Design Considerations for Direct RF Sampling Receiver in GNSS Environment

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1 Desig Cosideratios for Direct RF Samplig Receiver i GNSS Eviromet Ville Syrjälä, Mikko Valkama ad Markku Refors Tampere Uiversity of Techology Istitute of Commuicatios Egieerig Korkeakoulukatu 1, Tampere, Filad {ville.syrjala, mikko.e.valkama, markku.refors}@tut.fi Abstract I this paper, the applicability of advaced direct RF samplig receiver architecture is studied i the GNSS eviromet. The architecture is based o samplig the sigal directly at RF, which i the GNSS case is i the 1.5 GHz rage. The high-frequecies i the sigal to be sampled pose the very high demads for the accuracy ad quality of the samplig process, ad thus quatizatio ad especially the timig aspects must be cosidered i detail. Both system calculatios as well as computer simulatios are used to assess the essetial requiremets for the samplig process. I summary, the study shows that the quatizatio ad requiremets are i priciple feasible whe the pre-samplig filterig is doe properly. Idex Terms Direct RF Samplig, radio receiver desig, satellite avigatio systems, timig N I. INTRODUCTION ot oly the wide scale chages i basic techologies of Global Navigatio Satellite Systems (GNSS), but also the demads for low-cost ad flexible GNSS receivers have bee greatly icreasig durig the last few years i may applicatio areas. As practical examples, car avigatio systems are becomig almost a essetial igrediet of betterclass cars, ad the demads for GNSS itegrated cellular phoes are also icreasig [5]. The car avigatio systems eed to be as cheap as possible ad cellular phoe itegrated avigatio systems must also be small ad have very low power cosumptio. I additio, as the cellular phoes of course eed to capture the cellular sigals as well, there is geerally big iterest to receive Global System for Mobile Commuicatios (GSM), Uiversal Mobile Telecommuicatios System (UMTS) ad GPS/Galileo sigals, all with oe flexible receiver architecture. Direct RF Samplig (DRFS) receiver architecture is oe promisig approach for buildig flexible radio receivers. The idea of DRFS is to sample the sigal at as early stage of the receiver as possible. The dow-coversio of the highfrequecy sigals ca be doe withi the samplig process itself, usig aliasig i a cotrolled maer. So there is o This work was supported by the Fiish Fudig Agecy for Techology ad Iovatio (Tekes; uder the project Advaced Techiques for Persoal Navigatio ), the Academy of Filad (uder the project #11643 Uderstadig ad Mitigatio of Aalog RF Impairmets i Multiatea Trasmissio Systems ), ad the Techology Idustries of Filad Ceteial Foudatio. eed for aalog mixers ad thus the aalog compoet cout decreases. Aalog compoets are usually bulky, expesive ad use quite much power, so the basic cocept of the DRFS gets very iterestig. I additio, the flexibility of the DRFS receiver is at a very high level because the sigal is sampled directly from the radio frequecies (RF). Naturally, the sigal must be filtered to some extet before samplig but the filterig ca be doe so that the sigals of more tha oe commuicatios systems ca be processed ad received. I geeral, the topic of DRFS has ot yet bee very thoroughly ivestigated i the joit cellular/drfs receiver cotext, ad there are oly a few papers that cosider the practical implemetatio of the DRFS priciple. Thus, the idea is very promisig but more research eeds to be doe o the topic. The direct RF samplig receiver architecture has bee cosidered i [1], [] ad [1] with focus o the GNSS case, ad more geerally i [4]. Oe of the mai problems i a DRFS receiver is the high demads for the quality of the samplig process, due to the high frequecies of the sigals to be sampled [6], [15]. This paper cocetrates o the requiremets the DRFS receiver has for the samplig process i GNSS applicatios. First, the samplig ad the quatizatio effects o the effective sigal-to-oise ratios (SNR) are cosidered, usig system calculatio priciples at a geeral level. The, the samplig ad quatizatio level requiremets for samplig GNSS sigals cetered at MHz (E-L1-E1) bad are cosidered i detail. After the requiremets have bee derived by system calculatios, the results are verified usig simulatios. II. BASIC NON-IDEALITIES IN SAMPLING The mai sources of oise i samplig systems are the limited umber of bits i the quatizatio ad uitetioal deviatios called i the momets the samples are take [14]-[16]. Limits i these o-idealities are of iterest whe a high-performace samplig system is eeded i demadig eviromets such as i DRFS receiver [13]. I the followig system calculatios, we focus o power spectral desities () of the oise compoets geerated i the samplig process. I this Sectio, s for quatizatio ad oise are determied. These are the used i Sec-

