Introduction to CPM-OFDM: An Energy Efficient Multiple Access Transmission Scheme

Transcription

1 Joural of Commuicatio ad Computer 1 (015) doi: / / D DAVID PUBLISHING Itroductio to CPM-OFDM: A Eergy Efficiet Multiple Access Trasmissio Scheme Mohammad Irfa, Sag Hoo Lee ad Soo Youg Shi Wireless Emergig Networkig System Lab, Kumoh Natioal Istitute of Techology, South-Korea Abstract: I this paper we propose a eergy efficiet OFDM trasmissio scheme. Two CPM (cotiuous phase modulatio) schemes are itroduced to OFDM, keepig i view the costat evelope ad cotiuous phase chagig ature of CPM modulatio. Eergy efficiecy of the proposed scheme is ivestigated by simulatig PAPR (peak to average power ratio) ad is compared with the covetioal OFDM scheme. The impact of PAPR o BER is also ivestigated. BER (bit error rate) of the proposed scheme is simulated i differet chaels ad is compared with cov-ofdm (QPSK-OFDM) scheme. Key words: PAPR, BER, HPA, CPM. 1. Itroductio OFDM (orthogoal frequecy divisio multiplexig) is the most popular high data rate ad spectral efficiet multicarrier commuicatio system. I OFDM the subcarriers are orthogoal to each other, so they will ot iterfere with each other ad more umber of subcarriers ca be packed to the same spectrum to accommodate multiple users [1, ]. It s high data rate, spectral efficiecy ad robustess agaist multipath fadig make it oe of the most promisig cadidate for portable computig devices ad smartphoes. These devices demads high data rate but low power cosumptio as they are usually battery operated. Despite may advatages of OFDM, high PAPR of a OFDM sigal is its major limitig factor i practice. I practical OFDM systems, a HPA (high power amplifier) is used to obtai sufficiet trasmit power [3]. I a typical OFDM system, the trasmit power is oly 8% of the total cosumed power, 41% of power is wasted i HPA ad the rest of the circuit cosume about 51% power [1, 4]. There are two reasos of 41% of power loss i HPA, Correspodig author: Soo Youg Shi, professor, research fields: cogitive radio, WLAN, WiMAX. wdrago@kumoh.ac.kr. low efficiecy of HPA s ad high PAPR of OFDM sigal which further reduces the efficiecy of HPA. HPA has limited liear rage, such o-liear effects of HPA s seriously degrades OFDM sigal of high PAPR [5]. To solve this problem, the liear rage of HPA should be elarged, which meas the IBO (iput back off) of HPA should be greater tha the PAPR of the sigal (uless some pre-distortio techique is used) to avoid such sigal distortios [1, 6]. But icreasig IBO meas icreasig power cosumptio of HPA ad may decrease its efficiecy [5]. Improvig efficiecy of HPA by reducig PAPR of OFDM sigal will ot oly result i power savig, but the probability of bit error will also reduce as the sigal will be less distorted. The PAPR c for a cotiuous time OFDM trasmit sigal x(t) is give by Eq. (1), where N represets umber of subcarriers, symbol duratio is T, NT represets duratio of the sigal. PAPR c 10 log 10 max x ( t ) 0 t N T NT 1 x ( t ) d t NT 0 (1) Various schemes have bee developed to reduce PAPR of OFDM sigal. These schemes are summarize i Ref. [7]. Method of codig is discussed i Ref. [8] ad toe reservatio i Ref. [9].

