Poceedings of Meetings on Acoustics Volume 4, 2 http://acousticalsociety.og/ 62nd Meeting Acoustical Society of Ameica San Diego, Califonia 3 Octobe - 4 Novembe 2 Session 4pEA: Engineeing Acoustics 4pEA8. Capacity and Statistics of Measued Undewate Acoustic Paticle Velocity Channels Huaihai Guo, Chen Chen, Ali Abdi*, Aijun Song, Mohsen Badiey and Paul Husky *Coesponding autho s addess: Electical and Compute Engineeing, New Jesey Institute of Technology, 323 M.L.King Blvd, Newak, NJ 72, ali.abdi@njit.edu Acoustic paticle velocity channels can be used fo communication in undewate systems [A. Abdi and H. Guo, IEEE Tans. Wieless Communi. 8, 3326-3329, (29)]. In this pape, the infomation (Shannon) capacity of undewate acoustic paticle velocity channels is studied using measued data. Moe specifically, the maximum achievable data ates of a compact vecto senso communication eceive and anothe communication eceive with spatially sepaated scala sensos ae compaed. Some statistics of paticle velocity channels such as amplitude distibution and powe delay pofile ae investigated using measued data and pope models ae suggested as well. The esults ae useful fo design and simulation of vecto senso undewate communication systems in paticle velocity channels.the wok is suppoted in pat by the National Science Foundation (NSF), Gant CCF-839. Published by the Acoustical Society of Ameica though the Ameican Institute of Physics 22 Acoustical Society of Ameica [DOI:.2/.474639] eceived 3 Feb 22; published 3 Ap 22 Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
I. INTODUCTION Communication via acoustic paticle velocity channels using vecto sensos has been ecently poposed fo undewate systems [][2]. In addition to the acoustic pessue channel [3][4], acoustic paticle velocity channels povide exta channels fo communication [5]. Expeimental esults have shown the usefulness of such channels fo communication [6]. Some statistical chaacteistics of paticle velocity channels ae investigated in [7] and [8]. The inteested eade can efe to [5] fo a summay of channel modeling and communication system design eseach in paticle velocity channels. The infomation capacity of undewate acoustic pessue channels is studied in a numbe of publications, e.g., [9]-[3]. In this pape, we use expeimental data to study the capacity offeed by a multi-channel vecto senso eceive that measues the x, y and z components of the acoustic paticle velocity, as well as the acoustic pessue. The capacity povided by a eceive aay with fou spatially sepaated scala pessue sensos is investigated as well, using the collected data. As a benchmak, capacity of a fou channel eceive in ayleigh fading is also calculated. Measued capacities of both the vecto senso eceive and the scala aay eceive ae compaed with this ayleigh capacity efeence, to obtain futhe insight. Amplitude distibutions of the measued acoustic paticle velocity and pessue channels ae also compaed with ayleigh distibution, to study the suitability of the ayleigh model. The est of the pape is oganized as follows. The measued data and expeiment setup ae explained in Section II. In Section III naowband capacities of the vecto senso eceive and the scala aay eceive ae consideed, wheeas Section IV is devoted to wideband capacities. Concluding emaks ae povided in Section V. II. AT-SEA EXPEIMENTS AND MEASUED DATA A multi-channel vecto senso communication eceive is shown in Fig.. Thee we have one tansmit scala (pessue) senso, the black sphee, and a vecto senso eceive, the black cube which measues signals in pessue, x, y and z paticle velocity channels. Theefoe, this is a Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page 2 edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
