Impact of Inter-Channel Interference on Shallow Underwater Acoustic OFDM Systems

Nội dung text: Impact of Inter-Channel Interference on Shallow Underwater Acoustic OFDM Systems

1. Research and Development on Information and Communication Technology Impact of Inter-Channel Interference on Shallow Underwater Acoustic OFDM Systems Do Viet Ha1, Nguyen Tien Hoa2, Nguyen Van Duc2 1 Faculty of Electrical and Electronic Engineering, University of Transport and Communications, Hanoi, Vietnam 2 School of Electronics and Telecommunications, Hanoi University of Science and Technology, Hanoi, Vietnam Correspondence: Nguyen Van Duc, duc.nguyenvan1@hust.edu.vn Communication: received 27 July 2020, revised 27 August 2020, accepted 30 September 2020 Digital Object Identifier: 10.32913/mic-ict-research.v2020.n1.929 Abstract: This paper investigates the impacts of Inter- In shallow water environments, acoustic communication Channel Interference (ICI) effects on a shallow underwater systems are suffered from the Doppler shifts with two acoustic (UWA) orthogonal frequency-division multiplexing main sources, which are the relative movement between (OFDM) communication system. Considering both the turbu- the transmitter/the receiver and the disturbance from the lence of the water surface and the roughness of the bottom, a water surface [8, 9]. In particular, a surface displacement stochastic geometry-based channel model utilized for a wide- band transmission scenario has been exploited to derive a process usually varies very fast over time, thus an unpre- simulation model. Since the system bandwidth and the sub- dictable Doppler frequency shift creates many difficulties carrier spacing is very limited in the range of a few kHz, the in identifying and compensating the Doppler shifts in the channel capacity of a UWA system is severely suffered by the receiver [10, 11]. Therefore, system performance should be ICI effect. For further investigation, we construct the signal-to- evaluated under the Doppler effects. In this paper, we focus noise-plus-interference ratio (SINR) based on the simulation on analyzing the system capacity because it is an important model, then evaluate the channel capacity. Numerical results factor to design components in a communication system. show that the various factors of a UWA-OFDM system as subcarriers, bandwidth, and OFDM symbols affect the channel capacity under the different Doppler frequencies. UWA-OFDM system capacity studies are still an open Those observations give hints to select good parameters for area up to now as a consequence of the lack of standard UWA-OFDM systems. channel models [12, 13]. Besides, many studies have ig- nored the ICI effect in the channel capacity formulation Keywords: Underwater acoustic (UWA), geometry-based chan- [14–18]. For the sake of simplicity, the time-invariant UWA nel modeling, underwater OFDM systems channel model in which the ICI effect does not occurred has been used in [14–16] to analyze system capacity. The I. INTRODUCTION authors in [17, 18] have considered time-variant channels Underwater information systems have many applications to analyze the channel capacity versus the SNR, which in commerce and military [1]. Nowadays, the development means that the ICI effect has not been taken into account. and improvement of the service quality of the system is Furthermore, ICI is also computed by the time correlation facing many challenges such as frequency spectrum limita- function converted from the Doppler spectrum form of the tion, time and