Power Ratio Reduction with OFDM Signals for Broadband Wireless Mobile Communication

Transcription

1 Volume-4, Issue-, February-4, ISSN No.: Iteratioal Joural of Egieerig ad Maagemet Research Available at: Page Number: 66-7 Power Ratio Reductio with OFDM Sigals for Broadbad Wireless Mobile Commuicatio J.P. Pawar, Dr.Y.K.Jai Departmet of Techical Educatio, Haryaa, INDIA Professor Mewar Uiversity, Rajastha, INDIA ABSTRACT With the advacemet of techologies i commuicatio field, high data rate i additio to both power efficiecy ad lower bit error rate have always bee areas of iterest for scietist. The ever icreasig demad of high data rate ca be fulfilled by the sigle carrier modulatio alog with the tradeoff betwee the power efficiecy ad bit error rate. It is very difficult to achieve high data rate for this sigle carrier modulatio with a lower bit error rate performace i the presece of frequecy selective fadig eviromet. With cosiderig a advace step towards the multi carrier modulatio scheme it is possible to get high data rate i this multipath fadig chael without degradig the bit error rate performace. To achieve better performace usig multi carrier modulatio we should make the subcarriers to be orthogoal to each other i.e. kow as the Orthogoal Frequecy Divisio Multiplexig (OFDM) techique. But the great disadvatage of the OFDM techique is its high Peak to Average Power Ratio (PAPR). As we are usig the liear power amplifier at the trasmitter side so it s operatig poit will go to the saturatio regio due to the high PAPR which leads to i-bad distortio ad out-bad radiatio. This ca be avoided with icreasig the dyamic rage of power amplifier which leads to high cost ad high cosumptio of power at the base statio. I this paper, some of the importat PAPR reductio techiques which have bee compared based o computatioal complexity, badwidth expasio, spectral spillage ad performace i-bad sigal distortio ad out-of-bad radiatio. Keywords: Orthogoal; Frequecy; PAPR; CDF. I. INTRODUCTION Orthogoal frequecy divisio multiplexig (OFDM) is a modulatio techique used i may ew ad emergig broadbad techologies either wired like ADSL (asymmetric digital subscriber lie) or wireless as i DAB (digital audio broadcastig), DVB-T (digital video broadcastig-terrestrial), wireless LANs, ad so forth. I all these systems, the iformatio data stream is trasmitted i parallel o several orthogoal subcarriers, each subcarrier beig QAM or PSK modulated. The mai advatage of OFDM is its strog immuity to multipath fadig ad impulse oise, its great simplificatio of chael equalizatio ad its low computatioal complexity implemetatio based o usig Fast Fourier Trasform (FFT) techiques. Apart from lot of advatages, some drawbacks become apparet, while usig OFDM i trasmissio systems. A major obstacle is that the multiplex sigal exhibits a very high Peak-to-Average Power Ratio (PAPR). Large PAPR brigs the OFDM sigal distortio i the o-liear regio of high power amplifier (HPA) ad the sigal distortio iduces the degradatio of bit error rate (BER). Moreover, to prevet spectral growth of the multicarrier sigal i the form of iter modulatio amog subcarriers ad out-of-bad radiatio, the trasmit power amplifier has to be operated i its liear regio. If the HPA is ot operated i liear regio with large power back-offs, it is impossible to keep the out-of bad power below the specified limits. This situatio leads to very iefficiet amplificatio ad expesive trasmitters. The mai objective of this paper is to fid best data compressio techique that ca reduce PAPR sigificatly. To reduce the PAPR several techiques have bee proposed such as Partial Trasmit Sequeces (PTS) [,,3,4], Selective Mappig (SLM) [5,6], clippig [7,8] clippig ad filterig [9], Codig [], toe reservatio (TR), Active Costellatio Extesio (ACE) [], Phase Optimizatio[3], Noliear Compadig trasforms ad toe ijectio (TI) [4]. These techiques achieve PAPR reductio at the expese of trasmit sigal power icrease, bit error rate (BER) icrease, data rate loss, computatioal complexity icrease, ad so o. II. PAPR IN OFDM SYSTEM I this sectio, we review the basics of OFDM system ad the defiitio of PAPR. OFDM sigal may be geerated by a N-poit Iverse Fast Fourier Trasform (IFFT) i the trasmitter, ad the Fast Fourier Trasform (FFT) is employed at the receiver to restore the sigal. The 66

