Chapter 3. in this forward looking imaging sonar is chirp based. A chirp is a signal in which the

Transcription

1 Chaer 3 Performance Analysis of Chir Technology Sonar mouned on AUV 3.1 Inroducion Real ime underwaer environmen evaluaion and collision avoidance of Auonomous underwaer vehicle (AUV) wih he floaing or fixed objecs in he underwaer scenario needs eiher a rior knowledge of he oeraing environmen or sensing equimen. Having ariori knowledge is no feasible for unsrucured environmens and herefore sensing equimen mus be used for following second aroach. The sensing equimen in his case is he forward looking sonar ha is mouned on he AUV which scans he area in fron and rovides he images as he ouu. These images herefore mus be rocessed o deec he objecs in he ah of AUV in he underwaer environmen for is safe navigaion. The echnology used in his forward looking imaging sonar is chir based. A chir is a signal in which he frequency increases ('u-chir') or decreases ('down-chir') wih ime. In sonar, surface acousic wave devices such as reflecive array comressors are ofen used o generae and demodulae he chired signals. Chir echnology uses digially roduced linear frequency modulaion (FM) acousic ransmissions o roduce high resoluion images of seafloor conours and sub-boom layers. The chir signal generaion and he ulse comression echnique used in he sonar are discussed in deail in his chaer. To deec he underwaer objecs successfully, he eak of he received signal, he erformance of various windowing echniques and he range resoluion of chir echnology sonar and convenional sonar are also invesigaed in his chaer.

2 3. Forward Looking Sonar (FLS) During he underwaer survey, he AUV needs o mainain a consan aliude above he ocean ground. While oeraing a low aliude, he AUV is consanly a risk of colliding wih obsacles close o he ground or floaing in he waer (Doucee J. e al, 6). Therefore, Forward Looking Sonar (FLS) can be used as an effecive ool for avoiding ossible collisions. FLS is imaging sonar which works by ransmiing a series of narrow angle (encil beam) acousic ulses in he direcion erendicular o he axis of he sonar head cylinder. The azimuh angle of each successive ulse coninues o change as he sysem scans across he desired secor angle. The shae and sacing of he sonar ulses in a single scan varies in accordance wih he selecion of he ransducer frequency, scan seed, and oal secor angle (Cushieri J. e al, 1998). This sonar herefore can be used for obsacle avoidance and o exrac vehicle sae informaion (Dolbec M., 7). However, auonomous feaure exracion of images from he FLS is difficul due o he noise inheren in he sensor, underwaer environmen and he sensor s susceibiliy o inerference from oher acousic devices (Chanler M. J. e al, 1997). The forward looking sonar is of wo yes. They are he i) mechanically scanned and ii) muli beam variaions. Forward Looking Mechanically Scanned Sonar This ye of sonar is also used in a number of diverse alicaions, such as obsacle avoidance, mine deecion, and surveillance. The sonar consiss of a single hydrohone which is mechanically scanned along he horizonal axis by sweeing a secor. The reurns are hen used o creae an image. Mos sysems rovide he user wih he oion of choosing he size of he secor o scan and wih some degree of conrol on he resoluion. In mos cases higher resoluion resuls in a slower refresh rae. Tyical ranges are u o m. Forward-looking sonars have been used for many years by Remoely Oeraed Vehicle (ROV) ilos for

3 remoely conrolled navigaion, obsacle avoidance, and localizaion around known srucures (Zerr B. e al, 5). The major advanage of his ye of sonar is is caabiliy of deecing objecs or seabed feaures, such as roruding rocks, a large disances. Forward-Looking Muli-beam Sonar This ye of sonar uses a fixed array of hydrohones, scanned elecronically, which allows much faser udaes of secors. Some sonars are caable of udaing a secor u o 3 imes a second. In all oher accouns, his sonar is similar o mechanically scanned sonar. These sonars are more exensive han mechanical sysems; neverheless heir oulariy in he underwaer communiy has been growing. Auomaic mehods for obsacle avoidance, moion esimaion, and image recogniion using forward-looking muli-beam sonar images have already aeared. Chir echnology dramaically imroves he range resoluion comared wih convenional sonars. Infac, resoluion can be imroved by five imes. Wih his advancemen of echnology in he imaging sonars, coral reefs and oher such obsacles can now be deeced a a disance adequae enough o allow for a gradual ascen over he objec. Small forward-look sonars are in a relaively nascen hase of develomen. 3.3 Deerminaion of Range Resoluion of Monoonic and Chir echnology Sonar Monoonic Sonar In monoonic sonars, he ransmied acousic ulse consiss of an on/off swich modulaing he amliude of a single carrier frequency. Fig. 3.1 below shows how his relaionshi exiss beween he ransmied signal and he ouu roduced by he receiver circuiry in he sonar. I can be seen ha he receiver does no decode each cycle of he ransmied ulse, bu insead roduces he 'enveloe' of is overall amliude as shown in Fig. 3.1 Transmied signal Received decoded signal Pulse duraion Transmied circui Receiver

