A NEW DISCRETE HARTLEY TRANSFORM PRECODING BASED INTERLEAVED-OFDMA UPLINK SYSTEM WITH REDUCED PAPR FOR 4G CELLULAR NETWORKS

Joural of Egieerig Sciece ad Techology Vol. 6, No. 6 (211) 685-694 School of Egieerig, Taylor s Uiversity A NEW DISCRETE HARTLEY TRANSFORM PRECODING BASED INTERLEAVED-OFDMA UPLINK SYSTEM WITH REDUCED PAPR FOR 4G CELLULAR NETWORKS IMRAN BAIG*, VARUN JEOTI Electrical ad Electroic Egieerig Departmet, Uiversiti Tekologi PETRONAS, Malaysia *Correspodig Author: imra_baig_mirza@yahoo.com Abstract High peak-to-average power ratio (PAPR) reductio is oe of the major challeges i orthogoal frequecy divisio multiple access (OFDMA) systems sice last decades. High PAPR icreases the compleity of aalogue-to-digital (A/D) ad digital-to-aalogue (D/A) covertors ad also reduces the efficiecy of RF highpower-amplifier (HPA). I this paper, we preset a ew Discrete- Hartley trasform (DHT) precodig based iterleaved-ofdma uplik system for PAPR reductio i the upcomig 4G cellular etworks. Etesive computer simulatios have bee performed to aalyze the PAPR of the proposed system with root-raised-cosie (RRC) pulse shapig. We also compare simulatio results of the proposed system with the covetioal iterleaved-ofdma uplik systems ad the Walsh- Hadamard trasform (WHT) precodig based iterleaved-ofdma uplik systems. It is cocluded from the computer simulatios that the proposed system has low PAPR as compared to the covetioal iterleaved-ofdma uplik systems ad the WHT precoded iterleaved-ofdma uplik systems. Keywords: Iterleaved-OFDMA, Peak-to-average power ratio, Discrete-Hartley trasform, High-power-amplifier. 1. Itroductio Orthogoal frequecy divisio multiple access (OFDMA) is a multiple access versio of the orthogoal-frequecy-divisio-multipleig (OFDM). The OFDMA system splits the high speed data stream ito a umber of parallel low data rate streams ad these low rates data streams are trasmitted simultaeously over a umber of orthogoal subcarriers [1-4]. 685

686 A. Baig ad V. Jeoti Nomeclatures A Precodig matri a m,l m th row ad l th colum of DHT precoder matri A H Real umber k User ide L Precoder Size = User subcarriers M User subcarriers N System subcarriers Q Subchaels/Users (Q = N/M) r(t) Basebad pulse T Symbol duratio T ( Compressed symbol duratio after IFFT X A comple vector after S/P coverter (k ) A comple basebad iterleaved-ofdma uplik sigal for k th user Yˆ A comple vector after subcarrier-mappig Greek Symbols ω c Carrier frequecy Abbreviatios A/D CCDF DHT D/A HPA IFFT OFDM OFDMA PAPR RC RRC SNR S/P WHT Aalogue-to- digital Complemetary cumulative distributio fuctio Discrete- Hartley trasform Digital-to-aalogue High-power-amplifier Iverse fast Fourier trasform Orthogoal frequecy divisio multipleig Orthogoal frequecy divisio multiple access Peak-to-average power ratio Raised-cosie Root raised cosie Sigal-to-oise ratio Serial-to-parallel Walsh-Hadamard trasform The key differece betwee OFDM ad OFDMA is that istead of allocatig all the available subcarriers to oe user, the base statio assigs oe subset of carriers to oe user ad aother subset to aother user i order to accommodate several users at the same time. There are two differet approaches to do subcarrier mappig to users i OFDMA systems: localized subcarrier mappig ad distributed subcarrier mappig. I localized subcarrier mappig oe group of locally adjacet subcarriers are mapped to oe user ad aother to aother. The distributed subcarrier mappig aims to allocate a distributed set of subcarriers to oe user. It ca be further divided i to iterleaved subcarrier mappig mode ad radom iterleaved subcarrier mappig mode. I iterleaved subcarrier mappig, the mapped distributed subcarriers are equidistat to each other, while, i radom iterleaved subcarrier mappig, these subcarriers are distributed radomly. Joural of Egieerig Sciece ad Techology December 211, Vol. 6(6)