frequency-dependent channel characteristics UWA channel, which is assumed to be Jack, uniform or [2, 3]. It is a fact that the velocity of water sound waves two-path spectrum [11, 19, 20]. These assumptions may not is much lower than the velocity of electromagnetic waves. be applicable to UWA channels due to the complicated time Therefore, the prominent features of the UWA channels varying characteristics of the shallow UWA propagation en- are a large delay spread and strong Doppler effects [4]. vironments. In addition, the UWA channels are considered The OFDM technique is widely used thanks to its ability as non stationary channels such that the conversion between to eliminate the inter-symbol interference (ISI) which is the Doppler spectrum and the time correlation function caused by a large delay spread [5, 6]. However, OFDM should be accompanied by certain conditions. In [21], the systems are very easily influenced by the Doppler shifts capacity of UWA-OFDM has been derived from the SINR that result in the so-called inter-carrier interference (ICI) which is considered to be the same for all subcarriers. and degrade the system performance dramatically [7]. However, the UWA-OFDM system is inherently a wideband 42
2. Vol. 2020, No. 01, September system [16, 22], the Doppler shifts over subcarriers are thus y S1,n different from each other. Consequently, it is nesseary to DR investigate the channel capacity of UWA systems under the 1,n R VR y DT 1 ICI impacts over every subcarriers. 1,n R T 0 1,n V y1 Over the past few decades, although a large variety of D R  0 2,n x R UWA channel models have been proposed, there is still 1,n y2 0 no typical model that can be applied for all UWA chan- x Tx nels because of differences in geographical areas, weather 2,n R T D y 2,n conditions, and seasonal cycles [17]. The statistical char- 2 T D2,n S2,n acteristics of shallow UWA channels are greatly affected by the distribution of scatterers on the surface and the D bottom, which results in the different delays and Doppler frequency shifts of the transmit signals. The geometry- Figure 1. The Geometry-Based channel model for a shallow underwater based UWA channel model in [23] has been derived from acoustic channel. computing the number of scatterers and their positions using the wave-guide geometry, which does not represent UWA-OFDM system using this channel model are pre- the surface displacement. In [22, 24, 25], the proposed sented in detail in Section III. Section IV shows the simu- UWA channel models concentrate on analyzing the path lation results together with discussions. Finally, Section V loss and the multipath propagation whereas the Doppler draws the main conclusions of this paper. effect has not been integrated with the models. In this paper, we use the geometry-based channel model II. THE UNDERWATER ACOUSTIC for shallow water with rough surface conditions [26] to GEOMETRY-BASED CHANEL MODEL investigate the quality of the UWA-OFDM system. Partic- The geometry-based channel model [26] is illustrated ularly, the scattering points are assumed to be uniformly in Fig. 1, where denotes the distance between the distributed between the transmitter and the receiver. From transmitter (Tx) and receiver (Rx). The scatterers 푆푖,푛 (푛 = the assumption, the pulse response time variation of the 1, 2, . . . , 푖; 푖 = 1, 2) are assumed to be randomly dis- channel pattern is obtained. Using this channel impulse tributed on the surface (푖 = 1) and the bottom (푖 = 2) response, the SINR of each sub-carrier is derived for the of a