An Exact Analysis of Oscillator Noise in M-QAM-OFDM Communication Systems

Transcription

1 Iteratioal Joural of Iformatio ad Electroics Egieerig, Vol. 3, o. 5, eptember 3 Exact alysis of Oscillator oise i M-QM-OFDM Commuicatio ystems M. H. Madai,. bdipour, ad. Mohammadi bstract This paper presets a exact aalysis of oise effects of RF oscillators i M-QM Orthogoal Frequecy Divisio Multiplexig (OFDM) Commuicatio ystems. The phase oise ad the amplitude oise effects are studied i the performace of OFDM systems. theoretical aalysis for sigal to oise degradatio caused by phase ad amplitude oise i OFDM badwidth is preseted. It is show that bit error rate of aalytical results is closely match with simulatio results for OFDM system usig M-QM modulatio. system ad preset a bloc diagram of the system. I sectio III we derive the theoretical aalysis of phase ad amplitude oise effect i OFDM system ad itroduce power desity fuctio of oscillator phase oise. ectio IV gives performace aalysis ad simulatio results ad coclusios are preseted i ectio V. Idex Terms OFDM, QM, oscillator oise, sigal to oise degradatio. I. ITRODUCTIO Orthogoal frequecy divisio multiplexig is very attractive trasmissio techiques for future high data rate wireless multimedia commuicatio systems. OFDM has developed for widebad wireless digital commuicatio, used i applicatios such as Digital Video ad udio Broadcastig (DVB&DB), wireless etworig ad broadbad iteret access[]-[3]. The OFDM has advatages such as high spectral efficiecy, easy adaptatio to severe chael coditios without complex equalizatio, ad efficiet implemetatio usig FFT. It yields however some disadvatages, such as the sesitivity to frequecy offset, the high pea-to-average-power ratio (PPR) ad the sesitivity to oises [], [4], [5]. It is very importat to exactly predict ad aalyze the oscillator oise iflueces i OFDM commuicatio system ad quatify the tolerable level of oise. oscillator is a system that geerates a periodic sigal with a specified or cotrollable frequecy. There are the two ids of oise i a oscillator output, amely amplitude oise ad phase oise [6]. Phase oise effects i OFDM have bee aalyzed i may papers by several authors [4],[5],[7]-[9] but they did ot cosider the effect of amplitude oise ad always igore it relative to phase oise without ay acceptable reaso. The purpose of this paper is to extract the theoretical aalysis of impact of oscillator phase ad amplitude oise o the R (hece the ) performace of MQM- OFDM sigals over WG chael ad quatify the tolerable level of phase ad amplitude oises. This paper is orgaized as follows: I sectio II we itroduce OFDM Mauscript received eptember 5, ; revised ovember 3,. The authors are with the Microwave/mm-Wave ad Wireless Commuicatio Research Lab, Radio Commuicatio Ceter of Excellece, Electrical Egieerig Departmet, mirabir Uiversity of Techology, 44 Hafez ve, Tehra, Ira ( s: mh_madai@aut.ac.ir, abdipour@aut.ac.ir, abm5@aut.ac.ir). Fig.. Bloc diagram of OFDM commuicatio system. II. OFDM YTEM Orthogoal frequecy divisio multiplexig is a Frequecy Divisio Multiplexig (FDM) scheme utilized as a digital multi-carrier modulatio method. large umber of closely-spaced orthogoal sub-carriers are used to carry data. The data are divided ito several parallel data streams or chaels, oe for each sub-carrier. Each sub-carrier is modulated with a covetioal modulatio scheme such as Quadrature mplitude Modulatio (QM) or Phase hift eyig (P) at a low symbol rate, maitaiig total data rates