Design and Analysis of a High-Rate Acoustic Link for Underwater Video Transmission

Transcription

1 Desgn and Analyss of a Hgh-Rate Acoustc Lnk for Underwater Vdeo Transmsson by Konstantnos Pelekanaks Dploma, Electrcal Engneerng (001) Techncal Unversty of Crete, Greece Submtted to the Department of Ocean Engneerng In Partal Fulfllment of the Requrements for the Degree of Master of Scence n Ocean Engneerng at the Massachusetts Insttute of Technology June Massachusetts Insttute of Technology. All rghts reserved. Sgnature of Author... Department of Ocean Engneerng May 7, 004 Certfed by... Dr. Mlca Stojanovc Prncpal Scentst, MIT Sea Grant College Program Thess Supervsor Accepted by... Mchael Trantafyllou Professor of Ocean Engneerng Charman, Department Commttee on Graduate Studes

2 Desgn and Analyss of a Hgh-Rate Acoustc Lnk for Underwater Vdeo Transmsson by Konstantnos Pelekanaks Submtted to the Department of Ocean Engneerng on May 7, 004 n Partal Fulfllment of the Requrements for the Degree of Master of Scence n Ocean Engneerng ABSTRACT A hgh bt rate acoustc lnk for underwater vdeo transmsson s examned. Currently, encodng standards support vdeo transmsson at bt rates as low as 64 kbps. Whle ths rate s stll above the lmt of commercally avalable acoustc modems, prototype acoustc modems based on phase coherent modulaton/detecton have demonstrated successful transmsson at 30 kbps over a deep water channel. The key to brdgng the remanng gap between the bt-rate needed for vdeo transmsson and that supported by the acoustc channel les n two approaches: use of effcent mage/vdeo compresson algorthms and use of hgh-level bandwdth-effcent modulaton methods. An expermental system, based on dscrete cosne transform (DCT) and Huffman entropy codng for mage compresson, and varable rate M-ary quadrature ampltude modulaton (QAM) was mplemented. Phase-coherent equalzaton s accomplshed by jont operaton of a decson feedback equalzer (DFE) and a second order phase locked loop (PLL). System performance s demonstrated expermentally, usng transmsson rate of 5000 symbols/sec at a carrer frequency of 75 khz over a 10 m vertcal path. Excellent results were obtaned, thus demonstratng bt rates as hgh as 150 kbps, whch are suffcent for real-tme transmsson of compressed vdeo. As an alternatve to conventonal QAM sgnalng, whose hgh-level constellatons are senstve to phase dstortons nduced by the channel, M-ary dfferental ampltude and phase shft keyng (DAPSK) was used. DAPSK does not requre explct carrer phase synchronzaton at the recever, but nstead reles on smple dfferentally coherent detecton. Recever processng ncludes a lnear equalzer whose coeffcents are adjusted usng a modfed lnear least square (LMS) algorthm. Smulaton results confrm good performance of the dfferentally coherent equalzaton scheme employed. Thess Supervsor: Mlca Stojanovc Ttle: Prncpal Scentst, MIT Sea Grant College Program

3 Table of contents 1 Introducton Motvaton Coherent detecton for underwater acoustc channels Dfferentally coherent detecton Compresson technques for low bt-rate mage/vdeo codng Expermental systems Thess overvew Theory....1 JPEG mage compresson.... Underwater acoustc channels Bandwdth-effcent vs. power-effcent modulaton methods Jont adaptve equalzaton and phase estmaton for coherent detecton Dfferental Ampltude Phase Shft Keyng (DAPSK) modulaton and detecton Adaptve equalzaton for dfferentally coherent detecton Expermental descrpton Experment setup System descrpton Results Expermental results for phase coherent detecton Smulaton results for dfferentally coherent detecton Concluson Accomplshments Future work Bblography

4 Lst of Fgures Fgure 1: Autonomous Oceanographc Samplng Network [1]...8 Fgure : Block dagram of a JPEG encoder []....3 Fgure 3: Encodng and zgzag scannng []....8 Fgure 4: Sound propagaton paths n deep water....3 Fgure 5: Absorpton rate of acoustc energy n seawater [5]...35 Fgure 6: Shadow zone due to surface ductng...36 Fgure 7: Bandwdth effcency as a functon of SNR/bt (for constant P e =10-5) [6] Fgure 8: Recever structure for jont equalzaton and synchronzaton based on [5]...40 Fgure 9: Constellaton dagram of the 4x16DAPSK modulaton scheme...48 Fgure 10: Block dagram of the dfferentally coherent recever based on [11]...51 Fgure 11: Transducers wth pressure housng...56 Fgure 1: The transducers mounted on a 10m pole Fgure 13: Experment setup Fgure 14: Sgnal framng...58 Fgure 15: Block dagram of the transmtter and the recever...59 Fgure 16: Sgnal constellatons based on coherent detecton...60 Fgure 17: Sgnal constellatons based on dfferentalyl coherent detecton Fgure 18: 8PSK nput/output scatter. Input SNR/bt = 43 db...63 Fgure 19: 16QAM nput/output scatter. Input SNR/bt = 4 db...64 Fgure 0: 3QAM nput/output scatter. Input SNR/bt = 43 db...64 Fgure 1: 64QAM nput/output scatter. Input SNR/bt = 41dB...65 Fgure : (a) orgnal frame, (b) 16:1 compresson rato, (c) :1 compresson rato and (d) 30:1 compresson rato...67 Fgure 3: BER versus 10log 10 (E b /N o ) for the coherent and noncoherent x8dapsk recever...69 Fgure 4: BER versus 10log 10 (E b /N o ) for the coherent and noncoherent 4x4DAPSK recever...70 Fgure 5: BER versus 10log 10 (E b /N o ) for the coherent and noncoherent x16dapsk recever...70 Fgure 6: BER versus 10log 10 (E b /N o ) for the coherent and noncoherent 4x8DAPSK recever...71 Fgure 7: BER versus 10log 10 (E b /N o ) for the coherent and noncoherent 4x16DAPSK recever

5 Lst of Tables Table 1: Lumnance quantzaton table []...6 Table : Generaton of the ampltude s gven s -1 and the nformaton bts c 5 and c Table 3: Acheved bt rate and bandwdth effcency for all modulaton methods

6 Acknowledgements I gratefully acknowledge the patence and assstance of my advsor, Dr. Mlca Stojanovc and the support of Prof. Chryssostomos Chryssostomds, the drector of the MIT Sea Grant Program. Fundng for ths thess was suppled by the MIT Sea Grant College Program, NA16RG55 and the department of Ocean Engneerng. I thank Lee Fretag and Keenan Ball from WHOI for helpng me conduct the experments usng ther equpment. Thanks also to the AUV Lab engneers, Rob Damus, Jm Morash, Sam Desset for ther assstance throughout my thess work. I am very grateful to my former advsor Prof. Manols Chrstodoulou from the Techncal Unversty of Crete, Greece, who nspred me to pursut graduate studes n the USA. My father, mother and my younger brother John have been steadfastly behnd me all the way. Gve me where to stand, and I wll move the earth. Archmedes, 300 B.C. 6

7 Chapter 1 1 Introducton 1.1 Motvaton In the recent years, there has been an ncreasng nterest n underwater acoustc (UWA) communcatons brought by the growng need for wreless transmsson of nformaton for applcatons such as polluton montorng, remote control of submerged devces and collecton of scentfc data recorded n moored statons wthout retrevng the nstruments. The problem of real-tme wreless vdeo transmsson from an underwater vehcle to a surface platform represents one of the last mlestones n the development of autonomous systems for ocean exploraton and montorng. The majorty of today s underwater magery s obtaned by transmttng sgnals va optcal cables. However, cables lmt the operatonal range and maneuverng capablty. Advances n UWA communcatons make the transmsson of wreless vdeo sgnals possble, thus leadng to the vson of an autonomous oceanographc 7

8 samplng network (Fgure 1), a collecton of bottom-mounted nstruments and free-swmmng devces that provdes remote and almost nstantaneous access to oceanographc data. Fgure 1: Autonomous Oceanographc Samplng Network [1]. A partcular scenaro of nterest to ths work s transmsson over a vertcal channel at depths between several tens and several hundreds of meters. Ths scenaro s relevant to applcatons where an Autonomous Underwater Vehcle (AUV) s overshadowed by an Autonomous Surface Craft (ASC) so that the two reman n communcaton over a nearvertcal lnk. Vertcal transmsson mnmzes multpath propagaton so that the achevable bt rate s lmted only by the system bandwdth. 8

9 Vdeo transmsson nvolves large amount of data, whch must be compressed pror to transmsson n order to reduce the bt rate that s presented to the acoustc channel. The objectve of ths work s to demonstrate the capablty to acoustcally transmt dgtal sgnals over an underwater channel at rates that are suffcently hgh to accommodate real-tme vdeo nformaton. The challenge encountered n achevng ths goal s that the data rate requred for vdeo transmsson s hgh as compared to the avalable system bandwdth. Currently avalable commercal acoustc modems provde transmsson rates up to several kbps. For example, the Benthos acoustc modem operates at rates between 0.1 kbps and.4 kbps. Whle these rates may be suffcent for navgaton and control, data rates that are at least ten, f not a hundred tmes hgher are requred for reasonable qualty vdeo transmsson. 1. Coherent detecton for underwater acoustc channels The bt rate avalable over an UWA channel s lmted by the system bandwdth. For example, long range systems operatng over several tens of klometers are confned to few khz of bandwdth, medum range systems operatng over several klometers are lmted to tens of khz of bandwdth, whle only short range systems operatng over several tens of meters may have more than a hundred khz. Wthn ths lmted bandwdth, the sgnal s subject to dstortons caused by multpath propagaton. Whle n rado channels a typcal multpath spread spans a few symbol ntervals, the UWA channels suffer from extended multpath propagaton whch usually ncreases wth range, and, dependng on the sgnalng rate, causes the ntersymbol nterference to span up to several tens of symbol ntervals. 9