4 The abiliy of monoonic acousic sysems o resolve arges is beer if he ulse duraion is shor; his, however, has is drawbacks. Ideally, long ransmi ulses are needed o um enough acousic energy ino he waer for good idenificaion of he long range arges, bu due o he velociy of sound (VOS) hrough waer (yically around 15 meres / second), each ulse occuies an equivalen 'disance' relaed o is duraion - his is referred o as 'range resoluion', and is given by he following equaion. range resoluion = ulse lengh seedof sound (3.1) The duraion of he de-chired ulse equals he inverse of he bandwidh. ulse lengh 1 bandwidh (3.) For examle, if he smalles ulse duraion is 5 microseconds, and combining his wih he yical VOS of 15 meres / second, a range resoluion of 7.5mm is obained. The 'range resoluion' effecively deermines he abiliy of he sonar o disinguish wo close by arges; herefore using he above examle, if wo arges are less han 7.5mm aar hen hey canno be disinguished from each oher. The range resoluions for differen ulse duraions is shown in Table 3.1 and is erformance is shown in Fig The ne effec is ha he sysem will dislay a single large 'combined arge, raher han mulile smaller arges as shown in Fig. 3..

5 Range Resoluion in mm Targe searaion Targe Transmied ulse Targe 1 Individual echo Sonar range resoluion SONAR Targe1 Targe Individual echo Targe searaion + Combined echo seen by he sonar receiver Fig. 3. Monoonic sonar receiver resoluion Time Frequency used (khz) Pulse Duraion (micro seconds) Sound velociy (m/s) Range Resoluion (mm) Table 3.1 Range resoluions for differen ulse duraions of convenional sonar Pulse Duraion in microseconds

6 Chir Technology Sonar Insead of using a ulse of a single carrier frequency, in he chir echnology sonar he frequency wihin he ulse is changed (swe) hroughou he duraion of ransmission, from one frequency o anoher. For examle, a he sar of he ransmission he sonar may oerae a KHz, and a he end, i may have reached 5KHz. The difference beween he saring and ending frequency is known as he 'bandwidh' of he ransmission, and yically he cenre frequency of he ransmission is used o idenify he sonar (in his case i would be a 5KHz sonar). By consanly changing is frequency over ime, his 'chired' ransmission can be hough of as having a unique acousic signaure, and so if wo ulses now overla (as he arges are closer han he range resoluion), he known 'frequency versus ime' informaion can be used o searae hem aar. Wih new high-seed Digial Sonar Technology (DST) signal rocessing echniques, he sonar receiver conains a 'aern-maching' circui ha looks for is ransmied 'chir' being echoed back from arges, and is receiver now roduces a shar 'sike' when a good mach is found (whereas he monoonic sonar roduces an ouu having he same duraion as is ransmi ulse) as shown in Fig Transmied Received decoded Pulse duraion Transmied circui Fig. 3.4 Chir sonar acousic signals

7 Targe searaion Targe Transmied Pulse Targe1 Individual Echo Sonar Range Resoluion SONAR Targe1 Targe Searaion Targe Individual Echo Combined Echo seen by he Sonar Receiver + Boh Targes Visible Fig. 3.5 Chir sonar receiver resoluion Time In all sonar sysems, higher frequency conen is invariably associaed wih an increase in resoluion and a decrease in eneraion. Chir echnology, as imlemened in our chir sysems, reduces he rade-off beween signal range and image resoluion. Chir sonar receiver resoluion is shown in Fig The range resoluion of chir echnology sonar is given as Range resoluion = (velociy of sound) / (bandwidh x ) (3.3) The bandwidh of a yical chir sysem is 1 khz, and using he yical VOS of 15 meres / second, he range resoluion obained is 7.5mm which is beer han convenional sonar. The range resoluions for differen bandwidhs are shown in Table 3. and is erformance is shown in Fig Bandwidh Velociy of Range Resoluion (khz) sound (m/s) (mm)

