SIDELOBE SUPPRESSION IN OFDM SYSTEMS

SIDELOBE SUPPRESSION IN OFDM SYSTEMS Iva Cosovic Germa Aerospace Ceter (DLR), Ist. of Commuicatios ad Navigatio Oberpfaffehofe, 82234 Wesslig, Germay iva.cosovic@dlr.de Vijayasarathi Jaardhaam Muich Uiversity of Techology (TUM), 80333 Muich, Germay vijayasarathi.j@mytum.de Abstract I this cotributio, we develop a method for reducig out-of-bad emissio caused by high sidelobes i OFDM systems. The method is termed multiple-choice sequeces (MCS) ad operates i the frequecy domai of a OFDM system. The priciple of MCS is to map the origial trasmissio sequece oto a set of sequeces ad to choose, from this set, a sequece with the lowest power i sidelobes for the actual trasmissio. To eable successful sigal detectio, de-mappig of the received sequece oto the origial sequece is required at the receiver. Hece, a idex which uiquely idetifies the selected sequece is sigalled from the trasmitter to receiver. From this geeralized framework we derive several practical MCS algorithms. Simulatio results show that the MCS method achieves a cosiderable sidelobe suppressio which justifies the itroduced sigallig overhead. 1. Itroductio Orthogoal frequecy-divisio multiplexig (OFDM) systems have gaied a lot of popularity lately due to their high spectral efficiecy ad robustess to multi-path eviromets. OFDM has bee chose for may stadards like ADSL, DAB, DVB, IEEE 802.11a [1]. Oe of the drawbacks of OFDM is the high out-of-bad radiatio caused by the high sidelobes of the OFDM trasmissio sigal. The high sidelobes are particularly a critical issue i OFDM based overlay systems i which a broadbad OFDM system is overlaid o top of existig arrowbad systems [2]. As illustrated i Fig. 1, a overlay system exploits the u-

I. Cosovic ad V. Jaardhaam used parts of the spectrum assiged to the existig legacy systems, thus icreasig the spectral efficiecy. As this cocept requires successful co-existece betwee the legacy system ad the OFDM based overlay system, a crucial task i desigig such a overlay system is the avoidace of iterferece towards the legacy system. Therefore, the reductio of out-of-bad radiatio becomes a essetial topic, especially for the desig of OFDM based overlay systems. Power Existig legacy systems (digital ad/or aalog) OFDM overlay system Frequecy Figure 1. OFDM overlay cocept - exploitig the frequecy gaps i a existig frequecy badwidth. The topic of sidelobe suppressio i OFDM systems has ot bee extesively ivestigated so far. I [3], a multiplicatio of each OFDM symbol with a widowig fuctio i time domai ad isertio of empty guard bads are ivestigated. I [4] [5], isertio of a few dummy subcarriers at the edges of the used bads which are determied such that the sidelobes of the origial OFDM sigal are suppressed is preseted. I [6], a techique i which the subcarriers are weighted so that the sidelobes of the trasmissio sigal are miimized accordig to a optimizatio algorithm is proposed. I this paper, a differet method to sigificatly suppress the OFDM sidelobes is itroduced. This techique, referred to as multiple-choice sequeces (MCS), performs mappig of the origial trasmissio sequece oto a set of sequeces. From this set, a sequece which offers maximum reductio of out-of-bad radiatio is chose for the actual trasmissio. To eable successful sigal detectio, de-mappig of the received sequece oto the origial sequece is required at the receiver. To this purpose, a idex which uiquely idetifies the selected sequece i the set of several MCS has to be sigalled from the trasmitter to receiver. This results i a slightly reduced data throughput. However, umerical results show that this moderate loss i throughput is justified by the sigificat sidelobe suppressio achieved with this techique. The paper is structured as follows. I Sectio 2 the sigal model is itroduced. The priciple of MCS method is described ad several MCS algorithms are proposed ad aalyzed i Sectio 3. The proposed MCS