10 Consequently, bandwdth effcency of canddate systems becomes an mportant ssue n UWA communcatons. FSK (frequency shft keyng) modulaton, whch has been favored for underwater channels due to ts robustness to phase dstorton, neffcently uses the bandwdth, and, consequently, s not sutable for hgh data rate applcatons. To fully utlze the lmted system bandwdth and ncrease the speed of data transmsson, bandwdth-effcent sgnalng based on hgh-level PSK and QAM modulaton methods must be employed. Phase-coherent detecton systems, necessary for PSK/QAM modulatons, are based on adaptve equalzaton and synchronzaton technques, whch have been used n the majorty of hgh-rate acoustc communcaton lnks [],[3]. A representatve system based on phasecoherent modulaton operates over 60 m range at a carrer frequency of 1 MHz usng 15 khz bandwdth and achevng data rate of 500 kbps [4]. Ths system s used for communcaton wth an undersea robot whch performs mantenance of a submerged platform. A 16QAM modulaton scheme was used and the performance s aded by an adaptve LMS equalzer. The work by Stojanovc et al. [5] s based on an effectve algorthm that combnes decson feedback equalzaton wth a second-order PLL. Transmssons were made n long-range deep water (110 nautcal mles, 660 b/s), long-range shallow water (48 nautcal mles, 1kbps) and short-range shallow water ( nautcal range, 10kbps). Ths technque also forms the bass of the DSP mplementaton n the WHOI Utlty Acoustc Modem, whch has been successfully tested n a great number of horzontal acoustc channels over the past several years. Recently, the WHOI modem operaton was also demonstrated over a 3000 m deep vertcal lnk, where successful operaton was acheved at 15 kbps [6]. In the last two applcatons, the modulaton methods used were 4PSK or 8PSK. Thus, the maxmum bandwdth effcency of 3 b/s/hz was acheved. 10

11 1.3 Dfferentally coherent detecton The mplementaton and operaton of a coherent recever s, n general, a complex process nvolvng fne tunng of the PLL parameters that change from one acoustc channel to another. In many applcatons, smplcty and robustness of mplementaton take precedence over achevng the best possble performance. In these cases, dfferental detecton, whch obvates the need for explct phase synchronzaton offers an attractve alternatve to coherent detecton. Asde from mplementaton smplcty, dfferentally coherent detecton may offer a more robust performance wth hgh-level sgnal constellatons. As an alternatve to bandwdth-effcent modulaton methods, a multlevel dfferental modulaton technque, the so-called Dfferental Ampltude and Phase Shft Keyng (DAPSK) s nvestgated. DAPSK encodes nformaton n the sgnal phase and ampltude relatve to the prevous symbol, a strategy that leads to smple recever structure, at the expense of hgher bt error rate. The problem of concurrent dfferentally coherent detecton and equalzaton necessary for multpath channels s addressed n the early work by Seher and Kaleh [7], later by Masoomzadeh-Farad and Pasupathy [8] and more recently by Schober et al. [9]-[11]. These methods have not been consdered prevously for underwater channels. Below, a bref summary of the exstng solutons s gven. In [7], a lnear equalzer followed by the dfferentally coherent detector s employed. The tap coeffcents of the equalzer are adjusted to mnmze the mnmum square error (MSE) obtaned after dfferental detecton. The system of equatons to solve s of 3 rd order, as opposed to coherent recepton, preventng drect applcaton of stochastc gradent-based 11

12 algorthms such as LMS. To crcumvent ths dffculty, the tap coeffcents are consdered to be constant from one symbol nterval (teraton) to another. Then, the system of equatons becomes lnear yeldng a modfed LMS algorthm. Effectvely, the equalzer s appled to the nput sgnal pre-multpled by the complex conjugate of the prevously estmated symbol, whch accounts for dfferentally coherent phase compensaton pror to equalzaton. In [8] two recevers were mplemented: one based on lnear equalzaton and another based on nonlnear equalzaton both compatble wth DPSK sgnals. For lnear equalzers, a modfed recursve least squares (RLS) algorthm was consdered usng the same approach of lnearzng the post-detecton error as n [7]. For severe channel degradatons (.e. for channels wth spectral nulls), the authors proposed to perform dfferentally detecton frst, followed by a DFE. However, ths approach generates addtonal nonlnear dstorton and s not optmal. Scober et al. consdered both lnear equalzaton [9], [11] and nonlnear equalzaton schemes [10]. The nonlnear scheme, whch s compatble wth DPSK sgnals, ncludes a DFE followed by a dfferental demodulator and s optmal because maxmum-lkelhood sequence estmaton (MLSE) s appled to the nput sgnal contanng lnear ISI; thus, t can approach the performance of a coherent MMSE-DFE arbtrarly close. The lnear scheme of [9], whch s sutable for M-ary DPSK, approaches a coherent lnear MMSE equalzer and the lnear scheme of [11], whch s sutable for M-ary DAPSK, approaches a zero-forcng equalzer. The mprovement stems from generatng a reference symbol at the output of the equalzer to track the carrer-phase of the receved sgnal pror to demodulaton. The reference symbol s generated from N prevously detected symbols and as N tends to nfnty, optmum carrer reference s obtaned. Hence, these methods approach the performance of coherent detecton. When the reference symbol s generated from a sngle prevous observaton (N=1), the lnear 1

13 equalzer [9] reduces to that of [7]. For an effcent recursve adaptaton of the equalzer coeffcents, a modfed LMS and a modfed RLS are developed. 1.4 Compresson technques for low bt-rate mage/vdeo codng Vdeo transmsson over underwater acoustc channels requres extremely hgh compresson ratos. The approach currently favored by most of the expermental underwater mage transmsson systems s that of transmttng a sequence of stll mages. In ths approach, each mage from a sequence s encoded ndependently. Encodng s performed n an effcent manner to provde a certan compresson rato. The standard method for mage codng s the transform doman codng, usng the dscrete cosne transform (DCT). In ths method, the mage s frst transformed nto a set of DCT coeffcents. By elmnatng the (spatal) redundancy between pxels, ths transformaton provdes energy compacton,.e., the number of coeffcents needed to represent the mage s generally much smaller than the number of orgnal pxel levels. An alternatve to transform doman codng s subband codng. In ths approach, a dscrete wavelet transform (DWT) s taken, whch effectvely decomposes the sgnal (pxel levels) nto subbands of unequal length, where each subband s represented by ts transform coeffcents. In ths manner, subbands that contan more nformaton can be represented more precsely, thus achevng energy compacton. The coeffcents (DCT or DWT) are quantzed, usng, n the smplest form, a scalar quantzer. Vector quantzaton can be appled nstead to groups of coeffcents, to ultmately 13

14 provde better compresson. Fnally, the quantzed levels are encoded, usng an effcent method such as entropy codng n whch the levels that occur most frequently are represented by fewest bts. The resultng frame of bts s then transmtted. It s, of course, desrable to support as hgh a frame rate as possble. Commonly, t s requred to have a frame rate on the order of 10 frames per second for an acceptable vdeo qualty. Vdeo compresson s dfferent from compresson of stll mages n that t consders the ncremental dfference between mages, rather than compressng each mage ndvdually. In vdeo compresson, the frst mage of a sequence s transmtted as usually, but from then on, only the dfference between mages s encoded and transmtted. Because there s temporal redundancy among adjacent mages n a vdeo, the dfferental nformaton can be transmtted at a lower rate for the same vdeo qualty. Ths approach s analogous to Dfferental Pulse Code Modulaton (DPCM) used for voce transmsson, and many of the same deas that were orgnally developed for voce transmsson apply to vdeo as well. Moton-compensated predcton s a method frequently used for low-bt-rate vdeo codng. In ths method, further gans n compresson are acheved by encodng the dfference between the mage and ts predcted value, rather than the dfference between the current and prevous mage. Predcton s performed n an optmal manner based on the hstory of mages. The coeffcents of the predcton flter are then transmtted along wth the encoded sgnal. The encodng of the predcton error sgnal s performed usng any of the usual mage codng methods. Durng the past several years, there has been a prolferaton of work n the doman of lowbt-rate mage codng, drven largely by the demand for vdeo conferencng over bandlmted channels both wrelne and wreless. ITU standards H.63 and the efforts of MPEG-4 group 14