2 38 Itroductio to CPM-OFDM: A Eergy Efficiet Multiple Access Trasmissio Scheme Predistortio scheme i Ref. [10] ad clippig i Ref. [11]. All these methods ca be divide ito two categories distortio ad distortioless. Clippig [11], clips the peak power max x( t) 0 t NT to some pre-defied value ad thus distort the sigal which results i high BER at receiver ad reduces throughput. The distortio-less methods like toe reservatio [9] ad selective mappig [1] allows perfect recovery of the origial sigal at the cost of trasmittig some side iformatio which reduces throughput, icrease badwidth requiremet ad icreases sigal overhead. Ju ad Stuber [13] show a approach which trasforms the OFDM sigal ito costat evelope by phase modulatig the sigal after its IDFT (iverse discrete fourier trasform). Our approach is differet from Ref. [13]. We replaced the covetioal modulatio schemes used i OFDM such as QPSK, 16-QAM ad 64-QAM by GMSK (gaussia miimum shift keyig) ad MSK (miimum shift keyig) (kow as scheme 1 ad scheme i this work) (Fig. 1). I our proposed scheme, the iput data is first modulated by a CPM modulator, the modulated symbols are the trasformed from serial to parallel, a IDFT is the applied to the parallel modulated symbols. After IDFT cyclic prefixes are iserted the data is the agai chaged from serial to parallel followed by amplificatio by a HPA ad is trasmitted, at the receiver side a viterbi detector is used to detect the symbols after parallel to serial coversio. Fig. 1 Proposed CPM-OFDM block diagram. The rest of the paper is orgaized as follows: Sectio preseted fudametal of CPM, two CPM modulatio schemes that we have selected for this work ad some previous work is discussed; Sectio 3 preseted our system model, CPM based OFDM. I Sectio 3, we desiged CPM based trasmitter, PAPR aalysis of CPM based OFDM, receiver structure for CPM based OFDM ad the effect PAPR o BER. I Sectio 4, we preseted our umerical results ad coclusio is draw i Sectio 5.. Fudametals of CPM As compared to other modulatio schemes like QPSK, which is oe of the modulatio scheme used i LTE [14]. I such modulatio schemes, the carrier phase is abruptly reset to zero at the start of every symbol. I QPSK, whe the message sigal chages by oe bit a phase shift of 90 degrees occurs. This discotiuity of QPSK modulated sigal lead to high power cosumptio ad some percetage of power occurs outside of the iteded bad, which leads to poor spectral efficiecy [7]. While CPM has costat evelope ad the phase of the carrier sigal is modulated i a cotiuous maer, which yields high spectral efficiecy [7]. Due to its costat evelop the PAPR of such waveform is uity [7]. A CPM waveform is give by Eq. (), [15]. St ( ; ) exp{j (t; } () is the phase of the sigal ad is give by the followig equatio. (t; ) ihq i( tit) (3) β = β i represets the discrete time symbol sequece of M-ary symbols form i th user each symbol carries m=log M bits, T is the symbol duratio, h i is the modulatio idex. Smaller the modulatio idex the more arrower badwidth the sigal occupies. M is the value of M-ary sigalig. Throughout this work is M = 4. Two CPM schemes are selected for this work. Scheme 1: 4-ary sigalig is used, modulatio i

3 Itroductio to CPM-OFDM: A Eergy Efficiet Multiple Access Trasmissio Scheme 39 idex h i = 0.3, Raised cosie frequecy pulse with Pulse legth L = 4 ad miimum square Euclidea distace, d mi = Scheme : 4-ary sigalig with modulatio idex h i = 0.6, Gaussia frequecy Pulse with BT=0.5, Pulse legth, L = 3, ad miimum squared Euclidea distace, d mi = 4.6. The above two scheme differs i PAPR ad BER performace. Scheme 1 has smaller modulatio idex tha scheme, so it will occupy a arrow badwidth as compare to scheme, its power spectral desity will drop more abruptly, which will result i better PAPR performace. But o the other had, scheme 1 has small value of d mi, so Scheme will have better BER performace compare to Scheme 1. Icreasig d mi, lowers the probability of bit error [15]. 