GNSS software receiver sampling noise and clock jitter performance and impact analysis

Transcription

1 Inernaional Global Navigaion Saellie Sysems Soiey IGNSS Symposium 3 Ourigger Gold Coas, Qld Ausralia 6-8 July, 3 GNSS sofware reeiver sampling noise and lok performane and impa analysis Chen JianYun () College of Meharonis Engineering and Auomaion Naional Univ. of defense Tehnology China kdjy@sina.om Fen XuZhe () College of Meharonis Engineering and Auomaion Naional Univ. of defense Tehnology China kdjy@sina.om ZhouYonBin (3) College of Meharonis Engineering and Auomaion Naional Univ. of defense Tehnology China kdjy@sina.om ABSTRACT In he design of a muli-frequeny muli-onsellaion GNSS, sofware defined radio reeivers are beoming more and more popular due o is simple arhieure, flexible onfiguraion and good oherene in mulifrequeny signal proessing. I plays an imporan role in navigaion signal proessing and signal qualiy monioring. In pariular, GNSS sofware defined radio reeivers driving he sampling lok of analogue-o-digial onverer (ADC) by FPGA implies ha a more flexible radio ranseiver design is possible. Aording o he onep of sofware defined radio(sdr), he ideal is o digiize as lose o he anenna as possible. Whereas he arrier frequeny of GNSS signal is of he frequeny of Gz, onvering a his frequeny is expensive and onsumes more power. Band sampling mehod is a heaper, more effeive alernaive. When using band sampling mehod, i is possible o sample an RF signal a wie he bandwidh of he signal. Unforunaely, he inroduion of SDR onep and band sampling mehod indue negaive influene on he performane of he GNSS reeivers. ADC s suffer larger sampling lok generaed by FPGA; and a low sampling frequeny inrodues more noise o he reeiver. The influene of sampling noise an no be negleed. The paper analyzes he sampling noise, presens is influene on he arrier noise raio, and derives he ranging error by alulaing he synhronizaion error of he delay loked loop. Simulaions aiming a eah impa faor on sampling-noise-indued ranging error are performed. Simulaion resuls show ha if he arge ranging auray is a he enimeer level, he izaion lengh should be no less han 8 bi and he sampling lok should no exeed 3 ps. KEYWORDS: GNSS sofware reeivers, band sampling, sampling noise, lok, ranging error.

2 . INTRODUCTION Spread-sperum ranging has been widely applied wih he rapid developmen of GNSS ehnology, for is advanage of long unambiguous disane and high preision. Tradiional GNSS reeivers have been designed wih dediaed hannels eah apable of raking only a single saellie ode. In order o obain a good navigaion soluion, i is only neessary o operae enough raking hannels in a GNSS reeiver o obain suffiien saellies in view o ahieve good geomeri diluion of preision. Tha generally only requires beween six o welve Global Navigaion Saellie Sysem (GNSS) signals. As he number of odes and frequenies inrease, he demands on a onvenional GNSS reeiver ge higher. The inrease in he number of hannels using a onvenional reeiver design would also resul in inreased devie size and orrespondingly higher power operaion. Wih he inrease in he variey of GNSS signals required o be proessed by full-funion GNSS reeiver, he need for more flexible reeiver arhieures is neessary. As a resul, he sofware defined radio (SDR) onep was adoped o rak differen GNSS saellie odes and frequenies. SDR essenially allows he haraerisis of he GNSS reeiver o be hanged, enabling i o adap o differen GNSS appliaion sysems. This is possible by he use of programmable hardware (suh as a FPGA). In pariular, driving he sampling lok of analogue-o-digial onverer (ADC) by FPGA implies ha a more flexible radio ranseiver design is possible. Fig. shows a ypial reeiver sruure of a GNSS reeiver based on SDR. Aording o he onep of SDR, he ideal is o digiize as lose o he anenna as possible, bu when he arrier frequeny of GNSS signal is of he order of Gz, onvering a his frequeny is expensive and onsumes more power. Band sampling mehod is a heaper, more effeive alernaive. When using band sampling mehod, i is possible o sample a RF signal a wie he bandwidh of he signal. Unforunaely, he inroduion of SDR onep and band sampling mehod indue negaive influene on he performane of he GNSS reeiver. ADCs suffer larger sampling lok generaed by FPGA; and low sampling frequeny inrodues more noise o he reeiver. Obviously, he preision of spread-sperum ranging will be influened by he sampling noise. Espeially in high-auraely appliaions, he ranging error aused by sampling noise should no be ignored. As desribed in lieraure, sampling noise direly impas on he ranging error and bi error. There are few researhers ha ake sampling noise ino aoun on GNSS reeiver s spread-sperum ranging error and navigaion daa bi error. Yu Faxin e al. sudied he effe on ranging auray of regeneraive pseudo ode by he sampling lok. Yuan Jun e al. sudied he influene of izaion noise o muliple frequeny oninuous wave ranging radar. This paper fouses on he influene of he sampling noise on he arrier-noise-raio (C/N), inluding boh izaion noise and noise inrodued by aperure, sequenially examines he ranging error indued by he sampling noise. Simulaions and experimens in order o presen he numeri onneion beween ranging error and he impa faors of sapling noise are desribed a he end of he paper.

