time for parametric array aim at the location of the destination.
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3. Parametric array single carrier UAC scheme Fig. 2 shows the block diagram of single carrier UAC system based on parametric array, which consists of transmitting and receiving two parts. This paper is focus on the former. In the information transmission process, the source information is digitally quantified and packaged according to established protocols. Similarly, the training sequence in the protocol is inserted in the front of each frame of data to provide prior information for the receiver equalizer. After that, pulse shaping is an indispensable step in underwater acoustic channel with limited bandwidth. The roll-off factor of shaping filter should be selected depending on the underwater acoustic channel characteristics. Then, low frequency carrier is phase-modulated based on shaped symbols. At this point, we obtain the conventional excitation signal of single-carrier UAC system. In the application of directional communication, the pulse width of codes is usually small, to ensure the communication rate and transmit as soon as possible. In other words, it needs a relative wide bandwidth compared with the low frequency carrier to ensure the information integrity. However, narrow directivity of low-frequency broadband is difficult to achieve, which makes the parametric array has a potential value in single carrier secure UAC. As we know, parametric array is easy to implement highbandwidth and directional difference frequency signal, which is conducive to transmit single carrier signals with wide bandwidth. So we introduce a modulation scheme as shown in Fig. 1, to enhance the application value of parametric, that is to simplify the modulation method to improve the signal pre-processing speed, and to improve the reception distortion to ensure processing gain, respectively. In the system shown in Fig. 2, parametric array excitation signals are generated by proposed modulation scheme shown in Fig. 1. This transmit frame will reduce the receiver’s inter-symbol interference and device complexity, which is especially noticeable in shallow seas, as we will discuss in Section 4. An experiment for single carrier UAC based on parametric array has been carried out in channel sink, aiming to verify and analysis two important signal forms, Linear Frequency Modulation (LFM) signal and Continuous Wave (CW) pulse, respectively. LFM signal is often used in UAC as a synchronization information code. Here, we first use LFM signal as f ðtÞ in Eq. (3) without pre-processing. The difference frequency signal received by the hydrophone is shown in Fig. 3(a). We can find that there is a significant amplitude distortion as the frequency increases. The correlation curve for difference frequency signal and local signal at different bandwidths in
Fig. 1. Diagram of parametric array modulation recursive filter.
Fig. 2. Diagram of single carrier UAC system based on parametric array.
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Fig. 3. LFM signal recursive filtering modulation experiment. (a) Hydrophone received LFM signal without pre-processing; (b) LFM normalized correlation coefficients at different bandwidths without pre-processing; (c) the excitation signal pre-processed by the proposed modulation method; (d) Hydrophone received LFM signal with preprocessing; (e) the normalized correlation coefficient results of difference frequency signal and local LFM signal; (f) LFM normalized correlation coefficients at different bandwidths with pre-processing.
Fig. 4. CW pulse recursive filter modulation experiment. (a) The excitation signal obtained by the proposed modulation method; (b) Hydrophone received CW signal with pre-processing.
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Fig. 5. Channel comparison between parametric array and conventional sonar. Acoustic ray and CIR of (a) conventional transducer under the negative sound velocity gradient; (b) parametric array under the negative sound velocity gradient; (c) conventional transducer under the positive sound velocity gradient; (d) parametric array under the positive sound velocity gradient.
Fig. 6. Parametric array used in the experiment. (a) Structure of the parametric array; (b) Directivity of the parametric array.
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results of difference frequency signal and local LFM signal is shown in Fig. 3(e). We find that it matches well between received and desired signal. We also compare the correlations of signals with different bandwidth. As shown in Fig. 3(F), the proposed method do solves the issue (the correlation coefficient decreases as bandwidth increases). This presents a better performance for the broadband UAC system. Fig. 4 shows the experimental results of CW pulse signal whose frequency is 10 kHz and width is 1 ms. The excitation signal obtained by the proposed modulation method is shown in Fig. 4 (a). The acoustic signal is self-demodulated in the water, and the difference frequency wave received by hydrophone is shown in Fig. 4(b). Experiment shows that the recursive filter modulation is also appropriate for single-frequency signal. 4. Simulation and sea experiment
Fig. 7. Comparison of channel impulse responses. (a) Sound velocity gradient measured in the trail; (b) CIR of conventional transducer in experiment; (c) CIR of parametric array in experiment.