2 PAPR is the relatio betwee the maximum power of a sample i a give OFDM trasmit symbol divided by the average power of that OFDM symbol. PAPR occurs whe i a multicarrier system the differet sub-carriers are out of phase with each other. At each istat they are differet with respect to each other at differet phase values. Whe all the poits achieve the maximum value simultaeously; this will cause the output evelope to suddely shoot up which causes a 'peak' i the output evelope. Due to presece of large umber of idepedetly modulated subcarriers i a OFDM system, the peak value of the system ca be very high as compared to the average of the whole system. This ratio of the peak to average power value is termed as Peak-to- Average Power Ratio. A OFDM symbol cosists of N sub-carriers by the frequecy spacig of Δf. The total bad with B will be divided ito N equally spaced sub-carriers with all sub-carriers are orthogoal T = to each other withi a time iterval of legth f.each sub-carrier ca be modulated idepedetly with complex modulatio symbol X m,, where m is a time idex ad is a subcarrier idex. The m-th OFDM block period ca be described by equatio () as: N x () t = x g ( t mt ) m m, N = Where, g (t) is defied through equatio (). exp(jπ ft) t T g() t = else Where g (t) is a rectagular pulse applied to each subcarrier. The total cotiuous time sigal x(t) cosistig of all the OFDM block is give by equatio (3). N x() t = xm, g( t mt ) ( 3) N m= = Cosider a sigle OFDM symbol (m = ) without loss of geerality. This ca be show because there is o overlap betwee differet OFDM symbols. Sice m =, X m, ca be replaced by X. The, the OFDM sigal ca be described as follows, N jπ f xt () = Xe ( 4) N = If the bad-with of the OFDM sigal is B = N Δfad the sigal x(t) is sampled by the samplig time of t = = B N f, the the OFDM sigal is i discrete time form ad ca be writte as show i equatio (5). N jπ f N xk = Xe, k=,,,... N ( 5) N = PEAK PROBLEM A OFDM sigal cosists of a N umber of idepedetly modulated subcarriers, which ca give a very large PAPR whe added up coheretly. PAPR is the ratio betwee the maximum power ad the average power of the complex sigal. Geerally, the PAPR for the time domai OFDM sigal ca be defied as: P max x peak PAPR = = log ( 6) P average E x Where P peak represets peak output power, P average meas average output power. EE[.] deotes the expected value, xx represets the trasmitted OFDM sigals which are obtaied by takig IFFT operatio o modulated iput symbols XX kk. Mathematical, xx is expressed as: N k x = XW k k ( 7) N k = For a OFDM system with N sub-carriers, the peak power of received sigals is N times the average power whe phase values are the same. The PAPR of basebad sigal will reach its theoretical maximum at (ddbb) =log NN. Aother commoly used parameter is the Crest Factor (CF), which is defied as the ratio betwee maximum amplitude of OFDM sigal (tt) ad root-mea-square (RMS) of the waveform. The CF is defied as : max x CF( s( t)) = = PAPR ( 8) E x I most cases, the peak value of sigal s(tt) is equals to maximum value of its evelope (tt). CUMULATIVE DISTRIBUTION FUNCTION The Cumulative Distributio Fuctio (CDF) is oe of the most regularly used parameters, which is used to measure the efficiecy of ay PAPR techique. Normally, the Complemetary CDF (CCDF) is used istead of CDF, which helps us to measure the probability that the PAPR of a certai data block exceeds the give threshold. By implemetig the Cetral Limit Theorem for a multi carrier sigal with a large umber of sub-carriers, the real ad imagiary part of the time domai sigals have a mea of zero ad a variace of.5 ad follow a Gaussia distributio. So Rayleigh distributio is followed for the amplitude of the multi carrier sigal, where as a cetral chi-square distributio with two degrees of freedom is followed for the power distributio of the system. The CDF of the amplitude of a sigal sample is give by F (z) = -exp (z) (9) The CCDF of the PAPR of the data block is desired is our case to compare outputs of various reductio techiques. This is give by P (PAPR > z) = - P (PAPR z)() = - F (z) N () = - (-exp (-z)) N () III. OVERVIEW OF PAPR REDUCTION Block Codig Techiques The fudametal idea is that of all probable message symbols, oly those which have low peak power will be chose by codig as valid code words for trasmissio. No itroductio of distortio to the sigals. If there have N subcarriers, they are represeted by N bits usig QPSK modulatio ad thus N messages. Usig the whole message space correspods to zero bits of redudacy. Usig oly half of the messages correspods to oe bit of redudacy. The remaiig message space is the divided i half agai ad this 67