similar to covetioal sigle-carrier modulatio schemes i the same badwidth [],[]. Fig. shows a bloc diagram of OFDM trasceiver system. ( ) is a serial stream of biary digits. By iverse multiplexig, these are first demultiplexed ito parallel streams, ad each oe mapped to a (possibly complex) symbol stream usig some modulatio costellatio (QM, P, etc.). iverse FFT is computed o each set of symbols, givig a set of complex time-domai samples. These samples are the quadraturemixed to passbad i the stadard way. The real ad imagiary compoets are first coverted to the aalog domai usig digital-to-aalog coverters (DCs); the aalog sigals are the used to modulate cosie ad sie waves at the carrier frequecy, f c, respectively. These sigals are the summed to give the trasmissio sigal, () t.the receiver pics up the sigal rt (), which is the DOI:.7763/IJIEE.3.V

2 Iteratioal Joural of Iformatio ad Electroics Egieerig, Vol. 3, o. 5, eptember 3 quadrature-mixed dow to basebad usig cosie ad sie waves at the carrier frequecy. This also creates sigals cetered o f c, so low-pass filters are used to reject these. The basebad sigals are the sampled ad digitized usig aalog-to-digital coverters (DCs), ad a forward FFT is used to covert bac to the frequecy domai. This returs parallel streams, each of which is coverted to a biary stream usig a appropriate symbol detector. These streams are the re-combied ito a serial stream, ˆ( ), which is a estimate of the origial biary stream at the trasmitter[]. values for calculatig MQM-OFDM degradatio caused by phase ad amplitude oise i simulatio. TBLE I. OIE VRICE FOR DIFFERET,. B s (Hz) (OFDM 7 Badwidth) e-3 3.e-3 e- 3.6e III. OCILLTOR OIE LYI I OFDM YTEM. Phase ad mplitude oise oscillator is a system that geerates a periodic sigal with a specified or cotrollable frequecy. There are the two ids of oise i a RF oscillator output, amely amplitude oise ad phase oise. The output voltage of a oscillator ca be represeted by [6]: V () t ( + a ()). t Cos( π f t + ()) t () out V () t (). t Cos( πf t + ()) t () out Phase oise (dbc/hz) Here is the average amplitude of the output sigal ad f is omial frequecy of oscillatio. a () t ad () t represet the time varyig compoets of the amplitude ad phase, respectively. These compoets are cosidered as oise, because a oscillator would have costat amplitude ad phase varyig at a costat rate π f. It ca be show that white oise power of the amplifier electroics is equally partitioed ito amplitude ad phase oise compoets with zero mea ad, variace respectively [3]. The R performaces that ca be achieved i a OFDM system with a oisy oscillator ca be approximated by itegratig its phase ad amplitude oise power desity fuctio (PDF) over the chael badwidth. The phase oise PDF of a oscillator is approximated by a Lorezia fuctio with uiform phase distributio. It is parameterized by its total itegrated phase oise ad - 3dB badwidth B, to which we superimpose a oise floor (set 35dB above the thermal oise)as show i (3) [5]:. B L π f + B +. L f Fig. shows Phase oise PDF for differet ad -3dB badwidth of Hz. The amplitude oise power desity fuctio of a oscillator is similar to phase oise power desity fuctio, but is i average db less tha it i spectrum badwidth, which for practical parameter of a oscillator is ormally betwee to db relative to oscillators quality []. Therefore the phase ad amplitude oise variace are: Bs Bs π B. L( f ). df ( + L ). df f + B Table I shows phase ad amplitude oise variace of a oscillator for