PAPR and the Cubic Metric for Low PA Power consumption

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1 AR and he Cubic Meric for Low A ower consumpion Dr.Terence E. Dodgson Nokia iemens Neworks, Dr. Yanyan Wu Xi an Jiaoong Liverpool Universiy Absrac - Wih he every-increasing complexiy of signal waveforms generaed by ransmiers of modern digial communicaions sysems, here comes a corresponding demand for ransmiers o coninue o operae efficienly, producing minimum disorion, wihin specified limis. These days, equipmen requiremens also include he need o operae in an energy efficien way, minimizing power consumpion. In order o operae in he mos efficien manner possible, insananeous conrol of a ower Amplifier (A by measuring appropriae A inpu signal characerisics, for example he eak o Average ower Raio (AR or Cubic Meric (CM, should resul in seing he A Back-off (someimes referred o as de-raing as accuraely as possible. AR and a CM approaches o deermining A Back-off are compared for OFDM signals, ogeher wih a suiable AR reducion echnique, in erms of heir abiliy o minimize power consumpion and ensure efficien A operaion. Index Terms CM, Green Radio, AR, Opimum elecive Mapping I. INTRODUCTION When looking a services which require high user bi raes, wireless communicaion sysems have ended o lag behind wired sysems due o problems caused by he less benign radio ransmission environmen. To he end user service is all imporan, however, when considering he environmen, low power consumpion becomes as imporan. Curren percepion is ha users would like o have he same service offered over a wireless link as hey would be able o obain over a wired one, despie any addiional performance requiremens. This has led o he design of cellular wireless sysems which are capable of working wih relaively high daa raes, in paricular over he wireless link. Recen advances in he hird generaion (G sysem, currenly referred o as Wideband Code Division Muliple Access (WCDMA formerly he Universal Mobile Telecommunicaions ysem (UMT have resuled in conceps such as High peed acke Access (HA where heoreical daa raes of 4.4Mbps and 5.76Mbps in downlink and uplink respecively are achievable. The nex generaion mobile phone sysem (LTE aims o increase hese daa raes furher, in a specrum efficien manner, using bandwidh on demand echniques (he allocaion of appropriae resource blocks depending on, amongs oher iems, he amoun of daa a user requires. The main, driving, forces behind he design of WCDMA and LTE have been he hirs for increased daa raes and he requiremen for specrum efficiency (accessible bandwidh being a relaively rare resource. Due o environmenal consideraions, a hird driver, he requiremen for power efficiency, needs o be aken ino accoun, aiming ulimaely owards he developmen of ower Efficien Technology (or Green Technology. II. GREEN TECHNOLOGIE - GENERAL erhaps one of he firs, mos obvious, areas where high power efficiency has always been a requiremen is he ransmier A. The increase in daa rae, which allows for he delivery of enhanced user services needs o be complimened by he efficien delivery of ha service, ha is o say, resources should no be needlessly wased and power should no be unnecessarily consumed. Opimisaion of such sysem resources is a necessary ask in order o drive down he cos per bi o he end user and associaed Operaional Energy (OpEn coss. Muli-media (e.g. inerne service users require relaively high daa raes combined wih low daa access delays, ye inerne sessions end o be bursy in naure, wih defined periods of aciviy and inaciviy. To ensure efficien resource usage, users should be assigned only he minimum resources which would allow hem o remain conneced during hese inacive imes (i.e. when no daa is being sen on he Uplink. In imes of no user aciviy ideally (ignoring ransien off/on swiching aspecs A s should be urned off, oherwise heir back-off should be kep as small as possible, o ensure efficien operaion, whils also ensuring minimum signal degradaion which migh oherwise occur (for example hrough signal clipping. A low back-off value wihou signal disorion no only ensures increased efficiency bu also ensures power is channeled ino he desired signal and no wased on spurious signals. III. AR AND THE CM Inpu signals o a A end o be very dynamic and his is becoming increasingly rue wih modern communicaions sysems which involve he deploymen of an increased number of channels and associaed channel configuraions. The way hese channels are configured, and heir subsequen processing by he A, is likely o have an impac on any disorion ha migh be produced by ha A. Wih second generaion, G, sysems AR-based back-off schemes were deemed sufficien for efficien A operaion. However, more recen lieraure e.g. [], [], [4], [5] suggess ha AR back-off schemes are no sufficienly accurae when working wih he, increasingly, TO BE ADDED