3 process cotiues util N bits of redudacy have bee allocated which correspods to a rate oe-half code for N carriers. Large PAPR reductio ca be achieved if the log iformatio sequece is separated ito differet sub blocks, ad all sub block ecoded with System o a Programmable Chip (SOPC). The adaptive approach has bee adopted i order to reduce hardware for a slight icrease i complexity. The codig techique Error Correctio (EC) SLM usig covolutio code proposed by S.H.Ha ad J.H.Lee has bee studied. Block Codig Scheme with Error Correctio The method is proposed that desiged block codes ca ot oly miimize the PAPR, but also give error correctio capability. A k bit data block is ecoded by a (, k) block code with a geerator matrix G i the trasmitter of the system. Followed by the phase rotator vector b to produce the ecoded output x=a.g+b (mod ). After that geerator matrix G ad the phase rotator vector b are produced; which are used mappig betwee these symbols combiatio ad iput data vector a. The coverse fuctios of the trasmitter are executed i the receiver system. The parity check matrix H is achieved from the geerator matrix G, with a exceptio that the effect of the phase rotator vector b is removed before calculatios of sydromes. Selected Mappig (SLM) I the SLM techique, the trasmitter geerates a set of sufficietly differet cadidate data blocks, all represetig the same iformatio as the origial data block, ad selects the most favorable for trasmissio. Each of these alterative iput data sequeces is made the IFFT operatio, ad the the oe with the lowest PAPR is selected for trasmissio. A block diagram of the SLM techique is show i Fig.. Each data block is multiplied by Vdifferet phase sequeces, each of legth N, B(v) = [b v,, b v,,, b v, N ] T, v=,,,, V-, resultig i Vmodified data blocks. To iclude the umodified data block i the set of modified data blocks, we set B(v) as the all-oe vector of legth N. Let us deote the modified data block for the uth phase sequece X(v) = [X b v,, X b v,,, X N b v, N ] T, v=,,,, V-. After applyig SLM to X, the multicarrier sigal becomes N jπ ft u = Xbe v 3 N = x t Where t NT, v =,,.V- Amog the modified data blocks X(v), v=,,,, V-, oly oe with the lowest PAPR is selected for trasmissio. Iformatio about the selected phase sequece should be trasmitted to the receiver as side iformatio. Fig. Block Diagram of Selected Mappig Techique For implemetatio of SLM OFDM systems, the SLM techique eeds IFFT operatio ad the umber of required bits as side iformatio is for each data block. At the receiver, the reverse operatio is performed to recover the origial data block. This approach is applicable with all types of modulatio ad ay umber of subcarriers. The amout of PAPR reductio for SLM depeds o the umber of phase sequeces U ad the desig of the phase sequeces. Partial Trasmit Sequece PTS is aother very effective approach to reduce the PAPR; here a iput data block of N symbols is partitioed ito disjoit sub blocks. The subcarriers i each sub block are weighted by a phase factor for that sub block. The phase factors are selected such that the PAPR of the combied sigal is miimized. Fig. shows the block diagram of the PTS techique. I the ordiary PTS techique iput data block X is partitioed ito M disjoit sub blocks X m = [X m, o, X m,,, M X = X(m) X m, N ] T, m =,,,, M-, such that m= ad the sub blocks are combied to miimize the PAPR i the time domai. The L-times oversampled time domai sigal of X m, m =,,,, M-, is deoted x m = [xm,, x m,,, x m, NL ] T, m =,,, M-, is obtaied by takig a IFFT of legth NL o X m cocateated with (L )N zeros. These are called the partial trasmit sequeces. Complex phase factors, b m =є jѳm, m =,,,, M-, are itroduced to combie the PTSs. The set of phase factors is deoted as a vector b = [b, b b M- ] T. The time domai sigal after combiig is give by. M xb bx ( 4) = m m m= Where x (b) = [x (b), x (b), x NL- (b)] T. The objective is to fid the set of phase factors that miimizes the PAPR. Therefore, there are two importat issues should be solved i PTS: high computatioal complexity for searchig the optimal phase factors ad the overhead of the optimal phase factors as side iformatio eeded to be trasmitted to receiver for the correct decodig of the trasmitted bit sequece. 68