differet,. I ext sectio we use these (3) (4) Frequecy Offset (Hz) Fig.. Phase oise PDF for differet, BHz. B. Theoretical alysis s show i Fig. if sub-carriers are used, ad each sub-carrier is modulated usig M alterative symbols, the OFDM symbol alphabet cosists of M combied symbols. The low-pass equivalet OFDM sigal is expressed as []: j / () π t T t X e t < T (5) where j, X is the data symbol for the th subcarrier, is the umber of sub-carriers, ad T is the OFDM symbol time. The sub-carrier spacig of /T maes them orthogoal over each symbol period. () t is corrupted by the phase ad amplitude oise of TX local oscillator. lso, the received sigal is iflueced by the phase ad amplitude oise of RX local oscillator. It ca be assumed that the phase ad amplitude oises of the local oscillators at the trasmitter ad the receiver are idepedet ad idetical. o, it is expressed as follows: Y rt { t. ( t). e + t }. ( t). e (6) j TX ( t ) jrx ( t ) TX RX π j m r e m π j m j ( TX ( m ) + RX ( m )) TX RX e e m π j m j RX ( m ) + RX. e e m π π j lm j m j ( m ) ( X le ).. e e m l π j ( l ) m j ( m ) X l e e l m X lql l (7) 488

3 Iteratioal Joural of Iformatio ad Electroics Egieerig, Vol. 3, o. 5, eptember 3 where (t) is the complex Gaussia oise. TX (), t TX ()& t RX (), t RX () t are the time-varyig phase ad amplitude oise processes geerated by the RF local oscillator at the trasmitter ad the receiver. The sampled sigal for the th sub-carrier after FFT (fast fourier trasform) processig stage i the receiver ca be writte as: is a sampled FFT versio of the WG oise multiplied by the phase ad amplitude oise of RX local oscillator with variace. ( m ) ad ( m ) are equal to : m TX ( m ) RX TX + RX Q is give by : π j m j ( m ) (9) Q e e m The received sigal is composed of three cotributios: Y is the th desired sub-carrier, Y is the others ad is the WG, that is [7],[9],[],[3]-[5] : Y Y + Y + () or () Y X. Q + X l. Ql + l, l The expectatio value of X. Q is the desired sigal compoet. o, the desired sigal power ca be foud as : where: s desired s (8) P [ E[ X Q ]] P[ E[ Q ]] () j ( m ) j( m ) EQ [ ] Eme. E. ( me ) (3) m j ( m ) E ( m ) Ee e j j j... π. π. Ee e e d e d e Therefore: (4) s desired s. (5) P P e Variace of X. Q is the phase ad amplitude oise power caused by CPE(Commo Phase Error) ad P CPE is calculated as follows: where: P V ar[ X Q ] P V. ar[ Q ] (6) CPE s Var[ Q ] Var[ e ] Var( e ) j j m m Therefore : (7) j ( E. e. e ) (( + ) e ) (( CPE s ) ) P P + e (8) ext, is the iterferece compoet caused by X. Q l, l l l ICI (Iter-sub-Carrier Iterferece). o, calculated as: where: ICI s l l P P.{ Var[ Q ] Var[ Q ]} l l l m l m π j lm j Var[ Q ] Var[ { e e }] Therefore : PICI π j lm j Var[ { e e }] + e P P e ca be (9) () ICI s..( + ) () is a sampled FFT versio of the WG oise multiplied by the phase ad amplitude oise of RX local oscillator as see (7). o, for the sae of simple aalysis, we cosider Var[ ] as that of the WG sice it has zero mea ad variace is uchaged o the basis that FFT process is liear ad phase ad amplitude oise corruptig the WG wors as the phase rotatio factor. Pwith{, } Var[ ] P () From ()-(), the sigal-to-oise ratio icludig the phase ad amplitude oise ca be arraged as : P. e P. e ( CPE + ICI ) + ( + ) + Without{, } e + Without{, } ( + e ) With{, } P P P P e P (3) ext, the above-metioed powers are used to evaluate the performace degradatio of the OFDM system i the presece of phase ad amplitude oise of local oscillators. o, degradatio factor (DF) is calculated