A New DHT Precodig Based Iterleaved-OFDMA Uplik System 687 Figure 1 further eplais the cocept of localized subcarrier mappig mode ad iterleaved subcarrier mappig mode of the OFDMA. Moreover, the iterleaved-ofdma is oe of the promisig multiple access techiques for future mobile radio commuicatio systems [5]. OFDMA is widely adopted i the various commuicatio stadards like Worldwide Iteroperability for Microwave Access (WiMAX), Mobile Broadbad Wireless Access (MBWA), Evolved UMTS Terrestrial Radio Access (E-UTRA), Ultra Mobile Broadbad (UMB), OFDMA is also a strog cadidate for the Wireless Regioal Area Networks (WRAN) ad Layered OFDMA of LTE-Advaced. However OFDMA has some drawbacks, amog others, the peak-to-average power ratio (PAPR) is still oe of the major drawbacks i the trasmitted OFDMA sigals. (a) (b) Fig. 1. (a) Iterleaved OFDMA ad (b) Localized OFDMA. Therefore, for zero distortio of the OFDMA sigals, the high-power-amplifier (HPA) must ot oly operate i its liear regio but also with sufficiet back-off. Thus, HPA with a large dyamic rage are required for OFDMA systems. These amplifiers are very epesive ad are major cost compoet of the OFDMA systems. Thus, if we reduce the PAPR it ot oly meas that we are reducig the cost of OFDMA systems ad reducig the compleity of A/D ad D/A coverters, but also icreasig the trasmit power, thus, for same rage improvig received sigal-to-oise ratio (SNR), or for the same SNR improvig rage. A large umber of PAPR reductio techiques have bee proposed i the literature. Amog them, schemes like costellatio shapig [6], oliear compadig trasforms [7], clippig ad filterig [8], partial trasmit sequece (PTS) [9], selective mappig (SLM) [1-11] ad precodig based techiques [12-14] are popular. The precodig based techiques, however, show great promise as they are simple liear techiques to implemet without the eed of ay side iformatio. This paper presets a ew DHT precodig based OFDMA uplik system for PAPR reductio i 4G cellular etworks. This paper is orgaized as: sectio 2 describes the basics of the iterleaved-ofdma, i Sectio 3 we preset the Joural of Egieerig Sciece ad Techology December 211, Vol. 6(6)

688 A. Baig ad V. Jeoti proposed system model for PAPR reductio, ad Sectio 4 presets the computer simulatio results ad Sectio 5 cocludes the paper. 2. Iterleaved-OFDMA Uplik System Figure 2 illustrates the block diagram of iterleaved-ofdma uplik system. I iterleaved-ofdma uplik system, the basebad modulated symbols are passed through serial-to-parallel (S/P) coverter, which geerates the comple vector of size M. We ca write comple vector of size M as X = [X o, X 1, X 2,.., X M-1 ] T. After this, the N subcarrier mappig is carried out to the vector X i iterleaved mode, ad we get Yˆ [ ] T k = Yˆ, Yˆ 1, Yˆ 2,..., Yˆ N. For k th user, the comple basebad 1 iterleaved-ofdma uplik sigal with N system s subcarriers ad M user s subcarriers ca be writte as follows ( ) ( ) 1 k 1 M = ˆ k Yk N k=. e kq+ m j 2π N where =, 1, 2,... N-1, m =, 1, 2,... Q-1. Yˆ we get after subcarrier mappig, k j = 1, ad ( k ) Yˆ is modulated sigal o subcarrier k for k th user. The PAPR of the k covetioal iterleaved-ofdma sigal i Eq. (1) ca be writte as follows (1) PAPR ma =,1,... N 1 = 1 1 N M = ( k ) 2 ( k ) 2 (2) Fig. 2. Iterleaved-OFDMA Uplik System. Joural of Egieerig Sciece ad Techology December 211, Vol. 6(6)