Sidelobe Suppressioi OFDM Systems algorithms are compared by umerical simulatios i Sectio 4. Fially, i Sectio 5 coclusios are draw. 2. OFDM Sigal Model As illustrated i Fig.1, a real OFDM based overlay system might cosist of several cotiuous trasmissio sub-bads i-betwee the legacy systems. The proposed algorithm ca be applied to the OFDM trasmissio sigal by cosiderig all the sub-bads joitly or by cosiderig each of the sub-bads separately. As we cocetrate o the priciple of MCS i this cotributio, a simplified problem with a sigle cotiuous OFDM trasmissio bad is cosidered i the followig. A OFDM system with a total umber of N subcarriers is cosidered. The block diagram of the OFDM trasmitter is illustrated i Fig. 2. The iput bits are symbol-mapped ad N complex-valued data symbols d, = 1, 2,..., N, are geerated. These symbols are serial-toparallel (S/P) coverted resultig i a N-elemet data symbol array d = (d 1, d 2,..., d N ) T, where (.) T deotes traspositio. The array d is fed ito the MCS sidelobe suppressio uit which outputs the selected MCS, deoted with d = ( d 1, d 2,..., d N ) T, ad the idex of the chose MCS, deoted with Q. The MCS algorithms that determie d ad Q are described i the ext sectio. Fially, the selected MCS sequece d is modulated oto the N subcarriers usig the iverse discrete Fourier trasform (IDFT). After that, parallel-to-serial (P/S) coversio is performed ad a guard iterval that exceeds the delay spread of the multipath chael is added as cyclic prefix. I additio, the idex of the selected MCS sequece Q is coded i bits ad trasmitted over the correspodig sigalig chael. Note that i the followig, for simplicity, we assume that the cyclic prefix is cosiderably shorter tha the useful part of a OFDM symbol. d 1,, N S/P d 1 d N MCS SIDELOBE SUPPRESSION d 1 d N Q IDFT P/S CYCLIC PREFIX To sigalig chael Figure 2. Block diagram of the OFDM trasmitter with MCS sidelobe suppressio.

I. Cosovic ad V. Jaardhaam 3. Sidelobe Suppressio by Multiple-Choice Sequeces (MCS) The Priciple of MCS The priciple of MCS is illustrated i Fig. 3. A set of sequeces d (p) = (d (p) 1, d(p) 2,..., d(p) N )T, p = 1, 2,..., P, is produced from the sequece d. For each sequece d (p) the average sidelobe power, deoted with A (p), p = 1, 2,..., P, is calculated. To determie A (p), a certai frequecy rage spaig several OFDM sidelobes, called optimizatio rage, is cosidered usig discrete frequecy samples. Recallig that the spectrum of a idividual subcarrier equals a si-fuctio si(x) = si(x)/x, A (p) is give by A (p) = 1 2 K N d (p) si (π(y K k x )), p=1, 2,..., P, (1) k=1 =1 where x, = 1, 2,..., N, are the ormalized subcarrier frequecies ad y k, k = 1, 2,..., K, are ormalized frequecy samples withi the optimizatio rage. The idex Q of the sequece with maximum sidelobe suppressio is give by Q = arg mi p A (p), p = 1, 2,..., P. (2) Thus, the sequece d=d (Q) is chose for trasmissio ad output from the MCS uit. d GENERATE THE MCS SET (1) d (P) d MCS SELECT WITH MINIMUM SIDELOBE POW. (Q) d d Q Figure 3. Block diagram of the MCS sidelobe suppressio uit. To eable successful data detectio, the received sequece has to be de-mapped oto the origial sequece at the receiver. The MCS set is costructed such that the kowledge about the idex Q of the selected sequece is sufficiet to perform this de-mappig. Thus, the idex Q is coded i bits, passed from the MCS uit to the sigallig chael, ad set to the receiver. For example, assumig a OFDM system with N subcarriers modulated with M-ary phase-shift-keyig (M-PSK) or M- ary quadrature amplitude modulatio (M-QAM) symbols, the overhead

Sidelobe Suppressioi OFDM Systems eeded for the sigallig iformatio is log 2 (P ) / ( log 2 (M) N + log 2 (P ) ), (3) which is egligible for largen ad/orm. I (3), x deotes the smallest iteger greater tha or equal to x. At the receiver, a estimate d (Q) of the trasmitted sequece d (Q) is obtaied which is trasformed ito a estimate d of the origial sequece d usig the sigallig iformatio. Note that the sigallig iformatio is the idex Q which idicates that the sequece d (Q) out of the MCS set has bee chose for trasmissio. I the followig several computatioally effective, but yet efficiet algorithms to geerate MCS sets are proposed ad aalyzed. The proposed methods do ot degrade the bit-error rate performace at the receiver ad require oly a slightly icreased sigallig overhead. Symbol Costellatio Approach This algorithm geerates the set of MCS such that the elemets d (p), = 1, 2,..., N, of d (p) belog to the same symbol costellatio as the elemets of d. With this approach the fact that differet symbol sequeces have sidelobes with differet powers is exploited. Assume that the symbol costellatio cosists of M poits that are umbered as 0, 1,..., M 1. To each symbol d, =1, 2,..., N, a idex i {0, 1,..., M 1} is assiged which correspods to the umber of the respective costellatio poit. The, the idex i (p) the MCS symbol d (p) ( i (p) = I (4), r (p) (i + r (p) that correspods to, = 1, 2,..., N, p = 1, 2,..., P, is give by ) ) mod M, = 1, 2,..., N, p = 1, 2,..., P. (4) is a iteger radomly chose from the set r (p) {0, 1,..., M 1}. After determiig P idex vectors i (p) = (i (p) 1, i(p) 2,..., i(p) N )T the MCS vectors d (p), p = 1, 2,..., P, are obtaied by takig the data symbols from the symbol costellatio accordig to the vectors i (p). We assume that the same radom seed for geeratig r (p), = 1, 2,..., N, p = 1, 2,..., P, is used at both trasmitter ad receiver. Hece, the trasformatio of the received sequece back to the origial sequece ca be easily performed by exploitig the trasmitted sigallig iformatio. Let p α be the probability that a sequece at the iput of the MCS uit has a average power i the optimizatio rage above a certai threshold α. With the symbol costellatio approach the P geerated MCS sequeces belog to the same symbol costellatio as the sequece iput to the MCS uit. Therefore, the correspodig probability for