as follows: DF + + e R e Without{, } log log{( ( ). ) / } Without{, } With{, } (4) I (4), is the variace of radom variable TX ad ad R X is the variace of radom variable TX ad.these are calculated by itegratig the power R X spectrum desity of total output phase ad amplitude oise. IV. PERFORMCE LYI This paper presets performace aalysis of OFDM commuicatio system iflueced by the phase ad amplitude oise of the RF local oscillator i WG chael by both theoretical approach ad simulatio method. Phase ad amplitude oise i the OFDM system is difficult to be compesated because of the strog dispersive compoet. Therefore, it is importat to quatify the permissible level of phase ad amplitude oise i local oscillator to maitai system performace ad to desig local oscillator with limited maximum phase ad amplitude 489

4 Iteratioal Joural of Iformatio ad Electroics Egieerig, Vol. 3, o. 5, eptember 3 oise. The formula for system performace aalysis ca be foud by the R with phase ad amplitude oise istead of the R without phase ad amplitude oise. Equatios (5)-(6) shows probability of bit-error per carrier ad probability of bit-error for QM modulatio respectively[]. Where is umber of bits per symbol, M is umber of symbols i modulatio costellatio, E b is eergy-per-bit ad is oise power spectral desity P bc 3 E b ( ) Q(. ) M ( M ) b bc bc bc (5) P ( P ) P P (6) db 5 db db 5 db 6QM R (db) (a) Theory db 5 db db 5 db 6QM R (db) (b) imulatio Fig. 3. 6QM-OFDM system with phase oise (.) ad amplitude oise with differet orders. The phase ad amplitude oise variaces, achieved from above (4) ca be used to aalyze the performace i OFDM system with phase ad amplitude oise. Fig.3-4 show the (a) theoretical ad (b) simulatio performace of OFDM commuicatio system employig 6,64QM modulatios i the WG chael. For each modulatio we cosidered the highest level of phase oise variace that ca meet the -6 with differet order of amplitude oise relative to it ad do t cause Irreducible Error Rate(IER). Detail results for -6, every phae oise variace ad differet amplitude oise order relative to it, is show i Table II. s show i Fig. 3-4 ad Table II the relative R pealty (Degradatio) to meet -6 for differet amplitude oise order,, represeted i Table III. The results from Tables II-III shows that if the amplitude oise order relative to phase oise,, was higher tha 5 db (5- db), we ca igore the amplitude oise effect i performace aalysis but if it was less tha 5 db (-5 db) we must cosider the amplitude oise for exact aalysis ad determiig the tolerable level of amplitude oise. Fig. 5 shows the combiatio of two effects (CPE,ICI) o a 4-QM-OFDM sigal after demodulatio caused by phase ad amplitude oise. The first scatter plot (a) correspods to the demodulated sigal whe the variace of the phase oise that affects the OFDM sigal is zero, The secod scatter plot (b) correspods to the demodulated sigal whe the variace of the phase oise is.36 ad amplitude oise order relative to phase oise is db () ad The third scatter plot (c) correspods to the demodulated sigal whe the variace of the phase oise is.36 ad amplitude oise order relative to phase oise is db. s show i Fig.5 clouds i the costellatio of (c) has the higher spreadig tedecy ad cause higher performace degradatio db 5 db db 5 db 64QM R (db) (a) Theory db 5 db db 5 db 64QM 5 5 R (db) (b) imulatio Fig QM-OFDM system with phase oise (.3 ) ad amplitude oise with differet orders. 49

