CAPACITY OF UNDERWATER WIRELESS COMMUNICATION CHANNEL WITH DIFFERENT ACOUSTIC PROPAGATION LOSS MODELS Susan Joshy and A.V. Babu, Department of Eectronics & Communication Engineering, Nationa Institute of Technoogy Caicut, India soosanjoshy@gmai.com, babu@nitc.ac.in ABSTRACT In this paper, we cacuate the capacity of a point-to-point communication ink in an underwater acoustic channe. The anaysis takes into account the effects of various acoustic propagation oss modes. A physica mode of ambient noise power spectra density is aso considered. We perform a comparative assessment of the infuence of various acoustic transmission oss modes on the acoustic bandwidth and the capacity. KEYWORDS Channe Capacity, Optima Bandwidth, Point-to-Point Communication, Underwater Acoustic Channe,. INTRODUCTION Underwater (UW) acoustic networks are generay formed by acousticay connected ocean bottom sensor nodes, autonomous UW vehices, and surface stations that serve as gateways and provide radio communication inks to on-shore stations []. UW acoustic sensor networks consist of sensors and vehices depoyed underwater and networked via acoustic inks to perform coaborative monitoring tasks. However, the acoustic channes impose many constraints that affect the design of UW communication systems. These are characterized by a path oss that depends on both the transmission distance and the signa frequency. The signa frequency determines the absorption oss, which increases with distance as we [, ], eventuay imposing a imit on the avaiabe bandwidth. The Shannon capacity of a channe represents the theoretica upper bound for the maximum rate of data transmission at an arbitrariy sma bit error rate, and is given by the mutua information of the channe maximized over a possibe source distributions. The capacity of a time invariant additive white Gaussian noise (AWGN) channe with bandwidth and SNR is DOI :.5/ijcnc..5 9
og where the capacity achieving source distribution is Gaussian [5]. Authors of [] present numerica soution for the capacity of a very simpe UW acoustic channe without considering its frequency and distance dependant attenuation characteristics. In [], experimenta resuts on channe capacity for a shaow water wave-guide are presented. The capacity anaysis of UW acoustic OFDM based ceuar network is presented in []. In [], author presents the UW capacity based on an acoustic path oss mode and investigates the capacity distance reation. In this paper, the resuts of [] are extended. Based on the statistica and empirica acoustic path oss modes avaiabe in the iterature, we cacuate the capacity of a UW point-to-point ink. We anayze the effects of different propagation phenomena such as surface refection, surface duct, bottom bounce, and other effects such as acoustic absorption and spreading on the capacity.. ACOUSTIC TRANSMISSION LOSS AND AMBIENT NOISE In this section, anaytica modes for UW propagation oss and ambient noise are introduced. Acoustic transmission oss (TL) is the accumuated decrease in acoustic intensity as the sound traves from the source to the receiver.. Absorption and Spreading Loss Acoustic path oss depends on the signa frequency and distance. This dependence is a consequence of absorption (i.e., transfer of acoustic energy into heat). In addition, signa experiences a spreading oss, which increases with distance. Spreading oss refers to the energy distributed over an increasingy arger area due to the reguar weakening of a sound signa as it spreads outwards from the source. The overa transmission oss that occurs in UW channe over a transmission distance of meters at a signa frequency f is given by []: TL = k. og +. og a( f ) () where k is spreading factor ( k = for spherica spreading, k = for cyindrica spreading, and k =.5 for the so-caed practica spreading). In genera, for shaow water channes, cyindrica spreading is assumed ( k = ) whie for deep water channes spherica spreading is assumed ( k = ). Now og a( f ) is the absorption coefficient expressed using Thorp s formua, which gives a ( f ) in db/km for f in khz as foows []: 9
f f + f 4 + f 4 og a( f ) =. + 44 +.75. f +. () The absorption coefficient increases rapidy with frequency, and is a major factor that imits the maxima usabe frequency for an acoustic ink of a given distance. The transmission oss due to absorption and spreading (we refer this case as mode ) is shown in Figure for k =. 5. The oss increases rapidy with frequency and distance, imposing a imit on the avaiabe acoustic bandwidth.. Loss Due to Sound Propagation Characteristics Sound propagates in the sea through many different paths, which depend upon the sound-speed structure in the water as we as the source and receiver ocations. Further, mutipath propagation is affected by depth, frequency and transmission range. In the next sub-sections, we present the transmission oss expressions corresponding to three basic propagation paths between a sourcereceiver pair: surface refection, surface duct, and bottom bounce... Surface Refection Surface refection describes the refection of sound from the sea surface, and is affected by the roughness or smoothness of the sea. When the sea is rough, the transmission oss on refection can be found using the Beckmann-Spizzichino surface refection mode []: TL f + f (9 w) θ = + 6 f + f _ SR og where f = f and f = 78w, where w is the wind speed in knots, and θ is the ange of incidence to the horizonta measured in degrees. The tota acoustic path oss is computed (we refer this case as mode ) using Eqn. (4) beow and is shown in Figure ( w = m/sec, θ = 5 ). () TL = k.og +.og a( f ) + TL _ SR (4).. Surface duct In a surface duct, sound propagates to ong ranges by successive refections from the sea surface aong ray paths that are ong arcs of circes and the corresponding transmission oss, 94
