Spectrally Efficient Constant Envelope Modulation for GNSS Signals

Transcription

1 RADIOENGINEERING, VOL. 7, NO. 3, SEPEBER 8 83 Spetrally Effent Constant Envelope odulaton for GNSS Sgnals Xuan XIA, Zupng ANG, Jaolong WEI, Zhhu ZHOU Shool of Eletron Inforaton and Counatons, Huazhong Unversty of Sene and ehnology, Luoyu Road 37, 4374 Wuhan, Chna 63955@qq.o, tang_zupng@hust.edu.n, jlwe@hust.edu.n, zhh_zhou@63.o Subtted January, 8 / Aepted June, 8 Abstrat. As the L-band spetral resoures for GNSS serves are alost exhausted, new bands suh as S-band and C-band has been onsdered for new GNSS sgnals. In addton to the tradtonal sgnal features, out-of-band radaton s an portant fator to be onsdered for sgnal desgnng n these new bands. In ths paper, a atheatal odel for the optzaton of GNSS sgnal wavefors was onstruted by ntegratng rangng auray, antjang perforane and out-of-band radaton suppresson requreents. In obnaton wth nueral optzaton ethods, a spetrally effent onstant envelope odulaton shee based on phase trajetory optzaton was proposed. he odulated sgnal has a full-response ontnuous phase wavefor, whh faltates sgnal proessng and pleentaton at both ends of the transsson and reepton. In addton, n the sgnal desgn, the balane between sgnal auray, ant-nterferene perforane and out-of-band radaton suppresson an be aheved through the adjustent of the weght oeffent. he sulaton results show that the out-of-band radaton an be redued by about db opared wth the exstng shee when the sgnal perforane dfferene s lower than db. Keywords Spetrally effent, onstant envelope, GNSS, low out-of-band radaton. Introduton Wth the fast nreent of global navgaton satellte syste (GNSS) sgnals, the ontradton between sgnal deand and frequeny resoure restrtons has beoe nreasngly pronent, forng ore attenton to be dreted toward the spetral effeny when desgnng GNSS sgnals. Currently, the L-band spetral resoures for GNSS serves are alost exhausted, and thus, new bands, suh as S-band and C-band, ust be onsdered for new GNSS sgnals. At the World Rado Counatons Conferene n, the 5 Hz to 53 Hz part of the C- band was assgned for Rado Navgaton Satellte Serves (RNSS) ar-to-ground applatons, whereas the 5 Hz to 5 Hz part of the C-band was assgned for RNSS ground-to-ar applatons []. he adjaent frequeny bands for the Rado Astronoy Serve (RAS, 499 Hz to 5 Hz) and the rowave Landng Syste (LS, 53 Hz 55 Hz) have strt restrtons on out-ofband radaton, and the opatblty between uplnk GNSS sgnals and downlnk GNSS sgnals ust also be onsdered []. Aordng to the IU rules, the PSD (noralzed power spetral densty) of sgnals n frequeny band Hz annot exeed 9.5 db/hz, the PSD of sgnals n frequeny band Hz annot exeed 64.8 db/hz. GNSS s a typal power-onstraned syste, and thus, to axze the power effeny of the transtter, the hgh-power aplfer (HPA) ust work at the saturaton pont. o nze the nonlnear effets of the HPA, GNSS sgnals usually adopt onstant envelope odulaton shee [3]. here are two ways to redue out-of-band radaton. One s to desgn wavefors wth lower out-of-band spetral oponents, and the other s to flter the transtted sgnals. Generally, these two ethods ould both be used n board payload. Relatvely speakng, the frst ethod would nrease the oplexty of the base band sgnal generaton, the seond ethod would nrease the oplexty of RF hannel desgn. o enhane the out of band suppresson ablty, we need to use hgh-order flter, whh brngs addtonal nserton loss, larger group delay, and akes the sgnal wavefor qualty deterorated and unstable. Usng the frst ethod to desgn sgnals wth lower out of band radaton an redue the flter desgn requreents, whh has a postve effet on the qualty of the generated navgaton sgnals. However, gven the preondtons of onstant envelope haratersts and strt out-of-band radaton, optzng the perforane of the GNSS sgnals s dffult. he onstant envelope odulaton sgnals of L-band (e.g., bnary phase-shft keyng [BPSK], bnary offset arrer [BOC][4], and AltBOC [5]) all feature a rh hgh-frequeny oponent and low spetru roll-off speed, whh DOI:.364/re.8.83 SIGNALS