Fig. 3(b). Obviously, when the bandwidth of LFM signal is 12 kHz, the mutual correlation coefficient decreases to about 0.85, and the correlation coefficient decreases more rapidly as bandwidth increases. The amplitude modulation factor of the LFM signal will affect the performance of the communication system to a certain extent. Fig. 3(c) plots the output of excitation signal preprocessed by the proposed modulation method. The start and the end frequency of LFM signal is 8 and 12 kHz respectively. The pulse width is 0.05 s, and the frequency of high-frequency carrier is 150 kHz. Difference frequency wave received by hydrophone is shown in Fig. 3(d), and the normalized correlation coefficient
Equalizer is the core part in the single carrier UAC receiver, its taps number is proportional to the maximum multi-path delay of underwater acoustic channel. For shallow water UAC, multi-path expansion can reach tens or even hundreds of milliseconds, which greatly increases the computational complexity of the equalizer. Fig. 5 shows the channel impulse response (CIR) comparison between the conventional transducer and the parametric array with narrow directivity based on the Bellhop simulation [23]. The seabed is set to acoustics half space. Fig. 5(a) and (b) are the acoustic rays under the negative sound velocity gradient. Fig. 5(c) and (d) are the acoustic rays under positive sound velocity gradient. We can observe that the largest multi-path interference of parametric array is much less than that of the conventional transducer in the distance of 2 km. The narrow directional beam can effectively reduce the probability of contact boundaries, thus simplifying the channel structure and reducing the computational complexity of the equalizer. To verify the performance of the proposed modulation method and the communication system of parametric array, maritime communication test was carried out in Changhai of Dalian sea area
Fig. 8. Trial Experiment Data Structure.
Fig. 9. Receiver structure of single carrier UAC system based on parametric array.
S. Tang et al. / Applied Acoustics 145 (2019) 305–313 Table 1 Performance of parametric array and conventional transducer. Modulation mode
Mapping mode
Lff
Lfb
BER
Proposed method
QPSK 8PSK
10 15
10 10
6:67 104
Conventional method
QPSK
10
10
8PSK
10 15
80 10
15
150
0 1:96 104 0 2:46 101 1:28 102
in July 2015. The test water area was in the harbour of Xiaochangshan Island. The average depth of inner bay is 7 m. Offshore sediment are mostly sludge formed from people’s long-term job remnants. The waterway is busy because of the fishing industry. The hydrological conditions were abominable in this season. The parametric array used in the experiment is shown in Fig. 6. The
311
directivity of parametric array used in the test is about 6°. The center frequency of transmitting parametric array is 150 kHz. Fig. 7(a) shows the sound velocity gradient measured by the sound velocity profiler in the test, which is a negative gradient. Because the seabed absorption coefficient is large, the sound signal is difficult to achieve long-distance transmission. The transmission and receiving nodes were located near the edge of harbour and drifting boats respectively. In the trail, the parametric array is suspended at the same depth near the conventional transducer about 2 m below the surface. At the same time, in order to ensure the fairness between the two transducer as much as possible, we use the time division method to send all the data packets, that is, the parametric array and the conventional transducers alternate each other to send one data packet. There was slow movement between nodes due to storms. However, within the time of the data transmission, the nodes could be regarded as stationary approximately. According to the water condition, the communication distance of the sea experiment was about 200 m. The CIR comparison between the
Fig. 10. Decoding constellation of parametric array with recursive filtering modulation. (a) Input constellation of QPSK before equalization with input SNR = 9.44 dB; (b) Input constellation of 8PSK before equalization with input SNR = 4.98 dB; (c) Output constellation of QPSK after equalization, output SNR = 18.29 dB; (d) Output constellation of 8PSK after equalization, output SNR = 19.83 dB.