shallow-water environment. The symbols 훼푖,푛, 훽푖,푛, considered system. As aforementioned, the SINR of shallow (훽푖,푛 ≠ 0; 훼푖,푛 ≠ ) are the angle-of-departure (AOD) and UWA channels with rough surface transmission system the angle-of-arrival (AOA) of the 푛-th path, respectively. is strongly dependent on ICI effects which is caused by In the below subsections, the UWA channel parameters are Doppler shifts. We have, in contrast to other works, derived derived with reference to [26]. SINR expression of each sub-carrier with considering of the time-variant UWA channel model. We have also used the geometrical scattering model for representing the char- 1. The Channel Impulse Response acteristics of shallow water with rough surface conditions The time-variant channel impulse response (TVCIR) to evaluate the channel capacity. The channel capacity is ℎ (휏, 푡) of the shallow UWA environment is composed of further formulated as the superposition of all the single three components, which is given by [26] channel capacity from each sub-channel. By analyzing the 2 ∑︁ numerical results, a set of suitable parameters for the ℎ (휏, 푡) = ℎ푖 (휏, 푡). (1) considered UWA-OFDM system is found, which includes 푖=0 the number of subcarriers, signal bandwidth and the length In Eq. (1), the line-of-sight (LOS) component is denoted of the OFDM symbol. It should be noticed that these by ℎ0 (휏, 푡), whereas ℎ1 (휏, 푡) and ℎ2 (휏, 푡) stand for the are important parameters and they need to be determined scattered components from the surface and the bottom, appropriately in order to eliminate ISI while limiting the respectively. The LOS part ℎ0 (휏, 푡) is specified by ICI effects. √︂ 푅 푗 (2 0푡+휃0) The rest of the paper is organized as follows: Section II ℎ0 (휏, 푡) = 푠 ( 0) ( 0) 푒 훿(휏 − 휏0), 1 + 푅 presents the UWA geometry-based channel model which is (2) used to derive the time-variant channel impulse response in which 푅, 휏0, 0 and 휃0 denote the Rice factor, the and the channel transfer function. The calculations of the propagation delay, the Doppler frequency, and the phase SINR expression and channel capacity for the considered shift of the LOS path, respectively. The function 푠 ( 0) is 43
3. Research and Development on Information and Communication Technology 푅 the propagation loss coefficient due to spherical spreading, ,maxcos(훼푖,푛−훼푣 ), where ,max stands for the maximum which can be obtained by Doppler frequency. The propagation delays can be obtained 1 by 휏푖,푛 = 푖,푛/ 푠. The phase shift 휃푖,푛 is assumed to be ( ) = , (3) 푠 uniformly distributed over the range (− , ]. Finally, the where denotes the total propagation distance in meter. scattered components ℎ1 (휏, 푡) and ℎ2 (휏, 푡) of the TVCIR For the LOS path, the distance is defined by ℎ(휏, 푡) in Eq. (7) are derived. √︃ 2 푅 2 0 = + ( − ) . (4) 1 1 2. Channel Transfer Function The absorption loss coefficient ( ) is given by For further analysis of the UWA-OFDM system, the time- − 훽 ( ) = 10 2000 . (5) variant channel transfer function (TVCTF) ( , 푡) needs to be derived by taking the Fourier transform of the TVCIR The parameter 훽 in Eq. (5) is computed as ℎ(휏, 푡), which can be expressed by 2 2 ! 