3. CPM Based OFDM Cosider a OFDM system as show i Fig 1. N umber of symbols ad sub-carriers. Each symbol is mapped to oe sub-carrier. I our proposed scheme, the iput data is first modulated by a CPM modulator. The modulated samples are the coverted from serial to parallel by a serial to parallel coverter as show i Fig 1. S i s, s..., s where, i is the idex of a user. {i,0} {i,1} {i,n 1} Sil, exp{j (i;l)} (4) This is discrete time equivalet of Eq. (). The cotiuous time trasmitted OFDM sigal x(t) is expressed as: N 1 1 j kft x(t) Xke,0 t T (5) N k 0 where, T is the duratio of the OFDM symbol, X k = [X 0, X 1,.X N-1 ] is the iput data block, Δf = 1/T is the frequecy spacig betwee two adjacet subcarriers. The same way a discrete time CPM-OFDM sigal x() with Nyquist rate is obtaied by N-poit IDFT operatio of S {(i,l)}. T N 1 k 1 x() S e, 0, N k 0 The equatio above shows the waveform of a CPM j N il, N (6) based OFDM. After isertio of cyclic prefix ad digital to aalog coversio the sigal is amplified by a HPA (high power amplifier) ad is trasmitted. 3.1 PAPR Aalysis PAPR stads for Peak to Average Power Ratio. It is basically used as performace metric for evelop variatios i a sigal. As OFDM is a multi carrier system, a set of orthogoal frequecies are used. Mathematically these frequecies will ot iterfere with each other, but i practice they iterfere with each other. I this paper, N umber of sub carriers are used. Assumig amplitude of each sub-carrier is 1, as the costellatio poits are take from MSK ad GMSK modulators. These sub carriers ca costructively add up resultig i high peak powers. So the rage of PAPR is 1 to N. I case of o uity amplitude A like the case of QAM, the max PAPR is give by equatio below [16]. P APR A N max max (7) Aother reaso of high PAPR of a OFDM sigal is the spectral leakage of DFT. The samplig period Δt = 1/fs. The th array elemet i frequecy domai is kow as bi. The frequecy of bucket ca be related to the frequecy of iput sigal S{i, l} by equatio below [17]. f (8) Nt where, is the umber of bi, N is the umber of samples ad f is the frequecy of bi. Rearragig Nf f (9) N is the total umber of sub-carriers which is equal to 16 for this work, f s samplig frequecy ad f is the frequecy of th bi. For 900 Hz sigal the maximum amplitude occurs at = Nf /f s = 16*900/3000 = 4.8. As each bi represets a frequecy ot a rage of frequecies ad bi umber is a iteger, the the s

4 40 Itroductio to CPM-OFDM: A Eergy Efficiet Multiple Access Trasmissio Scheme questio is how ca DFT represet eergy at bi umber 4.8, actually it shows some leakage of eergy betwee bi 4 ad bi 5. I DFT for some frequecies there is some eergy leakage betwee bis, while i other frequecies, there is o eergy leakage. For example, for a 1,500 Hz waveform, = Nf /f s = 16*1500/3000 = 8, there is o spectral leakage betwee bi 8 ad bi 7 or bi 8 ad bi 9. I OFDM multi-carriers are geerated by IDFT ad due to the spectral leakage problem of DFT ad iterferece of the multi carriers OFDM exibits high PAPR. As the iput S{i, l} is radom so PAPR of x() give by equatio below is also a radom variable. PAPR 10log max x() 0 t * N 1 10 E x( ) (10) Therefore CDF (cumulative distributio fuctio) is used to describe its properties. CDF Prob PAPR Pr ob( PAPR ) 1 1 e N (11) where, γ is a costat. PAPR of a discrete time sigal x() is a accurate approximatio of the cotiuous time PAPRc, if the up-samplig factor τ 4, [7]. For this work we are usig up-samplig factor τ = Effect of PAPR o BER Performace I this sectio, we determie the relatio of PAPR ad BER performace of a OFDM sigal i the absece of IBO from HPA. A HPA exibits two kids of distortios, AM-AM ad AM-PM distortio. Whe the HPA is operatig i the liear regio, the output voltage is oly a scaled versio of the iput voltage. However whe the iput sigal has high peaks i the compressio regio, the output of the HPA is amplitude distorted. The resultat distortios are kow as AM-AM distortios. Similarly AM-PM is used for phase o liearity. I such kid of distortio the phase of the sigal is distorted. But here we will oly cosider the effect of AM-AM distortio. The