incuding oss due to absorption and spreading is given as foows (we refer this case as mode ) []: TL = k.og +.(og a( f ) + α L ) (5) S 6.6 f (.4) where H is the ayer depth in meters and α L = / [(45 +.5 t) H ]. Here S stands for the sea state number, and t is the temperature. The resuting transmission oss is potted in Figure (assumed parameters are S =, H = 9meters, and t = c )... Bottom bounce This corresponds to the refection of sound from the sea foor. The refection oss of sound incident at a grazing ange θ to a pain boundary between two fuids of density ρ and ρ and of sound veocity c and c is given by the ratio of intensity of the refected wave I r reated to the intensity of the incident wave I i []: where m = ρ / ρ and n = c / c. The attenuation coefficient α s due to the presence of sediments at the sea foor is α s = β f υ where υ is an empirica constant (typicay for many measurements on sands and cays) and β (db/m-khz) depends upon porosity and is approximatey equa to.5. The tota transmission oss is computed as (we refer this case as mode 4) []: I r msin θ ( n cos θ ) TL _ bottom = og og = I i msin θ ( n cos θ ) + ( ) ( ) ( α ) TL = k. og +. og a( f ) +. + TL _ bottom The attenuation corresponding to this oss mode is aso shown in Figure (parameters assumed are: m =.95, n =.86, θ = 5, β =.5, and υ = ). The graph corresponding to mode 5 in Figure considers the combined effect of oss modes -4.. Ambient Noise The ambient noise in ocean is modeed using four sources: turbuence, shipping, waves, and therma noise. Most of the ambient noise sources can be described by Gaussian statistics and a continuous power spectra density (PSD). The foowing empirica formua gives the PSD of the four noise components in db re µ Pa per Hz as a function of frequency in khz []: s (6) (7) 95
og N ( f ) = 7 ( og f ) og N ( f ) = 4 + ( s.5) + 6og f 6 og( f +.) og N og N (8) t s w th ( f ) = 5 + 7.5w / ( f ) = 5 + og f + og f 4 og( f +.4) where w is the wind speed in m/s and s is the shipping activity factor. Figure shows the overa PSD cacuated as N( f ) = N ( f ) + N ( f ) + N ( f ) N ( f ), The PSD decays with frequency..4 Underwater Signa-to-Noise Ratio t s w + Since the transmission oss in a UW channe depends both on frequency as we as the transmission distance, et it be represented by A (, f ). Using A (, f ) and noise PSD N ( f ), the signa to noise ratio (SNR) at the receiver at a distance and frequency f for a transmitted P / A(, f ) power of P and receiver noise bandwidth f is given by γ (. f ) =. Considering N( f ) f absorption and spreading oss aone, the frequency dependent factor in the SNR /[ A (, f ) N ( f )] is potted in Figure for different propagation oss modes. It may be noted that the optimum transmission band depends on ink distance. Further, for each, there exists an optima frequency f ( ) for which maximum SNR is obtained. This is the frequency for which the term / A(, f ) N ( f ) becomes maximum []. The optima frequency is shown in Figure 4 for various oss modes. th. UNDERWATER CHANNEL CAPACITY In this section, we rey on the UW capacity mode given in []. The channe is assumed to be time invariant for some interva of time and the ambient noise is assumed to be Gaussian. Two definitions are used for the capacity: the db acoustic bandwidth and the optima bandwidth.. Capacity Based on db Bandwidth The acoustic db bandwidth B ( ) is the range of frequencies around f ( ) for which γ (. f ) f γ (, f ( )) /. We choose the transmission bandwidth to be equa to B ( ). The transmitted signa power spectra density (PSD) S ( f ) is assumed to be fat over the transmission 96
bandwidth, i.e., S ( f ) = S for f B ( ) and esewhere. The tota transmission power is then P ( ) = S B ( ). The corresponding capacity expression is given as [] P B C = + ( ) / ( ) ( ) og df A f N f B (, ) ( ) ( ) (9) where P ( ) is the minimum transmission power required to ensure that the received SNR is equa to a target vaue γ and is computed as P ( ) = γ B () ( ) B ( ) B ( ) A N( f ) df (, f ) df. Capacity Based on Optima Bandwidth In this section, we consider the computation of capacity based on the notion of an optima bandwidth []. A case in which the transmitted signa PSD S ( f ) is adjusted in accordance with the given channe and noise characteristics was anayzed in []. This adjustment is equivaent to aocating power through water pouring. In the absence of mutipath and channe fading, the optima capacity of a point-to-point ink is given by [] () C( ) = B( ) K og df A(, f ) N( f ) where B () is the optimum band of operation and K is a constant. Here B() is the frequency range over which A(, f ) N( f ) K and ( f ).The corresponding transmitted power is S given by P( ) = S ( f ) df where the signa PSD shoud satisfy the water fiing principe B( ) S ( f ) = K A(, f ) N( f ), f B( ) () The transmission power P () is seected as the minimum power required such that the received SNR equas a target vaue γ and is computed as 97