15 are concerned wth vdeo transmsson at bt rates below 64 kbps. Codng and decodng algorthms that use reduced sze mages and reduced frame rates to comply wth bt-rate requrements as low as 9.6 kbps are commercally avalable, although the software s often propretary. In addton, there s on-gong research on vdeo codng algorthms whose desgn targets a pre-specfed bt-rate on the order of 10-0 kbps. For example, reference [1] descrbes a compresson scheme that transmts 144x176 pxel mages, wth 8 bts/pxel and 10 frames/sec usng 16 kbps. Bt rates n ths range can be well supported by a carefully desgned acoustc lnk. Despte the advances n low bt rate codng for vdeo transmsson over bandlmted channels, all but the most recent expermental underwater systems rely on encodng of stll mages usng JPEG prncples. JPEG s a standard method for mage compresson that s based on DCT, scalar quantzaton and Huffman codng. 1.5 Expermental systems The frst system to demonstrate mage transmsson over a vertcal path was developed n Japan [13]. The JPEG standard DCT was used to encode 56x56 pxel stll mages wth bts per pxel. Transmsson of about one frame per 10 seconds was acheved usng 4-DPSK at 16 kbps. The remarkable results obtaned wth ths system ncluded a vdeo of a slowlymovng crab, transmtted acoustcally from a 6,500 m deep ocean trench. Another vertcalpath mage transmsson system was developed n France and successfully tested n,000 m 15

16 deep water [14]. Ths system was also based on the JPEG standard and used bnary DPSK for transmsson at 19 kbps. More recently, an mage transmsson system has been developed n a Portuguese effort called ASIMOV [15]. In ths project, a vertcal transmsson lnk s secured by a coordnated operaton of an AUV and an ASC. Once the ste s chosen and the vehcles are postoned, transmsson of a sequence of stll mages of about frames/sec s accomplshed at 30 kbps usng an 8PSK modulaton method. Whle the approach of stll mage codng suffces for many underwater applcatons, mprovements are avalable from dedcated algorthms whch combne mage codng wth moton compensaton and predcton. The most recent expermental underwater vdeo transmsson system, developed n Japan [16], employs 4PSK, 8PSK and 16QAM sgnals wth 40 KHz bandwdth to acheve transmsson at up to 18 kbps. The system uses 100 khz carrer frequency and was tested over a short vertcal path of 30 m. The MPEG-4 standard was employed for vdeo compresson, and a frame rate of 10 frames/sec was supported. Effcent compresson can be acheved f there s a-pror nformaton avalable about the mages to be taken. Algorthms that explot the propertes nherent specfcally to underwater mages are such an example. Because underwater mages have low contrast, ther nformaton s concentrated at low frequences. Thus, by decomposng the mage nformaton nto low and hgh frequency subbands, and encodng the low bands wth more precson, t s possble to acheve hgher compresson ratos. Ths s the basc motvaton behnd the work n [17] whch used the DWT n place of the standard DCT. The DWT s combned wth entropy-constraned vector quantzaton (ECVQ) and moton-compensated predcton to acheve an average of 0.08 bts/pxel. Ths algorthm was appled to a sequence of underwater mages, taken at 30 16

17 frames per second, each havng 56x56 8-bt pxels. The acheved compresson rato of 100:1 provded very good qualty monochrome vdeo. The resultng bt rate needed to support such hgh qualty s on the order of 160 kbps, whch surpasses the capabltes of the current acoustc modem technology. However, the algorthm s equally applcable to reduced-sze mages. For example, a 144x176 pxel mage would requre 60 kbps wth 30 frames per second, or 0 kbps wth 10 frames per second. These values are approachng the capabltes of an acoustc modem, provded that a bandwdth-effcent modulaton/detecton scheme s used. Another system that explots wavelet-based compresson together wth motoncompensaton s proposed n [18]. Although t attans approxmately the same compresson rato (100:1) as n [17], t has better vsual ntellgblty because t employs a generalzed dynamc mage model (GDIM) that decouples the geometrc and photometrc varatons n an mage sequence commonly encountered n deep sea magery. Ths approach s n contrast wth ordnary terrestral moton-compensated algorthms, where steady and unform llumnaton s the underlyng assumpton. Usng 18x18 pxel frames and 30 frames/sec, the resultng bt rates needed to support real-tme vdeo transmsson s of the order of 40 kbps. The tradtonal methods descrbed above fall nto the category of hybrd methods, because they combne mage compresson wth moton compensaton. A dfferent approach s emergng n the form of model-based vdeo compresson methods. These methods explot the a-pror knowledge of shapes that appear n a partcular vdeo segment. A unque example s the algorthm proposed n [19], whch s desgned especally to capture the bubble emsson process from hot vents. Because they rely on the assumptons about a model, these algorthms have lmted applcablty; however, they can yeld hgh compresson ratos. At the moment, 17

18 custom-desgn of compresson algorthms for real-tme transmsson of underwater vdeo remans an open research area. 1.6 Thess overvew From the above dscusson, t s evdent that even after massve compresson, vdeo sgnals requre bt rates that are relatvely hgh accordng to the current standards of underwater acoustc modems. The key to achevng vdeo transmsson over the band-lmted underwater channels les n two approaches: 1. Effcent vdeo compresson.. Use of hghly bandwdth-effcent modulaton methods. The goal n combnng these two approaches s to close the gap between the bt rate needed for vdeo transmsson and that supported by the acoustc channel. The focus of ths thess s on the second approach. Hgher-level modulaton methods effcently use a fxed transmsson bandwdth by allocatng several bts of nformaton to a sngle transmtted symbol. In ths manner, several bts per second are transmtted per Hz of occuped bandwdth. The modulaton methods that can acheve ths come from the class of M-ary QAM and M-ary PSK methods, whch requre coherent detecton at the recever. For example, an 8PSK symbol carres 3 bts of nformaton, whle a 16QAM symbol carres 4 bts of nformaton. Over horzontal channels, where multpath propagaton causes strong nterference, these methods also requre sophstcated sgnal processng for equalzaton. For ths reason, ther 18

19 applcaton so far has mostly focused on the basc, bnary and quaternary PSK methods. In contrast, the vertcal path represents a better qualty communcaton channel, whch can be expected to support hgher-level modulaton schemes, thus makng full utlzaton of the bandwdth-effcent sgnalng. However, ths fact has not been exploted n the exstng systems that are often lmted to 8PSK sgnals. In comparson, some telephone channels and mcrowave rado lnks today use modulatons wth 56 levels. The focus of ths work s on the desgn and expermental demonstraton of hgh-level bandwdth-effcent modulaton methods wth bandwdth effcency greater than 3 bts/s/hz. As the number of bts per symbol ncreases, the performance, measured n terms of bt error probablty, degrades. However, the hgh sgnal to nose rato of a shallow or moderately deep vertcal channel and the modest bt error probablty requrement of mage transmsson offer favorable condtons for a trade-off between bandwdth-effcency and performance. The major concern n usng a hgh-level sgnal constellaton s ts senstvty to phase jtter and tme-varyng channel response. Whle the vertcal channel exhbts lttle multpath, vertcal moton due to waves causes substantal Doppler effects [0]. These effects are evdent both n the carrer phase varaton and n pulse compresson/dlaton. The frequency offset caused by vertcal moton cannot be assumed constant as the drecton of the moton changes n tme. In choosng the modulaton method, t s not only the constellaton sze that plays a role n the sgnal desgn, but also the constellaton shape. The conventonal shapes that are easy to mplement are the crcular shape of PSK and the square shape of QAM methods. In addton to these shapes, there are sgnal constellatons that are potentally more robust to the channel mparments. One such class of constellatons s the DAPSK (star shaped QAM), n whch concentrc crcles contan PSK-shaped sgnal ponts. These sgnals have been found to 19

20 provde mproved performance n stuatons wth dffcult phase trackng and sgnal level varaton [1]. The mprovement s based on dfferental sgnal encodng, n both ampltude and phase, whch permts dfferentally coherent demodulaton, thus elmnatng the need for explct phase trackng and gan control. In ths thess, a system employng varable rate modulaton based on coherent (M-ary QAM) or noncoherent (M-ary DAPSK) detecton was mplemented n software and tested over a 10 meter vertcal path usng transducers wth 5 khz bandwdth and center frequency of 75 khz. The system was used to transmt an underwater vdeo clp, encoded as a sequence of stll mages usng standard JPEG codng. Packet synchronzaton s acheved by matchedflterng to a 8-bt Barker sequence. Recever processng ncludes two optons: 1. Phase synchronzaton and channel equalzaton usng jontly optmzed decsonfeedback equalzer and decson-drected phase estmator. The weghts of the equalzer are adjusted by an adaptve algorthm (RLS or LMS) and second order dgtal PLL.. Dfferentally coherent detecton wth lnear channel equalzaton usng modfed LMS algorthm. All the equalzers were mplemented as fractonally spaced to elmnate the need for explct symbol delay trackng [5]. Excellent results were obtaned, thus demonstratng bt rates as hgh as 150 kbps, whch are suffcent for real-tme transmsson of qualty compressed vdeo. The thess s organzed as follows. In Chapter 1, an overvew s gven of the exstng work on coherent and dfferentally coherent equalzaton as well as ther applcatons n underwater vdeo transmsson over underwater acoustc channels. Chapter presents the theoretcal background of the JPEG standard, of the modulaton technques employed at the transmtter and of the sgnal processng employed at the recever. Chapter 3 descrbes the expermental 0

21 system. Results of data processng are gven n Chapter 4. Fnally, Chapter 5 summarzes conclusons and drectons for future work. 1