2 tios III ad IV for derivig the quatizatio ad requiremets for capturig ad receivig GNSS sigals usig the DRFS priciple. A. Quatizatio Noise The most basic o-ideality i a samplig system is the quatizatio oise [14]. If a sampled sigal has values from 1 to 1 ad bit quatizatio is used, the possible error value is uiformly distributed betwee ad. Thus the power of the quatizatio oise is var( ei ( )) = (1) 3 where e(i) is the error of the i-th sample. Assumig a siusoidal sigal with root mea square (RMS) power of (V rms ) =1/, the SNR due to quatizatio ca be writte as: SNR 1/ 3 /3 quat = = () I quatizatio, the white oise model is usually cosidered to be valid ad thus the of the quatizatio oise ca be writte as [14], [16]: quat P P P ( f ) = = = (3) quat sigal peak Fs SNRquat Fs 3Fs I (4), T =1/f is the cycle time of the assumed siusoid. Now, whe we multiply the RMS value of the voltage derivative by the RMS value of the Δt, we basically get the voltage error. The, by dividig the sigal power by oise power, the SNR due to ca be formulated as ( A / ) ( Aπ f Δt) SNR = = ( π f Δt) I [13], Shiagawa et al. have doe some calculatios with the same results ad oticed that this model is as accurate as expected. Now that the SNR is calculated ad we have coveietly got rid of the amplitude term, the power of the, P, ca be calculated as (5) P = P / SNR (6) total Here, P total is geerally the overall average power of the sampled sigal. If the oise is cosidered to be white oise ad thus spread over the Nyquist bad, we ca write the of the oise as ( f ) P P ( π f Δt) total = = (7) Fs Fs Similar results were got,e.g., by Valkama et al. i [16]. I (3), we have substituted P sigal =P peak sice actually the peak power (amplitude), P peak, is the most critical quatity i quatizatio, istead of the average power of the sigal, P sigal. White oise aturally falls over the whole badwidth determied by the used samplig rate F s. B. Jitter Noise As the frequecies of the sampled sigals rise, the timig of the sampler ca also become a limitig factor i the performace of the samplig process [3], [13]. I this sectio, we study the cotributio of the oise geerated by the timig o the overall SNR performace of the system. The oise aturally depeds o the shape ad especially the rate of chage (derivative) of the sigal we are samplig. Because the trasmitted modulated sigals are of oscillatig ature i telecommuicatios, we ca assume for aalysis purposes that the iterestig sigal is a siusoidal sigal as well. Thus, its voltage ca be preseted as V(t)=A cos(πf t), where A ad f are the amplitude ad the frequecy of the sigal, respectively. With this assumptio, we are able to calculate the voltage error of the sigal whe we cosider oly the error due to the. I the aalysis, we use the RMS value of the timig, like usually doe i the literature [13], [14]. First, we determie the RMS value of the derivate of V(t), yieldig T δv 1 δv( t) = δt rms T = δt Aπ f (4) III. JITTER REQUIREMENTS IN DIRECT RF SAMPLING RECEIVER Oe possible approach to determiig the requiremets i a GNSS receiver was itroduced by Dempster i [6]. The approach is very simple ad is based o the basic properties of the GNSS sigals. As is kow, the GNSS sigals are uder the thermal oise level. Accordig to the specificatios, GPS sigal is ot expected to exceed 15 dbw i ay situatio [11] ad is thus uder the thermal oise with its ~ MHz badwidth. Also, Galileo sigal specificatios say that its sigals i E-L1-E1 bad are ot expected to exceed 148 dbw [8], ad have wider badwidth of iterest tha sigals of the GPS. The Galileo sigals are also geerally uder the thermal oise. Thus, whe samplig a GNSS sigal at RF, the sampled sigal practically cosists of or is domiated by the thermal oise or other iterfereces that are ot filtered out. As was show i (7), the power of the oise depeds o the overall power of the sampled sigal. Now, if the oise geerated by the is say 1 db uder the thermal oise, its cotributio to the total system oise ca be cosidered isigificat. The selected target of 1 db here is, of course, somewhat idicative but illustrates the lie of thought here. The situatio assumed here is illustrated also graphically i Fig. 1. The thermal oise is at a higher level tha the iterestig sigals ad possible iterferig i-bad sigals. I additio, some out-of-bad iterferig sigals may also be preset. Although ideally the sigal we sample is at thermal oise level, there might be other iterferig sigals preset if our pre-samplig filterig is ot selective eough (see Fig. 1). I

