The PAPR Reduction in OFDM System with the Help of Signal Mapping Scheme

Transcription

1 Iteratioal Joural o Applied Sciece ad Egieerig 27. 5, : 75-8 The PAPR Reductio i OFD System with the Help o Sigal appig Scheme Jyh-Horg We, 2, Gwo-Ruey Lee ad Cheg-Yig Yag 3 * The Istitute o Electrical Egieerig, Natioal Chug Cheg Uiversity No.68, Uiversity Rd., i-hsiug, Chia-Yi, Taiwa, R.O.C. 2 Departmet o Electrical Egieerig, Tughai Uiversity No. 8 Sectio 3, Taichug Harbor Rd., Taichug, Taiwa, R.O.C. 3 Departmet o Computer Sciece, Taipei uicipal Uiversity o Educatio No., Ai-Guo W. Rd., Taipei, Taiwa, R.O.C. Abstract: The o-liear distortio caused by high peak-to-average power ratio (PAPR) o trasmitted sigal is a major drawback i the OFD systems. I this paper, the proposed PAPR reductio scheme is to choose the correspodig symbol patters with a low PAPR i the expaded sigal space. However, the scheme has a high complexity or the selectio o symbol patter with the smallest sigal power i a larger expaded sigal space. The scheme could be realized as a sigal mappig rom the origial iormatio symbols to the correspodig patters. With the selectio o the correspoded symbol patters, the PAPR could be greatly reduced. Accordig to the simulatio results with the proposed scheme, while the legth o the data rame is 6 ad the sigal expasio with addig bit ad 2 bits, the PAPR chagig rate could be 2 percets ad 6 percets o the origial PAPA, respectively. However, there is o promiet improvemet o PAPR reductio with more tha 8 bits or usig the sigal expasio scheme. Keywords: OFD system; PAPR reductio scheme; Sigal mappig scheme.. Itroductio Orthogoal requecy divisio multiplexig (OFD) techique has bee applied ito may applicatios such as digital audio broadcastig (DAB) systems, digital video broadcastig terrestrial TV (DVB-T) systems, asymmetric digital subscriber lies (ADSL), wireless local area etworks (WLAN), broadbad wireless access (BWA) etworks ad ultra-widebad systems [-4]. oreover, it could be expected to be the stadard or the Fourth Geeratio (4G) cellular system [5]. However, OFD sigal passes through a o-liear high power ampliier (HPA) beore it is trasmitted over the chael. Whe the iput sigal exceeds a certai value, the output o the ampliier becomes saturated ad, the, the OFD sigal results a great degradatio caused by the HPA [6, 7]. The HPA is commoly cosidered be memoryless, which meas that the curret output depeds o the curret iput oly. For applicatios with wider sigalig badwidths, however, the memory eects o the whole system caot be igored. [7] Especially, OFD sigal with a high PAPR is sesitive to the o-liear distortios caused by the HPA. The o-liear * Correspodig author; cyag@u.cyut.edu.tw Accepted or Publicatio: July 3, Chaoyag Uiversity o Techology, ISSN It. J. Appl. Sci. Eg., 27. 5, 75