4 single-input multiple-output (SIMO) communication system. The data sets analyzed in this pape wee collected duing the Makai expeiment in Hawaii in Septembe and Octobe of 25 [4]. The wate depth at the site was about m. A high fequency sound souce was mounted on the sea floo. A Wilcoxon TV- vecto senso aay was hung fom the eseach vessel, with the bottom element at the nominal depth of 4m. The element spacing was cm. The fifth, o the bottom, element did not function popely duing the expeiment. Each vecto senso element measued pessue, as well as x, y and z velocities. Duing the expeiment, the aay was consideed vetical since a 2 lbs. weight was attached to the end of the aay. Scala Senso y-velocity channel pessue channel y x-velocity channel x z-velocity channel Vecto Senso z pessue signal x-velocity signal y-velocity signal z-velocity signal Fig. A 4 vecto senso communication system with one pessue senso tansmitte. The vecto senso eceive measues the acoustic pessue, as well as the x, y and z components of the acoustic paticle velocity, all at a single point. Impulse esponses of the channels fom scala senso tansmitte to a fou-channel vecto senso eceive wee measued, as well as those between the tansmitte and fou scala senso eceives. A binay phase shift keying (BPSK) signal with a symbol ate of 6 kilosymbols/second was used to pobe the impulse esponses, at the caie fequency of f c = 2 khz. At the tansmit side, the pessue senso sent out a 3.5-second-long data packet which contained 54 sequences. At the eceive side, the eceived signals wee tansfomed to the baseband and Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page 3 edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
then wee factionally sampled at the ate of 3 samples/symbol. Theefoe, the sampling ate of the baseband signal was 8 khz. Then a 25ms-long channel impulse esponse was estimated using the least squae method. In this pape, the expeimental data collected fo the communication ange of 9 m ae analyzed. Fo example, magnitude of the measued channel x impulse esponse duing the 3.5 second packet fo the x-velocity channel, h [ n, l ], is shown in Fig. 2, whee n and l stand fo the geotime and aival time, espectively. Magnitudes of nomalized (unit-powe) impulse esponses of the pessue channel as well as x, y and z velocity channels ae shown in Fig. 3. Fequency esponse of each channel is obtained by taking the Fouie tansfom of the coesponding channel impulse esponse. Magnitudes of the fequency esponses of the channels in Fig. 3 ae shown in Fig. 4. x-velocity channel el. db.5-5 - Geotime (s).5 2-5 2.5-2 3-25 3.5 5 5 2 Aival time (ms) -3 Fig. 2 Measued impulse esponse of the x-velocity channel. Magnitudes of nomalized (unit-powe) tempoal coelation functions of the pessue channel, as well as x, y and z velocity channels ae shown in Fig. 5. Similaly to [5] and [6], * the tempoal coelation function fo a channel is defined as [ n] E{ h [ n] h[ n n]} whee E Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page 4 edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
Magnitude Magnitude Magnitude Magnitude pessue channel.2. 3.3333 6.26667 9.4 2.5333 5.6667 x-velocity channel.2. 3.3333 6.26667 9.4 2.5333 5.6667 y-velocity channel.2. 3.3333 6.26667 9.4 2.5333 5.6667 z-velocity channel.2. 3.3333 6.26667 9.4 2.5333 5.6667 Aival time (ms) Fig. 3 Magnitudes of aveage unit powe vecto senso channel impulse esponses at 9m. Magnitude(dB) Magnitude(dB) Magnitude(dB) Magnitude(dB) pessue channel -2-4 2 4 6 8 2 x-velocity channel -2-4 2 4 6 8 2 y-velocity channel -2-4 2 4 6 8 2 z-velocity channel -2-4 2 4 6 8 2 Fequency(kHz) Fig. 4 Magnitudes of aveage vecto senso fequency esponses at 9m. is mathematical expectation, * is complex conjugate, and hn [ ] is the zeo-mean unit vaiance complex channel esponse. Note that hn [ ] is elated to the channel impulse esponse hnl [, ] Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page 5 edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