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conventional transducer and the parametric array are shown in Fig. 7(b) and (c). It is obviously that the channel impulse response of parametric array system is more concise than the conventional one, since the high directivity reduces the scattering of media and the number of sound ray touching the interface. That brings great benefit on simplifying receiver complexity. What’s more, benefiting from the direction of the parametric array, the energy leakage of the acoustic signal outside the desired angle at this range is one millionth of that. Small acoustic leak reduced the mutual interference in multi-user communications, which is useful in UAC network where power control is difficult. In addition, this feature of parametric array can be used to realize the directional transmission to users if a specific direction is identified in coastal secure communication. The structure of sending data is shown in Fig. 8 for various communication rates. Training sequence is added before each frame of data as an equalizer priori information. We utilized a chirp signal as the synchronization signal of packets. Since the sea conditions were quit ideal, only coarse Doppler compensation was used on the receiver. A statistical average has been counted to evaluate the performance through 15 packets data with the receiving structure [24] shown in Fig. 9. We achieved 6 k symbols=s communication under QPSK and 8PSK modulation respectively based on parametric array to verify the directional communication and the proposed modulation method. Table 1 shows the decoding performance comparison between parametric array and conventional transducer. Here, we focus on the benefits that directionality brings to communications performance, so we try to make sure that the input signal to noise ratio (SNR) is the same as possible by power control and ocean noise
compensation so that it is a fair contrast. Parameters of decision feedback equalizer are as follows: Lff , the number of taps of the forward filter and Lfb is the number of taps for the feedback filter. P1 ¼ 0:0001 is proportionality coefficient of phase locked loop, P2 ¼ 0:00001 is integral coefficient of phase locked loop, r ¼ 0:5 is the initialization factor of correlation matrix of RLS algorithm, and k ¼ 0:995 is the forgetting factor. The bit error rate (BER) of the single carrier UAC system based on recursive filter modulation of parametric array is zero for QPSK mapping within statistical range, bit error rate of 8PSK mapping within the statistical range is 6:7 104 . The decoding constellation is shown in Fig. 10. In the Dalian experiment, we also compared the performance between modulation method without pre-processing and the proposed pre-processing way. Keeping other variables consistent in the experiment, the decoding constellation is shown in Fig. 11. From Fig. 11(a), (c) and (e), we observed that the decoding constellation gradually becomes divergence with the increases of the system bandwidth. The constellation is almost impossible to correctly judge as the system bandwidth reaches 6 kHz in Fig. 11(e). The interpretation may be that as the system bandwidth increases, the symbol period gradually decreases, and the phase changes of original frequency wave is faster, resulting in the additional phase of the difference frequency wave that makes the system performance worse, so that the conventional method is limited in the application of broadband UAC. Comparing Fig. 11(a) and (b), Fig. 11(c) and (d) respectively, we observed that the constellation of the proposed method is more divergent than the conventional one when the system bandwidth is not wide enough. This may benefit from the higher conversion efficiency of the conventional method. However, as the system
Fig. 11. Decoding Constellation of Two Methods at Different Bandwidths. 2 kHz bandwidth decoding constellation (a) without pre-processing modulation and (b) with preprocessing modulation; 4 kHz bandwidth decoding constellation (c) without pre-processing modulation and (d) with pre-processing modulation; 6 kHz bandwidth decoding constellation (e) without pre-processing modulation and (f) with pre-processing modulation.
S. Tang et al. / Applied Acoustics 145 (2019) 305–313
bandwidth increasing, reaching 6 kHz in Fig. 11(f) e.g., the performance of the proposed method is almost identical to that of the narrow band, while the conventional method can not decode the information of the packets. The reason is that the proposed method will not produce additional phase noise, and it is superior to the conventional one when the system bandwidth is large. 5. Conclusion A modulation method of parametric array is investigated in this paper for UAC. The source is assumed to be broadband signals for transmitting information in high communication rate. The method relies upon the theoretical time series relationship derived by Berktay. Utilizing the spirit of filter designing which is a relatively simple way to eliminate the distortion observed in difference frequency signal. The advantages of this method are that it needs low computation complexity and easy to implement. Two basic signal forms were verified by channel tank experiment. The performance of the broadband signal has been improved significantly. Single carrier UAC system based on parametric array is introduced. It not only provides a new idea for improving the shallow water acoustic communication performance, directional secure communication and acoustic multi-user network communication, but also is beneficial to support real-time transmission of highspeed communication tasks. Finally, the validity and reliability of the UAC scheme are verified by Dalian sea trial results. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 61471137, 61631008), the Fok Ying Tong Education Foundation, China (Grant No.151007), the Heilongjiang Province Outstanding Youth Science Fund (JC 2017017), and the Underwater Scientific Test and Control Technology Laboratory Foundation (Grant No. 9140C260401150C26114). References [1] L. Freitag, P. Koski, A. Morozov., S. Singh, Acoustic Communications and Navigation Under Arctic Ice, 2012 Oceans – VA, USA. [2] Qian Z. Nonlinear Acoustics. Beijing: Science Press; 1992.