8 Range Resoluion in mm Table 3. Range resoluions for differen bandwidhs of chir echnology sonar Bandwidh in khz Fig. 3.6 Variaion of range resoluion for various bandwidhs for chir echnology The resoluion of an imaging sysem is measured by is abiliy o searae closely saced objecs. In oher words, o deec discree echoes reurning from he inerfaces beween layers or arges on he seafloor. The verical resoluion of an acousic sub-boom rofiler refers o he minimum disance ha can be visually disinguished in he image roduced by he sysem. A sonar sysem wih a 1 cm resoluion will resolve layers ha are aleas 1 cm aar. In a convenional single-frequency sysem, he limi of resoluion is deermined by he ulse widh of he ransmied waveform. In a muli-frequency sysem, i is he bandwidh of he ransmied ulse ha ses he sysem's heoreical resoluion. The heoreical sonar range resoluion, eiher cross-rack in he case of side scan sonar or verical in he case of a subboom rofiling, is calculaed by mulilying he lengh of he comressed ulse by he seed

9 Amliude of sound, and dividing he roduc by wo o accoun for he ing's round ri ravel ime. 3.4 Chir echnologies used in Sonar There are wo yes of chir echnologies in use oday deending on he alicaion. They are i) Linear chir and ii) Exonenial chir Linear Chir In a linear chir, he insananeous frequency f( ) varies linearly wih ime as shown in Fig. 3.7 f() = f + k (3.4) where f is he saring frequency (a ime = ), and k is he rae of frequency increase or chir rae. The corresonding ime-domain funcion for a sinusoidal linear chir is given by x sin f d (3.5) sin ( f k) d x sin f k (3.6) Time in seconds Fig. 3.7 A linear chir waveform In he frequency domain, he insananeous frequency described by he equaion f() = f + k

10 is accomanied by addiional frequencies (harmonics) which exis as a fundamenal consequence of frequency modulaion. These harmonics are quanifiably described hrough he use of Bessel Funcions. However wih he aid of Frequency vs. Time rofile Secrogram, one can readily see ha he linear chir has secral comonens a harmonics of he fundamenal chir. Exonenial Chir In a geomeric chir, also known as an exonenial chir as shown in Fig. 3.8, he frequency of he signal varies wih a geomeric relaionshi over ime. In oher words, if wo oins in he waveform are chosen, i.e. 1 and, and he ime inerval beween hem 1 is ke consan, he frequency raio f( )/f( 1 ) will remains consan. In an exonenial chir, he frequency of he signal varies exonenially as a funcion of ime f() = f k (3.7) where f is he saring frequency (a = ), and k is he rae of exonenial increase in frequency. Unlike he linear chir, which has a consan chir rae, an exonenial chir has an exonenially increasing chir rae. The corresonding ime-domain funcion for a sinusoidal exonenial chir is given by x sin f d sin f k d x sin f k ln 1 k (3.8)

11 Amliude Time in seconds Fig. 3.8 An exonenial chir waveform As in he case for a linear chir, he insananeous frequency of he exonenial chir consiss of he fundamenal frequency f() = f k accomanied by addiional harmonics. A geomeric chir does no suffer from reducion in correlaion gain if he echo is Dolershifed by a moving arge. This is because he Doler shif acually scales he frequencies of a wave by a mulilier (shown below as he consan c). f() Doler = cf() Original (3.9) From he above equaions, i can be seen ha his acually changes he rae of frequency increase of a linear chir (k mulilied by a consan) so ha he correlaion of he original funcion wih he refleced funcion is low. Because of he geomeric relaionshi, he Doler shifed geomeric chir will effecively sar a a differen frequency, f mulilied by a consan, bu follow he same aern of exonenially increased frequency. For insance, he end of he original wave, will sill overla erfecly wih he beginning of he refleced wave and he magniude of he correlaion will be high for ha secion of he wave. A chir signal can be generaed wih analog circuiry via a volage conrolled oscillaor (VCO) and a linearly or exonenially raming conrol volage. I can also be generaed