22 Chapter Theory.1 JPEG mage compresson The goal of a stll-mage-codng algorthm s to explot spatal redundancy among neghborng pxels thereby reducng the sze of the -D data set. A popular approach s transform doman codng n whch the orgnal data s projected onto a set of bass functons such that a large number of the transform coeffcents contan lttle energy. By zerong out the coeffcents deemed nsgnfcant and effcently codng the remanng coeffcents, the orgnal data set becomes compressed. Vdeo compresson can be regarded as an extenson to the stll mage compresson problem snce dgtal vdeo s composed of a sequence of mages. The man dfference between the two problems s that vdeo may be compressed at much hgher rates snce temporal correlaton exsts among pxels across the frames of the sequence. A common mage compresson standard s JPEG. Accordng to ths standard, an mage s parttoned nto 8x8 non-overlappng pxel blocks form left to rght and top to bottom. Each

23 block s DCT coded, and the 64 transform coeffcents are quantzed to the desred qualty. The quantzed coeffcents are entropy-coded and output as part of the compressed mage data. Fgure llustrates the JPEG compresson algorthm. Each 8-bt sample s level shfted by subtractng 18 before beng DCT coded. The 64 DCT coeffcents are then unformly quantzed accordng to the step sze of a gven quantzaton matrx. Entropy codng s accomplshed n two stages. The frst stage s the translaton of the quantzed DCT coeffcents nto an ntermedate set of symbols. In the second stage, each symbol s dvded nto two parts; a varable length code (VLC) s assgned to the frst part (symbol 1), followed by a bnary representaton of the ampltude for the second part (symbol ). Fgure : Block dagram of a JPEG encoder []. 3

24 .1.1 Data compresson usng DCT The DCT s an orthogonal transform wth bass sequences that are cosnes; thus t s closely related to the DFT. In the development of the DFT, a perodc sequence s frst formed by appendng an nfnte number of shfted replcas of the fnte length sequence x[n] n such a way so that x[n] can be unquely recovered. Smlarly, snce cosnes are perodc and even functons, the DCT corresponds to formng a perodc and even sequence from x[n] n such a way so that x[n] can be unquely recovered. Snce there are many ways do to ths, the DCT has many defntons. The most commonly used s: X DCT [ k] = 1 x[ n] = N N 1 k = 0 N 1 n= 0 πk(n + 1) x[ n]cos( ), N β[ k] X DCT πk(n + 1) [ k]cos( ), N 0 k N 1 0 n N 1, 1/, k = 0 β[ k] = 1, 1 k N 1 (1) For a real sequence x[n], 0 n N-1, the DCT coeffcents X DCT [k] are real numbers whle the DFT coeffcents are, n general, complex, provdng a sgnfcant advantage of the DCT method n the case of data compresson algorthms. The relatonshp between DCT and DFT s developed n [3]: X DCT [ k] = Re j k /(N) { X [ k] e }, k = 0,..., N 1 DFT π () where X DFT [k] s the N-pont DFT of the N-pont sequence x[n] defned as follows X DFT [ k] = N1 n= 0 x[ n] e jπkn /(N ), k = 0,...,N 1 (3) The DCT s preferred to DFT n many data compresson algorthms because of ts energy compacton property. Wth respect to the DFT, the DCT of a fnte length sequence often has ts coeffcents hghly concentrated at low ndces. Ths means that one can force to zero many 4

25 hgh-ndexed coeffcents wthout a sgnfcant mpact on the energy of the sgnal. The energy compacton property can be ntutvely justfed by observng that the perodc, symmetrc expanson of a fnte-length sgnal often results n a smoother sgnal than ts smple perodc expanson producng low energy content at hgh frequences. Explotng the close relatonshp between the DCT and the DFT, fast algorthms such as the Fast Fourer Transform (FFT) can be used to compute the DFT n equaton () makng the DCT a very effcent method for data compresson. In mage compresson, the -D DCT s used whch s a separable transform, meanng the transform can be performed on each dmenson ndependently. Therefore, one can frst apply the 1-D DCT to the rows and then to the columns of a pxel matrx or vce versa. Ths property sgnfcantly reduces the complexty of the mplementaton..1. Quantzaton Accordng to Fgure above, the quantzaton block s used to lmt the range of the transform coeffcents. Ths block gves the compresson gan for the system; however, t ntroduces loss at the same tme. There are many quantzaton schemes used n the lossy mage compresson. The JPEG recommends a quantzer smlar to the optmal unform quantzer, but desgned specfcally for the block-based DCT coeffcents. Each frequency n the transformed block has a specfc quantzaton level. These levels are derved from expermental results based on many mages n order to gve the best vsual qualty for a gven bt rate. Table 1 contans the recommended quantzaton levels for the lumnescence 5

26 component accordng to the JPEG standard. The top left corner corresponds to the quantzaton level for the DC component. The bottom rght hand corner s the quantzaton level for the hghest frequency component of the transform coeffcents n -D. If the elements of the quantzaton table are represented by Q(u,v), then a quantzed DCT coeffcent wth the horzontal and the vertcal spatal frequences of u and v, F q (u,v), s gven by F( u, v) F q ( u, v) = (4) Q( u, v) where F(u,v) s the transform coeffcent value pror to quantzaton. At the decoder the quantzed coeffcents are nverse quantzed by to reconstruct the quantzed coeffcents. F Q q ( u, v) = F ( u, v) Q( u, v) (5) Table 1: Lumnance quantzaton table []. 6

27 .1.3 Entropy codng The entropy coder translates values or symbols nto a strng of bnary dgts. The encoder used n ths project s the run-length Huffman encoder confgured for JPEG. The run-length Huffman coder combnes regular Huffman codng wth the modfcatons of the quantzed coeffcents to acheve hgher compresson. Ths coder separates the coeffcents nto two parts: DC (commonly referred to as (0,0) coeffcent) and the 63 AC coeffcents. Each type s coded usng a dfferent method as shown n Fgure. The general concepts are descrbed below. The DC coeffcents have a very large range. For an 8-bt per pxel mage, the DC coeffcent les n the nterval [-047, 047]. Ths range requres 1 bts to represent. However, the value of the DC coeffcents of the adjacent blocks are close to each other because most mages are smooth and do not change abruptly. The DC coder uses dfferental pulse code modulaton (DPCM) to frst compute the dfference between adjacent blocks, and then encodes the dfference, as can be seen n Fgure 3. The separate treatment of DC coeffcents explots the correlaton between the DC values of adjacent blocks. Also, the DC coeffcents are encoded more effcently as they typcally contan the largest porton of the mage energy. The Huffman codeword for the DC coeffcents can be separated nto two parts: the category and the resdue. The category (CAT) s determned by the range of magntude of the DIFF (see Fgure 3) and s then varable length coded usng Huffman codng. The resdue s determned by the sgn and the ampltude of the DIFF. The CAT after beng varable length coded s appended wth addtonal bts to specfy the actual DIFF values 7

28 (ampltude). The Huffman table for the DC coeffcents of the DCT JPEG can be found n []. Fgure 3: Encodng and zgzag scannng []. As explaned prevously, the quantzed AC coeffcents of the DCT are lkely to be zeros at hgh frequences. The run-length coder counts the maxmum number of zeros before encounterng a non-zero coeffcent. The scannng method used for the AC coeffcents s called zgzag scan and s llustrated n Fgure 3. The maxmum number of zero-run code word s 16. Each non-zero coeffcent s represented n combnaton wth the run-length (consecutve number) of zero-valued coeffcents, whch precede t n the zgzag sequence. Each such run-length/non-zero-coeffcent combnaton s presented by a par of symbols: Symbol-1 (RUNLENGTH, CAT) Symbol- (AMPLITUDE) 8

29 Symbol-1 represents two peces of nformaton, RUNLEGTH and CAT. Symbol- represents a sngle pece of nformaton, whch s smply the ampltude of the non-zero coeffcent. RUNLEGTH s the number of the consecutve zero-valued coeffcents n the zgzag sequence precedng the non-zero coeffcent beng represented. CAT s determned by the range of magntude of the ampltude. The end of block (EOB) s used f the rest of the scannng coeffcents are zeroes. The run-length Huffman table coder for the AC coeffcents can be found n [].. Underwater acoustc channels Sound propagaton through sea water s affected by many factors. Vertcal gradent of sound speed causes refracton of rays, sometmes n a way that prevents recepton n certan locatons known as shadow zones. Also, the sgnal s subject to random fluctuatng Doppler shfts and spread because of surface and nternal wave moton. In addton, there exst multple propagaton paths from transmtter to recever n most underwater propagaton geometres. In deep water these paths are descrbed as rays or wavegude modes and n shallow water as reflectons from dscrete scatterers. Receved sgnal fluctuatons occur from medum fluctuatons along a sngle path (mcromultpath) and tme-varant nterference between several propagaton paths (macromultpath) [0]. The mechansms that cause dstortons to sgnals transmtted through the UWA channel are summarzed below. 9

30 ..1 Sngle-Path Fluctuaton From the vewpont of buldng a robust communcaton recever, the questons of prmary nterest are the types of ocean acoustc channels wth fluctuaton levels suffcently low to permt coherent sgnalng n order to acheve greater data throughput. Low fluctuaton geometres can be determned by nvestgatng regons where the Rytov approxmaton for weak scatterng holds [0]. The Rytov method yelds perturbaton log-ntensty and log-phase varance parameters: I + I I c ln (6) c where I c s the ntensty of the nonfluctuatng feld component and I s the fluctuatng (noncoherent) feld ntensty. For weak fluctuatons I c»i, so that I 1 = (7) I γ c where γ s a measure of acoustc fluctuatng ntensty defned as the rato of coherent to noncoherent feld ntensty. It s customarly accepted that the Rytov approxmaton s vald f <0.3 whch s also close to the phase trackng lmt for the coherent phase-locked loop [0]. The Rytov approxmaton valdty regon depends on the channel geometry and there s a strong expermental evdence of rapd system degradaton wth ncreasng transmsson angle from the vertcal [0]. For nstance, the deep-water vertcal path s amenable to coherent modulaton and several coherent systems currently exst [6], [13]. 30