efficiecy ƞ of HPA depeds o the iput voltage or iput power. A amplifier operates more efficietly if the iput is withi the rage of operatig poit. CPM has costat evelop, but due to the PAPR problem of multi-carrier systems there is a large evelope fluctuatio. So the efficiecy ƞ depeds o PAPR ad class of the amplifier [16]. gpapr G e db (1) where, G is the gai of a amplifier. As the probability of bit error depeds o SNR of the sigal. x ( ) SNR T (13) o where, o represets oise power ad [x()] is the trasmitted sigal power SNR depeds o the efficiecy ƞ of HPA. Ad the efficiecy of HPA depeds o PAPR of the sigal. So the probability of bit error depeds o PAPR of the sigal [16]. G x( ) T SNR (14) 1 PAPRSatLevel PAPR (10g/l10) (15) PAPRSatLevel Eq. (15) shows that low PAPR results i better HPA efficiecy ad high SNR which results i low eergy cosumptio by HPA ad low error rates. 4. Numerical Results 4.1 PAPR Numerical Results I this sectio, we first umerically aalyze PAPR ad BER properties of our proposed two schemes of CPM-OFDM ad the compare them to covetioal OFDM scheme. Relatio of PAPR to BER i the absece of IBO is also umerically aalyzed i this sectio. All the simulatios performed i this sectio cosists of (N = 16) N = umber of allocated sub carrier to oe user. Number of users = 1; Fig. shows umerically calculated CDF of PAPR of our two proposed schemes ad covetioal OFDM. Due to low modulatio idex of scheme 1 its power spectral desity will drop abruptly as compare to scheme of high modulatio idex ad covetioal OFDM. o

5 Itroductio to CPM-OFDM: A Eergy Efficiet Multiple Access Trasmissio Scheme 41 Therefore, scheme 1 has low PAPR as compare to scheme ad covetioal OFDM. The previous discussio i sectio, PAPR aalysis shows that CPM-OFDM will have costat evelop but as Fig. shows CPM-OFDM still has evelope variatios. The reasos are already discussed i the Sectio. Spectral leakage ad sub-carriers iterferece which results i high peaks. PAPR statistics of these three schemes are provided i Table 1. Proposed scheme 1 has almost 4 db performace gai over cov-ofdm ad almost 0.5 db performace gai over scheme i terms of their max PAPR. I order to operate the HPA i liear regio, so that it will ot distort the OFDM sigal, the iput back off must be higher tha the PAPR of the sigal. Iput back-off is the amout of power draw from dc (direct curret) source of HPA, i order to keep the HPA i liear regio. Table shows required amout of miimum iput back-off calculated from CDF plot of Fig.. Table shows that scheme 1 will draw little amout of power from the dc source which happes to be the most power efficiet scheme of all the three schemes. 4. PAPR effect o BER Numerical results of PAPR ad BER relatio are preseted i this sectio. Aalytically it is already developed i the previous sectio (18). Three differet HPA with iput saturatio level of, 4 ad 6 db are cosidered here. The output of amplifier is saturated ad distorted, oce the iput cross it saturatio limit. for such kid of HPA with o IBO, BER is simulated ad is show i Fig. 3. The Fig. 3 shows that BER is at low whe the iput sigal PAPR is with i HPA iput saturatio level. As the iput sigal PAPR crosses the iput saturatio of HPA the probability of bit error icreases abruptly. The probability of bit error icreases expoetially with icreasig PAPR. 4.3 Bit Error Rate (BER) Performace Fig. 4 shows BER performace of Scheme 1, Scheme ad cov-ofdm i AWGN chael. The effect of HPA distortios to OFDM sigal are also added i the form of IB-90% from Table. The actual BER performaces are plotted by solid lies for differet chaels. The BER performace with HPA distortios are plotted by dotted lies as a fuctio of E b /N o +IB 90%. As show without takig the effect of HPA o-liearity, scheme has better BER performace Fig. PAPR plots of scheme 1, ad cov-ofdm. Table 1 PAPR statistics of Fig.. Scheme Max [db] Mi [db] Mea [db] Scheme Scheme Cov-OFDM Table Required IBO from CDF plot. Scheme IB-90% [db] IB-99%[dB] Scheme Scheme Cov-OFDM Fig. 3 Effect of PAPR o BER, uder SNR = 10dB.