2 Back-Off Error Back-Off Error complex signals ha occur wih enhanced G sysems (and by implicaion fuure, fourh generaion, 4G, sysems. A measure is required which reflecs beer a signal s consiuen pars, e.g. for OFDM-ype signals his may include, for each channel, he number of samples used when implemening he Fas Fourier Transform (FFT and how many of hese samples are acive, he number of samples dedicaed o he Cyclic refix (C, he modulaion ype and he associaed bandwidh/number of resource blocks, as well as knowing he way in which he channels hemselves are formaed and how hey are combined, ogeher wih considering oher sysem aspecs such as how power conrol is implemened. Ref [] indicaes ha he (WCDMA CM has he required accuracy for deermining wha he A back-off should be for any given channel forma and combinaion for curren, modern, cellular sysems when considering WCDMA. Ref[] provides a similar (CM approach for LTE. IV. CM FOR LTE The modulaor oupu/inpu o he A can be represened as a complex sream of N samples, {v }, as indicaed in Figure ; Figure Modulaion Oupu From he lieraure, e.g. [9], he CM is given by; CM WCDMA Where, CEIL([.log (( v.log ( v ]/ ( norm rms normre f rms K v norm is he normalized volage waveform of he inpu signal. v Re is he normalized volage waveform of he reference norm f signal (.kbps AMR peech and.log ( v normre f rms. 5 db. K is a normalizing consan depending on he preading Facor (for WCDMA or he bandwidh/number of resource blocks (for LTE, see ref[] and ref[] The CM can be found using he modulaion oupu samples cubed power series and he power series iself. An alernaive, more explici, expression for he CM, ref[], is hus; rms N. / c ( Where, N is he number of samples considered, And, ( a ( a b N ( a ( a N ( a b b ( a b b... b ( a... ( a N N V. AR & CM COMARION b b N N In order o observe he accuracy of AR and CM back-off esimaions, signals represenaive of hose ha would occur in pracice migh be simulaed and he CM calculaion performed, making use of equaion (. Comparison of calculaed CMs of oher sysem signals is hen underaken. Using he empirical resuls from ref [] in he form of a graph he calculaed CM values can be mapped ono he required A power back-off values. A similar procedure can be carried ou for back-off as deermined by only AR measuremen. Boh ses of resuls can hen be compared o A back-off measuremens deermined hrough experimenaion wih appropriae A hardware. Considering LTE, he sandard error for AR back-off predicion, is found o be.56db which was also found o be, on average, more han.db poorer han he CM predicion Ref []. Approximaed Back-off esimaion plos for AR esimaion and CM esimaion can be seen in Figure and Figure respecively AR Back-Off Esimaion Error v. Measuremen No Measuremen No. Figure AR Back-Off Esimaion Error for a number of measuremens CM Back-Off Esimaion Error v. Measuremen No Measuremen No. Figure CM Back-Off Esimaion Error for a number of measuremens ( (4

3 IFFT Modulaion Mapping (eg. QK, 64QAM In order o avoid possible signal disorion, he variaion in he predicion error of eiher echnique should be aken ino accoun when deermining he A back-off value. As seen from he ideal drawings in Figure 4, his resuls in a smaller back-off value when using he CM. A Backoff AR predicion variaion Linear Region (a AR back-off predicion A Backoff CM predicion variaion (b CM back-off predicion Figure 4 AR/CM back-off predicion variaion VI. EAK TO AVERAGE OWER RATIO REDUCTION Linear Region To furher opimize he efficien operaion of he A he AR iself migh be reduced, hereby reducing he variaion of he acual signal and he associaed A backoff predicion error. Various echniques have been proposed o reduce AR, among hem elecive Mapping (LM, Ref [] and as shown in Figure 5, for an OFDMA sysem. LM is a non-disorion, sochasic, mehod ha incurs lile loss in efficiency. / X X X N ( u ( u ( u N Below AR Candidae equence Updae Figure 5 LM schemaic diagram for OFDM ransmission x x T... x N- X (5 A, phase adjused, symbol vecor is hen formed from he componen-wise produc of x wih a candidae phase sequence, s, given below: ( u... T N - u U Applying he Inverse Discree Fourier Transform (IDFT, wih L-imes over-sampling, o he phase adjused symbol vecor, produces a sampled version of he corresponding coninuous-ime muli-carrier signal: x T x