3 Fig. 1. The oise-domiated eviromet. The sigal with thicker lie is the sigal we are iterested i. additio, stroger other GNSS sigals might iterfere with the curret sigal of iterest (Fig. 1). Therefore, i determiig the overall power of the sampled sigal, these other sigals eed to be take ito accout. There is thus iterest to study cases where the total sampled power is, for example, 1 db, db ad 3 db over the thermal oise level, to make sure the study is extesive eough. This meas that the total sampled power, P total, ca be writte as: P = N (1 + x) = N + xn (8) total th th th i which x represets how may times stroger the overall out-of-bad iterferece is, compared to the thermal oise. For 1 db, db ad 3 db the values of x are 1, 1 ad 1 respectively. The of the thermal oise itself is [7]: 1 th ( f ) = kt (9) i which, T is the temperature ad k is the Boltzma s costat. Followig the the previous desig target of forcig the oise to be 1 db below the thermal oise level, the requiremets ca be derived from 1 ( f ) th ( f ) (1) 1 With the help of (7) ad (8), the requiremet ca the be formulated as Δt F s B(1 + x)( π f ) (11) Here, B is the sampled sigal badwidth. Now by deotig the oversamplig factor by osf=f s /B, this ca also be writte as Δt osf (1 + x)( π f ) (1) By usig (1), we get the basic results for the requiremets. The results are here evaluated for oversamplig factors of three, four ad eight as thought realistic i bad-pass samplig. These correspod to samplig rates of 9 MHz, 1 MHz ad 4 MHz with sigal badwidth of 3 MHz, which is sufficiet for Galileo receptio [1], [9]. Calculatig the results for more oversamplig factors is of course a trivial process. The obtaied results for requiremets are show i Table I. Based o these results, if there is o exteral iterferece i the system, the requiremets are relatively easy to meet with state-of-the-art samplig circuits. However, whe the iterferece icreases, the requiremets clearly get tighter ad tighter. Novel low-power aalog-to-digital coverters ad samplers have RMS value of about two picosecods [4]. Therefore, the tightest requiremet with oversamplig factor of eight is still feasible but already close to the limit. I iterferece-free eviromet, the samplig requiremets would ot be hard to achieve, but gettig such a semi-ideal eviromet would, i tur, result i very high requiremets for the selectivity of the RF froted filter stages. With more power-cosumig aalog-todigital coverters ad samplers, all the calculated requiremets are easily achievable, but the practical implemetatio i mobile receivers could ot yet be doe with the techology of today. Thus overall, the obtaied results icely summarize a tradeoff betwee the eeded frot-ed selectivity ad the eeded accuracy of the samplig process. IV. QUANTIZATION REQUIREMENTS IN DIRECT RF SAMPLING RECEIVER The quatizatio requiremets ca i priciple be calculated i a rather similar way as the requiremets. If the quatizatio oise is 1 db uder the thermal oise, the cotributio of quatizatio oise is o more tha that of the oise i the same situatio. As (3) shows, the quatizatio oise power depeds essetially o the peak power of the sampled sigal. Thus, the essetial differece betwee the ad the quatizatio studies is that while the oise depeds o the total sampled power, the quatizatio oise depeds o the peak power of the sigal. This is atural because the highest sigal amplitude must have its ow level i the quatizatio process. We also kow that i the GNSS eviromet, we practically sample bad-pass oise whose crest factor is aroud 1 (peak / RMS). We ca thus write: P total = 1/1 P (13) Puttig all these together, the requiremet for the quatizatio accuracy ca be formulated as peak 4 (1 + x) log / 3 osf (14) Here, is the amout of bits required. The requiremets ca be directly evaluated from (14). The results are show i Table II. As the results i Table II demostrate, the quatizatio requiremets are from three to eight bits depedig o the case. The requiremets are ot so high ad are achievable with ovel low-power aalog-to-digital coverters. Thus, the quatizatio oise does ot act as so strog limitig factor i a DRFS receiver as the samplig oise does.