3 Figure. Typial Sofware Defined Radio GNSS Reeiver Arhieures. SAMPLING NOISE DEFINE AND ANALYSE. Clok indued sampling noise Sine he primary purpose of a daa onverer is o ake regular ime digial samples and produe an analog signal, or o ake an analog oninuum and produe a series of regular ime digial samples, sabiliy of he sampling lok is very imporan. From a daa onverer perspeive, his insabiliy is alled lok or aperure and resuls in unerainy as o when he analog inpu is aually sampled. There is a wealh of informaion available on he opi of phase noise, is haraerisis, how i an be measured, and how i affes sysem performane. I is well known ha phase noise in osillaors and loks beomes one of he limiing degradaions in modern radio sysems. owever, mos radiional analysis onenraes on degradaions o sine wave signals in single arrier radio sysems. The effes of phase noise on GNSS wideband sysems are very rarely disussed. The easies way o alulae he degradaions inurred by phase noise in a sampled daa sysem is o onver phase noise o phase. This is mos easily aomplished by reognizing ha a ime delay is he same as a phase delay a a given frequeny. Exending his onep and wriing i in erms of noise power yields Equaion. () lk where is phase noise in rms radians, is phase in rms seonds, lk is lok frequeny in radians/se. Tha is, for a given error, a higher frequeny signal will have more phase error. Thus, Equaion relaes he oal inegraed phase noise, or lok, o he oal in he lok. Phase noise and lok are wo differen ways o look a he same phenomenon. Figure. Sample Clok in he Time Domain Showing Wha Clok Jier May Look Like Tradiional sampled daa analyses use Figure as an aid o deermine how noise on a lok generaes an error in he sampled daa. From his i is seen ha: v v () E v E v (3)

4 where () is he inpu GNSS signal wave funion, ' ( ) is he derivaive of GNSS signal, is sample lok, is sample lok indued signal ampliude error, he relaionship of and is E. Beause and v is zero mean and independen, err (4) E v E E v E v From his i is seen ha he noise power is a funion of he phase and he power in he signal derivaive. The of a signal sampled wih a lok is defined as Ev (5) E v For example, in a single sine wave, err sin v A (6) os v A (7) Therefore The of sine wave signal sampled wih a lok is, A A 4 f (8) This is he sandard equaion for a single sine wave sampled by a lok wih and an be found in many publiaions. Inuiively wha is happening is ha higher frequeny signals have larger slew raes. GNSS sysem using spread sperum ehnology o measuring range and veloiy, whih oupies a fairly wide sperum. In order o deermine how lik effes he for suh sysems, i mus onsider he GNSS signal power sperum disribued and signal bandwidh. One form of Parseval s heorem saes ha he power of a signal in he ime domain equals he power of he signal in he frequeny domain. Tha is, v d g d g f df (9) Where g f is he power speral densiy inwa/z. In addiion, using he differeniaion heorem of he Fourier ransform, whih saes ha he Fourier ransform of a derivaive is jus he Fourier ransform of he original funion muliplied by iω, as shown below, v jv () and ombining his wih Parseval s heorem, i is seen ha he power in v is he same as