5 Iteratioal Joural of Iformatio ad Electroics Egieerig, Vol. 3, o. 5, eptember 3 TBLE II: PHE D MPLITUDE OIE DEGRDTIO I 4, 6, 64,56 QM-OFDM FOR -6. for differet amplitude oise order,, is quatified. 3- The amplitude oise source of RF oscillator has a little effect o performace degradatio of M-QM OFDM system whe it is betwee 5- db, but whe is betwee -5 db we must cosider it for exact performace degradatio aalysis. REFERECE TBLE III: RELTIVE DEGRDTIO FOR DIFFERET MPLITUDE OIE ORDER I M- QM-OFDM FOR -6. Quadrature I-Phase I-Phase (a) RdB,, db (b) RdB,.36 Quadrature Quadrature I-Phase (c) RdB,.36, db Fig. 5. Costellatio poit of 4QM sigal V. COCLUIO -, db OFDM has bee stadardized i may recet wireless applicatios due to its ability to combat impulsive oise ad multipath effect ad mae better use of the system available badwidth. ice a accurate predictio of the tolerable phase ad amplitude oise ca allow the system ad RF egieers to relax specificatios, a exhaustive aalysis of phase ad amplitude oise effects o OFDM sigals has bee preseted. Results ca be arraged as follows: The performace degradatio of the OFDM commuicatio system caused by phase ad amplitude oise is quatified. lso, it is show that performace results by theoretical approach closely match with the simulatio results of the OFDM commuicatio system of the 4, 6, 64,56 QM modulatio format. The tolerable phase oise variace to meet differet []. R.. Bahai, B. R. altzberg, ad M. Erge, Multi Carrier Digital Commuicatios: Theory ad pplicatios of OFDM, priger, 4. [].. R. hamed, "Performace alysis of OFDM," Joural of Theoretical ad pplied Iformatio Techology, 8. [3]. G. rmada ad M. Calvo, "Rapid Prototypig of a Test Modem for Terrestrial Broadcastig of Digital Televisio, i Proc. of IEEE Tras. O Cosumer Electroics, vol. 43, o. 4, pp. 9, ov [4] E. Costa ad. Pupoli, "M-QM-OFDM ystem Performace i the Presece of a oliear mplifier ad Phase oise," i Proc. of IEEE Tras. o Commuicatios, vol. 5, o. 3, March. [5] B. Come, R. ess,. Doay, ad L. V. D. Perre, "Impact of Frot- Ed o-idealities o Bit Error Rate Performace of WL-OFDM Trasceivers," i Proc. of IEEE Radio ad Wireless Coferece, pp. 9 94,. [6] T. H. Lee, the Desig of CMO Radio Frequecy Itegrated Circuits, d ed. ew Yor, U: Cambridge Uiv. Press, pp , 4. [7] P. Liu, Y. B. ess, ad J. Zhu, "Effects of Phase oise at Both Trasmitter ad Receiver o the Performace of OFDM ystems," i Proc. of IEEE 4th ual Cof. o Iformatio cieces ad ystems, March 6. [8]. Wu ad Y. B. ess, "OFDM ystems i The Presece of Phase oise: Cosequeces ad olutios," i Proc. of IEEE Tras. o Commuicatios, vol. 5, o., ov. 4. [9] L. Xu, Y. Che, ad Z. Feg, "Effects of RF Oscillator Phase oise o Performace of Commuicatio ystem," i Proc. of 4th Iteratioal Cof. o Microwave/mm-Wave Techology, pp , ug. 4. []. R. Herlear, C. Zhag, H. C. Wu,. rivastava, ad Y. Wu, "OFDM Performace alysis i the Phase oise risig from the Hot-carrier Effect," i Proc. of IEEE Tras. o Cosumer Electroics, vol. 5, o. 3, 6. [] D. Petrovic, W. Rave, ad G. Fettweis, "Performace Degradatio of Coded-OFDM Due to Phase oise," i Proc. of 57th IEEE Vehicular Techology Coferece, vol., o. -5, pp. 68 7, pril 3. [] J. hetu,. Pata ad J. rmstrog, "Effects of Phase oise o Performace of OFDM ystems Usig a ICI Cacellatio cheme," i Proc. of IEEE Tras. o Broadcastig., vol. 49, o., pp. 4, Jue 3. [3] H. G. Ryu ad Y.. Lee, "Phase oise alysis of the OFDM Commuicatio ystem By the tadard Frequecy Deviatio," i Proc. of IEEE Tras. o Cosumer Electroics, vol. 49, o., pp. 4-47, Feb. 3. [4]. Wu ad Y. B. ess, "Performace alysis