RADIOENGINEERING, VOL. 9, NO., APRIL 7 The PAPR and Siple PAPR Reduction of the D Spreading Based Counication Systes Jiří BLUMENSTEIN, Zbyněk FEDRA Dept. of Radio Electronics, Brno University of Technology, Purkyňova 8, 6 Brno, Czech Republic xblue@stud.feec.vutbr.cz, fedraz@feec.vutbr.cz Abstract. This paper deals with Peak to Average Power Ratio (PAPR) characteristics and the theory of variable spreading factor orthogonal frequency and code division ultiplexing (VSF-OFCDM) systes. Coparison and evaluation of PAPR of VSF-OFCDM systes with various D spreading factors (SF) are done in tie and in frequency doain. The siple PAPR reduction approach based on rando chip interleaving is also evaluated. Keywords VSF-OFCDM, OFDM-CDMA, D Spreading, PAPR.. Introduction OFDM with its orthogonal subcarriers has been known since the 7 s, but due to high coputational requireents of the Fourier transfor, is used in the relatively new standards only (e. q. ADSL, LTE or DVB-T). CDMA was developed by the ilitary as a counication syste resistant to jaing, but CDMA can also be used as a channel access ethod. This feature is nowadays the ain advantage of CDMA that is used, for exaple, in the Qualco standard IS-95 and in GPS. The cobination of OFDM and CDMA techniques can be called variously OFDM-CDMA, Multi Carrier (MC) CDMA or Direct Sequence (DS) CDMA. All these systes are different, but only OFDM-CDMA offers twodiensional (D) spreading. OFDM-CDMA is the other nae for VSF-OFCDM []. Variable spreading is a very attractive feature. We can set the spreading factor in two diensions to get transitted data ore resistant to fading in the transission channel, but we can not leave behind the big disadvantage of a syste based on OFDM and CDMA - naely high envelope fluctuations of the transitted signal and thus the PAPR (Peak to Average Power Ratio) paraeter which is, as we consider, changing with changing spreading factor.. VSF-OFCDM as Cobination of CDMA and OFDM Data spreading in the VSF-OFCDM syste can be done in two diensions in the frequency doain and in the tie doain. This is the ain difference between the OFDM and the CDMA approach. Two-diensional spreading factor (SF) is expressed as: SF = SF tie SF f req () where SF tie is the spreading factor in tie doain and SF f req is the spreading factor in frequency doain. Variable spreading eans that we can change the spreading factor according to the actual transission channel conditions to achieve lower bit error rate (BER) []. It was shown in [7], that proper setting of the spreading factor is able to reduce the BER and. Moreover, to reduce BER, proper setting of separate SF tie paraeter as well as SF f req is of greater iportance than the whole spreading factor SF. We can suppose that PAPR will change with changing SF, SF tie or SF f req.. Siulation of VSF-OFCDM Fig. shows the schee of D spreading in the VSF- OFCDM syste. At first, a certain nuber of data sybols is spread by D spreading code of length SF. For this, the Hadaard sequences are used. After that, S/P block is used to divide the data strea fro D spreader into SF secondary D spread data streas according to the desired SF pattern. These streas for the input of the IFFT block. The IFFT block creates the orthogonality of the subcarriers according to the equation: s(t) = M n= = a n Rect T (t nt )e jπ t T () where is the subcarrier nuber, n is the sybol order, a n denotes the n-th sybol transitted in the -th subcarrier
8 J. BLUMENSTEIN, Z. FEDRA, THE PAPR AND SIMPLE PAPR REDUCTION OF THE D SPREADING BASED... M-QAM sybols: Hadaard spreading sequence of length SF = SF t * SF f A B... E x A A... A SF B B... B SF... E E... E SF A A... A SF t S/P... A SF - SFt A SF SFt +...... A SF B B... B SF t Optional Interleaver IFFT P/S E SF E SFt E SF SFt E +... E SF Fig.. Schee of D spreading in VSF-OFCDM. and finally Rect T is the rectangular window function with durability of T, which defines the OFDM sybol durability. Another illustration is shown in Fig., where we can observe a atrix of D spread and interleaved (arked as intv y, noninterleaved data are arked as intv n) signal just after IFFT operation. The siulated syste was 8 4, N = 3. The frequency doain is placed at x-axis, the tie doain is at y-axis and finally the power of the D signal is at z-axis. It is seen fro Fig. that one 6-QAM sybol is spread according to the desired spreading pattern on 4 subcarriers and on 8 tieslots. The values within the frae of one 6-QAM sybol in direction of axes x and y are not the sae due to rando interleaving and, in direction of x-asis, due to IFFT operation. The optional rando chip interleaving block can be used for reduction of PAPR, as proposed in soe papers [9]. The principle of such ethod is as follows. The data strea of an OFDM syste in the tie doain can be considered as a su of sinusoids. When the peak values of these sinusoids are optially utually shifted, the su of peaks in one tieslot (and also the PAPR paraeter) can be reduced. It was shown in [9], that the optial interleaving pattern gives alost the sae results as a rando pattern, which is used here and can be generated as a rando perutation of nuber of interleaved chips. 