푆 2 훽 = 8.68 ì 103 + ì ∑︁ 2 2 ( , 푡) = ( , 푡), (12) + (6) 푖 푖=0 ì(1 − 6.54 ì 10−4푃)[ / ], where −6 −6 where = 2.34 ì 10 and = 3.38 ì 10 , 푆 is salinity √︂ 푅 (in ppt), is the carrier frequency (in kHz), is the ( , 푡) = ( ) ( ) 0 1 + 푠 0 0 relaxation frequency (in kHz) and is temperature (in 푅 (13) 푗 [2 ( 푡− 휏 ) ] ◦C). The symbol 푃 denotes the hydro-static pressure (in ì 푒 0 0 , 2 kg/cm ), which is determined by 푃 = 1.01(1+0.1ℎ), where and ℎ is the water depth (in meter). The scattered components 1 ∑︁푖 ℎ1 (휏, 푡) and ℎ2 (휏, 푡) of the TVCIR ℎ(휏, 푡) are computed by ( ) ( ) ( ) 푖 , 푡 = √︁ 푠 푖,푛 푖,푛 2 푖 (1 + 푅) 푛=1 (14) 1 ∑︁푖 ( ) ( ) ( ) 푗 [2 ( 푖,푛푡− 휏푖,푛)+휃푖,푛] ℎ푖 휏, 푡 = √︁ 푠 푖,푛 푖,푛 ì 푒 2 푖 (1 + 푅) 푛=1 (7) 푗 (2 푖,푛푡+휃푖,푛) for 푖 = 1, 2. ì 푒 훿(휏 − 휏푖,푛), in which 푖,푛, 휏푖,푛, and 휃푖,푛 denote the Rice factor, the propagation delay, the Doppler frequency, and the phase III. CHANNEL CAPACITY ANALYSIS UNDER shift of the scattered path, respectively. With reference to INTERFENCE EFFECTS Fig. 1, the total propagation distance 푖,푛 can be computed This section uses the geometry-based UWA channel as 푅 simulation model to analyze the ICI effect in the UWA- 푖 푖 푖,푛 = + . (8) OFDM system. The SINR of each sub-carrier has been sin(훽 ) sin(훼 ) 푖,푛 푖,푛 formulated in terms of the time-variant channel transfer The parameters of the UWA channel are initiated by using function (TVCTF) ( , 푡) of the UWA channel model. optimum values of 푖,푛 The capacity estimation of UWA-OFDM system has been   opt 1 analyzed using the results of SINRs. 푖,푛 = 푛 − . (9) 푖 2 opt Using 푖,푛, the other values AOA 훼푖,푛 and AOD 훽푖,푛 can 1. SINR Computation be computed as follow The OFDM base-band signal is given as  −   + arctan 푖,푛 , if 0 ≤ ≤ .  2 푅 푖,푛 −1 1 1 ∑︁ 훼푖,푛 =  푅  (10) 푗2 푛 / + arctan 2 , if 0 ≤ ≤ . [푡푛] = √ [ ]푒 , (15)  − 푖,푛  =0 where is the number of sub-carriers, denotes the  1  arctan , if 0 ≤ 푖,푛 ≤ . th  푖,푛 data-modulated sub-carrier in the OFDM symbol. The 훽푖,푛 =   (11) 3 + arctan 푖,푛 , if 0 ≤ ≤ . OFDM signal at the receiver side is represented as  2 푖,푛  2 −1 Substituting 훼푖,푛 and 훽푖,푛 in Eq. (8) allows us to compute 1 ∑︁ 푖2 푛 / [푡푛] = √ [ , 푡푛] [ ]푒 + 푤[푡푛], (16) 푖,푛. The Doppler frequencies are computed by 푖,푛 = b =0 44
4. Vol. 2020, No. 01, September where [ , 푡푛] stands for the TVCTF of the UWA channel 2. Capacity Analysis and 푤[푡푛] denotes the ambient noise in the UWA commu- The channel capacity of th sub-carrier of an UW-OFDM nication system. After FFT at the receiver, the signal b[ ] in frequency domain can be expressed as system is computed from the SINR[ ] as follows −1 = Δ log2 (1 + SINR[ ]). (27) 1 ∑︁ −푖2 푛 / b[ ] = √ b [푡푛]푒 . (17) 푛=0 Suppose that each sub-carrier carries data, the total channel capacity of UWA-OFDM system is calculated by By using b [푡푛] from Eq. (16) in Eq. (17), the b[ ] is −1 given as in Eq. (25), where 푆[ ], [ ], 푊 [ ] denote the ∑︁ = 푆 Δ log (1 + SINR[ ]), (28) desired signal, the interference signal, and the frequency SINR + 2 푆 =0 domain of ambient noise 푤[푡푛], respectively, which are computed by where 푆, are the symbol duration and the guard length of the UWA-OFDM system, respectively. −1 1 ∑︁ 푆[ ] = [ , 푡 ] [ ], (18) In UWA communication systems, the spectral efficiency 푛 푛=0 / is a vital parameter in system performance evaluation because of the limited bandwidth. Substituting Δ = / −1 −1 into Eq. (28), we obtain the spectral efficiency / as 1 ∑︁ ∑︁ [ ] = [ , 푡 ]푒 푗2 ( − )푛/ [ ], (19) below 푛 =0 푛=0 −1 ≠ 1 ∑︁ = 푆 ì ì log (1 + SINR[ ]). (29) + 2 and 푆 =0 −1 1 ∑︁ − 푗2 푛 / 푊 [ ] = √ 푤[푡푛]푒 . (20) Observing Eq. (29), several constraints need to be con- 푛=0 sidered in determining OFDM transmission parameters to optimize the spectral efficiency. Assuming that the guard Assuming the Signal to Noise Ratio of the th subcarrier length is chosen to be equal to the maximal delay in the absence of ICI is denoted by the SNR[ ], which is spread 휏 to remove the ISI noise. With a given number given by max of