xnl- x... I is generally assumed, ref [], ha aking L = 4 allows a saisfacory esimae of he AR o be calculaed from x as follows: max xn n (NL- log AR x db. (8 E xn where E(. denoes expecaion. Afer he AR comparisons among he U ime signals x (u for u=, U, he one wih he minimum AR is seleced for ransmission. xˆ arg min ARx (9 uu Figure 5 shows a serial searching approach by which he search among he candidae phase sequences may erminae when a saisfacory AR is achieved. For each search, he complemenary cumulaive disribued funcion (CCDF of AR, i.e. he probabiliy ha AR exceeds a hreshold AR, can be esimaed by: r -AR N AR AR -(-e (6 (7 x ( This expression assumes ha he cenral limi heorem applies such ha he ime signal samples are independen complex Gaussian variables wih a mean of zero. This is however no accurae when over-sampling is applied. Insead empirical resuls are ofen used for he esimaion. Noneheless if U alernaive ime signals are muually independen, he AR CCDF can be obained from: AR AR r ARx r LM AR U ( ochasic approaches ofen demand more compuaions due o uncerain properies of he signal saisics, however he approach oulined in his paper, relevan o Figure 5, aims a minimizing he number of compuaions and associaed compuaion ime. The binary informaion sequence is mapped o complex symbols using QK, or 64QAM or a similar modulaion echnique, o produce a parallel daa sream denoed by he N-dimensional symbol vecor:

4 robabiliy(ar>ar robabiliy (AR>AR Original CCDF of AR (Oversampling =4 Opimum LM for U=6 by Eq. (7 Opimum LM for U=6 by Eq.(7 Opimum LM for U=6 by Eq.(7 Opimum LM for U=6 4 by Eq.(7 imulaion Resuls for U=6 imulaion Resuls for U=6 imulaion Resuls for U=6 imulaion Resuls for U= AR Figure 6 AR CCDFs using opimum LM wih incremenal phase sequences (wih oversampling Original AR CCDF (no oversampling Opimum LM for U=6 by Eq. (7 Opimum LM for U=6 by Eq. (7 Opimum LM for U=6 by Eq. (7 Opimum LM for U=6 4 by Eq. (7 imulaion Resuls for U=6 imulaion Resuls for U=6 imulaion Resuls for U=6 imulaion Resuls for U= AR Figure 7 AR CCDFs using opimum LM wih incremenal phase sequences (wihou oversampling Any wo phase sequences wih high cross-correlaion properies produce AR values which are very close o each oher hence, in order o keep he search space small, phase sequence design should ensure ha candidae sequences have relaively low cross-correlaion values. In his way he search ime is reduced wihou compromising he opimum LM approach, since he number of candidae sequences is hereby reduced. VII. AR REDUCTION LOW COT EARCH TECHNIQUE Referring o he schemaic diagram in Figure 5, searching is performed o find a phase sequence, idenified by a se of coefficiens {u, u,, u w }, whose AR is no bigger han he specified arge hreshold, using candidae phase sequences wih low cross-correlaion properies. ince each coefficien um has M possible values dicaed by he order of MK modulaion, a maximum of MW updaes has o be performed by he search. The order of MK modulaion is resriced on he one hand by he compuaional cos for he ransmier, and on he oher hand by he phase racking accuracy ha can be achieved a he receiver. A each updae, insead of calculaing a full NL-poin Inverse Fas Fourier Transform (IFFT for he complee ime-domain vecor x, i is more efficien o compue one sample, x n, a a ime. As soon as he value of x n appears for which i is clear ha he AR will exceed he hreshold, he corresponding phase sequence is dropped, and he search moves on o he nex one. The search erminaes when a phase sequence is found which gives a AR value ha is below he hreshold specified when all corresponding ime-domain samples have been used for ha AR calculaion. This process reduces he search space and hereby minimizes search laency. Furher complexiy reducion migh be achieved hrough employing a low complexiy search mechanism based on he parial IFFT. A he receiver, he correc demodulaion of all sub-carriers requires a cancellaion of he phase adjusmens ha were applied a he ransmier. The expecaion is ha a code-book approach would be adoped where he phase sequence used a he ransmier has is code-book number broadcas o he receiver as side informaion for phase recovery for every OFDM symbol. VIII. CONCLUION The AR or CM relaionship wih amplifier back-off is dependen on he complexiy of modulaed signals. Varying he number of componen signals and heir relaive signal srenghs affecs he AR/CM relaionship. For curren sysems, he AR/CM A back-off esimaion can be deermined empirically using experimenally obained daa from appropriae UE ower Amplifiers and hrough he generaion of he