An Oversampled Filter Bank Multicarrier System for Cognitive Radio

Transcription

1 An Oversample Filter Ban ulticarrier System for Cognitive Raio Qiwei Zhang, Anre B.J. Koeler an Gerar J.. Smit Department of Electrical Engineering, athematics an Computer Science University of wente, Enschee, he etherlans Abstract Due to small sieban power leaage, filter ban multicarrier techniques are consiere as interesting alternatives to traitional OFDs for spectrum pooling Cognitive Raio. In this paper, we propose an oversample filter ban multicarrier system for Cognitive Raio. he increase spacing between ajacent subcarriers in the oversample filter ban multicarrier system largely reuce the intercarrier interference, the ey limitation of the OFD base Cognitive Raio. he propose multicarrier system is compare with OFD for BER performance an sieban power rejection. Design traeoffs of the major parameters of the oversample filter ban will be iscusse. We also suggest a fast implementation of the propose filter ban moulation base on generalize DF filter ban moel, followe by a computational complexity analysis. I. IRODUCIO ultimeia wireless applications have been increasing rapily in recent years an this tren will continue in the future. he large eman for raio spectrum will mae it no room to accommoate new wireless applications. However, recent stuies have shown that most of the assigne raio spectrum is uner-utilize. Cognitive Raio [] is consiere as a promising technology to aress the paraox of spectrum scarcity an spectrum uner-utilization. In Cognitive Raio, a spectrum sensing process locates the unuse spectrum segments in a targete spectrum pool. hese segments will be use optimally without harmful interference to license users (users who have the legal license for the spectrum). his technology is calle spectrum pooling []. In spectrum pooling, orthogonal frequency ivision multiplexing (OFD) is use as the baseban transmission scheme. he cognition is realize by nullifying those subcarriers which cause interference to license users. he remaining frequency segments will be use optimally by Cognitive Raio. he aitional benefit of OFD is the reuse of the FF moule for spectrum sensing. However, ue to the rectangular winow in the time omain the OFD system has large sielobes which cause interference to ajacent bans. his fact has also been recognize in []. hey propose two methos to mitigate the interference to the license user: eactivating more subcarriers ajacent to the license system or applying non-rectangular winows to reuce the spectrum leaage. Both methos mitigate the interference at the cost of banwith efficiency. oreover, the two methos in t consier the system implementation issues. herefore, the inication is that other multicarrier schemes coul be interesting caniates for Cognitive Raio. his fact has also been observe in a recent publication [3]. A filter ban moulation calle filtere multitone (F) [4] has been applie to very high-spee igital subscriber line technology to achieve high-level spectral containment in subchannels. his is also the ey characteristic expecte for a spectrum pooling system, where sieban power leaage shoul be ept to a minimum. In this paper, we propose an oversample filter ban multicarrier system for Cognitive Raio base on the iea of F. he paper is organize as follows: Section II proposes the multicarrier system for Cognitive Raio base on the oversample filter ban. In section III, we present an efficient implementation of the propose system base on the generalize DF filter ban moel. he simulation results of the propose system are shown in section IV an followe by some iscussions. We will mention several interesting points for future wor in section V. Finally, we raw some conclusions in section VI. II. CR BASED O OVERSAPLED FILER BAK ULICARRIER he basic iea of multicarrier transmission is to ivie a broaban channel into parallel subchannels an the high-rate ata stream is split into low-rate streams an transmitte on eacubchannel. his transmission scheme can be moelle as a filter ban system [5], shown in figure. At the transmitter, complex symbols are upsample by a factor of an filtere by a base ban prototype filter. he output of each symbol stream will be properly shifte in frequency an ae for transmission. he receiver emoulates the signal by a matche filter an ownsampling by a factor of. he transmitter an the receiver are in fact ban synthesis ban an analysis filter. When critical sampling applies = an the prototype filter is selecte as a sinc shape filter in frequency, the multicarrier system becomes an OFD system. When >, the filter ban system is calle an oversample filter ban (OSFB). he oversampling will increase intercarrier spacing by a factor of (>), see figure. In suc way intercarrier interference (see the overlapping part between two subcarriers) is largely reuce, which is the basic iea of F [4]. One woul argue the increase intercarrier spacing results in less subcarriers in a given banwith, thus losing the banwith efficiency. However, compare with OFD systems where extra cyclic prefix always has to be introuce, /8/$5. 8 IEEE