accoding to hn [ ] hnl [, ]. By looking at the fequency domain [5], one can see hn [ ] is l the time-vaying naowband channel esponse, whee the signal bandwidth is much smalle than the channel bandwidth. On the othe hand, hnl [, ] is the time-vaying wideband channel esponse, whee the signal bandwidth is much lage than the channel bandwidth. These two coespond to fequency-nonselective and fequency-selective channels, espectively [5]. Coheence time T c of a time-vaying channel is the inteval ove which the channel emains nealy constant [5]. Using the -3 db point of the tempoal coelation function [6] [7], coheence times of the pessue and paticle velocity channels ae about 7 ms. On the othe hand, ou signaling ate is / T 6 kilo-symbols/second, which indicates T.7 ms. Theefoe, one can say ou channels ae nealy time-invaiant because T T c T c [5] [7]. Note that the length of the pobe signal, 25 ms, is much smalle than Tc 7 ms as well. So, the pessue and paticle velocity channels can be consideed to be time-invaiant duing shot signaling intevals of inteest. This allows to compute capacity using at-sea measued data, similaly to othe undewate channel capacity studies such as [2], [3], [6], [8], etc..9.8 pessue channel x-velocity channel y-velocity channel z-velocity channel.7 Magnitude.6.5.4.3.2..7.4 2. 2.8 n(s) Fig. 5 Magnitudes of aveage unit powe vecto senso tempoal coelation functions at 9m. Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page 6 edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
III. NAOWBAND CHANNEL CAPACITY In this section we study the naowband channel capacity of the 4 SIMO communication system with a vecto senso eceive. Let x and y denote the MT tansmitted signal vecto and the M eceived signal vecto, espectively, of an MT M multiple-input multiple-output (MIMO) system. Then the naowband input-output system equation is yhxv, () whee H is the naowband M M T complex channel esponse matix with elements hij, i =,, M and j =,, M T, and v is the M additive noise vecto. The capacity of this system, when channel is known at the eceive, is given by [9] 2 H C log H H, (2) whee log 2 is logaithm to the base 2 and signal / noise is the signal-to-noise atio (SN), with signal as the aveage signal powe and noise as the aveage noise powe at evey eceive channel, espectively. Moeove, () H is tanspose conjugate. In this pape we have M, M 4 and theefoe H [ h h2 h3 h4] T, whee () T is matix tanspose. In the vecto senso eceive, h, h 2, h 3 and h 4 epesent the pessue, x-velocity, y-velocity and z-velocity channels, espectively. In the scala aay eceive, h coesponds to the scala pessue senso at the top of the aay, wheeas h 4 coesponds to the one at the bottom of the aay. A. Naowband Channel esponse Distibution The cumulative distibution function () of the naowband channel amplitude n [ ] hn [ ] is shown in Fig. 6 and Fig. 7 fo the vecto senso and scala aay eceives, espectively, using 54 channel measuements. The unit powe ayleigh both figues as a efeence, and appeas to be close to the empiical s. B. Naowband Channel Capacity e 2 is plotted in Using eq. (2), the aveage capacity of the vecto senso eceive is plotted in Fig. 8, based on measued data, as well as the capacity of the scala aay eceive. The two eceives povide nealy the same capacity. As a efeence, the aveage capacity of a 4system in naowband T Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page 7 edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
.9.8.7 pessue channel x-velocity channel y-velocity channel z-velocity channel ayleigh.6.5.4.3.2..5.5 2 Fig. 6 s of the amplitudes of naowband esponses of diffeent channels in a vecto senso eceive at 9m..9.8.7 pessue channel # pessue channel #2 pessue channel #3 pessue channel #4 ayleigh.6.5.4.3.2..5.5 2 Fig. 7 s of the amplitudes of naowband esponses of diffeent channels in a fou-element scala aay eceive at 9m. Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page 8 edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
