The 9h Asia-Pacific Conference on Communicaions (APCC3) Bali - Indonesia Analog Single-Carrier Transmission wih Frequency-domain Equalizaion Thanh Hai VO Shinya KUAGAI Tasunori OBARA and Fumiyui ADACHI Dep. of Communicaions Engineering Graduae School of Engineering Tohou Universiy 6-6-5 Aza-Aoba Aramai Aoba-u Sendai iyagi 9579 Japan {vohanhhai umagai obara}@mobile.ecei.ohou.ac.jp adachi@ecei.ohou.ac.jp Absrac In his paper a new analog signal ransmission echnique called analog single-carrier ransmission wih frequency-domain equalizaion (analog SC-FDE) is proposed. The proposed analog SC-FDE applies discree Fourier ransform (DFT) frequency-domain specrum shaping and mapping inverse DFT (IDFT) and cyclic prefix inserion before ransmission. A he receiver one-ap frequency-domain equalizaion (FDE) is applied o ae advanage of he channel frequency-seleciviy. As an example in his paper he analog voice ransmission is considered. By compuer simulaion we evaluae he normalized mean square error (SE) performance o show ha analog SC-FDE achieves beer SE performance han convenional analog signal ransmission scheme. Keywords analog waveform ransmission; frequency-domain equalizaion; single-carrier ransmission I. ITRODUCTIO owadays alhough digial signal ransmission has been coninuously evolving []-[] analog signal ransmission (e.g. radio broadcasing) sill remains essenial. In wireless ransmissions he channel is composed of many propagaion pahs having differen ime delays. Therefore he channel becomes severely frequency-selecive as he signal bandwidh is wider [3]-[]. In analog signal ransmission he ime delays can be negleced because of is narrow bandwidh and hus he channel is considered as frequency-nonselecive fading channel [5]. As a consequence of suffering from he frequencynonselecive fading channel he received signal power drops over a consecuive period of ime and hence he received signal qualiy significanly degrades. In order o overcome his problem we focus on a soluion ha widens he bandwidh of he analog signal by using discree Fourier ransform (DFT) o uilize he advanage of frequency-selecive fading channel (i.e. frequency diversiy). The widening of signal bandwidh can be done by mapping he frequency componens which are obained by DFT over a broadband bandwidh. However in such he frequency-selecive fading channel he received signal specrum is severely disored and hus ransmission performance degrades significanly. This means ha some echniques ha can correc he specrum disorion need o be adoped. For digial signal ransmission i is well nown ha orhogonal frequency division muliplexing (OFD) [6] is robus agains he frequency-selecive fading channel bu is high pea-o-average power raio (PAPR) propery of he ransmied signal is he main drawbac [7]. On he oher hand single-carrier (SC) ransmission has lower PAPR while achieving a good ransmission performance by using he frequency-domain equalizaion (FDE) a receiver []-[]. As a consequence SC-FDE has recenly drawn grea aenion as a robus wireless signal ransmission echnique. In his paper we apply SC-FDE echnique in order o improve he performance of analog signal ransmission and propose a new analog signal ransmission echnique called analog single-carrier ransmission wih frequency-domain equalizaion (analog SC-FDE). The proposed analog SC-FDE applies DFT frequency-domain specrum shaping and mapping inverse DFT (IDFT) and cyclic prefix (CP) inserion before ransmission. A he receiver one-ap FDE is applied o ae advanage of he channel frequency-seleciviy. We evaluae by compuer simulaion he normalized mean square error (SE) performance of he proposed analog SC-FDE and show ha i achieves beer SE performance han convenional analog signal ransmission. In his paper single analog signal sream will be presened. However muliple analog signal sreams can be ransmied based on he principle of single-carrier frequency-division muliple access (SC- FDA) []. Therefore