12 digially by a digial signal rocessor (DSP) and a digial o analog converor (DAC) by varying he hase angle coefficien in he sinusoid generaing funcion. 3.5 Pulse Comression Mehod for Chir echnology Sonar Pulse comression is a signal rocessing echnique mainly used in radar and sonar o increase he range resoluion as well as he signal o noise raio (SNR). This is achieved by modulaing he ransmied ulse and hen correlaing he received signal wih he ransmied ulse. I involves he ransmission of a long coded ulse and he rocessing of he received echo o obain a relaively narrow ulse. The ransmied long ulse may be generaed from a narrow ulse. A narrow ulse conains a large number of frequency comonens wih a recise hase relaionshi beween hem. If he relaive hases are changed by a hase-disoring filer, he frequency comonens combine o roduce a sreched or exanded ulse. This exanded ulse is he ulse ha is ransmied. The received echo is rocessed in he receiver by a comression filer. The comression filer readjuss he relaive hases of he frequency comonens so ha a narrow or comressed ulse is again roduced. The ulse comression raio is he raio of he widh of he exanded ulse o ha of he comressed ulse. The ulse comression raio is also equal o he roduc of he ime duraion and he secral bandwidh (ime bandwidh roduc) of he ransmied signal. The received signal is he baseband signal recorded by he sonar afer i has been demodulaed. The received signal will conain overlaing waveforms a differen magniudes which have been refleced from he differen scaering oins of he arge. If he reflecion is from a single oin arge i will have he same form as he ransmied waveform alhough i will be disored by he sonar sysem. This received signal will hen be comressed o form a single imulse. The daa samles are he values of he received signal recorded by he sonar using he analog

13 o digial converers. These are comlex values recorded in airs from he in-hase and quadraure hase demodulaors. The ulse comressed received signal is he range rofile of he arge which consiss a series of cells where each cell has he widh of an ideal ulse i.e., he limi of he resoluion. This means ha he number of cells in he range rofile is equal o he number of daa samles in he received signal exce ha he ends of he signal canno be comressed as hey may only conain ar of a refleced waveform. I is he range rofile ha is required o carry ou furher rocessing. Pulse comression is he mehod used o calculae he range rofile, if he received signal and he ransmied waveforms are given. This can be done by eiher of he following wo mehods: 1. Deconvoluion Reversing he convoluion of he range rofile wih he ransmied waveform. This mus be done in he frequency domain.. Correlaion Searching for he waveform in he received signal. The range rofile is equal o he correlaion of he comlex ransmied waveform and he comlex received signal, wih a range shif. This is because he received signal conains coies of he ransmied signal all added ogeher, one for each ulse in he range rofile. A ime reversed and conjugaed coy of he ransmied waveform is convolved wih he received signal o roduce he correlaion. Unforunaely deconvoluion is less robus han correlaion, hence by defaul correlaion is referred. Block diagram of Pulse Comression Sonar In ulse comression echnique, he ransmied signal is eiher frequency modulaed or hase modulaed and he received signal is rocessed using a secific filer called "mached filer". In his form of ulse comression, a long ulse of duraion, T is divided ino N sub ulses each of widh, τ.

14 Inu signal Pulse modulaor Pulse coding Transmier/ Receiver Anenna Deeced arge Deec or/roc essor Weighing filer Mached filer Fig. 3.9 Block diagram of ulse comression sonar The block diagram shows he ulse modulaor resonsible for generaing he coninuousmodulaed ulse and he nex sage i.e. ulse coding echnique generaes frequency modulaed ulse or chir ulse (Fig. 3.9). In addiion o generaing he ransmied ulse, he frequency modulaor or hase coding echnique also lays a role in he design of he ulse comression filer. The ulse-comression filer is an examle of a mached filer because he filer is secially designed o recognise he characerisics of he ransmied ulse as hey are reurned o he receiver in he form of refleced ulses. To ha exen, he filer is been mached o he ransmied waveform. The received ulses wih similar characerisics o he ransmied ulse are recognised by he mached filer where oher received signals ass relaively unnoiced by he receiver. 3.6 Mached Filer for ulse comression A mached filer or ulse comression filer is basically used in he receiver o increase SNR and he range resoluion. The mached filer is usually included righ before he signal rocessor. In racical cases he ulse assed hrough he mached filer is no suffered from noise or aenuaion. Noise and aenuaion are a real roblem when oeraing sonar sysems. As indicaed in Fig. 3.1, if he inu o he mached filer is s(), he ouu will be s (). If he

15 inu is n hen he ouu will be n. o s() n() h() s () n () Mached filer Fig. 3.1 Block diagram of a mached filer If ransfer funcion, h is assumed as linear hen and (3.1) (3.11) so s h n n h o where denoes he convoluion. The oimizaion roblem in he frequency domain can be solved by using Fourier ransforms. H f h, (3.1) S f s (3.13) S f s o o and (3.14) So f H f S f.