I. Cosovic ad V. Jaardhaam each of the P geerated sequeces is also p α, whereas for the output MCS sequece this probability is p α = (p α ) P, (5) i.e., the probability is reduced from p α to (p α ) P, provig the beefits of the proposed approach. Iterleavig Approach The iterleavig approach produces P MCS sequeces by permutatig the iput sequece i a pseudoradom order. As a result, the resultig MCS symbols equal d (p) = d (p) Π, = 1, 2,..., N, p = 1, 2,..., P, (6) where Π (p) are permutatio idices stored at both trasmitter ad receiver. The permutatio idices Π (p) take values from the set Π (p) {0, 1,..., N 1} such that Π (p) Π (p) m if m. Similar to the symbol costellatio approach, the MCS symbols d (p) produced by the iterleavig approach stay i the same symbol costellatio as the origial symbols d. However, ulike the symbol costellatio approach, the umber of differet MCS d (p) possible with the iterleavig approach decreases whe the origial sequece d cotais reoccurrig data symbols. For example, if d = (1, 1,..., 1) T the iterleavig approach always produces d (p) = (1, 1,..., 1) T, p = 1, 2,..., P, irrespective of the selected permutatio idices. As a cosequece, the probability p α that a output MCS sequece has a average power i the optimizatio rage above a certai threshold α satisfies the coditio (p α ) P p α p α. (7) Note that the equality i (7) is valid oly if P = 1. Phase Approach I this approach the MCS symbols are obtaied by applyig radom phase shifts to the origial symbols. Hece, the resultig MCS symbols are formed as d (p) = d exp (jϕ (p) ), = 1, 2,..., N, p = 1, 2,..., P, (8) where the phase shifts ϕ (p) lie i the iterval [0, 2π) ad are geerated as ( ) r (p) = 2π. (9) M ϕ (p)

Sidelobe Suppressioi OFDM Systems I (9), M is a costat iteger ad r (p) is a iteger radomly chose from the set r (p) {0, 1,..., M 1}. Thus, ϕ (p) ca take oe of the M discrete phase values. Agai, the same radom seeds are used at the trasmitter ad receiver. Note that assumig a BPSK system ad M = 2, this approach becomes equivalet to the correspodig symbol costellatio approach. I the phase approach, the resultig MCS symbols do ot ecessarily belog to the same symbol costellatio as the origial symbols. Hece, a property similar to those described i (5) ad (7) caot be easily derived except for some special cases, e.g., M = 2. 4. Simulatio Results I this sectio, several umerical results are give that illustrate the effectiveess of the proposed MCS methods. BPSK modulatio is applied ad o chael codig is cosidered. The umber of used subcarriers is set to N = 12. The optimizatio rage cosists of 16 sidelobes at each side of the spectrum ad starts from the first sidelobe outside the OFDM trasmissio badwidth. Differet MCS methods are cosidered assumig differet sizes of the MCS set P. I Fig. 4, the ormalized power spectrum of the OFDM sigals averaged over all possible symbol vectors, i.e., 2 N symbol vectors, prior ad after the MCS uit are compared. The symbol costellatio approach is applied ad the size of the MCS set is fixed to P = 4. The beefits of the MCS techique are clearly visible. I compariso to OFDM without MCS the sidelobes are suppressed by aroud 6.1 db o average. I additio, from (3) it follows that these results are related to a reductio i system throughput of 14% for the chose system parameters. This sigallig overhead reduces if more subcarriers ad/or higher modulatio schemes are applied. I Fig. 5, the sidelobe suppressio averaged over all possible symbol vectors for differet sizes P of the MCS set ad differet MCS methods is give. To calculate the average sidelobe suppressio, stadard OFDM without MCS block is take as a referece. It ca be see that the symbol costellatio approach outperforms the other techiques. I particular, the iterleavig approach is outperformed as it offers less degrees of freedom i costructio of the MCS set tha the symbol costellatio approach. The performace of the phase approach depeds o the umber of possible radom phases M. To obtai these simulatio results M has bee set to M = 64. As already oted, settig M = 2 would lead to the same sidelobe suppressio results as obtaiable by the symbol costellatio approach. As expected, i all cosidered MCS approaches,

