PHASE CONJUGATION FOR UNDERWATER ACOUSTIC COMMUNICATIONS SŁAWOMIR JASTRZĘBSKI

Transcription

1 PHASE CONJUGATION FOR UNDERWATER ACOUSTIC COMMUNICATIONS SŁAWOMIR JASTRZĘBSKI Uiversity of Techology ad Agriculture i Bydgoszcz Kordeckiego 0, 85-5 Bydgoszcz, Polad s@ail.atr.bydgoszcz.pl I this paper a ultipath proble i shallow water acoustic chael ad phase cougatio techology will be preseted. Acoustic couicatios i shallow water had bee a difficult proble due to the characteristics of the uderwater acoustic chael. The shallow water chael is the eviroet which is of particular iterest to ay research workers ad presets a uber of challeges to the desigers of couicatios systes. Uderwater acoustic chaels are characterized by ultipath pheoeo whose characteristics are tie varyig. This is the aor factor that liits uderwater acoustic couicatios perforace. Couicatio systes ca be categorized as usig either icoheret or coheret odulatio strategies. This paper presets the phase cougatio techique, also called tie-reversal, which is the subect of active research i ay areas of acoustics. This is a ew ethod for coheret uderwater acoustic couicatio. Preliiary results cofir the potetial utility of the phase cougatio i uderwater acoustics with applicatios i uderwater couicatios. This ethod effectively itigates the ultipath propagatio ad ca be used to solve this proble. INTRODUCTION Over the last decade, acoustic phase cougatio or tie reversal has geerated steadily growig iterest i the uderwater research couity. TRM was origially developed usig ultrasoud i air. This ethod has uerous applicatios i edicie, o-destructive testig, geophysics, ad ow i uderwater acoustics. A series of carried out ocea acoustic experiets cofirig the robustess ad potetial utility of tie reversal irrors i uderwater acoustics with applicatios i active soar ad uderwater couicatios. Tie reversal ethod has applicatio i shallow water i the area of active soar [4], the echo-toreverberatio ehaceet [5], ad reverberatio ullig [5, 6]. I tie reversal acoustics a sigal is recorded by a array of trasducers, tie-reversed, ad the retrasitted ito the ediu. The retrasitted sigal propagates back through the sae ediu ad refocuses approxiately o the source.

2 TRM copesate for the ultipath propagatio that is coo i sea acoustics ad that liits the capacity of uderwater couicatios systes. The proble occurs i shallow water where soud travels as though i a waveguide. Acoustic sigals i shallow water orally iteract repeatedly with both the sea surface ad botto. A tie reversal irror i a ocea waveguide cosists of a vertical lie array of receivers ad trasitters. A probe sigal is trasitted fro a source at distace. The received sigal display a coplicated arrival structure ivolvig ay ultipaths specific to the shallow water waveguide. Whe the received sigals are tie reversed ad retrasitted ito the sea, the sea cobies the idividual ultipaths to produce a sigal close to the origial trasitted sigal at the probe source locatio. For uderwater acoustic couicatios ultipath arrivals cause iterferece betwee sybols resultig i sybol errors. Soeties a adaptive filter is used to reove such ultipath sigal. However if ay ultipath sigals are received, eve a adaptive filter caot reove all of the. Usig the sea to cobie the ultipath arrivals via a tie reversal process is a atural way to coduct uderwater couicatio [1]. The reflected ad refracted waves are coverged to focus i space ad tie ad the sigal level received at the focus icreases ad the sybol iterfereces are reduced. I the frequecy doai, tie reversal is equivalet to phase cougatio, which takes advatage of reciprocity, a property of wave propagatio i a static ediu ad a cosequece of the ivariace of the liear wave equatio to tie reversal []. Phase cougatio is a eviroetally self-adaptive process that ca fid applicatio i localizatio ad couicatio i coplex sea eviroets [3]. Tie reversal is a ovel for of acoustic couicatio that is based o spatial reciprocity ad tie syetry of the wave equatio. At the focal poit, tie reversal copresses dispersive acoustic eergy both i tie ad space. The teporal copressio recobies the dispersive ultipaths reducig itersybol iterferece. The spatial focus of the tie reversal process oderates the effect of chael fadig. Therefore, the receiver would ot eed spatial diversity. These two properties poit at tie reversal as a potetial ethod for couicatio [3]. 1. THE BASIC THEORY OF THE PHASE CONJUGATION TECHNIQUE Phase cougatio is syoyous with tie reversal i the tie doai. This is a twoway couicatios techique that first easures the chael respose with a PS, ad the trasits back the reversed couicatio sequeces. Tie reversal ethod ca be see as ipleetig a atched filter of the ipulse respose of the waveguide. Sigal x(t is trasitted fro a source i a waveguide, ad this sigal is covolved with the ipulse respose of the waveguide h i (t, ad the sigal y i (t=x(t*h i (t is received o the i-th eleet of the array of N source/receive trasducers (SRA. The SRA receives y i (t ad retrasits the tie reversed versio of the sigal, y i (-t. I this way tie reversal ipleets a liear atched filter givig the autocorrelatio of the ipulse respose of the waveguide. The sigal received back at the origial source locatio ca be writte as: N x (t = x ( t ( h( t h(t (1 r i= 1 i This equatio shows that quality of the tie reversal focus depeds o the uber of echoes received ad the uber of SRA eleets N. Fig.1 shows the basic geoetry for phase cougatio techique. A probe source seds out a pulse of soud. The array of source/receiver eleets records the coplicated arrival structure. The dispersed sigal with all its ultipath structure is tie reversed ad retrasitted by SRA ito the sea. The acoustic i i