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Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
A modulation method of parametric array for underwater acoustic communication Shengyu Tang a,b, Guangping Zhu a,b, Jingwei Yin a,b,⇑, Xiao Zhang c, Xiao Han a,b a
Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China c College of Computer Science and Technology, Jilin University, Changchun 130000, China b
a r t i c l e
i n f o
Article history: Received 9 October 2017 Received in revised form 13 June 2018 Accepted 25 July 2018
Keywords: Underwater acoustic communication Parametric array Covert communication
a b s t r a c t Focusing on the potential value of narrow directivity of parametric sonar in underwater acoustic communication, a broadband recursive filtering modulation method is proposed in this paper to generate parametric array excitation signal. The idea is to design the transient waveform by reversing the relationship between the envelope of original wave and difference frequency wave with the recursive filter. The method could process broadband and unknown arbitrary waveform signal (such as voice, image and video signal) in real time to get almost undistorted packets with low computation complexity. The feasibility and efficiency of the proposed method are verified by pool and trial experiments. The single carrier underwater acoustic communication system based on parametric array is applied to test the method in a distributed network. Performance of the system is improved effectively since the approximately distortion-free and narrow directivity compared with the conventional broadcast underwater acoustic communication system in Dalian sea trial. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction With the continuous exploration of the ocean, unmanned and intelligent vehicles were developed rapidly which result in the demand growth for acoustic devices, especially in Arctic Ocean [1]. Efficient, convenient and high-speed underwater information transmission greatly accelerated the understanding and utilization of marine science. Considering the complex variability of underwater acoustic channels (especially Chinese shallow waters) and the complexity of the underwater acoustic equipment implementation, directional communication implementations are an urgent issue in many applications such as secure communications and multi-user underwater acoustic communications (UAC) in a hot spot. Since oriented communication can not only increase channel capacity by spatial reuse, but also suppress multipath diffusion, and also has unique advantages in secure communication and network communication of multi-user groups. The parametric array utilizes the non-linear effect of the medium to produce the desired sound wave. In other words, the excitation signal of the parametric array is self-demodulated in water, resulting in the secondary wave field [2]. In general, the
⇑ Corresponding author. E-mail address: [email protected] (J. Yin). https://doi.org/10.1016/j.apacoust.2018.07.032 0003-682X/Ó 2018 Elsevier Ltd. All rights reserved.
structure and auxiliary equipment of the parametric array are not very complicated. The produced difference frequency component with narrow directivity in the secondary field is the desired signal in most underwater acoustic applications. This unique feature has been applied to UAC successfully [3–5]. However, few engineering applications are reported because the energy conversion of the parametric array is ineffective and difficult to align with receiver. In recent years, with the diversity of UAC nodes and the increasing use of large unmanned equipment, the energy supply and forwarding positioning issues are being addressed [6,7] or can be ignored. Therefore, parametric array for UAC is gradually coming back to our attention. For example, in a UAC network, which consists of fixed nodes (anchored platforms, shore-based underwater platforms or large surface vessels) with positioning function and mobile nodes (autonomous underwater vehicles, manned submarines, moving ships). The parametric array embedded in a fixed platform provides two important benefits based on the energy supply and source positioning of the system. Firstly, directional communication can improve the information capacity of a network. Secondly, one can send messages to the intended nodes without being intercepted. In this case, the energy consumption is even an acceptable overhead. As mentioned above, energy efficiency is an inevitable flaw of the parametric array. Besides, its excellent directionality, is like a
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double-edged sword that is hard to apply in practice, though appealing. Motivatived by solving these two disadvantages of parametric array in UAC practical application, this paper is committed to improve the gain loss caused by difference frequency signal distortion and the processing ability of parametric by innovativing modulation method, so as to better coordinate with the platform’s positioning and energy system. The earlier modulation methods of parametric array are conducting double-sideband modulation [8] and single side-band modulation [9] between carrier and data flow. Then the synthesized signal is sent as the excitation signal. These two methods are simple to realize, but distortion is observed in the received broadband communication signal after the nonlinear effect of aqueous medium. Square root modulation method [10] reduces the distortion of difference frequency wave by preprocessing the data flow. If 12 dB/oct compensation filter can be conducted before amplitude modulation, this method can achieve no distortion. However, the implementation of compensation filter with 12 dB/oct is not flexible enough for transient broadband signal (particularly when the signal’s parameters are unknown), which limits the application of this method. Double integral presquare rooting method [11,12] is in conformity with undistorted conditions in far field derived by Berktay [13]. However, integration results often lead to divergence when the method is used to design the excitation signal in practical application, due to the initial value and some factors. Other modulation methods [14–17] obtain the communication signal at the receiver without distortion approximately through the iterative calculation, but the large computations are not conducive to real-time processing. Motivated by the modulation distortions and engineering restrictions of above methods, this article presents an excitation signal modulation method of parametric array according to Berktay’s far field solution, which called the recursive filter to support the application of parametric array in UAC network. It is designed with the time series relationship between the envelopes of original frequency wave and difference frequency wave to obtain approximate undistorted communication signal. Meanwhile, its calculation effort is relatively less, which shows a potential value in real-time signal processing of transient, broadband, unknown arbitrary waveform signal. It is very conducive to the practical engineering application. Single carrier system combining equalizer with phase locked loop technology at the receiver, has been widely used in UAC network to achieve high-speed stable information transmission [18– 21] due to its trade-off between communication rate and robustness compared with Orthogonal Frequency Division Multiplexing (OFDM) and Direct Sequence Spread Spectrum (DSSS). In the application of UAC network and directional secure communication, single carrier may be a better choice with the parameter array. In this paper, we use single carrier system based on parametric array that works in moderate condition to transmit a large amount of data. The energy distribution of single carrier system depends on the constellation points and the roll-off factor of shaping filter. Its peak to average power ratio is lower and the equipment performance requirement is less than that of OFDM technique. In addition, the single-carrier avoids the issues caused by orthogonal mismatch of carriers. Its tolerance to synchronization error and Doppler shift is better [22]. The proposed modulation method is tested on a single carrier system based on parametric array for secure communication. The paper is organized as follows: In Section 2, the principle of the recursive filter modulation is introduced. Scheme of the single carrier parametric array UAC system is illustrated in Section 3, and we present the result of pool experiment to verify the effectiveness. In Section 4, the proposed system is verified by trial experiment. Finally, Section 5 concludes our work.