2 Jyh-Horg We, Gwo-Ruey Lee ad Cheg-Yig Yag distortio i the HPA results i such egative actors as () costellatio warpig which icrease the bit error rate (BER) i the system (2) spectrum outgrowth resultig i adjacet chael itererece (ACI) [6, 7]. I order to reduce the o-liear distortio, may schemes have bee proposed to reduce the PAPR o trasmitted sigal. Amog those PAPA reductio schemes, the simplest method is to use the clippig process [, 8, 9]. However, usig clippig process causes both i-bad distortio ad out-o-bad distortio. These udesired eects could be avoided with a liear peak cacellatio techique []. Besides, the orward-error-cotrol codig applied scheme is aother solutio to the PAPR reductio [, ]. oreover, based o the scramblig each OFD symbol with dieret phase, the small PAPR selectio is provided by symbol scramblig methods, such as selected mappig (SL) method, partial trasmitted sequece (PTS) method ad subblock phase weightig (SPW) method [-4]. I this paper, a ew PAPR reductio scheme with the help o the sigal mappig scheme is proposed. The correspodig symbol patters are chose with a low PAPR i the expaded sigal space. The scheme could be realized as a sigal mappig rom the origial iormatio symbols to the correspodig patters. With the selectio o the correspoded symbol patters, the PAPR could be greatly reduced. I the ollowig sectio, the OFD system with the proposed sigal mappig scheme is described. The umerical aalysis is show i Sectio III. Fially, a coclusio is give i Sectio IV. 2. The OFD System with the Sigal appig Scheme Basically, a OFD system cotais a series-to-parallel coverter, a sigal mappig scheme ad a ast Fourier trasorm (FFT)/ iverse FFT (IFFT) module [, 2, 4]. The series ad parallel coverter is cosidered to realize the cocept o parallel data trasmissio to provide a high data rate trasmissio. -ary phase shit keyig (PSK) or -ary quadrature amplitude modulatio (QA) mappig scheme is modulated i each parallel subcarrier to provide a dieret data rate service i the system. Besides, the IFFT ad FFT are employed to replace the baks o siusoidal geerator or the modulatio ad demodulatio with dieret carrier requecies to reduce the complexity o OFD modem implemetatio [, 2]. Additioally, cosider the sigal mappig or sigal space expasio, the proposed OFD system is show i Figure. First, source iormatio is mapped with -ary PSK scheme to obtai a serial message sequece. The message sequece a [a, a,, a K- ] with K symbols is coverted ito a parallel orm ad called as a iormatio symbol. I order to choose the modulated symbol patters with low PAPRs, the iormatio symbol is proposed to map the correspodig modulated symbol patter x (x, x,, x N-2, x N- ) with N symbols i the expaded sigal space. There are N patters i the expaded sigal space ad K patters with miimum PAPRs are chose or mappig. The N parallel modulated symbols are trasormed by a IFFT to be a data symbol, s [s, s,., s N- ]. The, the OFD symbol is trasmitted over a chael. The PAPR o the basebad OFD trasmitted symbol ca be deied as PAPR max N * ( s s) * ( s) E s () where * idicates the complex cojugate, max(s ) deotes the maximum value o s ad E(s s * ) is the average power o data symbol s. The probability desity uctio (pd) o, is power o data symbol s, ( ) ( ) e (2) 76 It. J. Appl. Sci. Eg., 27. 5,

3 The PAPR Reductio i OFD System with the Help o Sigal appig Scheme * where s s is the power o the -th sample i the OFD symbol ad is a i.i.d. chi-squared distributio with 2 degrees o reedom radom variable [5, 6]. At the receiver, the received symbol are coverted ito a parallel orm ad, the, trasormed by a FFT to get the estimated modulated symbols. The estimated modulated symbols are mapped with correspodig demodulated scheme. The, the estimated source iormatio is obtaied. essage Sequece Iormatio a odulated x Data s OFD Trasmitted Source Iormatio ary-psk apper a [ a,..., ak ] Serial-to- Parallel Coverter a ak Proposed apper x IFFT s xn 2 s N 2 Parallel-to- Serial Coverter xn sn Chael essage Sequece Iormatio odulated Received Data OFD Received Source Iormatio ary-psk Demapper Parallel-to- Serial Coverter â â aˆk Proposed De-mapper ˆx ˆx FFT xˆn 2 r N 2 r r Serial-to- Parallel Coverter r, r,..., r, r N N 2 xˆn rn Figure. The block diagram o the FFT-based OFD system The sigal expasio i the proposed mappig scheme could be cosidered as the traserrig the origial iormatio symbols ito the correspodig modulated symbol patters, as show i Figure 2. I the igure, there are K possible iormatio symbols i the origial sigal space. These iormatio symbols should be mapped ito those modulated symbol patters with lower PAPRs i the expaded sigal space where there are N possible modulated symbol patters. The circles with dash lies represet the symbol patters with higher PAPRs. I the proposed mappig scheme, with the selectio o the correspoded symbol patters, the PAPR o the OFD trasmitted sigal could be greatly reduced. Origial sigal space Expaded sigal space Figure 2. The cocept o sigal mappig i the proposed scheme I additio, the upper boud o PAPR with the proposed scheme could be derived as bellows. Withi mappig the symbol with K bits It. J. Appl. Sci. Eg., 27. 5, 77