he frequency uilizaion efficiency is he same as convenional analog signal ransmission inherenly narrowband. Furhermore since no source coding and channel coding are adoped he shor ransmission delay is achieved. The remainder of his paper is organized as follows. In secion II we propose he sysem model of he analog SC-FDE and describe he principle. Compuer simulaion resuls are given in Secion III. Then Secion IV provides he conclusion. II. AALOG SIGLE-CARRIER TRASISSIO WITH FREQUECY-DOAI EQUALIZATIO (AALOG SC-FDE) A. Sysem odel Sysem model of analog SC-FDE is illusraed in Fig.. A he ransmier afer he signal bandwidh is limied by lowpass filer (LPF) he analog signal s() is discreely sampled a yquis sampling rae. Then samples are grouped ino a signal bloc {s(; n=}. Each signal bloc is ransformed ino frequency-domain signal bloc by -poin DFT. From now on each frequency componen is called a subcarrier. Specrum shaping filer is inroduced in order o generalize he proposed analog SC-FDE in case of having a 97-673-65-/3/$3. 3 IEEE 7
The 9h Asia-Pacific Conference on Communicaions (APCC3) Bali - Indonesia specific specrum shaping design. Each bloc of subcarriers is mapped over a broad bandwidh having c (>) orhogonal subcarriers wih zeros occupying he unused subcarriers. Then each bloc of c subcarriers is ransformed bac ino complex ime-domain signal bloc {x(; n= c } by c -poin IDFT. Finally he las g samples of each ransmission bloc are copied as a CP and insered ino he guard inerval (GI) placed a he beginning of each ransmi bloc. The GI-insered signal bloc is ransmied over a frequency-selecive fading channel. A he receiver CP is removed from he each received signal bloc and hen each bloc is ransformed ino he frequency-domain signal bloc by c -poin DFT. Afer de-mapping is performed o pic up desired subcarriers of original signal one-ap FDE is performed o compensae he specrum disorion. Then each bloc is ransformed bac ino complex ime-domain signal. Real par of he signal is oupued and finally he analog signal s ( ) is reconsruced by auomaic gain conrol (AGC) [3] and LPF from discree signal s ( n ). s() H() -CP c -poin DFT LPF s( yquis-rae Sampling R() c De-mapping -poin DFT R ˆ( ) c - - Specrum shaping filer S() (a) Transmier W( c -) - apping -poin IDFT (b) Receiver Fig.. Sysem odel. X() c S ( ) s ( n ) - Real par oupu c - c -poin IDFT +CP W() FDE s ( ) AGC LPF B. Subcarrier apping A he ransmier we assume ha specrum shaping filer is an ideal bric wall LPF. The frequency componens (i.e. subcarriers) afer applying specrum shaping filer are denoed by {S(); =} and expressed as n S ( ) s( exp jπ. () n The ransmier hen maps subcarriers over a broadband bandwidh having c (>) orhogonal subcarriers expressed as {X(); = c } in () and (3). We consider wo mehods in order o map subcarriers: localized mapping and disribued mapping [5]. In localized mode subcarriers are confined o a coninuous specrum of subcarrier. Whereas in disribued mode hey are mapped equally space subcarrier. In boh of wo mapping mehods zeros occupy he unused subcarriers. In case of ransmiing muliple analog signal sreams each consising of subcarriers he subcarrier mapping is performed so ha muliple sreams do no overlap (or hey are orhogonal o each oher) in he frequency-domain similar o he principle of SC- FDA. An example of subcarrier mapping wih =6 c = and wo analog signal sreams (i.e. wo channels) is illusraed in Fig.. Localized mapping S( ) X ( ) () oherwise Disribued mapping c S( ) X ( ) (3) oherwise where = c and c / is he adjacen subcarrier inerval. C. Channel odel We assume ha he channel consiss of L disinc propagaion pahs in he proposed scheme. The channel impulse response h(τ) can be expressed as Channel Channel (a) Localized apping Channel c / Channel (b) Disribued apping Fig.. Subcarrier apping. L h l l h(τ) (τ τ ) () where h l and τ l are complex-valued pah gain wih L E [ l hl ] (E[.] denoes he expecaion operaio and symbol-spaced ime delay of he l-h pah (i.e. τ l =l) respecively. In () we assume ha he channel says consan during he signal ransmission period of one bloc. The channel ransfer funcion {H(); = c } (i.e. he channel gain a frequency-domai is given by L l l τ l H ( ) hl exp( jπ ). (5) c 97-673-65-/3/$3. 3 IEEE 75