2. Modulation method In 1965, Berktay derived broadband signal emission theory of parametric array [13] and supposed that acoustic signal is spread in plane waves. The sound pressure far away the equivalent sound center of parametric array is expressed as
h r r i pðt; rÞ ¼ Peap r f t cos xp t c c
ð1Þ
where t is the time, r is distance, c is the sound speed in the water, P is the amplitude of sound pressure, ap is the absorption coefficient of a signal with angular frequency xp . f t cr represents the envelope of the original frequency wave and its maximum frequency component is far less than the frequency of high-frequency carrier, which is the center frequency of original frequency wave. Berktay derived self-demodulation effect of plane waves. The axial sound pressure in the distance R is defined as
ps ðR; tÞ ¼
bP 2 Seas R @ 2 2 R f t 2 4 c 8pqc RaT @t
ð2Þ
where q is the density of water, b is the non-linear parameter of water, S is the beam cross-sectional area, as is the absorption coefficient of the center frequency of the difference frequency wave (assume that the bandwidth of the signal is smaller than the center frequency of the original frequency wave), and aT ¼ 2ap as . 2
as R
Regard A ¼ 8bPpqSec4 Ra as the amplitude factor. The expression for T
axial sound pressure of parametric array is
ps ðR; tÞ ¼ A
@2 2 R f t c @t 2
ð3Þ
Eq. (3) shows that the sound pressure of the receiver is only related to the envelope of the original frequency wave when communication distance is determined. The amplitude of sound pressure of difference frequency wave is a constant. When focusing on the signal envelope form caused by non-linear self-demodulation effect of water, the sound pressure at a fixed distance from the source could be expressed as 2
ps ðtÞ ¼ A
d
dt
2
xðtÞ
ð4Þ
2 where ps ðtÞ is the communication signal, and xðtÞ ¼ f t Rc . f ðtÞ is the envelope of original frequency wave. Eq. (4) is a second order differential equation with constant coefficients, where A can be taken as a constant for simplicity that does not influence the result. In order to obtain the communication signal at the receiving end, the communication signal is usually taken as f ðtÞ [4,8,9]. However, the wide-band difference frequency received by this method has obvious distortion, resulting in a decrease of processing gain. We hope to improve this shortcoming so that the parametric array can be better applied in UAC. we define Dt ¼ 1=f s as the sampling interval and discrete equation with central differencing scheme, then Eq. (4) is converted to
ps ðnÞ ¼ xðn þ 1Þ 2xðnÞ þ xðn 1Þ
ð5Þ
After that, we can design the recursive filter as the preprocessor of parametric array modulator, which is the most critical part of the parametric array in UAC. According to Eq. (5), its transfer function is
HðzÞ ¼
XðzÞ z ¼ P s ðzÞ ð1 zÞ2
ð6Þ
We observed that the system is unstable when its poles are on the unit circle. Therefore, in practical applications, the form of recursive filter is designed as
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xðn þ 1Þ ¼ ps ðnÞ þ axðnÞ bxðn 1Þ
ð7Þ
where a and b are the weighting coefficients of the filter. Considering the stability, transient characteristics and undistorted requirement of the equation, a and b can be chosen in range of 1:80 6 a 6 1:94 and 0:81 6 b 6 0:94 in practical applications. Fig. 1 shows the diagram of the recursive filter modulation of transient broadband exciting signal of parametric array, which consists of three parts, recursive filter, envelope calculating and side-band modulation, respectively. The recursive filter processing only needs two multiplications, two additions and one root operation for a symbol to be received by the hydrophone without distorted in the far field. Compared with the methods in literature [14–17], this method has lower algorithm complexity and higher computational efficiency. Register only needs to store the amplitude of current input signal and the output signal of filter, which reduces the cost of hardware, and it is conducive to real-time implementation. In the recursive filter, xðn þ 1Þ is the output alternating current (AC) signal, which is necessary to be carried a direct current (DC) bias to ensure that there is no imaginary root in the following modulation process. After the envelope calculating process, the envelope of original frequency wave is
f ðn þ 1Þ ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m þ xðn þ 1Þ
ð8Þ
where the constant m is DC bias. Its value is related to the amplitude dynamic range of the desired signal. After being sampled by interpolation filter, envelope f ðn þ 1Þ will be double-side-band modulated with digital carrier, then it is converted to analogy signals by digital-to-analogy (D/A) converter. Envelope f ðn þ 1Þ can also be converted to the analogy signals by D/A firstly, after that it is double-side-band modulated with analogy carrier to obtain excitation signals of parametric array transmission system. In the implementation of parametric array modulators, we find that the recursive filter is more simple and flexible than the compensating filter mentioned in literature [10], which compensates amplitude after the pretreatment of the square root. It is conducive to process unknown signal, which earn the valuable time for parametric array aim at the location of the destination.