2 x x e e e * e * y y Deactivate subcarriers from th to th x ˆx x ˆx x e C * e y x i i Oversample Synthesis Filter Ban Channel Oversample Analysis Filter Ban o emoulati on from th to th subcarrier s x x ˆ Fig.. A multicarrier system base on filter bans x x ˆ Fig. 3. An OSFB multicarrier system for Cognitive Raio f when f when Fig.. Intercarrier spacing of the critically sample an oversample filter ban, where enotes the symbol rate OSFB is no worse than OFD in terms of banwith efficiency. herefore, we thin the OSFB is a goo caniate for the multicarrier base Cognitive Raio. he basic iea of multicarrier base Cognitive Raio is to eactivate the subcarriers causing interference to license users an optimally use the remaining part of the targete spectrum. he eactivation can be realize by loaing zeros on the intene subcarriers while others are loae with moulate complex symbols at the transmitter which is an ban oversample synthesis filter ban. An ban oversample analysis filter ban on the receiver reconstructs the signal an sen only the symbols from those active subcarriers for emoulation. he eactivation information is sent to both the transmitter an the receiver throug control channel. he simplifie OSFB base multicarrier Cognitive Raio system is shown in figure 3. he moulation moe for the active subcarriers is aaptive to the channel s SR. he aaption can be one for all subcarriers as a whole or for each iniviual subcarrier base on subchannel s SR. he aaptive bit loaing for OFD base Cognitive Raio in [6] can be applie to the latter case. III. EFFICIE IPLEEAIO BASED O GEERALIZED DF FILER BAK he implementation of the OSFB is not as straightforwar as the critically sample filter ban. he authors in [4] inicate to implement perioically time-varying filters in the OSFB. However, this is ifficult in practice. herefore, we suggest an efficient implementation base on the generalize DF filter ban (GDF) moel in [7]. he transmitte analog signal s a can be expresse s a (t) = + m= n= x m (n ),m,a (t n ) (), where enotes the symbol uration, x m (n ) is the symbol on mtubcarrier at nth instance,,m,a (t) is the analog synthesis prototype filter on the mtubban. Since the symbol rate is, the sampling rate shoul be. For each sampling instance, the iscrete signal s() can be written s() = + m= n= x m (n),m ( n) = + n= s n ( n) (), where x m (n) = x m (n ),,m () enotes the igitize synthesis filter an only symbol instances for n are consiere. We efine signal s n () at each instance n s n () = m= x m (n),m () (3) he subban filter,m () is erive from a real value prototype filter p() by moulation,m () =p( L jπ(m )e )( L )/ (4), where L is the filter length, is set as carrier frequency an the elay of L is introuce to mae a causal system. From eq. 3, we can see s n () is the summation the multiplications of ban symbols with L filter coefficients. hus the length of s n () is L. We can write eq. 3 in a matrix form s n = H s x n (5), where x n is the symbol vector an H s is an L matrix: H s =[p( L jπ(m )e )( L )/ ] L (6) A matrix multiplication of Hs an x n can be one to prouce signal s n, however it costs L complex multiplications. o reuce the computational complexity, we reconstruct H s from

3 the generalize DF matrix [7] an a iagonal matrix Λ p where the iagonal hols L coefficients H s = [I ( ) I ] [I I... I he generalize DF matrix is expresse Î,u ] Λ p (7) =Λ W Λ (8), where W enotes an point DF matrix. Λ an Λ are iagonal matrices where the ith iagonal elements for Λ an jπ(i Λ are e )(L )/ an e jπi()/ respectively. In eq. 7, I an I enote the an ientity matrices respectively an Î,u is the first u column submatrix of I, where u is L moulo. From eq. 5, eq. 7 an eq. 8, we have: s n =Λ p [I I... I Î,u ] [I ( ) I ] Λ W Λ x n (9) Similarly at the receiver, the recovere symbol ˆx n can be written in matrix form: ˆx n = H a r n (), where ˆx n enotes the symbols from bans an r n is the receive signal with length L. In orer to satisfy the perfect reconstruction conition, the analysis filter matrix H a = Hs [5]. he recovere symbol ˆx n can be expresse ˆx n =Λ W Λ [I ( ) I ] [I I... I Î,u ] Λ p r n () he generalize DF implementation is base on eq. 9 an eq., where the filter coefficient matrices consist of perioically varying GDF matrices. Unlie the implementation in [4] where the coefficients are time varying, we can incorporate the perioicity into filter inputs. Figure 4 an 5 show the implementations of the GDF filter ban transmitter an receiver respectively. At the transmitter, symbols are first transforme by, which can be implemente as phase shifts of complex number an point IFF (here we consier that is a power-of-two integer ) base on eq. 8. he transforme symbols X i (i =,.., ) are use to mae sequence X = [X i=,,..., X i=,,..., ]. By