31 .. Multpath The mechansm of multpath formaton depends on the channel geometry and also on the frequency of transmtted sgnals. Understandng of these mechansms s based on the theory and models of sound propagaton. Fgure 4 llustrates the dfferent sound propagaton paths n deep water. Two prncpal mechansms of multpath formaton are reflectons from the boundares (bottom, surface and any objects n the water) and ray bendng. In shallow water propagaton largely occur n surface-bottom bounces n addton to a drect path and reflectons from other boundares, f any. Trappng of sound rays n the mxed layer through repeated surface reflecton and upward refracton due to the slghtly postve sound speed gradent creates the so-called surface duct. In deep water, there s a regon n the water column where sound speed frst decreases wth depth to a mnmum value and then ncreases wth depth. At that depth sound s trapped n the SOFAR (SOund Fxng And Rangng) channel wavegude and can travel extreme dstances wthout bouncng on the bottom or the surface. For steeper transmsson angles sound s not ducted n the sound channel but s refracted downward and then back up agan to the surface focusng n one regon. Typcal length of the so-formed convergence zone s km. Multpath propagaton gves rse to extended temporal sgnal spreadng n the ocean. The SOFAR channel has characterstc multpath spread from tens of mllseconds to several seconds. A commonly encountered multpath spread of 10 msec n medum-range shallow water channels causes the ISI to extend over 100 symbols f 10 khz s the transmtted sgnal bandwdth. At short ranges, reflectons from objects and channel boundares domnate the 31

32 multpath; the problem becomes geometrc specfc and no generc solutons are avalable [0]. D e p t h Sound Speed Drect Path Bottom Bounce Sound Channel Surface Duct Convergence Zone Fgure 4: Sound propagaton paths n deep water...3 Temporal varablty A tme-varyng multpath channel s characterzed by the tme spread T m and the Doppler spread B d. T m s the tme over whch most of the channel mpulse response des off, and B d s the ncrease n the frequency content of a receved sgnal over that whch was transmtted. The channel coherence tme s that tme over whch the mpulse response of the channel remans essentally constant. A smple approxmaton to the channel coherence tme s 3

33 T coh 1/B d. The channel spread factor s defned as the product T m B d. These values must be compared wth the correspondng sgnal parameters, T the symbol duraton and W 1/T the sgnal bandwdth. Channels whch do not ntroduce tme dsperson are those for whch T»T m. Channels whch are slowly varyng are those for whch B d «W. In a moble communcaton system relatve moton between the transmtter and the recever ntroduces addtonal Doppler spreadng and shftng. The tme and frequency dsperson of the UWA channel affects the selecton of sgnalng rate. Sgnalng at a low rate elmnates ISI but allows for hgh channel varaton from one symbol nterval to another. Sgnalng at a hgh rate results n ISI but also results n slower channel varaton over the symbol duraton. Ths allows an adaptve recever to effcently track the channel on a symbol to symbol bass. Thus, there s a trade-off n the choce of the sgnalng rate for a specfc channel. The trade-off n the choce of the sgnalng rate may be llustrated n the followng case. In shallow water, the domnant mechansm leadng to Doppler spreadng s the surface scatterng caused by waves. In [4], the estmated Doppler spread for telemetry systems s expressed as 4πf + 0 cosθ 1 h c = 0 Bw fw w (8) where w s the wnd speed, f w s the wave frequency, f 0 s the carrer frequency, θ 0 s the ncdent grazng angle, c s speed of sound and h w s the r.m.s. wave heght. Doppler spread can be estmated usng the followng emprcal formulas whch relate the frequency and the wave heght to the wnd speed: 33

34 f h w w = / w = 0.005w.5 (9) For example, consder the case where B w =10 Hz and the sgnal bandwdth s 1/T=1 khz. Then, the normalzed Doppler spread s B w T=10 - whch approaches the lmtng value for relable coherent detecton [3]. However, ncreasng the bandwdth reduces B w T; thus, phase coherent detecton s assured, provded a method for dealng wth the resultng ISI...4 Ambent nose Ambent nose strongly affects the receved SNR. The power spectral densty of ambent nose usually decays by 0 db/octave, thus t dctates the mnmum frequency lmt of the transmtted sgnal bandwdth. Ambent nose level depends on the ste of operaton, as well as on the presence of equpment, people, and marne organsms. Ar bubbles generated by waves or ran are the man cause of ambent nose n the 10-0 khz band [0]...5 Sound Attenuaton Attenuaton of the receved sgnal level s affected by range, frequency and channel wavegude propertes. Havng the range fxed, the rule of thumb to fnd the carrer frequency of transmsson s to use the followng equaton: absorpton rate range = 10 db [5]. In Fgure 5, the absorpton rate (db/km) versus frequency n seawater s llustrated. Clearly the 34

35 absorpton rate ncreases wth frequency; hence t dctates the maxmum frequency lmt of the transmtted sgnal bandwdth. Fgure 5: Absorpton rate of acoustc energy n seawater [5]. Moreover, transmsson loss depends on the channel wavegude propertes. There are shadow zones,.e. regons where data telemetry s nfeasble due to the excessve transmsson loss nduced by energy refracton. Fgure 6 shows the shadow zone caused by the splttng of the lmtng ray (defnes the deepest ray that remans n the mxed layer and the shallowest that escapes to the thermoclne) at the sonc layer depth (SLD). All rays transmtted at smaller angles reman n the mxed layer and all rays transmtted at greater angles escape to the 35

36 thermoclne. The depth at whch the lmtng ray reaches vertex speed s defned as the SLD. Theoretcally, no sound should enter the shadow zone, but some does due to scatterng and dffracton. Fgure 6: Shadow zone due to surface ductng.3 Bandwdth-effcent vs. power-effcent modulaton methods The choce of a sgnalng method n a communcaton system depends on the avalable bandwdth and SNR. A meanngful comparson of modulaton methods s based on the normalzed data rate (or bandwdth effcency) R b /W, whch s measured n bts per second per Hertz of occuped bandwdth. In a typcal communcaton system the data arrves at a rate of R b bts/sec and s converted nto a sequence of symbols chosen from the symbol constellaton of sze M. Thus, each symbol carres log M of nformaton. The symbol rate s R=R b /log M 36

37 symbols/sec and the symbol nterval s T=1/R. The requred bandwdth s W 1/T. The bandwdth effcency for M-ary PSK or M-ary QAM modulaton s R b /W=log M. Note that f a hgher-level symbol constellaton s used, for fxed bandwdth, the bt rate s ncreased. Orthogonal sgnalng, e.g. FSK, behaves dfferently as bandwdth ncreases. If the M orthogonal sgnals are constructed by means of orthogonal carrers wth mnmum frequency separaton 1/T for orthogonalty (1/T for noncoherent detecton), the bandwdth requred for transmsson s W 1 M = T log M = M R b (10) so as M ncreases the bandwdth-effcency decreases. Fgure 7 shows the graph of the normalzed data rate R b /W (bts/sec/hz) versus SNR per bt for PAM, PSK and QAM and orthogonal sgnals for the AWGN channel and for the case n whch the error probablty s Note that n the case of PAM, PSK and QAM, R b /W ncreases for ncreasng M at the cost of hgher SNR per bt. Consequently, these modulaton methods are approprate for bandwdth-lmted systems when R b /W>1 s desred, provded that there s suffcent SNR to accommodate greater M. In contrast, M-ary orthogonal sgnals are approprate for systems operatng when R b /W<1. These sgnals are effcent for powerlmted channels (low SNR regmes) provded that there s enough bandwdth to accommodate the large number of sgnals. As M, the error probablty can be made as small as desred provded that that the SNR/bt>-1.6 db. Ths s the result of Shannon s capacty theorem [6]. Fgure 7 llustrates the normalzed channel capacty of the bandlmted AWGN channel whch s expressed as 37

38 C C Ε b = log 1+ (11) W W N0 where E b s the energy per bt and N o s the nose power spectral densty. The rato C/W represents the hghest achevable bt rate to bandwdth rato. Therefore, t serves as the upper bound on the bandwdth effcency of any type of modulaton. Fgure 7: Bandwdth effcency as a functon of SNR/bt (for constant P e =10-5) [6]. 38