sub-carriers , the bandwidth efficiency coefficient 푃S [ ] SNR[ ] = , (21) 훽 = 푆/( 푆 + ) is increased by a larger symbol duration 푃N [ ] 푆. However, the larger 푆 = / makes the sub-carrier spacing Δ = / decrease. Consequently, the ICI effect where 푃S [ ] is the receiver power and 푃N [ ] stands for the noise power at the th subcarrier. Using (18) and (19), will be stronger, which results in degrading SINR. There- fore, the set of parameters , , should be considered the desired signal power 푃D [ ] and the ICI power 푃I [ ] 푆 of the th subcarrier can be obtained by thoughtfully to meet the quality requirements of the system. The numerical results of SINRs and system capacity in −1 !2 푃S [ ] ∑︁ section IV will evaluate the appropriate system parameters, 푃D [ ] = [ , 푡푛] , (22) 2 including thoes of 푆, , and to achieve optimal spectral 푛=0 efficiency for the UWA-OFDM system with ICI effects. and 2 −1 −1 IV. RESULTS AND DISCUSSIONS 푃S [ ] â∑︁ ∑︁ 푗2 ( − )푛/ ê 푃I [ ] = ư [ , 푡푛]푒 đ . 2 ư đ =0 푛=0 1. Simulation Setting ≠ ô ơ (23) The results of surveying system performance including The SINR of the kth sub-carrier is given by SINR and Capacity are averaged over 10 simulations, each 푃D [ ] running with a time of 10000 OFDM symbols. The main SINR[ ] = . (24) parameters running in the simulation are taken with central 푃I [ ] + 푃N [ ] carrier frequency = 30 kHz, SNR = 20 dB at receiver, th Using Eq. (21), Eq. (22), and Eq. (23), the SINR of the the number of subcarriers = 512, 1024 and 2048, and subcarriers can be obtained as in Eq. (26). the signal bandwidth varies between 1 kHz and 30 kHz. 45
5. Research and Development on Information and Communication Technology −1 " −1 ! # 1 ∑︁ ∑︁ [ ] = [ , 푡 ]푒 푗2 ( − ) [ ] + 푊 [ ] = 푆[ ] + [ ] + 푊 [ ]. (25) b 푛 =0 푛=0 1 Í −1 2 | [ , 푡푛]| SINR[ ] = 푛=0 . (26) 2 −1 1 Í −1 Í 푗2 ( − )푛/ 1 [ , 푡푛]푒 + =0, ≠ SNR[ ] 푛=0 20 20 19 15 18 10 17 SINR (dB) SINR SINR (dB) SINR 16 f =1Hz N =512 5 d c f =2Hz N =1024 d 15 c f =4Hz N =2048 d c 0 14 5 10 15 20 25 30 5 10 15 20 25 30 Bandwidth (kHz) Bandwidth (kHz) Figure 2. SINRs versus signal bandwidth for different Doppler frequen- Figure 3. SINR versus signal bandwidth for different numbers of subcar- cies. riers ( = 1Hz). 2. SINR Results Another aspect which should be considered in UWA- Figure 2 shows the SINR results of the UWA-OFDM OFDM system design is the number of subcarriers . For system with the number of subcarriers = 1024. It is a given bandwidth, the subcarrier spacing is narrower with noted that the SINR is calculated for each subcarrier and a larger . Consequently, the ICI effect on the OFDM the results in Fig. 2 is the average of all subcarriers. We system is more severe, and then the SINR decreases. As see the strong Doppler effect on the SINR when the signal the results show in Fig. 3, the SINR is lower in the case bandwidth is small. With a given number of subcarriers, of larger number of subcarriers . Using these results, the smaller signal bandwidth is, the subcarrier spacing the appropriate values of bandwidth and the number of Δ = / is narrower that causes more serious ICI effect sub-carrier can be determined to achieve a required and decreasing the SINR. On the contrary, when increasing SINR of the UWA-OFDM system. For even a very small the signal bandwidth, the larger carrier spacing mitigates value of Doppler shift = 1 Hz, the maximum number the ICI effect. If bandwidth is large enough, the ICI of subcarriers of = 1024 and the minimum bandwidth effect can be neglected and the SINR results approach to of 10 kHz should be