4 Jyh-Horg We, Gwo-Ruey Lee ad Cheg-Yig Yag to the symbol with K+b bits, the joit probability desity uctio (pd) is rewritte as (,...,,..., ) K+ b ( ) ( ) ( ) e K+ b K+ b (3) I the exteded sigal space, there are K+b symbol patters could be selected or the K dedicated symbols. Hece, the K miimum PAPR symbol patters could be chose. The, the PAPR upper boud up-boud i the proposed scheme could be obtaied with the Eq. (4), (,...,,..., K + b up boud ) K+ b up boud e d... d... dk+ b (4) K K+ b b < because there are K symbol patters should be chose amog K+b sigal patters. Besides, because is a i.i.d. radom variable, Eq. (4) is satisied. (,...,,..., K + b up boud ) < < up boud,..., < up boud,..., K + b < up boud (5) The, the PAPR upper boud up-boud i the proposed scheme could be obtaied as up boud ( ) ( ) K+ b ( e ) d K+ b b up boud up boud e d e d (6) Hece, the upper boud o PAPR, up-boud, could be obtaied as up boud l b K+ b (7) where l( ) deotes the logarithm uctio. Based o this proposed scheme, the simulatios are give i the ollowig sectio. 3. Numerical Aalysis At the begiig, assumig the umber o subcarriers ad the symbol umber o iormatio symbol to be 4 ad 3 (i.e. N4, K3), the umber o the possible iormatio symbols i the sigal space ad the possible symbol patters is 2 3 ad 2 4 idividually, whe the BPSK scheme is used. The histogram o PAPR i the 4-IFFT BPSK OFD system is show i Figure 3. I the igure, there are 2 4 possible symbol patters. The umbers o the patter with PAPR, PAPR2 ad PAPR4 are eight, our ad our, idividually. I the proposed scheme, the symbol patters withi the miimum 8 th PAPR could choose as the possible correspodig symbol patters i the proposed algorithm. Hece, the 8 patters with PAPR are chose or mappig. The PAPR has bee reduced rom 3 to i the proposed scheme. Besides, i Table, with the icrease o parameter K ad N, PAPR reductio is more outstadig. Numbers IFFT - BPSK PAPR Value Figure 3. The histogram o PAPR i the 4-IFFT BPSK OFD system 78 It. J. Appl. Sci. Eg., 27. 5,

5 The PAPR Reductio i OFD System with the Help o Sigal appig Scheme Table. PAPR o the covetioal OFD system ad the OFD system usig the proposed method K N odulatio scheme (-ary PSK) The PAPR o the covetioal OFD system with K subcarriers The PAPR o OFD system usig the proposed method 3 4 BPSK QPSK BPSK QPSK I additio, this is assumig the symbol umber o iormatio symbol to be6. With addig bits, the PAPR chagig rate is show i Figure 4. The PAPR chagig rate is deied as a ratio betwee the maximum PAPR value i the proposed scheme ad the maximum oe i origial PAPR. Without addig ay bit, the maximum PAPR value is ot chaged. While the legth o the data rame is 6 ad the sigal expasio with addig bit ad 2 bits, the PAPR is reduced rom 6 to 3.2 ad 2.6, idividually. Thus, the PAPR chagig rate could be 2 percets ad 6 percets o the origial PAPA, respectively. However, there is o promiet improvemet o PAPR reductio with more tha 8 bits or the sigal expasio..8 PAPR Chagig Rate The Added Bits, b Figure 4. The PAPR chagig rate i the proposed scheme 4. Coclusio I this paper, a ew scheme with sigal space expasio is proposed to reduce PAPR o the OFD trasmitted sigal. The scheme could be realized as a sigal mappig rom the origial iormatio symbols to the correspodig patters. With the selectio o the correspoded symbol patters, the PAPR could be greatly reduced. While the legth o the data rame is 3 ad the sigal expasio with addig bit, the PAPR is reduced orm 3 to whe the BPSK scheme is used. Besides, with the icrease o parameter K ad N, PAPR reductio is more outstadig. The PAPR chagig rate is large while the legth o the data rame is 6 ad the sigal expasio with addig bit. However, there is o promiet improvemet o PAPR reductio with more tha 8 bits or the sigal expasio. It. J. Appl. Sci. Eg., 27. 5, 79