repeating sequence X L/ ( enotes integer ivision) times an appening the first L mo elements in X at the en, an L-element sequence is prouce to be multiplie with L filter coefficients. he multiplication results are accumulate to a length L shift register D which is set to be zeros at the initialization. After the accumulation, the first samples in D are shifte out as transmitte symbols an all other samples are shifte positions ahea with zeros shifte in. At the receiver, L receive symbols in a shift register are multiplie with L filter coefficients. he i mo (i =,,..., L ) multiplication results are combine to form a sequence R. hen the secon half of R is negate x x x Fig. 4. new samples are shifte in Fig. 5. X X X X X X X X X () p X X ( ) u p L Accumulate to D he GDF filter ban transmitter implementation r r L p pi mo p L R R i R R R u R he GDF filter ban receiver implementation - - First samples are shifte out for transmission zeros are shifte in an combine with the fist half to prouce symbols to be transforme by which is the conjugate of. After the transform, recovere symbols are obtaine an new symbols will be shifte in. Base on the implementation, we mae an computational complexity analysis by counting the number of complex multiplications. o transmit an receive each symbols, we nee L complex multiplications with filter coefficients, 4 for the phase shift, an point IFF an an point FF. he total computational complexity of the OSFB C OSFB can be expresse C OSFB =L +4 + ( log ) () * x x x

4 he computational complexity of the OFD C OFD is: C OFD = ( log ) (3) From eq. an eq. 3, the OSFB is more computational complex than the OFD ue to the extra filtering. Especially if the length of prototype filter L is large, the computational complexity increases enormously. his complexity raises a question on how to mae efficient harware implementations. he regular computational structures in figure 4 an figure 5 are goo inications for parallel processing. BER OFD QPSK OSFB QPSK OFD 6QA OSFB 6QA IV. RESULS AD DISCUSSIOS A. Simulation setup In the simulation, we consier a CR with 3 subcarriers where 8 are eactivate to avoi the interference to license users. Both the OFD base an the OSFB base multicarrier systems are consiere. o simplify the evaluation of the system performance, the channel is assume to be Aitive White Gaussian oise (AWG) channel with no istortion for botystems. he moulation scheme is consiere to be the same for every subcarrier. In the OSFB, the oversampling ratio is chosen as =36. he square root raise cosine filter with rolloff factor.5 is assume to be the prototype filter. he atlab function rcosine is use to generate the require prototype filter. We set the parameter group elay K as 9, thus the filter length L =K + = 649. B. Comparison with OFD Figure 6 shows the BER performance comparison of the OFD an OSFB for the given scenario. For fair comparison, we assume no interference to botystems from license users. QPSK an 6QA moulation schemes are consiere. he BER performance of the OSFB is a little better than the OFD ue to its less intercarrier interference. Figure 7 shows the transmitte spectrum for botystems. We can see the sieban power rejection of the OSFB is much better than the OFD. he noise floor of the nullifie spectrum is below - 3 for OSFB, however it is much higher in case of OFD therefore causing significant interference to license users. Even if more ajacent subcarriers are turne off in the OFD as inicate in [], the interference to license bans is still high ue to big sielobes. herefore, the traitional OFD system without any moification is ifficult to be applie in spectrum pooling system. he alternatives sucs the OSFB are more promising in the context of spectrum pooling. C. he esign traeoffs in the OSFB here are a number of traeoffs in esigning an OSFB multicarrier system sucs choices of ifferent prototype filters, the length of filters an oversampling ratio. hese traeoffs have impacts on BER performance, sieban power rejection, banwith efficiency an computational complexity. Here we iscuss some traeoffs base on our system in the simulation SR() 3 Fig. 6. BER performance on AWG OSFB =36, K= OFD Fig. 7. ransmitte spectrum with null subcarriers he choice of group elay K: In figure 8 an figure 9, we show the BER performance an the transmitte spectrum of the OSFB by increasing the group elay K of the prototype filter from 4 to 9 while eeping the rolloff factor an the oversampling ratio unchange. QPSK moulation is use an the AWG channel is assume. Increasing K from 4 to 9 will increase the prototype filter length L from 89 to 649. We can see an improvement in the BER performance an especially the sieban rejection by increasing K. his is largely ue to the factor that the high orer prototype filter gives better frequency response an sieban rejection. However, the computational complexity increases by 9% accoring to eq.. herefore, the length of the prototype filter is an important traeoff between the system performance an the computational complexity. he choice of oversampling ratio : Intuitively, increasing the oversampling ratio will result in larger intercarrier spacing. he increase intercarrier spacing tens to reuce the power leaage to ajacent subcarriers, therefore better BER performance an less interference to license bans are expecte. If we consier only one sie of the spectrum leaage power P lea generate by one subcarrier, it can be efine P lea = + Δf Φ(f)f (4)