4 TABLE I THE JITTER REQUIREMENTS FOR VOLTAGE SAMPLING DRFS RECEIVER P total / N th Oversamplig factor db 39.1 ps 45.1 ps 63.8 ps 1 db 11.7 ps 13.6 ps 19. ps db 3.89 ps 4.49 ps 6.35 ps 3 db 1.3 ps 1.4 ps.1 ps TABLE II THE QUANTIZATION REQUIREMENTS (IN BITS) FOR DRFS RECEIVER. P total / N th Oversamplig factor db.74 (3).53 (3).3 (3) 1 db 4.47 (5) 4.6 (5) 3.76 (4) db 6.6 (7) 5.86 (6) 5.36 (6) 3 db 7.7 (8) 7.51 (8) 7.1 (8) Fig.. Bad-pass-oise sigal sampled with 37.5 MHz samplig rate with 63.9 ps samplig. V. JITTER REQUIREMENTS VERIFICATIONS Next, our target is to verify by simulatios the calculatios we made i the previous chapters. Eve though the used system calculatio priciples are relatively wellestablished i geeral, the obtaied results should ayway be verified. As we saw i the results i Table I, 63.9 ps should be sufficiet to get the power 1 db below the sampled pass-bad-oise sigal power, if oversamplig factor of 8 is used. Now we will verify this result usig computer simulatios. The overall simulator is implemeted usig MathWorks Matlab 7. I the simulator, a bad-pass-oise sigal with MHz badwidth at E-L1-E1 bad ( MHz cetered) is sampled. We use a iitial samplig rate of 3.8 GHz i the actual simulatio stage (for accurate modelig) ad the sigal is the decimated without filterig to get a practical samplig frequecy of 37.5 MHz. This is equivalet for the oversamplig factor of eight for a badwidth of MHz. With origial samplig rate of 3.8 GHz, decimatio by 16 without filterig aliases the oise to lower frequecies as it would have aliased if the 37.5 MHz samplig frequecy would have bee used i the first place. The spectrum at the simulator output ca be see i Fig.. Based o the spectral illustratio, the simulatios clearly verify the fact that the oise ideed stays 1 db uder the thermal oise with 63.9 ps samplig i case of oversamplig factor of eight. I additio, we verify oe more case with oversamplig factor of 4. This is equivalet to situatio where decimatio by 3 to the origial sigal with 3.8 GHz samplig rate is applied. Thus, the resultig samplig rate is MHz. I this case, the samplig of 45. ps should take the oise 1 db below the thermal oise level. The results are show i Fig. 3. It ca agai be see that the oise is, ideed, 1 db uder the bad-pass-oise sigal ad thus the requiremets are valid for both oversamplig factors assumed i the system calculatios. Fig. 3. Bad-pass-oise sigal sampled with MHz samplig rate with 45. ps samplig. VI. CONCLUSIONS We have studied the oise ad quatizatio oise effects i the samplig ad A/D process with special focus o direct RF samplig receiver i GNSS cotext, ad derived the equatios for power spectral desities of such oises. Furthermore, the equatios for ad quatizatio requiremets for direct RF samplig receiver i GNSS eviromet were derived. It was assumed that if the power of the samplig oise is 1 db uder the thermal oise, the cotributio to the total system performace is dimiishig. The ad bit-resolutio requiremets were cosidered i a few realistic situatios. The results showed that if the selectivity i the RF filters is sufficiet, the bit ad requiremets are feasible. O the other had, if the presamplig filterig is ot doe properly, the requiremets for the rise to levels that are ot yet practical i mobile commuicatios devices, at least with today s techologies. Jitters of aroud or eve less tha oe picosecods are actually achievable with high-power aalog-to-digital coverters of today but are by o meas practical i mobile devices due to their high power cosumptio. The resolutio requiremets, i tur, seemed quite relaxed eve with high iterfer-