16 (3.15) In he above equaions x denoes he Fourier ransform of x. Since n and n o are random rocesses he equaion can be wrien as N f E n n, No f E no n o and N f H f N f. o (3.16) As n and n are wide-sense saionary, o No f is a ower secral densiy and hus P N f df H f N f df. n (3.17) The eak signal ower is given by S o o P s. However, (3.18) s S f S f H f e df. 1 j fo o o o o (3.19) By combining Eqs. (3.17), (3.18) and (3.19) hen ge h PS : max max h P h n j f S f H f e o df H f N f df (3.)

17 A his oin, n is assumed as whie noise wih a noise ower secral densiy N f kt F G n and wrie (3.1) h : max h j f S f H f e o df kt F G H f df n (3.) In he above Eq. (3.), G is he gain of all receiver comonens beween he anenna and he inu o he mached filer. Thus, N f is he noise ower secral densiy a he inu of mached filer. The maximizaion rocess can be sared by alying one of he Cauchy-Schwarz inequaliies o he numeraor. The aricular Cauchy-Schwarz inequaliy of ineres is b b b A f B f df A f df B f df a a a (3.3) wih equaliy when A f KB f (3.4) where K is an arbirary consan. Aly Eq. (3.3) o he raio of (3.) he following equaion is obained A f H f (3.5) and

18 B f S f e j fo (3.6) I is obained as S f H j f f e o df H f df S f df kt F G H f df kt F G H f df n n (3.7) where j fo S f e S f. (3.8) Now Eq. (3.7) reduces o S f H j f o f e df S f df kt F G H f df n kt F G n. (3.9) Eq. (3.9) ells ha for all H f Tha is, he maximum value of PS he uer bound on he lef side is equal o he righ side., P, over all h is obained. To find he h ha yields n he maximum PS P n, he second ar of he Cauchy-Schwarz inequaliy given in Eq. (3.6) is used. Secifically, P max S h P n n S f df kt F G (3.3) when h is chosen as

19 h KS f e 1 j fo (3.31) Thus, he imulse resonse of he filer ha maximizes eak signal-o-average noise ower is found a he filer ouu. The equaion for he maximum eak signal-o-average noise in he form of Eq. (3.3) and have deermined ha he maximum occurs a From he Eq. (3.31) H f KS f o. (3.3) In oher words, he mached filer frequency resonse has he same shae as he frequency secrum of he signal. They simly differ by a scaling facor K. This is he reason h is called as a mached filer. From Eq. (3.3) secific form of h wih resec o s can be wrien as j fo j f j f o h KS f e e df K S f e df j f o K S f e df Ks o. (3.33) Thus, h is he conjugae of a scaled (by K ), ime reversed (because of he ) and shifed (by o ) version of he ransmi signal, s. Because of his reason h is called as a mached filer Mached filer resonse for an unmodulaed ulse In his secion, an equaion for he mached filer resonse for a signal, s() is derived, and hen i is used o derive he mached filer resonse for he case where s() is an unmodulaed ulse. From Eq. (3.33)

20 h Ks (3.34) Where K is an arbirary (comlex) consan and is he value of a which he mached filer resonse o s will reach is eak. Le us consider K 1 and. The laer saemen says ha he ouu of he mached filer will reach is eak a a relaive ime of zero. The equaion (3.33) can be given as h s. (3.35) The resonse of h o s is given by so h s s h d (3.36) Bu h s so h s s and so s s d. (3.37) For uroses of he res of he analyses s and s are reaed as searae funcions. Le s Ae j rec (3.38) and j s Ae rec.

21 (3.39) A lo of s is shown in Fig The lo of s would look he same as s exce ha he heigh would be j j Ae raher han Ae. s j Ae Fig Unmodulaed ulse In he so inegral i is noed ha is he searaion beween s and s as shown in Fig. 3.1 and i corresonds o he case where. s Ae j s Ae j Fig. 3.1 Plo of s and s for I should be clear ha if or, or, hen s and s will no overla, s s and s. Thus s. o (3.4) o For region he overla region of s and s is. Furher, over his j j s s Ae Ae A and hus so A d A.