3. PAPR PAPR in VSF-OFCDM systes can be observed in two diensions; in tie doain and in frequency doain. Considering that the ain drawback of high PAPR is the increase of BER caused by nonlinearity of a power aplifier, the tie doain PAPR has ore real usage than the PAPR paraeter in frequency doain. The reason for this is obvious fro Fig. 3 we consider the tie doain just behind the IFFT block. Behind this block, a power aplifier is inserted as well. The PAPR is critical for this block. PAPR can be coputed as: PAPR(x τ,τ) = ax τ τ x τ. (3) E { x τ } In (3), τ is the tie index used to represent the successive tie variable t and also the discrete tie index n. The ax τ τ x τ indicates { the axial value of the power of signal x and finally E x τ } denotes the ean value of the signal. Eq. (3) is the general expression of PAPR, [8] shows an alternative equation (4) used for coputing PAPR in the frequency doain: PAPR{x (t)} N ax X k E { X k } where N is the nuber of subcarriers. The arking of signals follows the way of arking in Fig. 3. A nuerical exaple of PAPR values in the frequency doain for 6-QAM odulation is deonstrated in Tab.. PAPR f [db] SF patterns N=8 6,8 8 N=6 9,8 4, 8 N=3,83 8 4, 4 8, 6 N=64 5,84 64, 8 8, 4 6 N=8 8,85 64 Tab.. PAPR f [db] values for 6-QAM odulation and various SF patterns. (4)
RADIOENGINEERING, VOL. 9, NO., APRIL 9 SF tie SF freq = 8 4 a N =3, intv y power 8 7 6 5 4 3 tie One interleaved and spread 6 QAM sybol 4 6 8 4 6 8 4 6 8 3 3 carriers.6.4...4.6 Fig.. A D spread signal after IFFT operation. D input data strea S/P X X X X N- Optional Interleaver IFFT x x x x N- P/S a CP In Fig. 6, the aplitude histogras of the transitted signal are plotted for SF= 6 settings and the interleaver is on and off, respectlively. The distribution of the aplitudes of systes with an interleaver is close to the Rayleigh distribution as well as in an OFDM syste. If no interleaver is used, the distribution is exponential. Power Aplifier x(t) Fig. 3. A OFDM transitter, signal arking. 4. Results D/A and LP filter Results of siulations are shown in Figs. 4, 5 and 6. PAPR was tested in the tie doain and the influence of changing SF tie, SF f req and N, which represents the nuber of subcarriers, was observed. The left part of Fig. 4 shows CCDF (Copleentary Cuulative Distribution Function) of PAPR for 6-QAM. SF f req stays const., SF tie = [8,6,3,64] and N =. Interleaver was not used. PAPR is not significantly rising with the rise of SF tie. The reference curve for a pure OFDM syste is illustrated in every figure for coparison. OFDM in this figure has significantly lower PAPR than D spreading based systes. The right part of Fig. 4 shows the situation when SF tie =, SF f req = [,,4,8] and N = 6. Interleaver was also not used. PAPR is rising with rising SF f req and is rising with N as well, which is shown in the left part of Fig. 5. The right part of Fig. 5 illustrates the ipact a of rando chip interleaver. A 6-QAM, SF = 8 6, N = 6 syste is considered. We can observe huge reduction of PAPR up to 9 db. The syste with an interleaver achieves nearly the sae PAPR as an OFDM syste with the sae nuber of subcarriers N. 5. Conclusions This paper describes the VSF-OFCDM syste with tie-frequency spreading and its Peak to Average Power Ratio (PAPR) perforance with different D spreading patterns. An iportant conclusion is that PAPR is not growing with growing SF tie, but with growing SF f req and N, PAPR is growing. This feature can be profitably used in designing various SF patterns in VSF-OFCDM systes. Another conclusion is that PAPR can be siply and effectively reduced nearly to OFDM PAPR level. Acknowledgeents This work has been prepared as a part of the solution of the Grant Agency of Czech Republic grants no. P//P53 Counication systes cobining OFDM and CDMA and their PAPR, no. GA/9/776 Algoriths and subsystes for software defined and cognitive ulticarrier radio. The research leading to these results has received funding fro the European Counity s Seventh Fraework Prograe (FP7/7-3) under grant agreeent no. 36. References [] FAZEL, K., KAISER, S. Multi-Carrier and Spread Spectru Systes. st ed. Chichester (England): Wiley, 3.