5 he power in j g, as desribed below, v d jg d f g f df () Suppose he GNSS signal disribued beween f L and f, he oal signal power is we have he follow resul, f f f f L E v g f df df,hen () f f E v f g f df f df (3) L In his paper, we researh and simulae he Beidou GNSS Open Servie Signal BI. The B signal is he sum of hannel I and Q whih are in phase quadraure of eah oher. The ranging ode and NAV message are modulaed on he BI arrier wih ener frequeny Mz, a hip rae of.46 Mps, and he PRN sequene lengh of 46 hips. These frequenies are all oheren wih a.3 Mz lok. The BeiDou BI signal is a phase-modulaed signal wih φ=,π; his ype of phase modulaion is referred o as bi-phase shif keying (BPSK). The phase hange rae is ofen referred o as he hip rae. The sperum shape an be desribed by he sin funion (sinx/x) wih he sperum widh proporional o he hip rae. The signal sperum of BeiDou BI an be expressed as follows, sin C ode where C he disree Fourier ransform of he spreading ode. f f g f T N ft X f (4) T is spread ode ime widh, N is he spread ode period number, and ode n N n X f is N X f x expj fnt (5) We an see ha he dominaing sperum sruure of g f is sin funion,and X ode f offer a refined sperum sruure. The dominaing sperum sruure g f is he primary elemen of BPSK and QPSK modulae ype GNSS signal, so we an ignore he influene of g f T N sin ft. X f, he g f an be expressed as ode f C sin C f (6) E v g f df NT ft df f 4 C sin f (7) E v f g f df NT f ft df ode

6 he resuling from a BPSK wideband signal beween f L and f being sampled by a lok wih is, E v 4 E v f f sin ft df f sin ft df (8) An alernaive expression is obained by leing f f BW L and. For his ase he expression beomes, 4 f BW f BW f BW f BW sin ft df f sin ft df (9) b For inegral equaion of sin ft df and sin a b a f ft df, we use malab symboli mah oolbox o alulae he resul. If signal power is P s, hen alernaive Ps expression of of signal sampled wih a lok an be express as, N where N is lok indued sample noise.. Quanizaion indued sampling noise The ADC izaion error an be expressed as () Q () where Q is he izaion sep size, N is he ADC izaion bis lengh and one bi is sign bi. Supposing he ampliude of he inpu signal is A, hen he of signal sampled wih izaion noise in all Nyquis sample bandwidh an be expressed as A 6A 3 N () Q If we onsider he deail informaion of sampling frequeny f s and signal bandwidh BW, he improved equaion of of sampled signal is, N 3 fs () 4BW As he same supposing, If signal power is P s, hen alernaive expression of of signal

7 sampled wih izaion noise an be express as Ps N 3 fs N 4BW..3 Whie noise indued sampling noise Noise ompees wih a man-made signal a he reeiver in almos all radio sysems. In his paper, we onern ourselves wih whie noise. The whie noise onsiss of noise omponens from all frequenies wih equal srengh, and so i has a power speral densiy ha is a N onsan W/z. Whie noise is an exellen model for he naural noise ha is reeived along wih BeiDou signals, beause naural noise has a onsan power speral densiy aross he GPS band. owever, whie noise may no be a good model for man-made signals ha may find heir way ino he BI band. We will disover ha he raio of he arrier wave signal power C o he oal noise power speral densiy is a key sysem parameer. The of a signal sampled wih whie noise is defined as he funion of C/N and BW. Ps C (3) N N BW.4 Toal sampling noise resul The oal should onsider he noise, izaion noise and hermal noise of he daa onverer. oal Ps N N N Ps Ps Ps Ps (4) Using his, he deailed for he oal may be expressed as, oal f BW f BW f sin ft df f BW 4BW BW 4 C f BW N 3f N sin ft df s (5) We will disover ha he raio of he signal power, C, o he oal noise power speral densiy is a key sysem parameer. We will denoe his raio as C/N, hen an expression of C/N for he sampled signal an be expressed as, C N oal BW oal (6) A ypial lok osillaor haraerisi is expressed as phase noise beause here is a dire relaionship beween phase noise and. In an aual GNSS reeiver, he sample lok frequeny is a muliple of he foundaion osillaor lok frequeny, so we should onsider