5 ig sigal levels. Practically, eight bits would be eough eve i very demadig applicatios. Simulatios were fially used to verify that with the calculated samplig requiremets, the oise ideed stays 1 db uder the thermal oise, which was used as the desig priciple i the system calculatios. REFERENCES [1] D. M. Akos, A. Ee, ad J. Thor, A Prototypig platform for multifrequecy GNSS receivers, i Proc. Istitute of Navigatio GPS/GNSS Meetig, Portlad, USA, 3. [] D. M. Akos, ad J. B. Y. Tsui, Desig ad implemetatio of a direct digitizatio GPS receiver frot ed, IEEE Trasactios o Microwave Theory ad Techiques, Vol. 44, No. 1, pp , December [3] B. Ami, ad A. G. Dempster, Samplig ad cosideratios for GNSS software radio receivers, i Proc. IGNSS Symposium 6, Gold Coast, Australia, 17 1 July 6. [4] V. J. Arkesteij, E. A. M. Klumperik, ad B. Nauta, Jitter requiremets of the samplig clock i software radio receivers, IEEE Trasactios o Circuits ad Systems II: Express Briefs, Vol. 53, No., pp. 9-94, February 6. [5] F. Behbahai, H. Firouzkouhi, R. Chokkaligam, S. Delshadpour, A. Kheirkhai, M. Narima, M. Cota, ad S. Bhatia, A fully itegrated low-if CMOS GPS radio with o-chip aalog image rejectio, IEEE Joural of Solid-State Circuits, Vol. 37, No. 1, pp , December. [6] A. G. Dempster Aperture effects i software radio GNSS receivers, i Proc. The 4 Iteratioal Symposium o GNSS/GPS, GNSS 4, Sydey, Australia, December 6-8, 4. [7] W. F. Ega, Practical RF System Desig, Joh Wiley & Sos, Ic. 3. ISBN p. [8] Europea Space Agecy (ESA) / Galileo Joit Udertakig, Galileo Ope Service i Space Iterface Cotrol Documet (OS SIS ICD) Draft, 6. [9] G. Heirichs, R. Bischoff, ad T. Hesse, Receiver architecture syergies betwee future GPS/Galileo ad UMTS/IMT-, i Proc. VTC -Fall, Vacouver, Caada,, pp Vol. 3. [1] H. Huttue, Sigaalikäsittely sovellukset, Tampere Uiversity of Techology, Istitute of Sigal Processig, Filad, 6. ISBN , ISSN p. [11] IS-GPS-. Iterface specificatio Navstar GPS space segmet/avigatio user iterfaces, IS-GPS-D, December 7, 4. [1] M. L. Psiaki, D. M. Akos, ad J. Thor, A compariso of direct RF samplig ad dow-covert & samplig GNSS receiver architectures, i Proc. Istitute of Navigatios GPS/GNSS meetig, Portlad, USA, 3, September 9-1, 3. [13] M. Shiagawa, Y. Akazawa, ad T. Wakimoto, Jitter aalysis of high-speed samplig systems, IEEE Joural of Solid-State Circuits, Vol. 5, No. 1, pp. -4, February 199. [14] J. Tsui, Digital Techiques for Widebad Receivers, Artech House, 1. ISBN p. [15] R. H. Walde, Aalog-to-digital coverter survey ad aalysis, IEEE Joural o Selected Areas i Commuicatios, Vol. 17, No. 4, pp , April [16] M. Valkama, J. Pirskae, M. Refors, Sigal processig challeges for applyig software radio priciples i future wireless termials: A overview, Iteratioal Joural of Commuicatio Systems, Vol. 15, No. 8, pp , September.

DESIGN CONSIDERATIONS FOR DIRECT RF SAMPLING RECEIVER IN GNSS ENVIRONMENT. Ville Syrjälä, Mikko Valkama, Markku Renfors

DESIGN CONSIDERATIONS FOR DIRECT RF SAMPLING RECEIVER IN GNSS ENVIRONMENT Ville Syrjälä, Mikko Valkama, Markku Renfors Tampere University of Technology Institute of Communications Engineering P.O Box 553,