39 .4 Jont adaptve equalzaton and phase estmaton for coherent detecton The vertcal underwater channel s bengn n comparson to the horzontal channel, prmarly due to the lack of boundary nteracton. Whle vertcal channels exhbt lttle tme dsperson, horzontal channels suffer from extended multpath propagaton that may cause the ISI to span up to several tens of symbol ntervals. Moreover, the receved sgnal undergoes carrer offset due to the relatve moton of the source and recever. In addton, the channel mpulse response vares wth tme, causng ampltude and phase dstorton. A soluton to the ISI problem s to desgn a recever that employs an equalzer whch compensates or at least reduces ISI n the receved sgnal. The optmum, from the probablty of error vewpont equalzer s based on the maxmum-lkelhood (ML) sequence detecton [6]. The major shortcomng of ths structure s ts complexty, whch grows exponentally wth the length of the delay dsperson, makng t mpractcal for hgh symbol rates when the channel response spans more than a few symbol ntervals. A suboptmum type of channel equalzer whch crcumvents the complexty problems s an adaptve decson feedback equalzer (DFE). Conventonal systems perform carrer phase recovery by usng a PLL structure and channel equalzaton separately. However, ths approach may not be well suted for a rapdly changng medum because resdual phase fluctuatons mpar the performance of the equalzer and may cause the problem of equalzer tap rotaton. Therefore, jont carrer phase estmaton and adaptve equalzaton has been developed and shown to be an effectve soluton for many underwater channels [5]. The recever structure s shown n Fgure 8. 39

40 u ( t + N ) 1T s T s τˆ ( k) { a * ( )} N k N1 p(k) ˆ e j θ ( k ) PLL d ˆ( k ) e(k) Decson Devce ~ d ( k ) Synchronze usng known channel probe q(k) { * M b ( k)} 1 Traned or Decson Drected Adaptve Flter Update Algorthm Error sgnal Fgure 8: Recever structure for jont equalzaton and synchronzaton based on [5]..4.1 Recever algorthm The receved sgnal, after beng brought to baseband and lowpass fltered, s frame synchronzed by matched flterng to a known channel probe. Then, the receved sgnal can be modeled as jθ( t) u(t) = d( k) h(t kt τ)e + w(t) (1) k where {d(k)} are the transmtted symbols taken from an M-ary constellaton, 1/T s the symbol rate, h(t) ncludes the physcal channel and any transmt and receve flterng and the delay uncertanty τ s wthn one symbol nterval after coarse synchronzaton n tme. The carrer phase θ(t) can be modeled as a sum of three terms: constant phase offset, varable Doppler shft and random phase jtter. w(t) s whte Gaussan nose. Past and future symbols cause the ISI, so a delay of N 1 samplng ntervals s ntroduced at the recever. The N=N 1 +N +1 tap weghts of the feedforward lnear transversal flter are 40

41 arranged n a row vector α and the nput vector at the n-th tme nstance stored n the feedforward flter s gven as T u k) = [ u( kt + N T + τ )... u( kt N + τ )]. (13) ( 1 s T s where T s =T/ (Nyqust rate). The output of the feedforward flter s produced once per symbol nterval yeldng: ˆ k p ( k ) ( k ( ) ) H ( k ) e j θ = a u. (14) where H denotes conjugate transpose. The feedback flter has tap weghts b and operates on the sequence of M prevously detected symbols collected n the vector ~ ~ ~ T d ( k) = [ d k 1... d k M ]. (15) The output of the feedback flter whch estmates the resdual ISI s expressed as ~ q( k) = b( k) H d ( k) (16) Ths estmate s subtracted from the output of the feedforward flter to produce the overall estmate of the data symbol d(k) whch s: dˆ ( k) = p( k) q( k) (17) By quantzng the estmate ˆ ~ d ( k ) to the nearest symbol value, the decson d ( k) s formed. In the MSE crteron, the recever parameters are adjusted to mnmze the mean square value of the error: e( k) = d( k) dˆ( k). (18) In the decson-drected mode, d(k) should be replaced by ~ d ( k ). The equatons that gve the gradent of the MSE wth respect to all the recever parameters are gven n [5] and are reproduced below for convenence: 41

42 E( e( k) α E( e( k) b E( e( k) ˆ θ E( e( k) ˆ τ ) = E ) = E ) = Im ) = Re * ( u( k) e ( k) ) ( ~ * d ( k) e ( k) ) e j ˆ θ * { E( p( k)( d( k) + q( k) ) } * { E( p& ( k) e ( k) )} (19) where and u&(k) ˆ k p ( k ) ( k ( ) ) H ( k ) e j θ & = a u&, (0) s the tme dervatve of the receved sgnal. Settng the gradents equal to zero results n the set of equatons whose soluton represents the jontly optmal soluton of channel equalzaton and phase synchronzaton. Snce the optmal values of the recever parameters are tme varyng we seek to obtan a soluton to the system of equatons n a recursve manner. To obtan the necessary trackng of the carrer phase estmate, a second order update equaton s used based on the analogy of the dgtal PLL but usng the expresson of the gradent of the MSE wth respect to the carrer phase n (19). The update equatons for the carrer phase estmate are: ˆ( θ k k + 1) = ˆ( θ k) + K1Φ( k) + K = 0 * Φ( k) = Im { p( k) ( d( k) + q( k) ) } Φ( ) (1) where K 1 and K are the proportonal and ntegral trackng constants. A good rule of thumb s K =K 1 /10. Two commonly used adaptve algorthms that produce the vector coeffcents update equatons are the least mean squares (LMS) algorthm and the recursve least squares (RLS) algorthm. 4

43 Update equatons for the LMS algorthm The update equatons for the LMS algorthm are derved n [7]: * c ( k + 1) = c( k) + µ e ( k) U( k), k = 0,1,... () where a( k) c ( k) = (3) b( k) s the composte weght vector, e(k) s gven n (18) and u( k) e U( k) = d( k) j ˆ( θ k ) (4) s the composte data vector. µ s a step sze parameter of the LMS algorthm. The ntal convergence rate s strongly nfluenced by the channel spectral characterstcs, whch are related to the egenvalues of the receved sgnal covarance matrx. If the egenvalue rato λ max /λ mn (condton number) s close to unty the equalzer converges to ts optmum tap coeffcents relatvely fast. On the other hand, f the channel exhbts poor spectral characterstcs, the egenvalue rato λ max /λ mn»1 and hence the convergence rate of the LMS algorthm wll be slow. A good rule of thumb to determne µ s by the followng equaton [6]: 0.5 µ = (5) ( N + N + 1 M ) 1 + P R where P R denotes the receved sgnal-plus-nose power, whch can be estmated from the receved sgnal. 43

44 Update equatons for the RLS algorthm The prce pad for the smplcty of the LMS algorthm s the slow convergence. Besdes allowng for shorter tranng perods, fast convergence s desred on rapdly changng channels snce t enables the recever to make full use of only temporarly present multpath components. The update equatons for the RLS algorthm are derved n [7]: 1) ( ) ( ) ( 1) ( ) ( ) ( ) ( 1) ( ) ( 0,1,... ) ( 1) ( ) ( ) ( ) ( 1) ( ) ( 1 ) ( 1) ( ) ( * = + Κ = = = + = Κ k k k k k k a k k k k k k k d k a k k k k k k H H H R U Κ R R c c U c U R U U R λ λ λ λ (6) where c(k) and U(k) are gven n (3) and (4) respectvely and the correlaton matrx R(k) s defned as = = k H k k R 1 ) ( ) ( ) ( U U λ (7) The applcablty of the RLS algorthm requres the ntalzaton of the recurson by choosng R -1 (0)=δ I (δ s a small postve constant) that assures the nonsngularty of the correlaton matrx. The use of the forgettng factor λ s ntended to ensure that data n the dstant past are forgotten n order to accommodate the tme varatons of the channel. λ s a postve constant close to, but less than 1. An adaptve algorthm has two sources of msadjustment error. The frst one s the estmaton nose of correlaton matrx that arses from computng estmates based on wndowed data sequences. The second one s lag nose caused by the reacton tme of the adaptaton algorthm to changes n ts envronment. Lag error s mnmzed by rapdly 44

45 dscountng the past observatons and computng estmates predomnantly based on recent data. These two errors place conflctng demands on the adaptaton algorthm. The estmaton nose s reduced by choosng λ close to 1; however, n the nonstatonary stuaton, the lag error s mnmzed by choosng a small forgettng factor. The optmzaton of the combnaton of these two errors requres a trade-off n the choce of λ..5 Dfferental Ampltude Phase Shft Keyng (DAPSK) modulaton and detecton In ths secton, we dscuss a multlevel dfferental modulaton technque, namely the DAPSK technque. The reason for consderng ths technque s that dfferental modulaton technques appear robust aganst carrer-phase varatons of the receved sgnal wthout requrng any carrer recovery. Moreover, a dfferental modulaton technque doesn t requre any explct knowledge about the channel propertes n the dfferental demodulaton process f flat fadng s assumed. It requres, however, that the channel remans relatvely constant over two consecutve symbol ntervals [8]. In ts generalzed form, the transmtter uses a star constellaton wth N concentrc ampltude rngs, each contanng M phasors and sequentally encodes nformaton onto the ampltude rato and phase dfference between current and prevously transmtted symbols. We refer to ths scheme as NxM DAPSK. The transmtted bt stream s frst grouped nto a sequence of real-valued pars {( β, γ ), =,0, 1,, } n whch β {0, 1,, N-1} and γ {0, 1,, M-1}. All N M possble pars are assumed equally lkely and Gray codng s used for bnary 45

46 representatons of β and γ. The pars ( β, γ ) are then used to determne the ampltude rato and phase dfference between current and prevous transmtted symbols. Wth α>1, the th transmtted complex-valued symbol s s gven by s β j(π / M ) γ = λa e (8) where Ν λ = Ν( α 1) /( α 1) (9) s used to normalze the sgnal constellaton to unt energy. In equaton (8), β and γ ndcate the ampltude and phase levels of s respectvely, and are related to ( β, γ ) by β = (β -1 + β ) mod N γ = (γ -1 + γ ) mod M (30) Note that the NxM DAPSK wth N=1 corresponds to the M-ary DPSK modulaton. Assumng a flat fadng stuaton, the effect of the channel s analytcally descrbed by a complex multplcaton: r = s h (31) where r s the receved -th data symbol. For a QAM modulaton/demodulaton technque, an estmaton of the channel transfer factor h would be necessary; however n the dfferental demodulaton process, the recever forms the rato between r and r -1 : ˆ r sh h d = = = s (3) r s h h where 46