22 (3.41) since,. Thus relace wih o ge so A. (3.4) The arrangemen of s and s for is shown in Fig s Ae j s Ae j Fig Plo of s and s for In his case he overla region is and so A d A. (3.43) Here since,. Thus relace wih o ge s A. o (3.44) Since his is he same form as for, combine hese o ge so A. (3.45) Finally, if his is combined wih he resul for hen

23 Amliude s o A A rec. (3.46) A lo of so is shown in Fig so Fig Mached filer ouu for CF ulse 3.6. Mached filer resonse for modulaed signal The above resuls can also be exended o find he mached filer resonse when s is a linear frequency modulaed (LFM) ulse or chir ulse. The ulse-comression filer or mached filer simly erforms a srong correlaion beween wha was ransmied i.e, LFM ulse or chir ulse and wha was received. The effecs of his form of rocessing on wo ulses wih he same duraion are shown in he following Fig In he coninuous frequency (CF) examle, he mached filer (correlaion) resonse shows he riangular enveloe as shown in Fig (a). However, in he chir examle wih he same duraion, he maching ulse-comression filer generaes an ineresing ulse called a sinc ulse wih a much narrower eak, and hence a suerior range resoluion as shown in Fig (b)

24 Amliude Amliude Fig a) Resonse of mached filer for a coninuous frequency signal 1 Chir Signal 5 Chir Signal Passed Mached Filer Time in seconds Time Time in seconds Time No. of samles Fig b) Resonse of mached filer for a chir signal Fig Tyical ouu from a ulse comression filer From Fig. 3.16, i is observed ha he widh of he sinc ulse is inversely roorional o he bandwidh of he uncomressed ulse and he heigh is roorional o he roduc of he bandwidh and uncomressed ulse widh. The ouu of he ulse-comression filer forms he inu o he deecor secion of he ulse-

25 comression sonar. I is herefore desirable o have a very narrow and all ulse (jus as i is in a sandard ulse sonar sysem). The main oins o noe from Fig are ha he inu o he filer is a relaively broad and low ower ulse. The ouu ulse, however, is very narrow and srong. These are he wo very desirable characerisics from ulse sonar. When looking a he ouu of he ulse-comression filer as shown in Fig 3.15, he sidelobes on eiher side of he cenral ulse are reasonably large. These sidelobes are called range sidelobes. The range sidelobes are a direc consequence of he ulse-comression filering rocess. They are undesirable because hey can lead o false alarms and range ambiguiy. The soluion o he range sidelobe roblem is o use a weighing facor in he ulsecomression filer or a ransmier side ha effecively deunes or mismaches he filer and consequenly aenuaes he sidelobe levels. Unforunaely, he advanages of he ulse comression rocess are slighly reduced by his echnique in which he comressed ulse will have reduced amliude and an increased ulse widh. 3.7 Invesigaion of suiable windowing echnique for underwaer objec deecion A chir signal has a ime-varying frequency, and rovides he righ kind of secral coverage. Chiring has some major advanages over coninuous signals. If he same frequencies are ransmied a all ime, one waveform will look like he oher one. There is los of informaion conens in he received signal however, one can' isolae ime evens roducing ha frequency conen. If he chirs are reduced o shor ime inervals, he ime resoluion imroves dramaically, hough i is harder o disinguish he frequency conen in he reurn signals. The abru edges of he squared ulse have some negaive side effecs. In he echo resuls, one can' ell which effecs come from he signal and which come from he arificial

26 Amliude edge disconinuiy. To avoid hese unresolvable roblems, windowing echniques are emloyed. Window funcions are used o obain a comromise beween a narrow main lobe for high resoluion and low side-lobes for low secral leakage. High resoluion rovides accurae esimaion of a arge and can addiionally searae wo arges ha are closely saced in frequency. In he saial domain i allows accurae esimaion of wo closely saced scaerers. Low secral leakage imroves he deecabiliy of a weak sinusoid in he resence of a srong sinusoid ha is no been cenered. In racical cases windowing echniques are mosly used afer mached filer secion of ulse comression echnique. Afer alying ulse comression o he received signal of he sonar, he resonse of he mached filer is shown in Fig Chir Signal Passed Mached Filer Time No. of samles Fig Resonse of mached filer for received signal Even afer assing signal hrough he mached filer he noise sill remains in he signal. So windowing echnique is alied afer he mached filer and he resonse of he signal is