4 are outside the allowed regio. For example, usig HPA with saturatio level below the sigal spa will automatically cause the sigal to be clipped. Fig.3. The OFDM trasmitter icludig clippig scheme. Fig. Block Diagram of Partial Trasmit Sequece Compadig The compader cosists of compressor ad expader. The compressor is a simple logarithm computatio. The reverse computatio of a compressor is called a expader. I this paper, the compressio at the trasmit ed after the IFFT process ad expasio at the receiver ed prior to FFT process are used. There are two types of compaders that are used here which are described i details i [4]. These two types are μ- law ad A-law compaders. μ-lawcompadig The μ-law compader employs the logarithmic fuctio at the trasmittig side. I geeral a μ law compressio characteristic: + µ x V log e y = V sg( x) ( 5) log e( + µ ) where μ is the μ-law parameter of the compader, where x: iput sigal. V : is the maximum value of the sigal x. μ: parameter cotrols the amout of compressio. The maximum value of output y is the same maximum of iput x is equal V. For ormalized iput sigal with x, the characteristic becomes: V log( + µ x) y = sg( x ) 6 log( + µ ) The μ-law expader is the iverse of the compressor: ( + µ ) V y log V x = ( e ) sg(y) 7 µ A-law Compadig The characteristic of this compader is give by: + l Ax sg( x) x l A A y = + ( 8) Ax sg( x) x + l A A where A: parameter cotrols the amout of compressio AMPLITUDE CLIPPING AND FILTERING The simplest ad most widely used techique of PAPR reductio is to basically clip the parts of the sigals that Geerally, clippig is performed at the trasmitter. However, the receiver eeds to estimate the clippig that has occurred ad to compesate the received OFDM symbol accordigly. Typically, at most oe clippig occurs per OFDM symbol, ad thus the receiver has to estimate two parameters: locatio ad size of the clip. However, it is difficult to get these iformatio. Therefore, clippig method itroduces both i bad distortio ad out of bad radiatio ito OFDM sigals, which degrades the system performace icludig BER ad spectral efficiecy. Filterig ca reduce out of bad radiatio after clippig although it caot reduce i-bad distortio. However, clippig may cause some peak regrowth so that the sigal after clippig ad filterig will exceed the clippig level at some poits. To reduce peak regrowth, a repeated clippigad-filterig operatio ca be used to obtai a desirable PAPR at a cost of computatioal complexity icrease. Fig.4 OFDM Sigal Amplitude As improved clippig methods, peak widowig schemes attempt to miimize the out of bad radiatio by usig arrowbad widows such as Gaussia widow to atteuate peak sigals A threshold value of the amplitude is set i this case to limit the peak evelope of the iput sigal. Sigal havig values higher tha this pre-determied value are clipped ad the rest are allowed to pass through u-disturbed. For amplitude clippig that is x x T B(x) = j (x) ( 9 ) Ae x < A where, B(x) = The amplitude value after clippig. x = the iitial sigal value. A = the threshold set by the user for clippig the sigal ad it is a positive real umber. 69