47 s = a e ( β β1 ) j(π / M )( γ γ 1 ) (33) If we assume that the channel changes neglgbly over two consecutve symbols,.e., h h -1, no channel estmaton s necessary, thus reducng the complexty of the recever. The dfferental demodulaton (3) yelds dˆ s. The phase and ampltude reference n the demodulaton process s known by the prevously receved state r-1; therefore, we can decode the transmtted bts by observng s. As an example, consder the 4x16DAPSK wth four dfferent ampltude levels and 16 dfferent phase states. The symbol constellaton s shown n Fgure 9 below. It conssts of four concentrc crcles wth ncreasng ampltude values λ, λα, λα, λα 3. On each crcle there are 16 dfferent phase states. The par ( β, γ ) s calculated from the 6-bt bnary nput sequence (c 1, c,, c 6 ). The nformaton of the frst four bts (c 1,, c 4 ) s mapped to one of the 4 = 16 possble phase states postoned on a sngle rng. Thus, γ {0, 1,, 15} and adjacent phase states n the constellaton dagram have a phase dfference of π/16. The nformaton remanng n the two bts c 5 and c 6 s used for the transton among the possble ampltude levels n the constellaton. Snce there are = 4 possble ampltude states, then β {0, 1,, 3}. In order to construct the symbol constellaton shown n Fgure 9 the transton between the dfferent phase and ampltude states s calculated from (30) where N=4 and M=16. Although the phase transtons are drectly appled as n 16DPSK, the ampltude transtons among the four rngs must be appled n a cyclc manner. From (33), observe that (β -β -1 ) {-3, -, -1, 0, 1,, 3} so seven dfferent ampltude ratos can occur related to seven possble transtons among the four dfferent ampltude rngs n the constellaton dagram. Table llustrates the 47

48 procedure. The ampltude s s calculated by the two bts c 5 and c 6 and the ampltude s -1 of the prevously transmtted symbol. Fgure 9: Constellaton dagram of the 4x16DAPSK modulaton scheme. Informaton bts c 6 and c 5 s s -1 = λ 1 α α α 3 s -1 = λα 1 α α 1/ α s -1 = λα 1 α 1/α 1/ α s -1 = λα 3 1 1/α 3 1/ α 1/ α Table : Generaton of the ampltude s gven s -1 and the nformaton bts c 5 and c 6. 48

49 The ampltude factor α between two adjacent ampltude crcles s a system parameter. In [8], the ampltude factor has been optmzed for the AWGN channel n order to mnmze the bt error rate and has been calculated as α=1.4. The ampltude factor characterzes the dstance between the ampltude rngs and addtonally nfluences the average power of all complex states on the constellaton. Note that the two propertes have opposte effect on the resultng bt error rate. In the dfferental demodulaton process the bnary nformaton s obtaned from the complex state d ˆ (see equaton (33)). For the phase decson, only the phase of dˆ s of nterest. Thus, the complex plane s dvded nto 16 sectors correspondng to the 16 possble values (πm/16, m=0,, 15) of the phase of s and the estmated phase s quantzed nto the closest possble value. The two bts c 5 and c 6 are recovered from the magntude of dˆ. The decson rule s the followng: f s s 1 = 1 then : 1, a, = a, 3 a, f d f d f d f d (1 + a) / f (1 + a) / f ( a + a f ( a + a ) / 3 ) / and s and s ( a + a ( a + a ) / 3 ) / f s s 1 = a then : 1 a, 1, = a, a, f d f d f d f d ( a f ( a 1 1 f (1 + a) / f ( a + a + 1) / + 1) / ) / and and s s (1 + a) / ( a + a ) / 49

50 = = = = 1) / ( f 1, 1) / ( and ) / ( f, ) / ( and ) / ( f, ) / ( f, then : f ) / (1 f, ) / (1 and 1) / ( f 1, 1) / ( and ) / ( f, ) / ( f, then : f a d a s a a d a a a s a a d a a a d a s a s a d a a s a d a s a a d a a a d a s a s f f f f f f (34).6 Adaptve equalzaton for dfferentally coherent detecton DFE s an effcent, practcal approach for the transmsson of hgh speed data over slowly varyng, fadng multpath channels. For slow channel varatons, the tap weghts of a conventonal adaptve equalzer remove the phase dfference between the transmtter and recever clocks and the carrer phase doesn t have to be recovered. For fast channel varatons, however, the conventonal DFE cannot compensate for carrer phase. One approach to solve ths problem s to ncorporate a PLL at the recever whch s a complex process nvolvng many ancllary functons assocated wth the carrer synchronzaton loop. An easer way to mtgate carrer phase varatons s to employ noncoherent sgnalng such as DAPSK and a correspondng recever based on dfferentally coherent detecton. Ths choce reduces the computatonal complexty at the recever at the expense of hgher probablty of error. 50

51 The combnaton of a lnear equalzer and a decson-aded dfferental detector that works for both N-DPSK and NxM-DAPSK has been proposed n [11]. Usng the equalzer output sgnal, a reference symbol s generated recursvely or nonrecursvely. For adaptaton of the equalzer coeffcents a modfed LMS algorthm s mplemented. Fgure 10 llustrates the recever structure employed for dfferentally coherent detecton [11]. r ( t + N ) 1T s { c * ( )} N k N1 e(k) q (k) d(k) reference symbol (k) q ref ( ) 1 Decson Devce sˆ ( k) Fgure 10: Block dagram of the dfferentally coherent recever based on [11].6.1 Recever algorthm In ths secton, the dfferentally coherent equalzer of Schober et al [11] s descrbed. The DAPSK symbols s(k) (see (8)) are transmtted over the UWA channel and the baseband equvalent receved sgnal at the nput of the fractonally spaced equalzer s modeled as 51

52 u( t) = s( k) h( t kt ) e k jθ ( t) + w(t) (35) where T s the symbol nterval, h(t) s the combned mpulse response of the cascade of transmt flter, channel, and recever nput flter. The unknown carrer phase s denoted as θ(t). w(t) s whte Gaussan nose. Past and future symbols cause ISI so a delay of N 1 samplng ntervals s ntroduced at the recever. The N=N 1 +N +1 tap weghts of the lnear transversal flter are arranged n a row vector c and the nput vector at the n-th tme nstance stored n the equalzer s gven as T u ( k ) = [ u( kt + N1Ts )... u( kt N T s )] (36) where T s =T/. It s assumed that proper tme algnment has been acheved so that ths sgnal contans sgnfcant contrbutons from the data symbol s(k). The output of the flter s produced once per symbol nterval yeldng: q( k) = c( k) H u( k). (37) The next stage of the recever s a decson-aded dfferental detector whch determnes the estmate ŝ(k) for the transmtted symbol s(k)=s(k)/s(k-1). To do so, a reference symbol s generated recursvely as qref ( k ) q( k 1) + W * sˆ ( k 1) qref ( k 1) = (38) W 1+ sˆ( k 1) where W, W 0 s a desgn parameter. Alternatvely, the reference symbol may be generated nonrecursvely as: 5

53 q m1 v= 1 ref ( k 1) = m1 v1 v1 1 q( k v) * µ = 1 sˆ ( k µ ) 1 sˆ( k µ ) v= 1 µ = 1 (39) where m s the number of equalzer output symbols used to determne ŝ(k). Note that for m=, q ref (k-1)=q(k-1),.e., the prevous equalzer output symbol s employed to provde a phase and ampltude reference for the current equalzer output q(k). Ths reference s used for conventonal dfferental detecton [7]. Snce q(k-1) s a nosy reference, the performance of the resultng noncoherent recever s worse than that of a coherent recever that assumes perfect knowledge of the ampltude and phase reference. In order to allevate ths problem, m equalzer output symbols may be used to mprove the phase and ampltude reference. The decson varable for estmaton of ŝ(k) s gven by d( k) = q ref q( k) ( k 1) (40) and the decson rules are descrbed n Secton.5. The equalzer mnmzes the varance of the post-detecton error: e( k) = sˆ( k) qref ( k 1) q( k). (41) Ths error s used to determne the equalzer vector c accordng to the MMSE crteron. However, an unconstraned mnmzaton of E{ e(k) } yelds the all zero vector c=0. Therefore a unty energy constrant s ntroduced,.e., c H c=1. An effcent soluton can be obtaned usng the stochastc gradent approach. The adaptve gradent algorthm s obtaned from 53

54 cˆ ( k + 1) = c( k) µ e( k). * (4) c ( k) and cˆ( k + 1) c ( k + 1) = (43) cˆ( k + 1) where µ s the adaptaton step sze parameter and s equal to the step sze parameter of the conventonal LMS algorthm. Equaton (43) ensures that the unty energy constrant s satsfed. Note that q ref (k-1) depends only on c(k-v), v 0 but not on c(k). Therefore, t has to be treated lke a constant when dfferentatng wth respect to c(k). Hence, (4) s rewrtten to ˆ * c( k + 1) = c( k) + µ e ( k) u( k) (44) Note that e * (k)r(k) s not a functon of θ therefore the resultng modfed LMS algorthm s noncoherent. 54