selected to avoid the ICI effect. For the SNR=20 dB. = 2048, the minimum bandwidth is required to be greater than 20 kHz. However, on one hand, a small number From the SINR results in Fig. 2, it is observed that with of subcarriers results in mitigating the Doppler effect; on a bandwidth greater than 10 kHz, the ICI effect for the the other hand, it makes the efficiency of the spectrum Doppler frequencies of = 1 Hz and 2 Hz is negligible. and the system capacity decrease. The next section will For the case of = 4 Hz, a bandwidth greater than 20 kHz evaluate the capacity to determine the appropriate number is required to significantly reduce the ICI effect. Therefore, of subcarriers for the UWA-OFDM system. depending on the hardware capabilities of the system, the impact of ICI on system performance can be significantly reduced if a wide bandwidth is chosen. 46
6. Vol. 2020, No. 01, September 200 6.5 N =512 c 6 N =1024 150 c N =2048 c 5.5 100 5 Capacity (kbps) Capacity Capacity (bit/s/Hz) Capacity N =512 50 c 4.5 N =1024 c N =2048 c 4 0 0 200 400 600 800 1000 0 5 10 15 20 25 30 T (ms) Bandwidth (kHz) S Figure 4. System capacity (Kbps) versus bandwidth for different Figure 5. Spectral efficiency / (b/s/Hz) versus symbol length 푆 for numbers of subcarriers ( = 1Hz). different numbers of subcarriers. 3. Capacity Results 6.4 f =1 Hz 6.2 d f = 2 Hz The system capacity of the UWA-OFDM system versus d 6 f = 4 Hz the signal bandwidth for different numbers of subcarriers d 5.8 (with = 1Hz) is shown in Fig. 4. For the bandwidth range of 204.8 ms. The reason 10 kHz to 15 kHz, one should choose = 1024 to ensure is that the larger 푆 (i.e. the smaller subcarrier spacing Δ ) that the system capacity is not significantly reduced, but to makes the ICI effect more serious on the UWA channel. limit the ICI effect. For a bandwidth of more than 20 kHz, Hence, 푆 > 204.8 ms also results in the decrease of = 2048 is suitable. both SINR and the spectral efficiency / as shown in Besides the system capacity (Kbps), the spectrum Eq. (29). As observed in Fig. 5, the spectral efficiency all efficiency / (b/s/Hz) is also an important factor in the achieves the maximal value / max = 6.265 (b/s/Hz) at OFDM system design due to the limited bandwidth of 푆 = 204.8 ms. Using this result, we can determine the UWA channels. Figure 5 shows the results of the spectrum optimal bandwidth for each different number of subcarriers efficiency / (b/s/Hz) versus the symbol duration 푆 for . 47
7. Research and Development on Information and Communication Technology TABLE I for OFDM-Based Cognitive Radio Systems,” in Pro- THE UWA-OFDM SYSTEM PARAMETERS FOR DIFFERENT DOPPLER ceedings of the 7th International Conference on Ubiq- FREQUENCIES. uitous Information Management and Communication, ( / ) (kHz) max (ms) ICUIMC ’13, (New York, NY, USA), Association for (b/s/Hz) 푆 N=512 N= 1024 N =2048 1 Hz 6.265 204.8 2.5 5.0 10.0 Computing Machinery, 2013. 2 Hz 6.059 128.0 4.1 8.2 16.4 [4] T. Ebihara and K. Mizutani, “Experimental Study of 4 Hz 5.757 78.8 6.5 13.0 26.0 Doppler Effect for Underwater Acoustic Communi- cation Using Orthogonal Signal Division Multiplex- ing,” Japanese Journal of Applied Physics, vol. 51, Moreover, depending on the Doppler shift , an appro- p. 07GG04, jul 2012. priate should be chosen to achieve the maximum / . 