ormalized power spectrum i db 10 0-10 -20-30 -40-50 sidelobes -16 0 16 ormalized frequecy I. Cosovic ad V. Jaardhaam sidelobes origial sequece selected MCS Figure 4. OFDM spectrum of the origial trasmissio sequece ad of the trasmissio sequece after the MCS uit averaged over all possible data sequeces; symbol costellatio approach; BPSK, N = 12, P = 4. a icrease i size of the MCS set improves sidelobe suppressio, but simultaeously leads to a further icrease i sigallig overhead. As a cosequece, there is a trade-off betwee the additioal sidelobe suppressio obtaied by elargig the set size P ad the icreased sigallig overhead. Settig P = 2, 4, or 8 seems to be a good compromise. A further icrease of P appears to be ujustified as it leads to a relatively high sigallig overhead with oly moderate further improvemet i sidelobe suppressio. The probability that average power i the cosidered sidelobes of the chose MCS exceeds the threshold α is preseted i Fig. 6. Simulatio results are give for P = 4 ad P = 16 assumig differet MCS algorithms. As referece, correspodig probability for stadard OFDM without MCS block is give. As it ca be see, the symbol costellatio approach with P = 16 performs better tha other cosidered alteratives. Moreover, for P = 4, there is almost o differece i performace betwee the symbol costellatio ad iterleavig approach, whereas the phase approach performs cosiderably worse. Agai, for the phase approach M has bee set to M = 64. Fially, we ote that the preseted umerical results agree with the aalytical results give i (5) ad (7). Note that the MCS techique ca be easily combied with other sidelobe suppressio methods, e.g., methods from [3]- [6]. However, due to the space limitatio of this paper we skip details of such aalysis.

Sidelobe Suppressioi OFDM Systems 20 average sidelobe suppressio i db 18 16 14 12 10 8 6 4 2 symbol costellatio approach iterleavig approach phase approach 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 size of the MCS set, P Figure 5. Average sidelobe suppressio for differet sizes of the MCS set P ad for differet MCS methods; BPSK, N = 12. Pr[average sidelobe power i db > α] 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 P = 16 without MCS phase approach iterleavig approach sym. costellatio approach P = 4 0-50 -40-30 -20-10 0 threshold i db, α Figure 6. Probability that average power i the cosidered sidelobes of the chose MCS exceeds the threshold α; BPSK, N = 12. 5. Coclusios I this paper, we have itroduced a ew techique, termed multiplechoice sequeces (MCS), to suppress sidelobes of OFDM trasmissio sigals. The MCS techique ca be used to improve the spectral effi-

I. Cosovic ad V. Jaardhaam ciecy of OFDM based trasmissio systems ad/or to reduce iterferece of OFDM based overlay systems towards the legacy systems sharig the same frequecy bad. The proposed sidelobe suppressio scheme is capable of easily reducig the sidelobes of OFDM trasmissio sigals by several db. The price to pay for this achievemet is a moderate reductio i system throughput, sice the trasmissio of additioal sigallig iformatio is required. Ackowledgmet This work was supported by the Broadbad VHF Aeroautical Commuicatios System Based o MC-CDMA (B-VHF) project [7] which is fuded by the Europea Commissio withi the 6th Framework Programme. Refereces [1] K. Fazel ad S. Kaiser. Multi-Carrier ad Spread Spectrum Systems. Joh Wiley & Sos, 2003. [2] T. Weiss ad F. Jodral. Spectrum poolig - a iovative strategy for the ehacemet of spectrum efficiecy. I IEEE Commuicatios Magazie, Radio Commuicatios Supplemet, pages S8 S14, Mar. 2004. [3] T. Weiss, J. Hillebrad, A. Kroh, ad F. Jodral. Mutual iterferece i OFDM-based spectrum poolig systems. I Proceedigs IEEE Vehicular Techology Coferece (VTC 04, Sprig), May 2004. [4] J. Bigham. RFI suppressio i multicarrier trasmissio systems. I Proceedigs IEEE Global Telecommuicatios Coferece (GLOBECOM 96), Nov. 1996. [5] S. Brades, I. Cosovic, ad M. Schell. Sidelobe supressio i OFDM systems by isertio of cacellatio carriers. I Proceedigs IEEE Vehicular Techology Coferece (VTC 05 Fall), Sept. 2005. [6] I. Cosovic, S. Brades, ad M. Schell. A techique for sidelobe suppressio i OFDM systems. I Proceedigs IEEE Global Telecommuicatios Coferece (GLOBECOM 05), Nov. 2005. [7] http://www.b-vhf.org.