6 Jyh-Horg We, Gwo-Ruey Lee ad Cheg-Yig Yag Reereces [ ] Nee, R. V. ad Prasad, R. 2. OFD wireless multimedia commuicatio, Artech House. lc. Norwood A. U.S.A. [ 2] Egels,. 22. Wireless OFD Systems: How to ake Them Work? Kluwer Academic Publishers, st editio. assachusetts. U.S.A. [ 3] Prasad, R. 24. OFD or Wireless Commuicatios Systems, Artech House. lc. Norwood A. U.S.A. [ 4] Zou, W. Y., ad Wu, Y COFD: A overview, IEEE Trasactios o Broadcastig, 4, : -8. [ 5] Hazo, L., Webb, W., ad Keller T. 2. Sigle- ad multi-carrier quadrature amplitude modulatio Priciples ad applicatios or persoal commuicatios, WLANs ad broadcastig, Joh Wiley & Sos, Ltd, Eglad. [ 6] Wag, T., ad Ilow J. 24. Compesatio o o-liear distortios with memory eects i OFD trasmitters, Proceedig o IEEE Globecom 4, 4: [ 7] Li, J., ad Ilow, J. 26. Adaptive volterra predistorters or compesatio o o-liear eects with memory i OFD trasmitters, Proceedig o CNSR 6: -3. [ 8] Ochiai, H., ad Imai, H. 2. Perormace o the deliberate clippig with adaptive symbol selectio or strictly bad-limited OFD systems, IEEE Joural o Selected Areas i Commuicatios, 8, : [ 9] Ryu, H. G., Hoa, T. P., Hieu, T. H., ad Ji, J. 24. BER aalysis o clippig process i the orward lik o the OFD-FDA commuicatio system, IEEE Trasactios o Cosumer Electroics, 5, 4,: [] Richard D. J. Va Nee, 996. OFD codes or peak-to-average power reductio ad error correctio, Proceedig o IEEE Globecom 96: [] üller S. H., ad Huber J. B A compariso o peak power reductio schemes or OFD, Proceedig o IEEE Globecom 97: -5. [2] Breilig,., üller-weiurter S., ad Huber J. 2. SL peak-power reductio without explicit side iormatio, IEEE Commuicatios Letters, 5, 6: [3] üller S. H., ad Huber J. B OFD with reduced peak- to-average power ratio by optimum combiatio o partial trasmit sequeces, IEE Electroics Letters, 33, 5: [4] Ryu H. G., ad You K. J. 22. A ew PAPR reductio scheme: SPW (subblock phase weightig), IEEE Trasactios o Cosumer Electroics, 48, : [5] Ochiai H., ad Imai H. 2. O the distributio o the peak-to-average power ratio i OFD sigals, IEEE Trasactios o Commuicatios, 49, 2: [6] Abramowitz., ad Stegu, I. A Hadbook o athematical Fuctios with Formulas, Graphs, ad athematical Tables, Dover Publicatios, Ic. New York, U.S.A. 8 It. J. Appl. Sci. Eg., 27. 5,