o Effect of Phase oise i OFDM ystems," i Proc. of IEEE 7th It. ymp. O pread-pectrum Tech. ad ppl.,. [5]. G. rmada, "Uderstadig The Effects of Phase oise i OFDM," i Proc. of IEEE Tras. o Broadcastig, vol. 47, o., pp , Jue. [6]. athaatha ad C. Tellambura, "Performace alysis of a OFDM ystem with Carrier Frequecy Offset ad Phase oise," i Proc. of 54th IEEE Vehicular Tech. Coferece, pp ,. [7] L. Tomba, "O The Effect of Wieer Phase oise i OFDM ystems," i Proc. of IEEE Tras. o Commu., vol. 46, o. 5, pp , May 998. [8] C. Muschalli ad T. Multimedia, "Ifluece of RF Oscillators O OFDM igal," i Proc. of IEEE Tras. o Cosumer Electroics, vol. 4, o. 3, ug [9] T. Pollet, M. V. Blade, ad M. Moeeclaey, " esitivity of OFDM ystems to Carrier Frequecy Offset ad Wieer Phase oise," i Proc. of IEEE Tras. o Commu., vol. 43, o., 995. [] Wiipedia. [Olie]. vailable: /wii/ofdm. [] B. chie, I. Rolfes, ad H. J. iweris, oise i High-Frequecy Circuits ad Oscillators, Joh Wiley & os, 6. []. ampei, pplicatios of Digital Wireless Techologies to Global Wireless Commuicatios, Pretice-Hall,

6 Iteratioal Joural of Iformatio ad Electroics Egieerig, Vol. 3, o. 5, eptember 3 Techology. M. H. Madai was bor i Ira i 976. He received the B.c., M.c ad P.h.d degrees i Electrical Egieerig i 998, ad, respectively. His research areas iclude wireless commuicatio systems. He is curretly a member of Microwave/ mm-wave ad Wireless Commuicatio Research Lab i Electrical Egieerig Departmet of mirabir Uiversity of. bdipour was bor i lashtar, Ira, i 966. He received the B.c. degree i electrical egieerig from Tehra Uiversity, Tehra, Ira, i 989, the M.c. degree i electroics from Limoges Uiversity, Limoges, Frace, i 99, ad the Ph.D. degree i electroics from Paris XI (Orsay) uiversity, Paris, Frace, i 996. He is curretly a Professor with the Electrical Egieerig Departmet, mirabir Uiversity of Techology (Tehra Polytechic), Tehra, Ira. He authored three boos about oise i Electroic Commuicatio Circuits ad ystems ad Trasmissio Lies. His research areas iclude wireless commuicatio systems (RF techology ad trasceivers), RF/microwave/mm-wave circuit ad system desig, electromagetic (EM) modelig of active devices ad circuits, high-frequecy electroics (sigal ad oise), oliear modelig, ad aalysis of microwave devices ad circuits. He has authored or coauthored over papers i refereed jourals ad local ad iteratioal cofereces.. Mohammadi received the B.c. degree i Electrical Egieerig from Tehra Uiversity, Ira i 988, the M.c. ad Ph.D. degrees i Electrical Egieerig from the Uiversity of asatchewa, Caada, i 995, ad 999, respectively. He was a researcher at Telecommuicatios Research Lab (TRLabs), Caada, from 995 to 998. I 998, he joied to Vecima etwors Ic., Microwave Research Lab, Victoria, Caada, as a seior research egieer where he coducted research o Microwave ad Wireless Commuicatios. ice March, he has bee with the Electrical Egieerig Departmet of mirabir Uiversity of Techology (Tehra Polytechic), Tehra, Ira. I 8, he joied to Electrical ad Computer Egieerig Departmet of the Uiversity of Calgary, Caada as a visitig professor. He has published over Joural ad Coferece papers ad holds three U.. ad oe Caadia Patets. His curret research iterests iclude broadbad wireless commuicatios, adaptive modulatio, MIMO ystems, Mesh ad dhoc etwors, Microwave ad Wireless ubsystems, ad direct coversio trasceivers. Curretly he is Director of Radiocommuicatio Ceter of Excellece of mirabir Uiversity of Techology (Tehra Polytechic). 49