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3. Parametric array single carrier UAC scheme Fig. 2 shows the block diagram of single carrier UAC system based on parametric array, which consists of transmitting and receiving two parts. This paper is focus on the former. In the information transmission process, the source information is digitally quantified and packaged according to established protocols. Similarly, the training sequence in the protocol is inserted in the front of each frame of data to provide prior information for the receiver equalizer. After that, pulse shaping is an indispensable step in underwater acoustic channel with limited bandwidth. The roll-off factor of shaping filter should be selected depending on the underwater acoustic channel characteristics. Then, low frequency carrier is phase-modulated based on shaped symbols. At this point, we obtain the conventional excitation signal of single-carrier UAC system. In the application of directional communication, the pulse width of codes is usually small, to ensure the communication rate and transmit as soon as possible. In other words, it needs a relative wide bandwidth compared with the low frequency carrier to ensure the information integrity. However, narrow directivity of low-frequency broadband is difficult to achieve, which makes the parametric array has a potential value in single carrier secure UAC. As we know, parametric array is easy to implement highbandwidth and directional difference frequency signal, which is conducive to transmit single carrier signals with wide bandwidth. So we introduce a modulation scheme as shown in Fig. 1, to enhance the application value of parametric, that is to simplify the modulation method to improve the signal pre-processing speed, and to improve the reception distortion to ensure processing gain, respectively. In the system shown in Fig. 2, parametric array excitation signals are generated by proposed modulation scheme shown in Fig. 1. This transmit frame will reduce the receiver’s inter-symbol interference and device complexity, which is especially noticeable in shallow seas, as we will discuss in Section 4. An experiment for single carrier UAC based on parametric array has been carried out in channel sink, aiming to verify and analysis two important signal forms, Linear Frequency Modulation (LFM) signal and Continuous Wave (CW) pulse, respectively. LFM signal is often used in UAC as a synchronization information code. Here, we first use LFM signal as f ðtÞ in Eq. (3) without pre-processing. The difference frequency signal received by the hydrophone is shown in Fig. 3(a). We can find that there is a significant amplitude distortion as the frequency increases. The correlation curve for difference frequency signal and local signal at different bandwidths in
Fig. 1. Diagram of parametric array modulation recursive filter.
Fig. 2. Diagram of single carrier UAC system based on parametric array.
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Fig. 3. LFM signal recursive filtering modulation experiment. (a) Hydrophone received LFM signal without pre-processing; (b) LFM normalized correlation coefficients at different bandwidths without pre-processing; (c) the excitation signal pre-processed by the proposed modulation method; (d) Hydrophone received LFM signal with preprocessing; (e) the normalized correlation coefficient results of difference frequency signal and local LFM signal; (f) LFM normalized correlation coefficients at different bandwidths with pre-processing.
Fig. 4. CW pulse recursive filter modulation experiment. (a) The excitation signal obtained by the proposed modulation method; (b) Hydrophone received CW signal with pre-processing.
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Fig. 5. Channel comparison between parametric array and conventional sonar. Acoustic ray and CIR of (a) conventional transducer under the negative sound velocity gradient; (b) parametric array under the negative sound velocity gradient; (c) conventional transducer under the positive sound velocity gradient; (d) parametric array under the positive sound velocity gradient.
Fig. 6. Parametric array used in the experiment. (a) Structure of the parametric array; (b) Directivity of the parametric array.