A New DHT Precodig Based Iterleaved-OFDMA Uplik System 689 3. Proposed Model 3.1. Discrete Hartley trasform (DHT) The DHT is a liear trasform. I DHT, N real umbers o, 1,.., N-1 are trasformed ito N real umbers H o, H 1,.., H N-1. Accordig to [15], the N-poit DHT ca be defied as follows H k N 1 N 1 2πk 2πk 2πk = cos + si = = N N = N ( ). cas where cas θ = cos θ +si θ ad k =, 1 N-1 2πm a m, 1 = cas N The precodig matri A ca be costructed as follows a a1 K a( L 1) a1 a11 K a1 ( L 1) A = M M O M a( ) ( ) ( )( ) L 1 a L 1 1 K a L 1 L 1 A is precodig matri of size L L show i Eq. (5), m ad l are itegers from to L-1. The DHT is also ivertible trasform which allows us to recover the from H k ad iverse ca be obtaied by simply multiplyig DHT of H k by 1/N. (3) (4) (5) 3.2. DHT precodig based iterleaved-ofdma uplik system Figure 3 shows a DHT precodig based iterleaved-ofdma uplik system. I DHT precodig based iterleaved-ofdma uplik system a precodig matri A of dimesio L L is applied to costellatios symbols before the subcarrier mappig ad IFFT to reduce the PAPR. I the proposed system, the basebad modulated data is passed through the S/P coverter which geerates a comple vector of size M that ca be writte as: X = [X o, X 1, X 2,.., X M-1 ] T. After that, the DHT precodig is applied to this comple vector which trasforms this comple vector ito ew vector of legth L = M that ca be writte as: Y=AX = [Y o, Y 1, Y 2,.., X L-1 ] T ad Y M ca be writte as follows L = 1 m l= Y a X, m =, 1,., L-1 (6) m, l. l a m,l meas m th row ad l th colum of precoder matri. After the precodig, the subcarrier mappig is doe i iterleaved mode. Mathematically, the subcarrier mappig i iterleaved mode ca be doe as follows Y l Y ˆ =, l = Q.k k M-1 otherwise (7) l Q where l N-1, N = Q.M, N is system subcarriers, M is user subcarriers, ad Q is subchaels/users (Q = N/M). Joural of Egieerig Sciece ad Techology December 211, Vol. 6(6)

69 A. Baig ad V. Jeoti The k th subcarrier of each group is assiged to the k th user with ide set {(k), (k+q),, (k+(m-1)q)} where k =, 1, 2,., Q-1. Suppose the k th user is assiged to subchael k the the comple basebad DHT precoded iterleaved-ofdma uplik sigal for k th user ca be writte as follows ( ) ( ) 1 k 1 M = ˆ k Yl N l=. e lq+ k j2π N, =, 1, 2,... N-1 (8) where, user ide k =, 1,, Q-1 ad ( k ) Yˆ is modulated sigal o subcarrier l l for k th user. The comple pass ad sigal of DHT precoded iterleaved-ofdma after RRC pulse shapig ca be writte as follows ( ω (9) N 1 j ct ( k ) ( t) = e. r( t T ) = ( where ω c is carrier frequecy, r(t) is basebad pulse, T = ( M / N )T is compressed symbol duratio after IFFT ad T is symbol duratio i secods. The root raised cosie (RRC) pulse shapig filter ca be defied as follows r ( t) π si ( t = T + t T 2 π t 16α t ( 1 ( 2 T T πt T ( 1 α ) 4α ( cos ( 1+ α ) 2, α 1 (1) Fig. 3. DHT Precodig Based Localized-OFDMA System. The PAPR of DHT precoded iterleaved-ofdma sigal i Eq. (9) with pulse shapig ca be writte as follows Joural of Egieerig Sciece ad Techology December 211, Vol. 6(6)

A New DHT Precodig Based Iterleaved-OFDMA Uplik System 691 ma ( t NT NT PAPR = ( 1 ( NT ( t) ( t) 2 2 dt (11) The PAPR of DHT precoded Iterleaved-OFDMA sigal i Eq. (8) without pulse shapig ca be writte as follows PAPR ma =,1,... N 1 = 1 1 N M = ( k ) 2 ( k ) 2 (12) 4. Simulatio Results Etesive simulatios i MATLAB have bee performed to aalyse the PAPR of the proposed DHT precodig based iterleaved-ofdma uplik system. We evaluate the PAPR statistically by usig complemetary cumulative distributio fuctio (CCDF). The CCDF of PAPR, for iterleaved-ofdma uplik sigal, is used to epress the probability of eceedig a give threshold PAPR (i.e., CCDF = Pr(PAPR>PAPR )). We also compared our simulatio results with the covetioal iterleaved-ofdma uplik systems ad WHT precoded iterleaved-ofdma uplik systems. Simulatio parameters used i the simulatio are chose to reflect the LTE stadard ad are tabulated i the Table 1 as follows Table1. System Parameters. Chael Badwidth 5MHz User Subcarriers 16 System Subcarriers 512 Modulatio Precodig QPSK, 16-QAM ad 64-QAm DHT ad WHT Pulse Shapig Root Raised Cosie (RRC) RRC Roll-off Factor Alpha=.22 CCDF Clip-Rate 1-3 Figure 4 shows the CCDF compariso of PAPR of the DHT precodig based iterleaved-ofdma uplik system with the covetioal iterleaved-ofdma uplik systems ad the WHT precodig based iterleaved-ofdma uplik systems. At clip rate of 1-3, with user subcarriers M = 16 ad system subcarriers N =512, the PAPR is reduced to 9.9 db, 8.8 db ad 7 db respectively, for the covetioal iterleaved-ofdma uplik system, WHT precoded iterleaved- OFDMA uplik system ad DHT precoded iterleaved-ofdma uplik system. Figure 5 shows the CCDF compariso of PAPR of the DHT precodig based iterleaved-ofdma uplik system with the covetioal iterleaved-ofdma uplik systems ad the WHT precodig based iterleaved-ofdma uplik systems. At clip rate of 1-3, with user subcarriers M = 16 ad system subcarriers N =512, the PAPR is reduced to 9.9 db, 8.9 db ad 7.9 db respectively, for the covetioal iterleaved-ofdma uplik system, WHT precoded iterleaved- OFDMA uplik system ad DHT precoded iterleaved-ofdma uplik system. Joural of Egieerig Sciece ad Techology December 211, Vol. 6(6)