5 BER 3 4 K=4, L=89 K=9, L= SR() Fig. 8. BER performance of the OSFB with ifferent K an QPSK moulation in AWG Fig K= K= ransmitte spectrum of the OSFB with ifferent K, where Φ(f) enotes the power ensity spectrum of subcarrier an Δf is the subcarrier spacing. If an ieal raise cosine filter is use as prototype filter in the OSFB, eq. 4 can be expresse P lea = H rc (f) f (5), where is the symbol uration an H rc (f) is frequency response of raise cosine filter. Ieally from eq. 5, the power leaage is reuce to zero when the sampling ratio > regarless of the choice of rolloff factor. However, in practice the ieal raise cosine filter can never be realize therefore the spectrum power leaage will always exists. evertheless eq. 5 can still serve as rough guiance to mae traeoffs between the oversampling ratio an the sieban power leaage in the OSFB base on the raise cosine prototype filter. However, increasing oversampling ratio obviously loses the banwith efficiency. Furthermore, the increase oversampling ratio will also result in an increase of computational complexity. he type of prototype filter: In our iscussion, only the raise cosine filter is consiere. However, there is freeom for prototype filter esign if the reconstruction error is on an acceptable level. uch research has been one for the prototype filter esign for filter ban systems. For example in [8], a small sie-lobe prototype filter may be an interesting option for filter ban multicarrier for Cognitive Raio. V. FUURE WORK Although the OSFB is a promising option in the context of Cognitive Raio, there are still a number of challenges for the practical system. Compare with OFD, filter ban base multicarrier is more subject to istortion an elay from channel. herefore, channel equalization in filter ban base multicarrier systems is an important issue to be consiere. he other rawbac of filter ban base multicarrier systems is the high computational complexity. Our future wor will also focus on how to mae efficient harware implementations for parallel processing. Besies, other filter ban base multicarrier systems for Cognitive Raio are also worttuying such as cosine moulate filter ban in [9] an wavelet multicarrier base on nonuniform filter ban in []. VI. COCLUSIO In this paper, we propose an oversample filter ban multicarrier for Cognitive Raio. It can achieve better BER performance an less sieban power leaage compare with OFD. herefore, the OSFB is a goo caniate for multicarrier base Cognitive Raio. We suggeste an efficient implementation base on the generalize DF moel followe by a computational complexity analysis. his implementation can be further exploite for efficient parallel processing. We also iscusse some esign traeoffs for the propose OSFB multicarrier system. ACKOWLEDGE he wor is sponsore by the Dutch inistry of Economic affairs Freeban AAF project. he authors woul lie to than their colleagues from the IRC of the echnical University Delft (UD) for the fruitful iscussions in the AAF project. REFERECES [] J. itola III. Cognitive Raio: An Integrate Agent Architecture for Software Define Raio, PhD hesis, Royal Institute of echnology, Sween, ay.. [].A. Weiss an F.K. Jonral, Spectrum pooling: An innovative strategy for the enhancement of spectrum efficiency, IEEE Commun. ag., ar. 4 [3] P. Amini, R. Kempter, R-R. Chen, L. Lin an B. Farhang-Boroujeny, Filter ban multitone: A caniate for physical layer of Cognitive Raio, SDR Forum echnical Conference, 5, USA [4] G. Cherubini, E. Eleftheriou, S. Olcer, J.. Cioffi, Filter ban moulation techniques for very higpee igital subscriber lines, IEEE Commun. ag., ay. [5] P.P. Vaiyanathan, ultirate System an Filter Bans, Prentice-Hall, 993 [6] Qiwei Zhang, Anre B.J. Koeler an Gerar J.. Smit, A reconfigurable raio architecture for Cognitive Raio in emergency networs, European Conference on Wireless echnology, September 6, anchester, UK [7] R.E. Crochiere an L.R. Rabiner, ultirate Digital Signal Processing Prentice-Hall, 983 [8] Kenneth W. artin, Small sie-lobe filter esign for multitone atacommunication applications IEEE rans. Circuit an System, Aug. 998 [9] B. Farhang-Boroujeny, ulticarrier moulation with blin etection capability using cosine moulate filter bans, IEEE rans. Commun., Dec. 3. [] Lashmanan,.K. Buiarjo, I. iooar, H., aximally frequency selective wavelet pacets base multi-carrier moulation scheme for Cognitive Raio systems, IEEE GLOBECO conference, 7