55 Chapter 3 3 Expermental descrpton 3.1 Experment setup The experment took place at the Woods Hole Oceanographc Insttuton (WHOI) dock. Two electroacoustc transducers were used. One acted as the sound projector and the other as the hydrophone. The transducers have a 6 concal beampattern provdng approxmately 5 khz of usable bandwdth centered at 75 khz. Fgure 11 llustrates the two RD Instruments Long Ranger transducers used for the experment. Fgure 1 shows a 10 m pole, on whch the two transducers were mounted. The pole was vertcally submerged, wth the recever meters below the surface, and the transmtter at the lower end. Also at the lower end, a ROS 0/0 underwater camera was attached provdng the nput vdeo frames to the system for transmsson. The gray-scale vdeo had the followng specfcatons: 15 frames/sec, 144x176 pxels/frame and 8 bts/pxel. 55

56 Fgure 11: Transducers wth pressure housng. Fgure 1: The transducers mounted on a 10m pole. 56

57 All the sgnal processng was mplemented n Matlab, runnng on two laptop computers. Both of the laptops were connected wth the transducers through a Natonal Instruments DAQ Card-606E whch was used for dgtal-to-analog and analog-to-dgtal converson of the sgnals used durng the experment. The laptop connected wth the sound projector had also an Imperx VCE-B5A01 frame grabber whch was used to acqure the frames from the camera and then to delver them to the routne responsble for data compresson. Fgure 13 shows the expermental set-up and llustrates the hardware nterconnectons. 110 A/D BPF Rx 3 o 10 m 011 D/A AMP Tx Frame Grabber C Fgure 13: Experment setup. 3. System descrpton Transmsson was organzed n packets of fxed duraton. Each packet contaned 4158 data symbols, and an addtonal block of tranng data. The tranng sequence was generated as a 57

58 pseudo-random bnary sequence, mapped nto the same sgnal constellaton as the rest of the data block. Each data block was preceded by a synchronzaton probe whch was a 8-bt Barker code and a guard tme whose duraton need not be longer than the expected multpath spread. The desgn parameters used n the experment, 500 tranng symbols and 50 ms guard tme, were chosen wth a larger-than-necessary safety margn. Fgure 14 llustrates how the symbols are organzed nto a packet. Sequental packet transmsson was employed so as to provde perodc frame synchronzaton and retranng for the equalzer. The transmsson rate was 5000 symbols/sec for all the modulaton methods consdered. For all the data packets, average transmsson power per bt was equal. The passband samplng rate was 00 khz (8 samples/symbol). probe sgnal tranng data data 50 ms 500 symbols 4158 symbols 50 ms Fgure 14: Sgnal framng. The system block dagram s shown n Fgure 15. At the nput to the system are 8-bt grayscale 144x176-pxel vdeo frames, whch are frst compressed usng a selected method. In the current mplementaton, frames n the vdeo sequence are compressed ndvdually, by applyng the JPEG algorthm. The resultng bt stream s mapped nto the symbols of desred sgnal constellaton. The followng have been mplemented: 1. 8PSK, 16QAM, 3QAM and 64QAM for use wth coherent detecton 58

59 . 4x4DAPSK, x8dapsk, 4x8DAPSK, x16dapsk and 4x16DAPSK for use wth dfferentally coherent detecton The sgnal constellatons for the frst and second modulaton methods are llustrated n Fgure 16 and Fgure 17 respectvely. After addton of tranng data and organzng transmsson n packets, transmtter flterng s performed usng a rased cosne pulse wth roll-off factor 0.5 and truncaton length of ±4 symbol ntervals. The sgnal s then modulated onto the carrer and passed to the output stages of the transmtter. The receved sgnal, after A/D converson s shfted to baseband, low-pass fltered and down-sampled to samples/symbol. Packet coarse synchronzaton s acheved by matchedflterng to the 8-bt Barker sequence. Adaptve flterng by a T/ fractonally-spaced equalzer s used. For coherent detecton, jont decson feedback equalzaton and phase trackng s employed. The adaptve equalzaton algorthm s a combnaton of RLS or LMS and a second order PLL. For dfferentally coherent detecton, lnear equalzaton s mplemented usng a modfed LMS algorthm. The detected data symbols are fnally converted to bts and passed on to the vdeo decoder. vdeo frames DCT Quant. Huffman Encoder Symbol Mappng Packetzng Tx. Flter j fct e π Tx M-QAM M-DAPSK to vdeo decoder Bt Decson Adaptve Flterng Packet Sync. 4 Low-pass Flter Rx e jπf t c Fgure 15: Block dagram of the transmtter and the recever. 59

60 Fgure 16: Sgnal constellatons based on coherent detecton. 60

61 Fgure 17: Sgnal constellatons based on dfferentalyl coherent detecton. 61

62 Chapter 4 4 Results 4.1 Expermental results for phase coherent detecton Expermental data obtaned from the experment conducted at WHOI were processed employng the coherent recever descrbed n Secton.4. 8PSK, 16QAM, 3QAM and 64QAM modulaton methods were used. In all the modulaton schemes, the DFE had 10 T/- spaced feedforward taps and two feedback taps. The PLL trackng constants were K 1 =10-3 and K =K 1 /10. The forgettng factor of the RLS algorthm was chosen by tral to be λ= The step sze µ of the LMS algorthm s gven n (5). The short vertcal channel chosen for the tests proved to have very lttle dstorton (neglgble multpath), allowng for excellent sgnal detecton usng all modulaton formats. Fgure 18 - Fgure 1 present the results for all the modulaton methods employed. Shown n the left and rght-hand columns are the scatter plots before and after equalzaton respectvely. In addton, the mean square error for each adaptve algorthm (RLS/LMS) s gven. Note that n all cases RLS converges faster than LMS. No errors were observed n any of the packets. 6

63 Table 3 summarzes the acheved bt rates and bandwdth effcency for the modulaton schemes employed. Note that for the 64QAM case, the bandwdth effcency of 6 bts/sec/hz was acheved, correspondng to the rate of 150 kbps. Fgure 18: 8PSK nput/output scatter. Input SNR/bt = 43 db. 63

64 Fgure 19: 16QAM nput/output scatter. Input SNR/bt = 4 db. Fgure 0: 3QAM nput/output scatter. Input SNR/bt = 43 db. 64

65 Fgure 1: 64QAM nput/output scatter. Input SNR/bt = 41dB. The transmtted vdeo had the followng specfcatons: 15 frames/sec, 144x176 pxels/frame and 8 bts/pxel. If no compresson were used an acoustc lnk of 3,041 kbps would be needed to support transmsson of the selected vdeo clp. Employng JPEG compresson at each ndvdual frame, the requred rate was reduced to 101 kbps (30:1 compresson rato). Therefore, n the current mplementaton, bandwdth effcency greater than 3 bt/sec/hz,.e. 16QAM, 3QAM or 64QAM, s adequate n order to support real tme underwater vdeo transmsson. Note also that the rates summarzed n Table 3 suffce for real-tme transmsson f 64 kbps vdeo encodng s employed whch s a typcal rate for the vdeo encodng standards MPEG-4, H

66 Modulaton method Bt rate Bandwdth effcency 8PSK 75 kbps 3 bts/sec/hz 16QAM 100 kbps 4 bts/sec/hz 3QAM 15 kbps 5 bts/sec/hz 64QAM 150 kbps 6 bts/sec/hz Table 3: Acheved bt rate and bandwdth effcency for all modulaton methods. The 144x176 sample frame was extracted from an underwater clp. The frame exhbts low contrast and detal nherent to underwater magery. Fgure llustrates the orgnal mage frame and three JPEG compressed mages produced from the orgnal one. The varous compresson ratos were acheved by zerong hgh spatal frequency DCT coeffcents (AC coeffcents). Fgure (b) s generated wthout zerong any AC coeffcents (pure JPEG compresson), Fgure (c) s produced by zerong all the AC coeffcents wth absolute value less than 1 and Fgure (d) s produced by zerong all the AC coeffcents wth absolute value less than. Note that as the threshold s ncreased, the compresson rato ncreases at the expense of vsual ntegrty. The blockness dstorton nherent to JPEG compresson s due to the processng of an mage by 8x8 subblocks and the zerong of many AC coeffcents produces rough pxel transtons across the boundares of the subblocks. The results demonstrate that the JPEG algorthm yelds hgher qualty compressed mages for bt-rates of 0. bts/pxel and up. However, n a very low bt-rate scenaro ( 0. bts/pxel) the qualty of the JPEG reconstructed mage drops off dramatcally. 66

67 (a) (b) (c) (d) Fgure : (a) orgnal frame, (b) 16:1 compresson rato, (c) :1 compresson rato and (d) 30:1 compresson rato. 4. Smulaton results for dfferentally coherent detecton In ths secton the performance of the lnear equalzer followed by a reference-aded dfferentally detector s evaluated for 4x4DAPSK, x8dapsk, 4x8DAPSK, x16dapsk and 4x16DAPSK by computer smulatons. For all sgnal constellatons, the ampltude factor between two adjacent rngs was α=1.4. The packets transmtted n the experment are used to conduct the smulatons. All the packets had a tranng sequence of 500 symbols. The 67