2 84 X. XIA, Z. P. ANG, J. L. WEI, E AL., SPECRALLY EFFICIEN CONSAN ENVELOPE ODULAION FOR GNSS are benefal for optzng the sgnal perforane. However, these features are not avalable for the preondton of strt out-of-band radaton. herefore, the onstant envelope ontnuous phase odulaton ethod s preferred n the desgn of C-band navgaton sgnals. For exaple, the Galleo tea reoended the use of Gaussan nu shft keyng (GSK) [6], and Lu et al. proposed nu shft keyng-bnary oded sgnal (SK-BCS) odulaton [7]. hs paper proposes a new onstant envelope odulaton ethod. hrough the jont optzaton of the n-phase and quadrature (I&) hp wavefor, ths odulaton ethod aheves perforane equvalent to that of GSK- BPSK(), GSK-BOC(5,5), SK-BCS and SK- BCS. Furtherore, the onstant envelope feature and sgnfantly redued out-of-band radaton of ths ethod ndate that t has better spetral effeny.. Spetrally Effent Constant Envelope odulaton (SPECE) SPECE defnes two dret sequene-spread spetru sgnal oponents as follows: k s t a p t k I I k k s t b p t k d k where a k, b k are pseudo-rando sequenes wth values of ±, s the hp wdth; p I (t) s the pulse wavefor of the n-phase oponent; p (t) s the pulse wavefor of the quadrature-phase oponent, whh are both equal to when t < or t ; and d s the pseudo ode phase dfferene between the two sgnals, d [,). When the sgnal pulse wavefor of the two sgnals satsfes the followng equatons, the obned sgnal s t sit jst s onstantly enveloped. p t p t d t d I pi t ptd d t where s a onstant. If these two branh sgnal ode phases are perfetly algned (d = ), one branh sgnal or both sgnals wll exhbt a sudden hange at the edge of the hp, resultng n a large hgh-frequeny spetral oponent. Learnng fro SK odulaton, d = / s hosen n ths paper to redue the out-of-band spetral oponent and beneft the syetry of the hp wavefor. Based on the trgonoetr funtons' feature sn + os = and d = /, the followng pulse wavefor funtons are onstruted:, () () I p t os t t pi t os t t p t sn t t p t sn t t where (t) s a funton defned n [, /). It an be verfed that the pulse wavefor defned by (3) satsfes the ondtons requred by (). hus, the I& wavefor jont optzaton proble was transfored nto a phase trajetory optzaton proble, whh s shown as follows. t t ax U s.t. C where U[ ] s a utlty funton that reflets the perforane of the odulaton sgnals based on the phase path funton (t). C[ ] s a onstrant funton that reflets the out-of-band radaton and other ndex values. he utlty funton was onstruted frst. For the GNSS sgnal, rangng auray, ant-jang perforane and ant-ultpath perforane are rtal desgn fators. heoretally, the rangng auray depends on the ode trakng perforane, whose lower bound s nversely proportonal to the Gabor bandwdth of the odulated sgnal; lterature studes have shown that ant-ultpath perforane has a slar relatonshp wth the Gabor bandwdth. herefore, a utlty funton ould be used wth the Gabor bandwdth to reflet the rangng auray and ultpath perforane of the odulated sgnals, as follows: S (3) (4) U f G ( f)df (5) where B f s the front-end bandwdth, and G S (f) s the noralzed power spetru densty of the odulated sgnal s(t). he followng equaton shows the relatonshp between G S (f) and the sgnal wavefor: G f p t t p t t j ft j ft S( ) Ie d e d (6) where p I (t) and p (t) an be derved fro (3). he ant-jang perforane s uh ore oplated to evaluate. hs phenoenon s related to dfferent proessng steps, suh as aquston, trakng, and deodulaton, and dfferent types of jang. Xue et al. proposed a set of ndators, and evaluaton of the ant-jang perforane an be onstruted based on these ndators [8]. In fat, under the assuptons of long ode, these ndators exhbt the sae trend when they are nfluened by sgnal odulaton, and seletng representatve ndators an splfy the wavefor optzaton proess. he ant-athed-spetru-jang ert fator DeAJS

3 RADIOENGINEERING, VOL. 7, NO. 3, SEPEBER 8 85 was adopted to easure the odulaton ant-jang perforane. he ant-athed-spetru-jang ert fator DeAJS s defned as: log (db) (7) R GS ( f)df DeAJS B f d where R d denotes the essage rate. herefore, the perforane of the ant-jang utlty funton an be defned as: S U G ( f )df. (8) In suary, the ntegrated utlty funton of a GNSS sgnal s as follows: U log U log U (9) where s the weghtng fator of the ant-jang perforane and ant-ultpath perforane wth respet to the rangng perforane. Applyng the logarth operaton an avod the probles aused by dfferent sales. he desgn of the onstrant funton s related to the out-of-band radaton ltaton of the frequeny band n whh the sgnal s loated, assung that N adjaent frequeny bands of the GNSS sgnal are nvolved, that the frequeny range of the -th frequeny band s fl, f U, the out-of-band radaton onstrants are onstruted as follows f U G ( )d S f f fl C I f f () U where N, I s the axu average PSD(APSD) n the -th frequeny band derved fro IU rules. 3. Nueral Optzaton ethod Frst, the sgnal wavefor s sapled; the saplng rate f s = KR, K s an nteger, and R s the ode rate. hen, the phase trajetory saples to be optzed an be expressed as a vetor L θ,,..., K. () he wavefor saplng values of the I& branh sgnals defned n (3) are as follows: p p os θθ,, sn θ, θ () I f f where [ ] denotes the atrx transpose. f s the flpped vetor of, whh s defned as θ f K, K,...,. A frequeny vetor s defned as follows: R f [ K, K,..., K ] (3) where (an nteger) denotes the nteger ultple of the oversaplng power spetru. he power spetru vetor ould be alulated as Dag Vp Dag I VpI Vp Vp S (4) 4K R where () denotes onjugate transposton, Dag[ ] eans extratng the an dagonal eleents, and S s a olun vetor. V s a vanderonde atrx wth K rows and K oluns that s onstruted by vetor exp[jπf /(K)], whh s defned as: K j f j f j f K K K V,e, e,..., e. (5) he above proess ay also be pleented on a zero-padded fast Fourer transfor (FF). he orrespondng utlty funton s: 3 R U K S U S, (6) where S s the -th eleent of vetor S, R KR B f f, KR B R R (7) where eans roundng down. By defnton, the utlty funton of the dsrete wavefor s U 3 R log K S log S log. (8) Note that, a noral letter U s used to express the utlty funton of the dsrete wavefor, and thereby dstngush t fro the utlty funton of the ontnuous wavefor. Consderng the onotonty of the log funton, and assung that R,, and ω are onstants, so log(r /) 3 ω s a onstant, n the proess of searhng the axu of (8), we ould gnore t. he phase path optzaton an be expressed as arg axu arg ax log K S log S (9) wth the followng restrtons:

4 86 X. XIA, Z. P. ANG, J. L. WEI, E AL., SPECRALLY EFFICIEN CONSAN ENVELOPE ODULAION FOR GNSS U R C S I L KR f L f KR fu f L, U R R () hs optzaton proble ay be solved by any tehnques n optzaton theory. In ths paper, the penalty funton ethod s adopted. he penalty funton tehnque onverts the onstraned optzaton nto an approxate equvalent but unonstraned searh of the objetve funton. he unonstraned optzaton proble s nzng the followng N F( ) U( ) r C. () p(t) t(hp) Fg.. Optzed wavefor. I Here we use the uas-newton ethod to get the optal result of the optzaton proble. r s the penalty fator of out-of-band suppresson RAS RNSS uplnk RNSS downlnk LS 4. Sulaton Results In ths seton, usng the C-band as an exaple and an RNSS ar-to-ground applaton loated at 5 to 53 Hz, the anly out-of-band restrtons oe fro the RAS band, and the opatblty between the RNSS downlnk sgnal and the RNSS uplnk sgnal ust be onsdered. In the optzaton proess, the I& branh sgnals are staggered by half a hp to satsfy the onstant envelope feature, and the ode rate s Hz. o obtan a balane between bandwdth ltaton and perforane proveent, the penalty fator r s vared. r = e5 s set to fnd the optzed wavefor n Fg., and the weghtng fator ω =. Fgure shows the PSDs of the proposed SPECE, GSK-BPSK(), GSK-BOC(5,5), SK-BCK and SK-BCS ethods, where SK-BCS eans SK- BCS([,,,,,,,,, ],), and SK-BCS eans SK-BCS([,,,,,,,,,],) [7]. Aordng to Fg., the proposed SPECE ethod has an obvous an lobe n the RNSS downlnk band and uh lower APSD than the other odulatons n adjaent bands. hus, ths ethod has less out-of-band radaton and better opatblty wth the RAS and RNSS uplnk bands. In ab. the Gabor bandwdth, DeAJS, RAS band APSD and RNSS uplnk band APSD of SPECE and other odulatons are opared. he Gabor bandwdth s the root-ean-square (RS) bandwdth n hertz [8], and as the Gabor bandwdth nreases, the nherent ablty to avod sall ode trakng errors proves. It s defned as Gabor. () f Gs( f)df PSD(dBW/Hz) SPECE GSK-BPSK() GSK-BOC(5,5) SK-BCS SK-BCS frequeny(hz) Sgnal opton Fg.. Sgnal opton power spetra. Gabor bandwdth (dbhz) DeAJS (db) RAS Band APSD (dbw/hz) Uplnk Band APSD (dbw/hz) SPECE GSK- BPSK() GSK- BOC(5,5) SK-BCS SK-BCS ab.. he ndators of the sgnal optons. able shows that the Gabor bandwdth of SPECE s larger than GSK-BPSK(), GSK-BOC(5,5), SK-BCS, and SK-BCS. SPECE has a.9dbhz advantage opared to GSK-BPSK(). GSK-BOC(5,5), SK-BCS and SK-BCS's Gabor bandwdth are.9 dbhz, 3. dbhz, 3.8 dbhz, respetvely. DeAJS evaluates the ant-nterferene perforane of the GNSS sgnal, and larger values of ths ndex reflet better sgnals. In ab., the DeAJS of SPECE s slghtly lower than those of GSK-BPSK(), GSK- BOC(5,5) and SK-BCS but slghtly hgher than that of SK-BCS.

5 RADIOENGINEERING, VOL. 7, NO. 3, SEPEBER 8 87 o easure SPECE's opatblty wth the RAS band, ther APSDs were opared. he APSD of SPECE s 35.8 dbw/hz, whle the APSDs of GSK- BPSK(), GSK-BOC(5,5), SK-BCS and SK- BCS are 3. dbw/hz, 8. dbw/hz,.6 dbw/hz, and 5.3 dbw/hz respetvely. hus, SPECE aheves an proveent of dbw/hz opared to the other odulatons. Slarly, for RNSS uplnk sgnals, the APSD of SPECE s 3.4 dbw/hz, whle those of GSK-BPSK(), GSK-BOC(5,5), SK-BCS and SK-BCS are 96 dbw/hz,. dbw/hz, 88.7 dbw/hz and 93.4 dbw/hz, respetvely. herefore, SPECE aheves an proveent of dbw/hz opared to the other odulatons. hese lower APSD values allow the C-band to transt power and redue the nfluene of the C-band free spae loss growth, thereby dereasng the oplexty of the on-board load requred. he ultpath error envelope and ean ultpath error are used to reflet the ultpath perforane. Fgure SPECE GSK-BPSK() GSK-BOC(5,5) SK-BCS SK-BCS shows that the ultpath error envelope of SPECE s slghtly larger than those of the other odulatons when the ultpath delay s loated n (, ). In ontrast, when the ultpath delay s loated n (, ) and (, 4), SPECE's perforane s equal to those of the other odulatons. Fgure 4 presents the ean ultpath errors of the odulatons; all the odulatons exhbt slar perforane n ters of ths value. 