3 eergy coverges to the origial PS depth ad rage. A vertical receive array (VRA is collocated with the PS to easure the vertical structure of the acoustic field. VRA PS SRA tie reversal VRA PS SRA Fig.1 Basic geoetry for phase cougatio techique. MATHEMATICAL FOUNDATIONS OF THE PHASE CONJUGATION I this sectio the basic of atheatical forulatios of phase cougatio i ragedepedet odel will be preseted [8]. Probe source is located a distace R fro the source/receive array. Poit source eits a tie-haroic wave of agular frequecy, which is deteried fro the Helholtz equatio: G (r;z,z + k (zg(r;z,z = δ(r r δ( z z ; k(z = ( c(z A oochroatic poit source with frequecy located at (r,z geerates a acoustic pressure field that ay be decoposed ito a su of oral ode fuctios: ( iπ / 4 ie φ(z φ(z (ikr G(r;z,z = e (3 ρ(z ( 8π r k where k are the odal wave ubers ad φ (z are the eigefuctios of eigevalue proble defied by the ordiary differetial equatio: d φ + [k (z k ] (z = 0 φ (4 dz The ode fuctios satisfy the depth eigevalue equatio at every rage poit ad are ortooral, i.e.: φ(z φ(z dz = δ (5 ρ(z 0 ad have a for: φ (z φ (zs = δ(z zs (6 ρ(z s

4 The phase cougatio process cosists of excitig the SRA sources by the coplex cougate of the received field G * (R;z. The resultig acoustic field trasitted fro the J sources i SRA satisfies the wave equatio: pc pc J P (r,z + k (zp (r,z = = 1 δ(z z The solutio of (7 is the volue itegral of the product of the Gree s fuctio as specified by ( ad the source ter of (7. For a vertical lie of discrete sources, the itegral reduces to a su over the source positios: P (r,z;r = pc J = 1 G (r;z,z The data are give by G (R;z,z ad the replica field by G w (r;z,z. P pc (r,z focuses at the positio of the probe source (R,z that was deostrated by substitute (3 ito (8, which specifies that over all odes ad array sources are sued: φ(z φ(z φ(z φ(z i(kr kr Ppc(r,z; e (9 ρ(z (z k k rr I case of a array which spas the alost whole water colu ad actually saples ost of the odes, the su of sources ay be approxiate as a itegral ad satisfy the orthoorality coditio (5. I this case the su over selects out odes = ad the equatio (9 siplifies to: φ(z φ(z ik(r R Ppc(r,z; e (10 ρ(z k rr G (R;z,z G (R;z 3. ACOUSTIC COMMUNICATION USING PHASE CONJUGATION A possible applicatio of phase cougatio techology is uderwater acoustic couicatio. For phase cougatio couicatios, the sigal fro the probe source, received o the source receiver array (SRA, will be tie reversed, odulated with a sigalig schee (e.g. BPSK ad trasitted ito the sea. The sigal arrivig at the probe source locatio should be free of itersybol iterferece ad the essage ca the be extracted fro the received data by siple deodulatio. The ai disadvatage of this ethod is that it requires the establishet of a two way lik. For phase cougatio couicatios to work, the ocea eeds to be statioary fro the tie the probe sigal is trasitted fro the probe source to the tie the back-propagated sigal is received by the probe source. A ew probe sigal will be required every tie the ocea eviroet chages. Phase cougatio ca be ipleeted i either a active or passive ode. For couicatio purposes, the ai differece betwee active ad passive ipleetatios is the directio i which the iforatio flows. I the active case, iforatio ca be set fro the array to a distat source, while i the passive case the source seds iforatio to the array. Active phase cougatio is the couicatio fro array to poit. It has bee ipleeted i the sea ad has also bee proposed as a ethod for couicatio [3, 7, 8]. I this techique pulses are trasitted fro source ad ext received at each eleet of the SRA ad tie reversed. This tie reversal pulses are ultiplied oe by oe with the sybols of digital data sequece ad i this way tie reversal sigals are coposed. These sigals are retrasitted fro each eleet of the SRA, ad the they coverge to the focus poit. I this tie reversal sigals trasitted fro the SRA, tie-reversal pulses are superiposed at a,z (7 (8