The 9h Asia-Pacific Conference on Communicaions (APCC3) Bali - Indonesia D. Subcarrier De-mapping and Frequency-Domain Equalzaion Afer removing CP he receiver ransforms he received signal bloc ino he frequency-domain signal using c -poin DFT. The frequency-domain received signal a he -h frequency R() for = c can be expressed as R( ) S H ( ) X ( ) ( ) (6) where S and () are he average received signal power and he noise componen a he -h frequency respecively and () for = c is given by c ( ) n( ) exp jπ (7) c c wih n() being he zero-mean complex-valued addiive whie Gaussian noise (AWG) having he variance. Then de-mapping is performed o obain subcarriers of original signal and desired channel gain which is expressed as Rˆ ( ) Hˆ ( ) respecively for =. Localized de-mapping Rˆ( ) R( ) ˆ H ( ) H ( ) Disribued de-mapping. () ˆ( ) c R R ˆ ( ). (9) H H c Afer he subcarrier de-mapping one ap FDE is carried ou as S ( ) W ( ) Rˆ( ) SW ( ) Hˆ ( ) S( ) W ( ) ˆ ( ) () where W() ˆ ( ) for = are he FDE weigh noise componen corresponding o R ˆ( ) respecively. We consider hree FDE weighs based on zero-forcing () crierion maximal-raio combining (RC) crierion and minimum mean square error (SE) crierion [] expressed as Hˆ ( ) W ( ) H ˆ ( ) RC () ˆ H ( ) SE ˆ H ( ) γ where γ is he average received signal-o-noise power raio (SR) and [*] denoes he complex conjugae operaion. Afer ransforming he frequency-domain signal bloc (i.e. subcarriers) bac ino he ime-domain signal bloc by - poin IDFT only he real par of he ime-domain signal { s ( n ) ; n=} is oupued as s ( Re K s( Re S ( )exp jπn () μ ( μ ( ISI where /K μ ISI ( n ) and μ noise ( n ) are normalizaion facor of AGC residual signal disorion and equivalen noise respecively which are given by K S H ( ) n n μ ISI( S H ( ) s( n )exp jπ K n n n μ noise( ( )exp jπn K (3) wih ˆ H ( ) W ( ) H ( ) and ( ) W ( ) ˆ ( ) being he equivalen channel and he equivalen noise componen a he -h frequency respecively. Finally he analog signal s ( ) is reconsruced by LPF from discree signal s ( n ). E. Convenional analog signal ransmission For comparison convenional double-sideband suppressedcarrier (DSB-SC) ransmission [] is considered. A he ransmier afer applying LPF he analog signal is ransmied wihou any processing. Due o he narrow bandwidh of signal we assume ha he channel consiss of one pah (i.e. frequency-nonselecive fading channel). A he receiver in order o suppress he flucuaion of received signal power ideal fas AGC is assumed. Afer an ideal coheren deecion he demodulaed signal s ( ) of DSB- SC using fas AGC can be expressed as s ( ) s( ) Re η( ) S h( ) () where h() s() and η( ) are complex-valued pah gain ransmied signal and he zero-mean complex-valued AWG having he variance respecively. Signal ransmission noise TABLE I. COPUTER SIULATIO CODITIO Analog SC-FDE Toal no. of subcarriers c =9 Time-domain bloc size =6 o. of channels U= Specrum shaping filer Ideal bric wall LPF GI lengh g =6 Sampling rae /T=Hz apping Localized Disribued Channel FDE weigh Channel esimaion & Fas AGC Frequency-selecive bloc Rayleigh fading L=6-pah uniform power delay profile RC SE Ideal Convenional DSB-SC Frequency non-selecive Rayleigh fading 97-673-65-/3/$3. 3 IEEE 76