5. Conluson In ths paper, a atheatal odel for the optzaton of GNSS sgnal wavefors was onstruted by ntegratng rangng auray, ant-jang perforane and out-of-band radaton suppresson requreents. By adjustng the paraeters ω and r, the balane between sgnal auray, ant-nterferene perforane and out-of-band radaton suppresson ould be aheved. he sulaton results show that the out-of-band radaton an be redued by about db opared wth the exstng shee when the sgnal perforane dfferene s lower than db. Aknowledgents ultpath error envelope() ean ultpath error() ultpath() Fg. 3. ultpath error envelope. SPECE GSK-BPSK() GSK-BOC(5,5) SK-BCS SK-BCS ultpath() Fg. 4. ean ultpath error. hs work s supported by the Natonal Sene Foundaton of Chna (NSFC), Grant 647. Referenes [] IRSIGLER,., HEIN, G. W., PEIFFER, A. S. Use of C-band frequenes for satellte navgaton: benefts and drawbaks. GPS Solutons, 4, vol. 8, no. 3, p DOI:.7/s [] XUE, R., CAO,.., WEI,. A flexble odulaton shee desgn for C-band GNSS sgnals. atheatal Probles n Engneerng, 5, artle ID 6597, p. 8. DOI:.55/5/6597 [3] HUANG, X., ZHU, X., OU, G. Constant-envelope dual PSK-lke odulaton and ts generalsed for for odern GNSS sgnals. Eletrons Letters, 5, vol. 5, no., p DOI:.49/EL [4] BEZ, J. W. Bnary offset arrer odulatons for radonavgaton. Navgaton: Journal of he Insttute of Navgaton,, vol. 48, no. 4, p DOI:./J B47.X [5] LAUREN, L., ARAUD, G., ISSLER, J. AltBOC for dues or everythng you always wanted to know about AltBOC. In Proeedngs of the st Internatonal ehnal eetng of the Satellte Dvson of he Insttute of Navgaton (ION GNSS 8). Savannah (USA), Sep. 8, p [6] AVILA-RODRIGUEZ, J. A., WALLNER, S., WON, J. H., et al. Study on a Galleo sgnal and serve plan for -band. In Proeedngs of the st Internatonal ehnal eetng of the Satellte Dvson of he Insttute of Navgaton (ION GNSS 8). Savannah (USA), Sep. 8, p [7] LIU,., ZHAN, X., LI, W., JING, S., CHEN,. An proved SK-BCS odulaton for global navgaton satellte systes n C

6 88 X. XIA, Z. P. ANG, J. L. WEI, E AL., SPECRALLY EFFICIEN CONSAN ENVELOPE ODULAION FOR GNSS band. IEEJ ransatons on Eletral and Eletron Engneerng, 6, vol., no. 4, p DOI:./tee.64 [8] XUE, R., SUN, Y., ZHAO, D. CP sgnals for satellte navgaton n the S and C bands. Sensors, 5, vol. 5, no. 6, p. 384 to 3. DOI:.339/s56384 About the Authors... Xuan XIA was born n Hube, Chna n 987. He reeved hs B.S. fro Huazhong Unversty of Sene and ehnology n 9. He s urrently workng toward the Ph.D. degree at the Shool of Eletron Inforaton and Counatons, Huazhong Unversty of Sene and ehnology, Chna. Hs researh nterests nlude next generaton GNSS sgnals and sgnal proessng algorth of GNSS reevers. Zupng ANG (orrespondng author) was born n Chongqng, Chna n 98. He reeved hs B.S.,.S. and Ph.D. degrees fro Huazhong Unversty of Sene and ehnology, Wuhan, Chna, n, 5 and 9, respetvely. He s urrently an assoate professor of the Shool of Eletron Inforaton and Counatons, Huazhong Unversty of Sene and ehnology. Hs researh nterests nlude GNSS sgnal desgn theory, sgnal qualty evaluaton and GNSS reever tehnque. Jaolong WEI was born n Jangx, Chna n 965. He reeved hs B.S.,.S. and Ph.D. degrees fro Huazhong Unversty of Sene and ehnology, Wuhan, Chna, n 986, 99 and 4, respetvely. He s urrently a professor, Ph.D. supervsor and ve-dean of the Shool of Eletron Inforaton and Counatons, Huazhong Unversty of Sene and ehnology. Hs researh nterests nlude wreless ounatons and networks, ntellgene oputaton and satellte navgaton. Zhhu ZHOU was born n Hunan, Chna n 988. He reeved hs B.S. fro Huazhong Unversty of Sene and ehnology n. He s urrently workng toward the Ph.D. degree at the Shool of Eletron Inforaton and Counatons, Huazhong Unversty of Sene and ehnology, Chna. Hs researh nterests nlude next generaton GNSS sgnals and sgnal proessng algorth of GNSS reevers.