3 J. BLUMENSTEIN, Z. FEDRA, THE PAPR AND SIMPLE PAPR REDUCTION OF THE D SPREADING BASED... 3 8, N=, intv n 6, N=, intv n 3, N=, intv n 64, N=, intv n OFDM, N= 3 6, N=6, intv n 6, N=6, intv n 6 4, N=6, intv n 6 8, N=6, intv n OFDM, N=6 4 5 7 9 3 5 7 9 4 5 7 9 3 5 7 9 3 5 Fig. 4. CCDF of PAPR for 6-QAM. In the left part, SF f req stays constant, SF tie = 8,6,3,64 and N =. Interleaver was not used. In the right part, SF tie =, SF f req = [,,4,8], N = 6. Interleaver was not used. 3 6, N=, intv n 6, N=4, intv n 6, N=8, intv n 6, N=6, intv n OFDM, N=6 3 8 6, N=6, intv y 8 6, N=6, intv n OFDM, N=6 4 5 7 9 3 5 7 9 4 5 7 9 3 5 7 9 3 5 Fig. 5. CCDF of PAPR for 6-QAM. In the left part, N = [,4,8,6] and SF= 6. Interleaver was not used. In the right part, the influence of an interleaver on 6-QAM, SF= 8 6, N = 6 syste is shown. x 5 Aplitude histogra, 6, N=, intv y 8 6 4.5..5. Aplitude values 3.5 x 6 Aplitude histogra, 6, N=, intv n 3.5.5.5.5..5. Aplitude values Fig. 6. Aplitude histogras of SF= 8 6, N = systes. The left part with an interleaver, the right part without interleaver.
RADIOENGINEERING, VOL. 9, NO., APRIL 3 [] MAEDA, N., KISHIYAMA, Y., ATARASHI, H., SAWAHASHI, M. Variable spreading factor-ofcdm with two diensional spreading that priorizes tie doain spreading for forward link broadband wireless access. IEICE Transactions on Counications, 5, vol.e88-b, no.. [3] HANZO, L., MÜNSTER, M., CHOI, B. J., KELLER, T. OFDM and MC-CDMA for Boardband Multi-User Counications, WLANs and Broadcasting, st ed. Chichester (England): Wiley, 4. [4] HENG, K., ZENG, G., WANG, W. Perforance analysis for OFDM- CDMA with joint frequency-tie spreading. IEEE Transactions on Broadcasting, 5, vol. 5, no., p. 44-48. [5] ATARASHI, H. Broadband Packet Wireless Access and Its Experients. [Online] Cited 8-4-6. Available at: www.ctr.kcl.ac.uk/pages/4gforu/3/presentations/asia/atarashi. [6] JOYDEEP, A. Two Diensional Spreading for Doubly Dispersive Channels. Diploa thesis. New Jersey: The State University of New Jersey, 5. [7] BLUMENSTEIN, J., FEDRA, Z. The characteristics of the D spreading based counication systes. In Proceedings of 9th International Conference Radioelektronika 9. Bratislava (Slovakia), 9, p. 77-79. [8] TELLADO J. Multicarrier Modulation with Low PAR Applications to DSL and Wireless. Norwell (USA): Kluwer Acadeic Publishers,. [9] FEDRA Z., MARŠÁLEK R., ŠEBESTA V. Chip interleaving and its optiization for PAPR reduction in MC-CDMA. Radioengineering, 7, vol. 6, no. 4, p. 9-3. About Authors... Jiří BLUMENSTEIN was born in Prostějov, Czech Republic in 984. He received his Master degree in electrical engineering fro the Brno University of Technology in 9. At present, he is a PhD student at the Departent of Radio Electronics, Brno University of Technology. His research interests are counication systes based on cobination of OFDM and CDMA and siulations. Zbyněk FEDRA was born in Dačice, Czech Republic in 98. He graduated fro Brno University of Technology in 4 and received the Ph.D. degree in 8. He is currently an assistant professor at Departent of Radio Electronics, Brno University of Technology. His research interests are ulticarrier counication and signal processing.