ayleigh fading is also plotted in Fig. 8, which appeas to be a good model fo measued capacities. ayleigh capacity can be calculated using eithe [2] 3 C log 2( ) e d 6, (3) o eq. (34) in [2] 4 ( )/ 5 i C e d i ln 2, (4) whee ln is natual logaithm to the base e. 5 Theoetical (ayleigh) Empiical (vecto senso) Empiical (scala aay) Channel capacity (bits/sec./hz) 5 5 5 2 25 3 SN (db) Fig. 8 Naowband channel capacities at 9m. IV. WIDEBAND CHANNEL CAPACITY The wideband channel capacity of the 4 SIMO communication system with a vecto senso eceive is studied in this section. The geneal wideband MIMO system equation with L channel taps is given by L y[ n] H x[ nl] v [ n], (5) l l whee H l is an M M T complex matix that epesents the l th tap of the MIMO channel esponse. By applying N-point discete Fouie tansfom (DFT) to both sides of (5), we obtain Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page 9 edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
the system equations in the fequency domain Hee L j2 lk/ N H k H le is the M l MT y, x k and fequency bin, wheeas y k y k H x v, k k k k,, N. (6) fequency domain channel matix in the k th v k ae fequency domain epesentations of the eceived signal vecto, tansmitted signal vecto and noise vecto in the k th bin, espectively. The capacity of this system with channel known at the eceive is given by [22] N C log H 2 det M N I H H k k, (7) k whee signal /( N noise ) is the SN pe eceive channel, with signal as the aveage signal powe and noise as the aveage noise powe pe eceive channel pe fequency bin. A. Powe Delay Pofile Powe delay pofile (PDP) is an impotant chaacteistic of wideband channels, as it shows the distibution of powe at diffeent delays [23]. It is the basis of the wideband channel capacity simulation. Hee we conside the multi-exponential PDP model [23] whee m, M [ l] mexp[ m( llm)], (8) m m. and l m ae the weight, decay ate and position of the m th one-side exponential (cluste), espectively. In Fig. 9a, the empiical PDPs of all channels of the vecto senso eceive ae shown, such that each PDP is nomalized to have unit aea. Accoding to this figue thee ae M 4 clustes in each channel. Upon choosing l m s fom Fig. 9a, the paametes m and m ae estimated using a numeical least-squaes method, which ae.58.57.85.39.452.535.94.735 VS γ,.93.392.43.92.23.927.474.33 Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
β VS.468.4736.287.425.4443.4287.353.973, (9).3846.3296.299.7562.478.4797.376.356 26 43 66 26 43 66 VS l. 26 43 66 26 44 66 The supescipts VS in (9) stands fo vecto senso and each m th column coesponds to the m th cluste. Moeove, ows fom top to bottom in each matix coespond to the pessue, x- velocity, y-velocity and z-velocity channels, espectively. Using the estimated paametes, multiexponential PDP models of all the channels in the vecto senso ae plotted in Fig. 9b, which closely mimic the empiical PDPs. PDP.2.5..5 Expeimental PDP pessue channel x-velocity channel y-velocity channel z-velocity channel PDP.2.5. 2 4 6 8 2 4 Aival time (symbol) (a) Multiple exponential PDP pessue channel x-velocity channel y-velocity channel z-velocity channel.5 2 4 6 8 2 4 Aival time (symbol) (b) Fig. 9 Powe delay pofiles of a vecto senso eceive: (a) Estimated diectly fom measued data, (b) Multi-exponential model with paametes estimated fom measued data. The empiical PDPs of all the channels of the scala aay (SA) eceive ae shown in Fig. a, and the coesponding estimated multi-exponential PDP models ae pesented in Fig. b, Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