27 Magniude shown in below Fig So comared o he above Fig he noise is reduced o much exen. 1 Resonse of window funcion for received signal No.of samles Fig Enveloe of mached filer ouu assed hrough window There are wo common siuaions: deecion of a secral comonen in he resence of broadband noise; or disinguishing beween narrow band secral comonens. The choice of window funcion may be differen in he wo cases of deecion or resoluion. The choice of he window is imoran. I deermines he rade-off of ime versus frequency resoluion which affecs he smoohness of he secrum and he deecabiliy of he frequency eaks. The mos commonly used windows are Recangular, Triangular, Hamming, Hanning, Kaiser, Blackman Harris windows and many ohers. In he subsequen aragrahs, some of he windowing echniques are analyzed and comared Recangular Window The recangular window is someimes known as a Dirichle window. I is he simles window, aking a orion of he signal wihou any oher modificaion leads o disconinuiies

28 Magniude Magniude a he endoins.the recangular window, is herefore rarely used for is low soband aenuaion. The firs lobe has aenuaion of 13dB and he narrowes ransiion region. Unlike oher window funcions which are designed based on he comromise beween Narrow Transiion and Soband Aenuaion his window is characerized by exreme values. I is easy o find recangular window coefficiens as all coefficiens beween and N-1 (Nfiler order) are equal o 1, which can be exressed in he following way: W[n] = 1; n N 1 (3.47) When alying his funcion o he received signal of ulse comression sonar, he magniude resonse boh in saial and frequency domain is shown in Fig. 3.19(a) and (b). 1 Resonse of Recangular Window for received Signal Resonse of Recangular Window for received Signal Number of Samles Number of Samles (a)time domain (b) Frequency domain Fig Magniude resonse of received signal afer recangular window 3.7. Hann window The Hann window is used o reduce effecs on frequency characerisic roduced by he final samles of a signal being filered. This window has higher so band aenuaion han hose designed wih riangle funcion. The firs side lobe in he frequency domain of his filer has 31dB aenuaion. The Hann window coefficiens can be exressed as:

29 Magniude Magniude 1 n W[ n] 1 cos( ) ; n N N 1 1 (3.48) The magniude resonse of received signal afer assing hrough he Hann window is shown in Fig. 3.. Resonse of Hann Window for received Signal 1 1 Resonse of Hann Window for received Signal Number of Samles Number of Samles (a) Time domain (b) Frequency domain Fig. 3. Magniude resonse of received signal afer hann window Hamming Window The Hamming window is one of he mos oular and mos commonly used windows. Hamming window belongs o he family of raised cosine windows. The window is oimized o minimize he maximum (neares) side lobe giving i a heigh of abou one-fifh ha of he Hann window, a raised cosine wih simler coefficiens. A filer designed wih he Hamming window has minimum soband aenuaion of 53dB. The ransiion region is somewha wider han he soband aenuaion, which is considerably higher. The Hamming window coefficiens are exressed as: n W[ n] cos ; n N N 1 1 (3.49)

30 Magniude Magniude The magniude resonse of he received signal afer assing hrough he Hammimg window is shown in Fig Resonse of Hamming Window for received Signal 1 1 Resonse of Hamming Window for received Signal Number of Samles Number of Samles (a) Time domain (b) Frequency domain Fig. 3.1 Magniude resonse of received signal afer hamming window Kaiser Window The windows described above are kind of a comromise beween requiremens for a narrow ransiion region (greaer seleciviy) and a higher soband aenuaion. All he windows described here are no oimal. An oimal window is a funcion ha has maximum aenuaion according o he given widh of he main lobe. The oimal window is also known as Kaiser Window. Is coefficiens are exressed as: n I 1 1 M W[ n], I n M = oherwise (3.5) Where, I is he zero h order Modified Bessel funcion of he firs kind and α is an arbirary real number ha deermines he shae of he window. In he frequency domain, i deermines