8 he relaionship of and f s. To deermine he, he firs sep is o deermine oal noise power by inegraing he noise over he bandwidh. For a lok osillaor, he differen regions of phase noise urve may be inegraed separaely and hen added ogeher o provide he oal resuls. An example of ypial phase noise urve is show as Figure 3. Figure 3. Sample Jier Calulaion Assuming Broadband Phase Noise The firs sep in alulaing he equivalen rms is o obain he inegraed phase noise power over he frequeny range of ineres, i.e., he area of he urve, A. The urve is broken ino a number of individual areas (A, A, A3, A4), A lg( A A A3 A4 ) (7) os_ lk os_ lk os_ lk os_ lk os_ lk Generally speaking, he upper frequeny range for he inegraion should be wie he osillaor frequeny. If he sample lok frequeny is M muliple of foundaion osillaor lok frequeny, hen we have, sample _ lk os _ lk A log M A (8) The inegraion of eah individual area yields individual power raios. The individual power raios are hen summed and onvered bak ino db. One he inegraed phase noise power is known, he rms phase in radians is given by he equaion. sample _ Asample _ lk / ( rad) M (9) lk _ and dividing by fsample _ lk onvers he in radians o in seonds, M M (3) sample _ lk _ sample _ lk _ fsample _ lk fsample _ lk 3. RANGING ERROR DUE TO SAMPLING NOISE As we shall see, he ranging performane also depends on he signal-o-noise raio C/N, and he averaging ime used by he reeiver. Delay loked loop (DLL) is widely employed o rak he pseudo-noise (PN) ode in spread sperum ranging sysems. Ranging error in an ideal

9 senario in whih here is no mulipah, ionspheri or ropospheri errors is aused by he synhronizaion error of DLL, whih mainly onsiss of hermal noise indued error and dynami sress indued error. Carrier noise raio (C/N) is used o analyze he synhronizaion error. The equivalen noise bandwidh of DLL is always muh narrower han he bandwidh of he sampling noise. Considering a dire sequene spread sperum (DSSS) sysem wih binary phase shif keying (BPSK) modulaion, ake he well known nonoheren DLL using early lae power disriminaor for insane, he synhronizaion error DLL due o hermal noise and sampling noise is DLL B n R T D, D C/ N TC/ N( D) Bfe B n BfeT R R T D, D C/ N BfeT BfeT TC/ N ( D) Bfe B fe B n R T, D C/ N BfeT TC/ N Bfe (3) where T is he period of PN ode (s), Bn is he equivalen loop noise bandwidh of DLL (z), D is he ime spaing of he early lae orrelaor normalized wih respe o one PN ode hip, T is he predeeion inegraion inerval (s), R is he PN ode hip rae (hips/s); and B fe is he double-sided bandwidh of he analogue fron end (z). Based on he AGWN hypohesis of sampling noise, he sampling noise indued ranging errors an be separaed simply as s e (3) DLL DLL where DLL is he synhronizaion error due o hermal noise, and is he speed of radio signal. 4. SIMULATION RESULTS Assoiaing formula (5) wih formula (3), he impa faors of ranging error due o sampling noise inlude izaion bis, sampling lok, inermediae arrier frequeny, sampling rae, and signal srengh. When designing band-sampling sysems, all he faors menioned above should be onsidered omprehensively. Four simulaions are performed and analyzed in his seion, for purpose of presening he numerial relaionship beween ranging 8 error and sampling noise. For simulaion examples, 3 m/s, f 4Mz, flk Mz, B n =8z, D =hip, T ms, R =.46Mps, B = fe R, lk _ 5ps, and he ondiion all for he seond equaion in formula (3) o alulae he ranging error. Fig. 4 shows he ranging error urves for he siuaions where he izaion bis range from o and he C/N of he inpu analogue signals are 3dB-z, 35dB-z, 4dB-z, 45dB- z and 5dB-z. In addiion, ranging error due o sampling lok is ignored o bring influene of izaion noise ino prominene, and for simpliiy, he sampling rae is wie as he frequeny of osillaor, hus Mz. From Fig.4, i is observed ha he ranging error exeeds m when izaion bis are less han 6, and he weaker he inpu signal is, he ranging error dereases faser wih he inrease of he izaion bis. Wha s more, in spie of he assumed signal srengh, he ranging error falls off nearly o sabilizaion when he izaion bis are more han 8. Aordingly, he izaion bis equal o 8 in he following simulaions.