whee the paametes ae.782.67.88.4.879.744.727.266 SA γ,.22.829.774.322.277.886.64.283.538.573.334.333.5426.5643.3442.28 SA β, ().5785.647.499.256.5498.579.454.2238 4 29 46 68 4 29 46 67 SA l. 4 29 47 67 4 29 47 67 Similaly to eq.(9), in each of the above matices the m th column epesents the m th cluste, wheeas the fist and last ows coespond to the scala sensos at the top and bottom of the aay, espectively. PDP.2.5..5 Expeimental PDP pessue channel # pessue channel #2 pessue channel #3 pessue channel #4 PDP.2.5. 2 4 6 8 2 4 Aival time (symbol) (a) Multiple exponential PDP pessue channel # pessue channel #2 pessue channel #3 pessue channel #4.5 2 4 6 8 2 4 Aival time (symbol) (b) Fig. Powe delay pofile of a scala aay eceive: (a) Estimated diectly fom measued data, (b) Multi-exponential model with paametes estimated fom measued data. Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page 2 edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
B. Wideband Channel esponse Distibution As shown in Fig. 9 and Fig., thee ae fou channel taps with the maximum powe in fou clustes. Since these taps contibute the most to the eceived powe, hee we study thei amplitude distibutions. Expeimental s of these channel taps ae shown in Fig. and Fig. 2 fo the vecto senso eceive and the scala aay eceive, espectively. The unit powe ayleigh e 2 is also shown in these figues, the dashed cuve labeled with. As expected, we obseve some deviations fom ayleigh distibution compaed to the naowband case. This is because the numbe of multipath components in some taps might be small and theefoe cental limit theoem is less likely to hold. Tap # Tap #26.8.8.6 P.4 Vx Vy.2 Vz 2 Tap #43.6 P.4 Vx Vy.2 Vz 2 Tap #66.8.8.6 P.4 Vx Vy.2 Vz 2.6 P.4 Vx Vy.2 Vz 2 Fig. s of the amplitudes of fou channel taps in all the channel impulse esponses of a vecto senso eceive at 9m. C. Wideband Channel Capacity Using eq. (7) and with N 2, aveage capacities of the vecto senso eceive and the scala aay eceive ae calculated fom measued data and ae shown in Fig. 3. The two systems appea to have nealy the same capacity. Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page 3 edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
Tap #4 Tap #29.8.8.6 P.4 P2 P3.2 P4 2 Tap #46.6 P.4 P2 P3.2 P4 2 Tap #67.8.8.6 P.4 P2 P3.2 P4 2.6 P.4 P2 P3.2 P4 2 Fig. 2 s of the amplitudes of fou channel taps in all the channel impulse esponses of a fouelement scala aay eceive at 9m. As a basic model, the aveage capacities of 4 wideband ayleigh fading with the multi-exponential PDPs given in (9) and () ae povided in Fig. 3. Each individual wideband L ayleigh channel is simulated accoding to a [ ] l l nl, in which L 5 accoding to the 2 measued data and a l is zeo-mean complex Gaussian whose powe E{ a l } is given by the associated PDP value [] l. Accoding to Fig. 3, wideband ayleigh capacity seems to be close to the measued wideband vecto senso capacity. V. CONCLUSION In this pape and using at-sea data, the channel statistics and capacity of a vecto senso eceive that measues the scala and vecto components of the acoustic field ae investigated. It is obseved that ayleigh fading and multi-exponential powe delay pofile models accuately chaacteize the aveage capacity of acoustic paticle velocity channels, measued by vecto sensos. The esults ae useful fo design and simulation of vecto senso communication systems in acoustic paticle velocity channels. Capacity s, noise distibutions and possible noise Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page 4 edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