692 A. Baig ad V. Jeoti 1 DHT Precodig Based Iterleaved-OFDMA Uplik System for QPSK Covetioal Iterleaved-OFDMA WHT Precoded Iterleaved-OFDMA DHT Precoded Iterleaved-OFDMA Prob(PAPR > PAPR ) 1-1 1-2 1-3 2 4 6 8 1 12 14 PAPR (db) Fig. 4. CCDF Compariso of the PAPR of the DHT Precoded Iterleaved- OFDMA Uplik with the Covetioal Iterleaved-OFDMA Uplik ad the WHT Precoded Iterleaved-OFDMA Uplik with M=16 (User Subcarriers) ad N=512 (System Subcarriers) for QPSK Modulatio. 1 DHT Precodig Based Iterleaved-OFDMA Uplik System for 16-QAM Covetioal Iterleaved-OFDMA WHT Precoded Iterleaved-OFDMA DHT Precoded Iterleaved-OFDMA Prob(PAPR > PAPR ) 1-1 1-2 1-3 2 4 6 8 1 12 14 PAPR (db) Fig. 5. CCDF Compariso of the PAPR of the DHT Precoded Iterleaved- OFDMA Uplik with the Covetioal Iterleaved-OFDMA Uplik ad the WHT Precoded Iterleaved-OFDMA Uplik with M=16 (User Subcarriers) ad N=512 (System Subcarriers) for 16-QAM Modulatio. Figure 6 shows the CCDF compariso of PAPR of the DHT precodig based iterleaved-ofdma uplik system with the covetioal iterleaved-ofdma Joural of Egieerig Sciece ad Techology December 211, Vol. 6(6)

A New DHT Precodig Based Iterleaved-OFDMA Uplik System 693 uplik systems ad the WHT precodig based iterleaved-ofdma uplik systems. At clip rate of 1-3, with user subcarriers M = 16 ad system subcarriers N = 512, the PAPR is reduced to 9.9 db, 9 db ad 8 db respectively, for the covetioal iterleaved-ofdma uplik system, WHT precoded iterleaved-ofdma uplik system ad DHT precoded iterleaved- OFDMA uplik system. Thus, it ca be see that the PAPR performace of the DHT precodig based iterleaved-ofdma uplik system is better tha the o-precodig or the popular WHT precodig based OFDMA systems. The improvemet is most for QPSK costellatio based system tha for 16 QAM or 64 QAM based systems. 1 DHT Precodig Based Iterleaved-OFDMA Uplik System for 64-QAM Covetioal Iterleaved-OFDMA WHT Precoded Iterleaved-OFDMA DHT Precoded Iterleaved-OFDMA Prob(PAPR > PAPR ) 1-1 1-2 1-3 2 4 6 8 1 12 14 PAPR (db) Fig. 6. CCDF Compariso of the PAPR of the DHT Precoded Iterleaved- OFDMA Uplik with the Covetioal Iterleaved-OFDMA Uplik ad the WHT Precoded Iterleaved-OFDMA Uplik with M=16 (User Subcarriers) ad N=512 (System Subcarriers) for 64-QAM Modulatio. 5. Coclusios I this paper, we proposed a ew DHT precoded iterleaved-ofdma uplik system with improved PAPR for 4G cellular etworks. MATLAB simulatio shows that DHT precoded iterleaved-ofdma uplik system shows better PAPR gai as compare to the covetioal iterleaved-ofdma uplik systems ad the WHT precoded iterleaved-ofdma uplik systems. Hece, it is cocluded that the proposed DHT precodig based iterleaved-ofdma uplik system is more favourable tha the covetioal iterleaved-ofdma uplik systems ad the WHT precoded iterleaved-ofdma uplik systems. The DHT precoded OFDMA uplik system also take the advatage of the frequecy variatios of the commuicatio chael ad ca also offer substatial performace gai i fadig multipath chaels. Joural of Egieerig Sciece ad Techology December 211, Vol. 6(6)