The 9h Asia-Pacific Conference on Communicaions (APCC3) Bali - Indonesia Average SE Fig. 3. SE performance in case of cosine wave ransmission. Average SE Convenional DSB-SC COSIE WAVE (f=hz) =6 c =9 g =6 Subcarrier inerval=5hz 5 5 5 Average received SR (db) Fig.. SE performance in case of voice ransmission. III. COPUTER SIULATIO In his paper in order o evaluae ransmission performance of proposed analog SC-FDE scheme we use normalized mean square error (SE) crierion which is defined as SE s ( s( n Proposed analog SC-FDE Convenional DSB-SC Proposed analog SC-FDE VOICE =6 c =9 g =6 Subcarrier inerval=5hz n s ( where is he oal number of ransmied signal samples. Localized Disribued RC SE Localized Disribued RC SE 5 5 5 Average received SR (db) (5) A. Compuer Simulaion Condiion The compuer simulaion condiion is summarized in Table I. In he proposed analog SC-FDE we assume he bandwidhresriced ( Hz) voice ransmission. We use a sampling rae of Hz a ime-domain signal bloc wih lengh of =6 samples an adjacen subcarrier inerval of 5 Hz and a bandwidh afer subcarrier mapping of c =9 subcarriers. The channel is assumed o be a frequency-selecive bloc Rayleigh fading channel having a symbol-spaced L=6-pah uniform power delay profile. Ideal channel esimaion is assumed. On he oher hand in convenional analog signal ransmission he channel is assumed o be a frequencynonselecive fading channel. Ideal fas AGC is also assumed in he convenional scheme. B. ormalized ean Square Error performance The SE performance of he proposed scheme in case of cosine wave ransmission and voice ransmission are showed in Fig. 3 and Fig. respecively. For comparison SE performance of he convenional DSB-SC ransmission is also ploed. I can be seen ha boh of cosine wave and sound ransmission have almos he same performance. The proposed analog SC-FDE achieves much beer performance han convenional DSB-SC. Among hree FDE weighs he performance in case of using -FDE is almos same as convenional DSB-SC. SE-FDE wih disribued mapping achieves he bes performance for all average received SR. The reasons are discussed below. Using he weigh (i.e. W()= Hˆ ( ) ) he equivalen channel becomes fla (i.e. H ( ) =) and as a consequence he residual signal disorion disappears in () (i.e. μ ISI ( n ) ). Therefore i can o be seen ha he oupu in proposed scheme (i.e. s ( n ) in ()) is same as he oupu in convenional DSB-SC (i.e. s ( ) in ()). Consequenly he proposed scheme using -FDE has almos same performance as convenional DSB-SC. However i should be noed ha he noise of analog SC-FDE using -FDE and he noise of convenional DSB-SC using fas AGC are boh enhanced when he channel gain H ˆ ( ) drops. The RC weigh (i.e. W()= Hˆ ( ) ) can avoid he noise enhancemen problem and maximizes he SR bu i enhances he frequency-seleciviy of he equivalen channel (he channel afer FDE) in case of disribued mapping and hus disribued mapping wih RC-FDE canno improve he performance even SR increases. Bu in case of localized mapping RC-FDE does no really enhance he frequencyseleciviy of he equivalen channel because he original signal bandwidh afer localized mapping is inherenly narrowband (he signal bandwidh is ep he same as he original analog signal). Therefore RC-FDE improves significanly he SE performance as shown in Fig.3 and Fig.. The SE weigh minimizes he SE beween frequency-domain signal afer he FDE and before he subcarrier mapping. If ˆ H ( ) γ he SE weigh approximaes he weigh. On he oher hand if ˆ H ( ) γ SE weigh approaches γhˆ ( ) and approximaes he RC weigh. As a consequence SE- FDE can resore a near frequency-nonselecive channel while alleviaing he noise enhancemen problem. Besides using disribued mapping frequency diversiy gain is achievable 97-673-65-/3/$3. 3 IEEE 77