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results of difference frequency signal and local LFM signal is shown in Fig. 3(e). We find that it matches well between received and desired signal. We also compare the correlations of signals with different bandwidth. As shown in Fig. 3(F), the proposed method do solves the issue (the correlation coefficient decreases as bandwidth increases). This presents a better performance for the broadband UAC system. Fig. 4 shows the experimental results of CW pulse signal whose frequency is 10 kHz and width is 1 ms. The excitation signal obtained by the proposed modulation method is shown in Fig. 4 (a). The acoustic signal is self-demodulated in the water, and the difference frequency wave received by hydrophone is shown in Fig. 4(b). Experiment shows that the recursive filter modulation is also appropriate for single-frequency signal. 4. Simulation and sea experiment
Fig. 7. Comparison of channel impulse responses. (a) Sound velocity gradient measured in the trail; (b) CIR of conventional transducer in experiment; (c) CIR of parametric array in experiment.
Fig. 3(b). Obviously, when the bandwidth of LFM signal is 12 kHz, the mutual correlation coefficient decreases to about 0.85, and the correlation coefficient decreases more rapidly as bandwidth increases. The amplitude modulation factor of the LFM signal will affect the performance of the communication system to a certain extent. Fig. 3(c) plots the output of excitation signal preprocessed by the proposed modulation method. The start and the end frequency of LFM signal is 8 and 12 kHz respectively. The pulse width is 0.05 s, and the frequency of high-frequency carrier is 150 kHz. Difference frequency wave received by hydrophone is shown in Fig. 3(d), and the normalized correlation coefficient
Equalizer is the core part in the single carrier UAC receiver, its taps number is proportional to the maximum multi-path delay of underwater acoustic channel. For shallow water UAC, multi-path expansion can reach tens or even hundreds of milliseconds, which greatly increases the computational complexity of the equalizer. Fig. 5 shows the channel impulse response (CIR) comparison between the conventional transducer and the parametric array with narrow directivity based on the Bellhop simulation [23]. The seabed is set to acoustics half space. Fig. 5(a) and (b) are the acoustic rays under the negative sound velocity gradient. Fig. 5(c) and (d) are the acoustic rays under positive sound velocity gradient. We can observe that the largest multi-path interference of parametric array is much less than that of the conventional transducer in the distance of 2 km. The narrow directional beam can effectively reduce the probability of contact boundaries, thus simplifying the channel structure and reducing the computational complexity of the equalizer. To verify the performance of the proposed modulation method and the communication system of parametric array, maritime communication test was carried out in Changhai of Dalian sea area
Fig. 8. Trial Experiment Data Structure.
Fig. 9. Receiver structure of single carrier UAC system based on parametric array.
S. Tang et al. / Applied Acoustics 145 (2019) 305–313 Table 1 Performance of parametric array and conventional transducer. Modulation mode
Mapping mode
Lff
Lfb
BER
Proposed method
QPSK 8PSK
10 15
10 10
6:67 104
Conventional method
QPSK
10
10
8PSK
10 15
80 10
15
150
0 1:96 104 0 2:46 101 1:28 102
in July 2015. The test water area was in the harbour of Xiaochangshan Island. The average depth of inner bay is 7 m. Offshore sediment are mostly sludge formed from people’s long-term job remnants. The waterway is busy because of the fishing industry. The hydrological conditions were abominable in this season. The parametric array used in the experiment is shown in Fig. 6. The
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directivity of parametric array used in the test is about 6°. The center frequency of transmitting parametric array is 150 kHz. Fig. 7(a) shows the sound velocity gradient measured by the sound velocity profiler in the test, which is a negative gradient. Because the seabed absorption coefficient is large, the sound signal is difficult to achieve long-distance transmission. The transmission and receiving nodes were located near the edge of harbour and drifting boats respectively. In the trail, the parametric array is suspended at the same depth near the conventional transducer about 2 m below the surface. At the same time, in order to ensure the fairness between the two transducer as much as possible, we use the time division method to send all the data packets, that is, the parametric array and the conventional transducers alternate each other to send one data packet. There was slow movement between nodes due to storms. However, within the time of the data transmission, the nodes could be regarded as stationary approximately. According to the water condition, the communication distance of the sea experiment was about 200 m. The CIR comparison between the
Fig. 10. Decoding constellation of parametric array with recursive filtering modulation. (a) Input constellation of QPSK before equalization with input SNR = 9.44 dB; (b) Input constellation of 8PSK before equalization with input SNR = 4.98 dB; (c) Output constellation of QPSK after equalization, output SNR = 18.29 dB; (d) Output constellation of 8PSK after equalization, output SNR = 19.83 dB.