694 A. Baig ad V. Jeoti Refereces 1. Morelli, M. (24). Timig ad frequecy sychroizatio for the uplik of a OFDMA system. IEEE Trasactios o Commuicatios, 52(2), 296-36. 2. Selvakeedy, S. (26). Performace study of distributed coordiatio fuctio over IEEE 82.11a physical layer. Joural of Egieerig Sciece & Techology (JESTEC), 1(1), 1-2. 3. Omar, M.H.; Hassa, S.; Shabli, A.H.M. (29). COGRADNET: Ubiquitous heterogeeous wireless etworks. Joural of Egieerig Sciece & Techology (JESTEC), 4(2), 184-195. 4. Idumathi, K.; Murugesa, K. (211). A cross-layer resource schedulig with QoS guaratees usig adaptive toke bak fair queuig algorithm i wireless etworks. Joural of Egieerig Sciece & Techology (JESTEC), 6(3), 26-267. 5. Frak, T.; Klei, A.; Costa, E.; ad Schulz, E. (25). IFDMA A promisig multiple access scheme for future mobile radio systems. IEEE 16th Iteratioal Symposium o Persoal, Idoor ad Mobile Radio Commuicatios (PIMRC), 2, 1214-1218. 6. Kou, Y.J.; Lu, W.S.; ad Atoiou, A. (27). A ew peak-to-average powerratio reductio algorithm for OFDM systems via costellatio etesio. IEEE Trasactios o Wireless Commuicatios, 6(5), 1823-1832. 7. Jiag, T.; Yao, W.; Guo, P.; Sog, Y.; ad Qu, D. (26). Two ovel oliear compadig schemes with iterative receiver to reduce PAPR i multicarrier modulatio systems. IEEE Trasactios o Broadcastig, 52(2), 268-273. 8. Wag, L.; ad Tellambura, C. (25). A simplified clippig ad filterig techique for PAR reductio i OFDM systems. IEEE Sigal Processig Letters, 12(6), 453-456. 9. Ha, S.H.; ad Lee, J.H. (24). PAPR reductio of OFDM sigals usig a reduced compleity PTS techique. IEEE Sigal Processig Letters, 11(11), 887-89. 1. Baig, I.; ad Jeoti, V. (21). DCT precoded SLM techique for PAPR reductio i OFDM systems. Proceedigs of 21 Iteratioal Coferece o Itelliget ad Advaced systems (ICIAS), 1-6, Kuala Lumpur, Malaysia. 11. Baig, I.; ad Jeoti, V. (211). O the PAPR reductio i OFDM systems: A ovel ZCT precodig based SLM techique. Joural of Egieerig Sciece ad Techology (JESTEC), 6(3), 357-368. 12. Slimae, S.B. (27). Reducig the peak-to-average power ratio of OFDM sigals through precodig. IEEE Trasactios o Vehicular Techology, 56(2), 686-695. 13. Baig, I.; ad Jeoti, V. (21). PAPR aalysis of DHT-Precoded OFDM system with M-QAM. Proceedigs of 21 Iteratioal Coferece o Itelliget ad Advaced systems (ICIAS), 1-4, Kuala Lumpur, Malaysia. 14. Baig, I.; ad Jeoti, V. (211). O the PAPR reductio: A ZCMT precodig based distributed-ofdma uplik system. Proceedigs of 211 Iteratioal Coferece Electrical, Cotrol ad computer Egieerig (INECCE), 55-51, Kuata, Pahag, Malaysia. 15. Bracewell, R.N. (1983). Discrete Hartley trasform. Joural of the Optical Society of America, 73(12), 1832-1835. Joural of Egieerig Sciece ad Techology December 211, Vol. 6(6)