10 addiion sampling noise indued ranging error(m) C/N=3dBz C/N=35dBz C/N=4dBz C/N=45dBz C/N=5dBz izaion bis Figure 4. Ranging error vs. Quanizaion bis and signal srengh In Fig. 5 and Fig. 6, he ranging error versus he sampling lok is presened. The sampling rae is he same as he previous simulaion, izaion lengh is 8 and f 4Mz, and C/N of he inpu signal is 45dB-z in Fig. 6. We an see he ranging error exeeds m a he given signal srengh and arrier frequeny. addiion sampling noise indued ranging error(m) C/N=3dBz C/N=35dBz C/N=4dBz C/N=45dBz C/N=5dBz osillaor lok (ps) Figure 5. Ranging error vs. Sampling lok and signal srengh.

11 addiion sampling noise indued ranging error(m) f = Mz f = 3Mz f = 4Mz f = 5Mz f = 6Mz osillaor lok (ps) Figure 6. Ranging error vs. Sampling lok and inermediae arrier frequeny. I should be noied ha in he simulaions above, he sampling rae is fixed o Mz, he onneion beween he ranging error and he sampling frequeny wih differen inermediae arrier frequenies is demonsraed in Fig. 7. The izaion lengh is 8; he osillaor lok is 5ps and C/N of he inpu signal is 45dB-z. I an be seen ha hough ranging error redues wih he inrease of he sampling frequeny, he urves show a paraboli figure, so here exiss a minimum ranging error in all sampling frequenies. Sysem design should give aenion o sampling rae and proessing abiliy. addiion sampling noise indued ranging error(m) f = Mz f = 3Mz f = 4Mz f = 5Mz f = 6Mz sampling frequeny(mz) Figure 6. Ranging error vs. Sampling frequeny and inermediae arrier frequeny. 5. CONCLUSION

12 The arile analyzed he sampling noise wih an emphasis on is influene upon ranging preision of a sofware defined radio spread-sperum sysem. Sampling noise is dominaed by izaion noise and sampling-lok--indued noise. Sampling noise, whih an be reaed as AGWN when a DLL is adoped, adds hermal noise and degrades he C/N of he sampled daa. By virue of he C/N, ranging errors aused by sampling noise an be alulaed. Quanizaion bis, sampling lok, inermediae arrier frequeny, sampling rae, and signal srengh are he main faors ha impa ranging error. Simulaions aiming a hose faors show ha if he arge ranging auray is he level of enimeers, he izaion lengh should be no less han 8 and he sampling lok should no exeed 3ps. Simulaions also demonsrae ha he effe of inreasing he sampling frequeny on he ranging error is limied. REFERENCES ZANCI A SAMORI C. Analysis and haraerizaion of he effes of lok in A/D onverers for subsampling[j], IEEE Trans. On Ciruis and Sysems, 8,55(): DEMPSTER A. Aperure effes in sofware radio GNSS reeivers[j]. Journal of Global Posiioning Sysems, 5, 3(-): DUAN Z L, LIU Y. Analysis on navigaion reeivers error soures[j].radio Engineering, 9,39( 7): YU F X, XU X L, GUAN J, e al. Effe on pseudo ode ranging preision by A/D sampling lok [J].Chinese Journal of Sensors and Auaors, 7, (5):8-85. YUAN J Q, CEN Z, CAO P J. The effe of ifiaion noise o performane of muliple frequeny CW ranging radar[j]. Eleroni Informaion Warfare Tehnology, 7,, No. 3, pp. 3-35, May. BRANNON B. Aperure unerainy and ADC sysem performane[ol] p:// ZINEROFER C M. Quanizaion noise as superposiion of frequeny-modulaed sinusoids. IEEE Signal Proessing Leers, Vol. 6, No., pp , Nov. 9. YU C, DUAN D P, WANG J Y. A/D onverers signal-o-noise raio analysis and is appliaion in moonle erminals[j], Chinese Journal of Spae Siene, 4,4(5): KAPLAN E D, CRISTOPER J. egary, Undersanding GPS: Priniples and Appliaions (Seond Ediion)[J].Areh ouse In., 6:-73. Brad Brannon, Sampled Sysems and he Effes of Clok Phase Noise and Jier, p://