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conventional transducer and the parametric array are shown in Fig. 7(b) and (c). It is obviously that the channel impulse response of parametric array system is more concise than the conventional one, since the high directivity reduces the scattering of media and the number of sound ray touching the interface. That brings great benefit on simplifying receiver complexity. What’s more, benefiting from the direction of the parametric array, the energy leakage of the acoustic signal outside the desired angle at this range is one millionth of that. Small acoustic leak reduced the mutual interference in multi-user communications, which is useful in UAC network where power control is difficult. In addition, this feature of parametric array can be used to realize the directional transmission to users if a specific direction is identified in coastal secure communication. The structure of sending data is shown in Fig. 8 for various communication rates. Training sequence is added before each frame of data as an equalizer priori information. We utilized a chirp signal as the synchronization signal of packets. Since the sea conditions were quit ideal, only coarse Doppler compensation was used on the receiver. A statistical average has been counted to evaluate the performance through 15 packets data with the receiving structure [24] shown in Fig. 9. We achieved 6 k symbols=s communication under QPSK and 8PSK modulation respectively based on parametric array to verify the directional communication and the proposed modulation method. Table 1 shows the decoding performance comparison between parametric array and conventional transducer. Here, we focus on the benefits that directionality brings to communications performance, so we try to make sure that the input signal to noise ratio (SNR) is the same as possible by power control and ocean noise
compensation so that it is a fair contrast. Parameters of decision feedback equalizer are as follows: Lff , the number of taps of the forward filter and Lfb is the number of taps for the feedback filter. P1 ¼ 0:0001 is proportionality coefficient of phase locked loop, P2 ¼ 0:00001 is integral coefficient of phase locked loop, r ¼ 0:5 is the initialization factor of correlation matrix of RLS algorithm, and k ¼ 0:995 is the forgetting factor. The bit error rate (BER) of the single carrier UAC system based on recursive filter modulation of parametric array is zero for QPSK mapping within statistical range, bit error rate of 8PSK mapping within the statistical range is 6:7 104 . The decoding constellation is shown in Fig. 10. In the Dalian experiment, we also compared the performance between modulation method without pre-processing and the proposed pre-processing way. Keeping other variables consistent in the experiment, the decoding constellation is shown in Fig. 11. From Fig. 11(a), (c) and (e), we observed that the decoding constellation gradually becomes divergence with the increases of the system bandwidth. The constellation is almost impossible to correctly judge as the system bandwidth reaches 6 kHz in Fig. 11(e). The interpretation may be that as the system bandwidth increases, the symbol period gradually decreases, and the phase changes of original frequency wave is faster, resulting in the additional phase of the difference frequency wave that makes the system performance worse, so that the conventional method is limited in the application of broadband UAC. Comparing Fig. 11(a) and (b), Fig. 11(c) and (d) respectively, we observed that the constellation of the proposed method is more divergent than the conventional one when the system bandwidth is not wide enough. This may benefit from the higher conversion efficiency of the conventional method. However, as the system
Fig. 11. Decoding Constellation of Two Methods at Different Bandwidths. 2 kHz bandwidth decoding constellation (a) without pre-processing modulation and (b) with preprocessing modulation; 4 kHz bandwidth decoding constellation (c) without pre-processing modulation and (d) with pre-processing modulation; 6 kHz bandwidth decoding constellation (e) without pre-processing modulation and (f) with pre-processing modulation.
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bandwidth increasing, reaching 6 kHz in Fig. 11(f) e.g., the performance of the proposed method is almost identical to that of the narrow band, while the conventional method can not decode the information of the packets. The reason is that the proposed method will not produce additional phase noise, and it is superior to the conventional one when the system bandwidth is large. 5. Conclusion A modulation method of parametric array is investigated in this paper for UAC. The source is assumed to be broadband signals for transmitting information in high communication rate. The method relies upon the theoretical time series relationship derived by Berktay. Utilizing the spirit of filter designing which is a relatively simple way to eliminate the distortion observed in difference frequency signal. The advantages of this method are that it needs low computation complexity and easy to implement. Two basic signal forms were verified by channel tank experiment. The performance of the broadband signal has been improved significantly. Single carrier UAC system based on parametric array is introduced. It not only provides a new idea for improving the shallow water acoustic communication performance, directional secure communication and acoustic multi-user network communication, but also is beneficial to support real-time transmission of highspeed communication tasks. Finally, the validity and reliability of the UAC scheme are verified by Dalian sea trial results. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 61471137, 61631008), the Fok Ying Tong Education Foundation, China (Grant No.151007), the Heilongjiang Province Outstanding Youth Science Fund (JC 2017017), and the Underwater Scientific Test and Control Technology Laboratory Foundation (Grant No. 9140C260401150C26114). References [1] L. Freitag, P. Koski, A. Morozov., S. Singh, Acoustic Communications and Navigation Under Arctic Ice, 2012 Oceans – VA, USA. [2] Qian Z. Nonlinear Acoustics. Beijing: Science Press; 1992.
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