appropriae Uplink Modulaed Waveforms wih heir associaed power levels. Wih a low CM/AR, a low A back-off is needed which leads o a higher A efficiency and lower power consumpion (Greener operaion. CM back-off esimaion has a lower error variaion around he ideal back-off poin han AR back-off esimaion does. To caer for his error he final CM back-off esimaion can be lower han he corresponding AR back-off esimaion. To furher increase he accuracy of he A back-off esimaion, an effecive AR reducion mehod, of low complexiy, having minimum associaed overhead, inroducing no disorion, and inroducing lile laency, such as he mehod oulined in his paper, is required. The AR echnique is also applicable o all ypes of subcarrier modulaion (eg. K or QAM and any number of subcarriers and low complexiy is achieved by reducing he saisics search space associaed wih he opimum LM, and

5 employing a low complexiy search mechanism based on he parial IFFT. Finally, usage of AR reducion echniques will reduce he errors in A back-off for boh CM and AR usage, bu he relaive gains of CM over AR for back-off esimaion will sill remain, and hence i migh be concluded ha use of AR reducion ogeher wih CM esimaion for deermining A back-off will resul in he Greenes mehodology. [] Y Wu, " A polynomial phasing scheme o realize minimum cres facor for mulicarrier ransmission, roc. WT, pp. -5. [4] Liu, and J Chong, A sudy of join racking algorihms of carrier frequency offse and sampling clock offse for OFDM-based WLANs, IEEE Inernaional Conference on Communicaions, Circuis and ysems, vol., pages:9-, 9 June - July. [5] Y Wu, Ka Man and Y Wang, Opimum selecive mapping for AR reducion, roceedings of Wireless Telecommunicaions ymposium, New York Ciy, UA, -5 April. IX. REFERENCE [] Dodgson, T.E. Horgan, M. Wireless Mulimedia Coninuous acke Conneciviy (CC, ower Amplifier (A Back-off and he Cubic Meric (CM, WINY, July 7. [] G TG RAN WG4#, Tdoc#R4-467, Comparison of AR and Cubic Meric for ower De-raing, Beijing, China, May -4, 4. [] G TG RAN WG4#, Tdoc#R4-47, Mapping of cubic meric o addiional A headroom, hin-yokohama, Japan, 5-9 November 4. [4] G TG RAN WG4#8, Tdoc#R4-64, Change Reques UE maximum oupu power wih H-DCCH and E-DCH, Denver, Colorado, UA, h 7h February 6 [5] Rohde & chwarz, Applicaion Noe, High peed Downlink acke Access (HDA: Challenges for UE ower and Amplifier Design, hp:// [6] G T 5. v6.5., preading and Modulaion (FDD Release 6, ecion 4... [7] G T 5.4 v6.9., hysical Layer rocedures (FDD Release 6, ecion 5. [8] G TR 5.9 v.4., Coninuous Conneciviy for acke Daa Users, Release 7, ecion 4.. [9] G T 5. v6.. User Equipmen (UE radio ransmission and recepion (FDD Release 6, ecion 6... [] G TG RAN WG LTE Adhoc: Tdoc#R-6, Cubic Meric in G-LTE, Helsinki, Finland, January -6, 6. [] A.D.. Jayalah and C. Tellambura, LM and T peak-power reducion of OFDM signals wihou side informaion, IEEE ransacion on wireless communicaions, Vol. 4, No.5, pp.6-, ep. 5 []. H.Han and J.H. Lee, An overview of peak-o average power raio reducion echniques for mulicarrier ransmission, IEEE Wireless Communicaion. Mag., vol., no., pp.56-65, April, 5. [] B.. Krongold and D.L. Jones, AR reducion in OFDM via acive consellaion exension, IEEE Trans. Broadcas., vol.49, no., pp.58-68, ep.. [4] A.T. Erdogan, A low complexiy mulicarrier AR reducion approach based on subgradien opimizaion, iganl rocessing, vol.86, no., pp.89-9, Dec.6. [5] Renao L. G. Cavalcane, and Isao Yamada, A flexible eak-to-average ower raio Reducion scheme for OFDM sysems by he adapive rojeced ubgradien Mehod, IEEE ransacion on signal processing, Vol.57, No. 4, April, 9. [6] Leonard J. Cimini, and Nelson R. ollenberger, eak-o-average power raio reducion of an OFDM signal using parial ransmied sequences, IEEE communicaion leers, vol.4, No, pp86-88,. [7] eung Hee Han, John M. Cioffi, and Jae Hong Lee, On he use of Hexagonal Consellaion for eak-o-average ower Raio Reducion of an OFDM ignal, IEEE Transacions on Wireless Communicaions, vol.7, no., pp , March. 8. [8] J.. Kahane, ur les polynomes a coefficiens unimodulaires, Bull. London Mah. oc., no, pp-4,98. [9] M. Friese, Mulione signals wih low cres facor, IEEE Transacion on Communicaions, vol.45, no., pp8-44, Ocober, 997. [] Dae-Woon Lim e. al. On he phase sequence se of LM OFDM scheme for a cres facor reducion, ignal rocessing, IEEE Transacions, 54 (5, May 6, pp: [] N. Ohkubo and T. Ohsuki, Design crieria for phase sequences in seleced mapping, roc. VTC -pring, Vol., pp [] eng Cheng; Yue Xiao; Lilin Dan; haoqian Li; Improved LM for AR Reducion in OFDM ysem, IMRC ep. 7, pp: 5.