5 The problem i this case is that due to amplitude clippig distortio is observed i the system which ca be viewed as aother source of oise. This distortio falls i both i bad ad out of bad. Filterig caot be implemeted to reduce the i bad distortio ad a error performace degradatio is observed here. O the other had spectral efficiecy is hampered by out of bad radiatio. Out of bad radiatio ca be reduced by filterig after clippig but this may result i some peak re growth. A repeated filterig ad clippig operatio ca be implemeted to solve this problem. The desired amplitude level is oly achieved after several iteratio of this process. Iterleavig Techique The otio that highly correlated data structures have large PAPR ca be reduced, if log correlatio patter is broke dow. The basic idea i adaptive iterleavig is to set up a iitial termiatig threshold. PAPR value goes below the threshold rather tha seekig each iterleaved sequeces. The miimal threshold will compel the adaptive iterleavig (AL) to look for all the iterleaved sequeces. The mai importat of the scheme is that it is less complex tha the PTS techique but obtais comparable result. This method does ot give the assurace result for PAPR reductio. Toe Reservatio (TR) The mai idea of this method is to keep a small set of toes for PAPR reductio. This ca be origiated as a covex problem ad this problem ca be solved accurately. Toe reservatio method is based o addig a data block ad time domai sigal. A data block is depedet time domai sigal to the origial multicarrier sigal to miimize the high peak. This time domai sigal ca be calculated simply at the trasmitter of system ad stripped off at the receiver. The amout of PAPR reductio depeds o some factors such as umber of reserved toes, locatio of the reserved toes, amout of complexity ad allowed power o reserved toes This method explais a additive scheme for miimizig PAPR i the multicarrier commuicatio system. It shows that reservig a small fractio of toes leads to large miimizatio i PAPR ever usig with simple algorithm at the trasmitter of the system without ay additioal complexity at the receiver ed. Here, N is the small umber of toes, reservig toes for PAPR reductio may preset a o egligible fractio of the available badwidth ad resultig i a reductio i data rate. The advatage of TR method is that it is less complex, o side iformatio ad also o additioal operatio is required at the receiver of the system. Toe Ijectio (TI) Toe Ijectio (TI) method has bee recommeded by S. H. Muller ad J. B. Huber [9]. This techique is based o geeral additive method for PAPR reductio. Usig a additive method achieves PAPR reductio of multicarrier sigal without ay data rate loss. TI uses a set of equivalet costellatio poits for a origial costellatio poits to reduce PAPR. The mai idea behid this method is to icrease the costellatio size. The, each poit i the origial basic costellatio ca be mapped ito several equivalet poits i the exteded costellatio, sice all iformatio elemets ca be mapped ito several equivalet costellatio poits. These additioal amouts of freedom ca be utilized for PAPR reductio. The drawbacks of this method are; eed to side iformatio for decodig sigal at the receiver side, ad cause extra IFFT operatio which is more complex. IV. CONCLUSIONS OFDM is a very attractive techique for commuicatios due to its spectrum efficiecy ad chael robustess. Oe of the serious drawbacks of OFDM systems is that the composite trasmit sigal ca exhibit a very high peak power whe the iput sequeces are highly correlated. Although a lot of PAPR reductio techiques have bee proposed i the recet years. I this paper some PAPR reductio techiques for multicarrier trasmissio have bee discussed. May techiques to reduce the PAPR have bee proposed all of which have the potetial to provide substatial reductio i PAPR at the cost of loss i data rate, trasmit sigal power icrease, BER icrease, computatioal complexity icrease ad so o. No specific PAPR reductio techique has bee the best solutio for all multicarrier trasmissio system. It has bee suggested that the PAPR reductio techique should be carefully chose accordig to various system requiremets. REFERENCES [] A.Ghassemi ad T.A. Gulliver, PAPR Applicatio of OFDM Usig PTS ad Error-Correctig Code Sub Blockig, IEEE Tras. O Wireless Commuicatios, Vol.9, No.3, pp , March. [] S.H.Ha ad J.H.Lee, PAPR Reductio of OFDM Sigals usig a Reduced Complexity PTS Techique, IEEE Sigal Processig Letters, Vol., No., pp , Nov.4. [3] S. H. Muller ad J. B. Huber, OFDM with reduced peak-toaverage power ratio by optimum combiatio of partial trasmit sequeces, IEEE Electro. Letter, Vol. 33,pp , Feb [4] L. J. Cimii Jr. ad N. R. 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