6 4 Itroductio to CPM-OFDM: A Eergy Efficiet Multiple Access Trasmissio Scheme o-liearity. I the presece of HPA o-liearity which is more realistic approach our proposed scheme outperforms the cov-ofdm (QPSK-OFDM). Ackowledgmet Fig 4 BER Plots of scheme 1, ad Cov-OFDM i AWGN Chael. as compare to scheme 1 ad Cov-OFDM. The reaso is the large miimum square Euclidea distace d mi = 4.6, of scheme as compared to d mi = 1.48 of scheme 1. At BER of 10-4 i AWGN chael scheme has almost 1.5 db gai over cov-ofdm ad almost db gai over scheme 1. Whe the HPA o-liearity is take ito accout i the form of E b /N o +IB 90%, we otice that scheme 1 ad scheme have almost the same BER performace, although the previous discussio shows that scheme has better BER performace. Scheme has better BER performace tha scheme 1, but it has high PAPR as well, so i presece of HPA o-liearity, both the scheme has almost the same BER performace. The cov-ofdm shows the worse performace of all due to its high PAPR as compare to scheme 1 ad scheme. 5. Coclusio I this work, we have compared PAPR properties of our proposed two schemes with cov-ofdm, ad have show that how the proposed schemes will have better PAPR performace as compare to covetioal scheme. High PAPR results i worse BER performace i the absece of HPA Iput Back-off, ad high power cosumptio ad low efficiecy i the presece of iput Back-off. BER performace is also evaluated i the presece ad absece of HPA This research was supported by the MSIP(Miistry of Sciece, ICT ad Future Plaig), Korea, uder the ITRC(Iformatio Techology Research Ceter)) / CITRC(Covergece Iformatio Techology Research Ceter) support program (IITP-015-H ) supervised by the IITP(Istitute for Iformatio & commuicatios Techology Promotio). Refereces [1] Abraham, P., ad Ruiz, A Frequecy Domai Data Trasmissio Usig Reduced Computatioal Complexity Algorithms. Preseted at the IEEE Iteratioal Coferece o Acoustics, Speech, ad Sigal Processig. [] Saltzberg, B Performace of a Efficiet Parallel Data Trasmissio System. IEEE Trasactios o Commuicatio Techology 15: [3] Tao, J., Li, C., ad Ni, C. X Effect of PAPR Reductio o Spectrum ad Eergy Efficiecies i OFDM Systems with Class-A HPA over AWGN Chael. IEEE Trasactios o Broadcastig 59: [4] Tao, J Multicast Broadcast Services Support i OFDMA-Based WiMAX Systems [Advaces i Mobile Multimedia]. IEEE Commuicatios Magazie 45: [5] Krogold, B. S., ad Douglas, L. J A Active-Set Approach for OFDM PAR Reductio via Toe Reservatio. IEEE Trasactios o Sigal Processig 5: [6] Gree, W., Marily, P., Perris, E., ad Svesso, T Itroductio to CPM-SC-FDMA: A Novel Multiple-Access Power-Efficiet Trasmissio Scheme. IEEE Trasactios o Commuicatios 59: [7] Hee, H. S., ad Lee, J. H A Overview of Peak-to-Average Power Ratio Reductio Techiques for Multicarrier Trasmissio. IEEE Wireless Commuicatios 1: [8] Davis, J. A., ad Joatha, J Peak-to-Mea Power Cotrol i OFDM, Golay Complemetary Sequeces, ad Reed-Muller Codes. IEEE Trasactios o Iformatio Theory 45: [9] Krogold, B. S., ad Douglas, L. J A Active-Set Approach for OFDM PAR Reductio via Toe

7 Itroductio to CPM-OFDM: A Eergy Efficiet Multiple Access Trasmissio Scheme 43 Reservatio. IEEE Trasactios o Sigal Processig 5: [10] Adrea, D., Aldo, N., Vicezo, L., ad Ruggero, R Noliear Predistortio of OFDM Sigals over Frequecy-Selective Fadig Chaels. IEEE Trasactios o Commuicatios 49: [11] Armstrog, J. 00. Peak-to-Average Power Reductio for OFDM by Repeated Clippig ad Frequecy Domai Filterig. Electroics letters 38: [1] Lee, Y. L Peak-to-Average Power Ratio i MIMO-OFDM Systems Usig Selective Mappig. IEEE Commuicatios Letters 7: [13] Ju, T., ad Stuber, G. L Frequecy-Domai Equalizatio for Cotiuous Phase Modulatio. IEEE Trasactios o Wireless Commuicatios 4: [14] Che, Y Research o the Modulatio ad Codig Scheme i LTE TDD Wireless Network. Preseted at the Iteratioal Coferece o Idustrial Mechatroics ad Automatio. [15] Aderso, J. B., Auli, T., ad Sudberg, C. E Digital phase modulatio. Spriger. [16] Dov, W. L Defiitio of Efficiet PAPR i OFDM. IEEE Commuicatios Letters 9: [17] Lyo, D. A The Discrete Fourier Trasform, Part 4: Spectral Leakage. Joural of object techology 8.