P( ) = K B( ) A(, f ) N( f ) df B( ) () The optima PSD is then determined through the numerica agorithm in []. 4. NUMERICAL RESULTS The numerica resuts for the capacity and the bandwidth are obtained using MATLAB. The parameters used are wind speed w = m/s, moderate shipping activity s =. 5, and spreading factor k =. 5. The SNR threshod is set to γ db. Figures 5 & 6 respectivey show the = bandwidth and the capacity versus distance based on db bandwidth definition. The resuting bandwidth efficiency is 6.65bps/Hz. Tabe shows the comparison of capacity and bandwidth for different oss modes. It may be noted that both the capacity and the bandwidth decreases drasticay as the transmission distance increases. Assuming absorption and spreading aone, channe capacity is amost equa to 7.kbps for = 4 km whie for the combined oss mode 5, the capacity is.kbps which is equivaent to amost 95% reduction in capacity. For the case of optima bandwidth, the transmitted signa PSD for each distance and for the desired threshod SNR γ is determined using the numerica agorithm mentioned earier. Figures 7 & 8 respectivey show the bandwidth, and the capacity obtained based on the notion of optima bandwidth. The resuting bandwidth efficiency is approximatey equa to 8.5bps/Hz and is isted in Tabe ( = 4 km). The capacity improves by approximatey 78% as compared to that achievabe based on db bandwidth definition. The numerica resuts aso revea that for a the oss modes described in this paper, both bandwidth and capacity decays amost ineary with distance on a ogarithmic scae. 5. CONCLUSION In this paper, numerica resuts for the capacity of time invariant UW point-to-point ink were presented, considering the effects of various acoustic path oss modes and a specific mode of ambient noise PSD. The path oss corresponding to different acoustic propagation phenomena such as surface refection, surface ducts, and bottom bounce, were considered for the capacity cacuation. A comparative assessment of the infuence of these oss modes on the capacity and achievabe bandwidth were presented. 98
6 Attenuation, A(,f) (db) 5 4 mode mode mode mode 4 mode 5 4 6 8 4 6 8 Frequency (khz) Fig.. Attenuation for different propagation oss modes ( ( = km) 5 noise p.s.d (db re micro Pa) 45 4 5 5 5 5 5 frequency (khz) Fig.. Ambient Noise PSD 99
-5 - /A(,f)N(,f) (db) -5 - -5 - mode mode mode mode 4 mode 5-5 4 6 8 4 6 8 Frequency (khz) Fig.. / A (, f ) N ( f ) for different oss modes Optima Frequency (khz) 8 7 6 5 4 mode mode mode mode 4 mode 5 4 5 6 7 8 9 Distance (meters) x 4 Fig. 4. Optima frequency f ( ) vs distance
Bandwidth (khz) mode mode mode mode 4 mode 5-4 5 6 7 8 9 Distance (meters) x 4 Fig. 5. Bandwidth vs distance (db bandwidth definition) Capacity (kbps) mode mode mode mode 4 mode 5 4 5 6 7 8 9 Distance (meters) x 4 Fig. 6. Capacity vs distance (db bandwidth definition)
Bandwidth (khz) mode mode mode mode 4 mode 5-4 5 6 7 8 9 Distance (meters) x 4 Fig. 7. Bandwidth vs distance (optima bandwidth definition) Capacity (kbps) mode mode mode mode 4 mode 5 4 5 6 7 8 9 Distance (meters) x 4 Fig. 8. Capacity vs distance (optima bandwidth definition)
Tabe. Capacity & Bandwidth ( = 4 km) Loss mode Bandwidth( B khz) Capacity( C kbps) Spectra Efficiency Absorption & Spreading Absorption, Spreading & Surface Refection Absorption, Spreading & Bottom Bounce Absorption, Spreading & Surface Duct Combined mode db bandwidth definition Optima bandwidth definition db bandwidth definition Optima bandwidth definition db bandwidth definition ( C / B b/s/hz) Optima bandwidth definition 4. 9. 7.987 75.98 6.658 8.58 4. 9.4 7.987 8. 6.658 8.755.6.75.995.45 6.658 7.5..5.9975.854 6.658 7.656..45.6.78 6.658 8.66 REFERENCES [] I.Akyidiz, D.Pompii and T. Meodia, (5) Underwater acoustic sensor networks: Research chaenges, Esevier Journa on Ad Hoc Networks, vo., issue, pp. 57-79. [] Mari Carmen Domingo, (8) Overview of channe modes for underwater wireess communication Networks, Esevier Journa on Physica Communication, vo., issue, pp. 6-8. [] James Preisig and Miica Stojanovic, (9) Underwater acoustic communication channes: Propagation modes and statistica characterization, IEEE Communications Magazine, vo. 47, no., pp.84-89. [4] M. Stojanovic, (8) Underwater acoustic communications: Design considerations on the physica ayer, proceedings of IEEE/IFIP conference on Wireess On demand Network Systems and Services (WONS 8).
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