31 Magniude Magniude he rade-off beween main-lobe widh and side lobe level, which is a cenral decision in he window design. M is an ineger, and he lengh of he sequence is N=M+1. The magniude resonse of received signal afer assing hrough he Kaiser window is shown in Fig Resonse of Kaiser Window for received Signal Resonse of Kaiser Window for received Signal Number of Samles Number of Samles (a) Time domain (b) Frequency domain Fig. 3. Magniude resonse of received signal afer Kaiser window Blackman-Harris Window The Blackman-Harris window is one of he mos well-known and mos commonly used windows. I is quie similar o Hann and Hamming window, bu i has one addiional cosine erm o furher reduce he rile raio. Blackman windows have slighly wider cenral lobes and less sideband leakage han he equivalen lengh of Hamming and Hann windows. I is characerized by high so band aenuaion and he wides ransiion region comared o all windows. The Blackman-Harris window coefficiens are exressed as: n 4 n 6 n W[ n] cos.1418cos.1168cos ; n N N 1 N 1 N 1 1 (3.51)

32 Magniude Magniude The magniude resonse of received signal afer assing hrough he Blankman Harris window is shown in Fig Resonse of Blackman Harris Window for received Signal Resonse of blackman harris Window for received Signal Number of Samles Number of Samles (a) Time domain (b) Frequency domain Fig. 3.3 Magniude resonse of received signal afer Blackman Harris window From above resuls i observed ha by using Blackman Harris window, noise in he received signal of ulse comression sonar is reduced by a large value comared o all oher window funcions. In sonar alicaions, he Blackman-Harris window is he convenional choice. The Blackman-Harris window has good roeries for low disorion and good sideband rejecion. Window echnique Maximum side lobe level (db) Side lobe roll-off rae (db/decade) Recangular 13 Hann 31 4 Hamming 53 4 Kaiser 48

33 Blackman-Harris 71 6 Table 3.3 Comarison of windowing echniques for chir sonar From he Table 3.3, i is concluded ha Blackman-Harris window erforms beer for chir echnology sonar wih maximum side lobe level of 71dB and Side lobe Roll-off rae of 6 db/decade. 3.8 Facors Affecing Choice of Pulse Comression Sysem The selecion of a ulse comression sysem is deenden uon he ye of waveform and he mehod of generaion and rocessing. The rimary facors influencing he selecion of a aricular waveform are usually deenden on he sonar requiremens of range coverage, waveform flexibiliy, inerference rejecion, and signal-o-noise raio (SNR). In general, he mehods of imlemenaion are divided ino wo classes, acive and assive deending uon wheher acive or assive echniques have been used for he generaion and rocessing. Acive generaion imlies generaing he waveform by hase or frequency modulaion of a carrier wihou he occurrence of an acual ime exansion for examle digial hase conrol of a carrier. On he oher hand, Passive generaion imlies exciing a device or a nework wih a shor ulse o roduce a ime-exanded coded waveform. An examle of his is an exansion nework comosed of a surface-acousic wave (SAW) delay srucure. Acive

34 rocessing also involves mixing delayed relicas of he ransmied signal wih he received signal which is a correlaion-rocessing aroach, whereas assive rocessing involves he use of a comression nework which is he conjugae of he exansion nework and is also known as mached-filering aroach. Alhough he combinaion of acive and assive echniques may be used in he same sonar sysem, mos sysems emloy he same mehods for boh i.e. for generaion and for rocessing e.g., a assive sysem uses boh assive generaion and assive rocessing. 3.9 Conclusions Unlike radar which is based on radio communicaion rincile, sonar emloys he acousic energy for use in underwaer environmen. In his chaer he imorance of chir echnology and is generaion has been exlained. The ulse comression echnique and differen windowing echniques have been analyzed so as o oimally deec he eak of he received signal. The Range Resoluion characerisics of fixed frequency ulse sonar vis-a-vis chir echnology based sonar have also been invesigaed. From he resuls i is concluded ha he range resoluion of chir echnology based sonar is far suerior in comarison wih he fixed frequency ulse SONAR. I is also observed ha due o high range resoluion of chir echnology, he images ha are obained are simler o analyze. The resoluion a 1 khz bandwidh has been of he order of 7.5mm which is 5imes beer han he convenional sonar. However, in chir echnology based sonar he range resoluion imroves a he exense of increased bandwidh. The erformance of various windowing echniques ha suis he ulse comression of chir echnology sonar is invesigaed. I is concluded ha he Blackman- Harris window erforms beer wih a maximum side lobe level of 71dB and side lobe roll-off rae of 6 db/decade.