푆 [5] J. Tao, “DFT-Precoded MIMO OFDM Underwater Figure 6 depicts the / results versus for different 푆 Acoustic Communications,” IEEE Journal of Oceanic Doppler shifts for the case of = 1024. When the Engineering, vol. 43, no. 3, pp. 805–819, 2018. Doppler frequency increases, the optimal value of to 푆 [6] L. Zhang, T. Kang, H. C. Song, W. S. Hodgkiss, and achieve maximum / is decreased. The optimal and 푆 X. Xu, “MIMO-OFDM Acoustic Communication in values for different Doppler frequencies are shown in Shallow Water,” in 2013 OCEANS - San Diego, pp. 1– Table I. Based on these results, one can determined the 4, 2013. parameters , , , for UWA-OFDM systems to not only 푆 [7] H. Tran Minh, S. Rie, S. Taisuki, and T. Wada, “A achieve maximum spectral efficiency and channel capacity Transceiver Architecture for Ultrasonic OFDM with but also limit the ICI effect and minimize complexity at the Adaptive Doppler Compensation,” in OCEANS 2015 receiver under different transmission conditions. - MTS/IEEE Washington, pp. 1–6, 2015. [8] S. Yoshizawa, H. Tanimoto, and T. Saito, “Experimen- V. CONCLUSIONS tal results of OFDM rake reception for shallow wa- ter acoustic communication,” in 2016 Techno-Ocean This paper has investigated the capacity of the UWA- (Techno-Ocean), pp. 185–188, 2016. OFDM system under the impact of ICI effect. Using the [9] H. Do Viet, T. Chien, and V. Nguyen, “Propos- time variant geometry-based channel model for the shallow als of Multipath Time-Variant Channel and Additive water environment, the SINR of each sub-carrier has been Coloured Noise Modelling for Underwater Acous- derived. The channel capacity is computed from the SINR, tic OFDM-Based Systems,” International Journal of which takes the Doppler effect into account. The numerical Wireless and Mobile Computing, vol. 11, pp. 329–338, results of SINR, channel capacity, and spectral efficiency Jan. 2016. give us guidance in UWA-OFDM system design, specifi- [10] G. Qiao, Z. Babar, L. Ma, L. Wan, X. Qing, X. Li, and cally in choosing the transmission parameters including the M. Bilal, “Shallow water acoustic channel modeling number of subcarriers, the symbol length, and the signal and mimo-ofdm simulations,” in 2018 15th Interna- bandwidth for the different Doppler shifts. tional Bhurban Conference on Applied Sciences and Technology (IBCAST), pp. 709–715, 2018. ACKNOWLEDGEMENT [11] D. Nguyen, H. Nguyen, and H. Ho, “Methods to Esti- This study was funded by the Vietnam National Foun- mate the Channel Delay Profile and Doppler Spectrum dation for Science and Technology Development (NAFOS- of Shallow Underwater Acoustic Channels,” Archives TED) under the project number 102.04-2018.12. of Acoustics, vol. 44, pp. 375–383, Jan. 2019. [12] X. Wang, J. Wang, L. He, and J. Song, “Doubly Se- lective Underwater Acoustic Channel Estimation with REFERENCES Basis Expansion Model,” in 2017 IEEE International [1] G. Marani, S. K. Choi, and J. Yuh, “Underwater Conference on Communications (ICC), pp. 1–6, 2017. Autonomous Manipulation for Intervention Missions [13] M. Naderi, D. V. Ha, V. D. Nguyen, and M. Patzold, AUVs,” Ocean Engineering, vol. 36, no. 1, pp. 15–23, “Modelling The Doppler Power Spectrum of Non- 2009. Stationary Underwater Acoustic Channels Based on [2] D. W. Kim, “Tracking of REMUS Autonomous Un- Doppler Measurements,” in OCEANS 2017 - Ab- derwater Vehicles with Actuator Saturations,” Auto- erdeen, pp. 1–6, 2017. matica, vol. 58, no. C, pp. 15–21, 2015. [14] H. Nouri, M. Uysal, E. Panayirci, and H. Senol, “In- [3] N. T. Hoa, N. T. Hieu, N. Van Duc, G. Gelle, and formation Theoretical Performance Limits of Single- H. Choo, “Second Order Suboptimal Power Allocation carrier Underwater Acoustic Systems,” IET Commu- 48
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