coelations will be discussed in anothe pape. 5 Expeimental (vecto senso) Expeimental (scala aay) Simulation (vecto senso) Simulation (scala aay) Channel capacity (bits/sec./hz) 5 5 5 2 25 3 SN (db) Fig. 3 Wideband channel capacities at 9m. VI. ACKNOWLEDGEMENT This wok is suppoted in pat by the National Science Foundation (NSF), Gant CCF- 839. EFEENCE [] A. Abdi and H. Guo, A new compact multichannel eceive fo undewate wieless communication netwoks, IEEE Tans. Wieless Commun., vol. 8, pp. 3326-3329, 29. [2] A. Abdi, H. Guo and P. Sutthiwan, A new vecto senso eceive fo undewate acoustic communication, in Poc. Oceans, Vancouve, BC, Canada, 27. [3] D. B. Kilfoyle and A. B. Baggeoe, The state of the at in undewate acoustic telemety, IEEE J. Oceanic Eng., vol. 25, pp. 4-27, 2. [4] M. Stojanovic, High speed undewate acoustic communications, in Undewate Acoustic Digital Signal Pocessing and Communication Systems.. S. H. Istepanian and M. Stojanovic, Eds, Boston, MA: Kluwe, pp. -35, 22. Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page 5 edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
[5] A. Abdi, H. Guo, A. Song and M. Badiey, An oveview of undewate acoustic communication via paticle velocity channels: Channel modeling and tansceive design, in Poc. Meetings on Acoustics (59th Meeting of Acoustical Society of Ameica), Baltimoe, MD, 2. [6] A. Song, A. Abdi, M. Badiey, and P. Husky, Expeimental demonstation of undewate acoustic communication by vecto sensos, IEEE J. Oceanic Eng., vol. 36, pp. 454-46, 2. [7] H. Guo, A. Abdi, A. Song and M. Badiey, Delay and Dopple speads in undewate acoustic paticle velocity channels, J. Acoust. Soc. Am., vol. 29, pp. 25-225, 2. [8] A. Abdi and H. Guo, Signal coelation modeling in acoustic vecto senso aays, IEEE Tans. Signal Pocessing, vol. 57, pp. 892-93, 29. [9] M. Stojanovic, On the elationship between capacity and distance in an undewate acoustic communication channel, ACM SIGMOBILE Mobile Comput. Commun. ev., vol., pp. 34-43, 27. [] D. E. Lucani, M. Stojanovic and M. Medad, On the elationship between tansmission powe and capacity of an undewate acoustic communication channel, in Poc. Oceans, Kobe, Japan, 28. [] P. King,. Venkatesan and C. Li, A study of channel capacity fo a seabed undewate acoustic senso netwok, in Poc. Oceans, Quebec City, QC, Canada, 28. [2] T.C. Yang, Channel Q function and capacity, in Poc. Oceans, Washington, DC, pp. 273-277, 25. [3] M. Zatman and B. Tacey Undewate acoustic MIMO channel capacity, in Poc. Asiloma Conf. Signals, Systems, Computes, Pacific Gove, CA, pp. 364-368, 22. [4] M. B. Pote, The Makai expeiment: High fequency acoustics, in Poc. Euopean Conf. Undewate Acoustic, Cavoeio, Potugal, 26. [5] J. G. Poakis, Digital Communications, 4th ed., McGaw-Hill, 2. [6] A. adosevic, J. G. Poakis and M. Stojanovic, Statistical chaacteization and capacity of shallow wate acoustic channels, in Poc. Oceans, Bemen, Gemany, 29. [7] T. S. appapot, Wieless Communications: Pinciples and Pactice, 2nd ed., Pentice Hall PT, Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page 6 edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45
22. [8] A. adosevic, D. Fetonani, T. Duman, J. G. Poakis, and M. Stojanovic, Capacity of MIMO systems in shallow wate acoustic channels, in Poc. Asiloma Conf. Signals, Systems, Computes, Pacific Gove, CA, pp. 264-268, 2. [9] D. Tse and P. Viswanath, Fundamentals of Wieless Communication. Cambidge Univesity, 25. [2] E. Telata, Capacity of multi-antenna Gaussian channels, Euopean Tans. Telecommun., vol., pp. 585-595, 999. [2] M. Kang, and M.S. Alouini, Capacity of MIMO ician channels,, IEEE Tans. Wieless Comm. vol. 5, pp. 2-22, 26. [22] A. Paulaj,. Naba and D. Goe, Intoduction to Space-time Wieless Communications. Cambidge Univesity, 23. [23] A. F. Molisch, Wieless Communications. Wiley-IEEE, 25. Poceedings of Meetings on Acoustics, Vol. 4, 36 (22) Page 7 edistibution subject to ASA license o copyight; see http://acousticalsociety.og/content/tems. Download to IP: 72.79.5.74 On: Wed, 6 Jul 26 :2:45