The 9h Asia-Pacific Conference on Communicaions (APCC3) Bali - Indonesia more han localized mapping and hus SE-FDE wih disribued mapping provides he bes performance among combinaions of hree FDE weighs and wo subcarrier mappings in he proposed scheme. Fig. 5 shows a one-sho observaion of sound ransmission when γ= db in order o compare convenional DSB-SC scheme o he bes combinaion beween subcarrier mapping and FDE (i.e. SE-FDE wih disribued mapping) in proposed scheme. In convenional scheme he channel is assumed he frequency-nonselecive fading channel wih maximum Doppler frequency f D = Hz and ideal fas AGC is also assumed. While proposed scheme considers he L=6- pah uniform power delay profile and he oher simulaion condiion is shown in Table I. As discussed above i could be clearly seen for convenional DSB-SC scheme ha where he channel gain h() drops he received voice power becomes high due o he noise enhancemen. On he oher hand proposed scheme using SE-FDE wih disribued mapping can achieve he received voice waveform approximaing he original voice. This is because he combinaion of SE- FDE and disribued mapping no only provides he bes compromise beween he noise enhancemen and he suppression of frequency-seleciviy bu also obains significan frequency diversiy gain. IV. COCLUSIO In his paper we proposed a new analog signal ransmission echnique called analog single-carrier ransmission wih frequency-domain equalizaion (analog SC- FDE) in order o improve he performance of analog signal ransmission. In he proposed scheme he frequency componens of analog signal are mapped over a broad bandwidh in order o obain he frequency diversiy gain. Besides he FDE is applied o miigae he disadvanage of he channel frequency-seleciviy (i.e. he specrum disorio. We showed by compuer simulaion ha he proposed analog SC-FDE achieves beer normalized mean square error (SE) performance han convenional DSB-SC ransmission. In his paper single analog signal sream was presened. However i should be noed ha muliple analog signal sreams can be ransmied based on he principle of singlecarrier frequency-division muliple access (SC-FDA). Ideal channel esimaion was assumed. Channel esimaion for he analog SC-FDE is lef as an ineresed fuure sudy. [5] A. Goldsmih Wireless communicaions Cambridge Universiy Press 5. [6] V. Charavarhy A. S. unez and J. P. Sephens TDCS OFD and C-CDA: a brief uorial IEEE Commun. ag. vol.3 pp.s-s6 Sep. 5. [7] S. H. Han and J. H. Lee An overview of pea-o-average power raio reducion echniques for mulicarrier ransmission IEEE Wireless Commun. vol. no. pp.56-65 April 5. [] H. Sari G. Karam and I. Jeanclaude Frequency-domain equalizaion of mobile radio and erresrial broadcas channels IEEE Globecom vol. pp.-5 San Francusco ov.-dec. 99. [9] D. Falconer S.L. Ariyavisaul A. Benyamin-Seeyar and B. Eidson Frequency domain equalizaion for single-carrier broadband wireless sysems IEEE Commun. ag. vol. no. pp.5-66 April. [] F. Adachi H. Tomeba and K. Taeda Frequency-domain equalizaion for broadband single-carrier muliple access IEICE Trans. Commun. vol.e9-b no.5 pp.56 ay 9. [] F. Adachi H. Tomeba and K. Taeda Inroducion of frequencydomain signal processing o broadband single-carrier ransmission in a wireless channel IEICE Trans. Commun. vol.e9-b no.9 pp.79- Sep. 9. [] H. G. yung J. Lim and D. J. Goodman Single carrier FDA for uplin wireless ransmission IEEE Vehicular Technol. ag. vol. no.3 pp.3-3 Sep. 6. [3] Y. Han Z. Wang L. Li and Y. Zhao A fas auomaic gain conrol scheme for IEEE.5. receiver Proc. IET nd Inernaional Conference on Wireless obile and ulimedia ewors (ICW) pp.67-7 Beijing Oc.. [] B. Kanmani The ransformer-less double-side band suppressed carrier generaion IET Inernaional Conference on Wireless obile and ulimedia ewors pp. umbai Jan.. s() s() h() Sampling rae=hz Original Voice Convenional DSB-SC Channel Gain fd=hz Received Voice Ideal fas AGC s() Fig. 5. One-sho observaion of voice ransmission (γ= db). Proposed analog SC-FDE Disribued apping SE c =9 =6 g =6 L=6 Subcarrier inerval=5hz Ideal channel esimaion Received Voice REFERECES [] Y. Kim B. J. Jeong J. Chung C.-S. Hwang J.S. Ryu K.-H. Kim and Y. J. Kim Beyond 3G; vision requiremens and enabling echnologies IEEE Commun. ag. vol. no.3 pp. arch 3. [] Y. Par and F. Adachi Enhanced radio access echnologies for nex generaion mobile communicaion Springer 7. [3] J. G. Proais and. Salehi Digial communicaions 5h ed. cgraw- Hill. [] T. S. Rappapor Wireless communicaions Prenice Hall 996. 97-673-65-/3/$3. 3 IEEE 7