5 sybol rate, so that the sigal received at the focus is the sequece of pulses without ultipaths. That is alost the sae as the data sequeces to be set. Fig. showed the active phase cougatio process. source tie reversal array focused data tie reversal pulses Fig. Active phase cougatio process Aother way to achieve ultipath cobiatio is to use passive phase cougatio. As a ethod for couicatio this procedure is passive i that the array eed oly receive sigals ad does ot eed to trasit. Passive-phase cougatio for uderwater couicatios is carried out as follows. The process begis with trasissio of a sigle probe pulse fro the distat soud source ad receptio of the respose at each eleet of the array. The data strea is the trasitted by the soud source ad recorded by each eleet of the array. The sigal processig step ivolves cross correlatig the probe receptios ad data streas as observed at a array eleet. This cross correlatio is doe i parallel at each array eleet ad the results are sued across the array to achieve the fial couicatio sigal ready for deodulatio. As the ocea chages, it becoes ecessary to break up the data strea by isertig ew probe pulses [1]. The passive phase cougatio process is show i Fig.3. probe sigal data strea sigals received at the array trasit sigal... cross-correlatio cross-correlatio coheret suatio Fig.3 Passive phase cougatio process The probe pulse ad the data strea trasitted by the source are showed at the left side of the Fig.3. At the right side there are the probe ad data strea which are observed at each of the eleets i the receivig array. The true power i the techique coes fro usig the

6 spatial diversity provided by the array. The cross-correlatios are the coheretly sued across the array. 4. CONCLUSIONS This paper presets the properties of the phase cougatio process. This ethod ca have applicatio i active soar ad udersea couicatios. Phase cougatio techique potetially is a effective uderwater acoustic couicatios techique that reduces chael fadig i shallow water ad effectively deals with itersybol iterferece origiatig fro ultipath tie spread. This ethod is a stad aloe syste that requires o coputatioally itesive algoriths. I case of uderwater couicatios phase cougatio provides a possibility to ipleet space-tie ultiplexig i coplicated uderwater eviroet. REFERENCES [1] T.C. Yag, Differeces Betwee Passive-Phase Cougatio ad Decisio-Feedback Equalizer for Uderwater Acoustic Couicatios, IEEE Joural of Oceaic Egieerig, vol. 9, o., pp , April 004 [] T. Folegot, P. Billad, S. Tauvry, S. Hibral, L. Beriere, J. Rosy, D. Cloreec, J.G. Miozio, C. Prada, M. Fik, B. Celesti, Desig of a Tie Reversal Mirror for Mediu Scale Experiets, Oceas-Europe 005, pp , 005 [3] G.F. Edela, W.S. Hodgkiss., S Ki, W.A. Kupera, H.C Sog, T. Akal, Uderwater acoustic couicatio usig tie reversal, Oceas 001, Hawaii, pp , 001 [4] H.C Sog., P. Roux, T. Akal, G.F Edela, W. Higley, W.S. Hodgkiss, W.A. Kupera, K. Raghukuar, M. Steveso, Tie reversal ocea acoustic experiets at 3.5 khz: Applicatios to active soar ad udersea couicatios, High Frequecy Ocea Acoustics, La Jolla, CA, 004 [5] S. Ki, W.A. Kupera, W.S. Hodgkiss, H.C. Sog, G. Edela, T. Akal, Echo-to- Reverberatio ehaceet usig a tie reversal irror, JASA 115, pp , 004 [6] H.C. Sog, S. Ki, W.S. Hodgkiss, W.A. Kupera, Eviroetally adaptive reverberatio ullig usig a tie reversal irror, JASA 116, pp , 004 [7] G.F. Edela, T. Akal, W.S. Hodgkiss, S. Ki, W.A. Kupera, H.C. Sog, A iitial deostratio uderwater acoustic couicatio usig tie reversal, IEEE Joural of Oceaic Egieerig, vol. 7, pp , 00 [8] W. A. Kupera,W. S. Hodgkiss, H. C. Sog, T. Akal, C. Ferla, D. R. Jackso, Phase cougatio i the ocea: Experietal deostratio of a acoustic tie-reversal irror, J. Acoust. Soc. Aer., vol. 103, o. 1, pp. 5 40, 1998