4 Telfor Journal Vol. 4 No.. OFDM AF Varable Gan Relay System for the Next Generaton Moble Cellular Networs Ens Kocan Member IEEE and Mlca Pejanovc-Djursc Member IEEE Abstract In ths paper we present analytcal performance evaluaton of a dual-hop OFDM amplfy-andforward (AF) varable gan (VG) relay system mplementng ordered subcarrer mappng (SCM) at the relay staton (R) consdered to be a very nterestng soluton for the next generaton moble cellular networs. A scenaro wth no drect communcaton between the source of nformaton (S) and destnaton termnal (D) wth the Raylegh fadng statstcs on both hops s assumed. A closed form analytcal expresson for the bt error rate (BER) performance of the consdered system wth DPSK modulaton s derved whle for ts ergodc capacty performance a tght upper bound expresson s obtaned. The accuracy of the undertaen analytcal approach s confrmed through comparson wth smulaton results. It s shown that sgnfcant capacty enhancement can be acheved through SCM mplementaton at R for all the sgnal-to-nose rato (SNR) values on both hops but especally n the regon of small SNRs on hops. BER analyss reveals that n the regon of small and medum average SNRs on both hops BER performance may also be mproved wth SCM at R staton. Key words BER ergodc capacty OFDM AF relay system subcarrer mappng varable gan. R I. INTRODUCTION ELAY systems have become a subject of ntensve research nterest as t s recognzed that they can mprove capacty and extend the coverage area of wreless communcaton systems. Addtonal attenton s focused on them snce they were proposed for the mplementaton n moble cellular networs of the new generaton []. Many research efforts conducted from that perod have led to the acceptance of two standards that are recognzed as IMT-Advanced or 4G systems []. Both of them assume mplementaton of relay (R) statons n dual-hop scenaros wth three communcaton termnals where there s no drect communcaton between the source of nformaton (S) and destnaton termnal (D). The R staton performs sgnal processng based on a decode-and-forward (DF) paradgm whch means that the sgnal receved from S s fully decoded and then agan re-encoded before forwardng towards D. However t s expected that some of the upcomng IMT-Advanced systems specfcatons wll nvolve amplfy-and-forward (AF) relayng where the R staton only amplfes the sgnal receved from R and then forwards t to D [] [3]. In such a scenaro the R Ens Kocan Faculty of Electrcal Engneerng Podgorca. Dzordza Vasngtona bb 8 Podgorca Montenegro ( e-mal: ens@ac.me ) Mlca Pejanovc-Djursc Faculty of Electrcal Engneerng Podgorca. Džordža Vašngtona bb 8 Podgorca Montenegro (e-mal: mlca@ac.me ). staton may amplfy the receved sgnal wth a fxed gan (FG) or wth a varable gan (VG) dependng on ts ablty to estmate S-R channel. AF relay systems are smpler for realzaton and ntroduce shorter latency than the DF relay systems. Thus n ths paper we analyze the performance of relay systems mplementng AF VG relayng. Le most of the modern broadband wreless communcaton systems the next generaton cellular networs wll employ orthogonal frequency dvson multplexng (OFDM) on a physcal layer due to ts proven ablty to provde hgh data rates even n frequency selectve channels [3]. Nowadays numerous researches are ongong wth the am to defne new solutons for performance mprovement of the standardzed OFDM relay systems for cellular networs. One of the nterestng solutons for performance mprovement s the mplementaton of subcarrer mappng (SCM) at the R staton whch can enhance the system capacty [4]-[8] and/or mprove bt error rate (BER) performance [7]-[]. For the capacty maxmzaton the so called best-to-best SCM (BTB SCM) scheme should be used where the subcarrer wth the hghest SNR from the frst hop should be mapped to the subcarrer wth the hghest SNR on the second hop then the subcarrer wth the second hghest SNR from the frst hop to the subcarrer wth the second hghest SNR on the second hop etc [4]-[8]. However for dual-hop OFDM AF relay systems t has been shown n [9] that BTB SCM scheme mproves the BER performance only n the regon of small and medum SNRs on both hops whle for hgh SNRs the SCM scheme denoted as BTW SCM should be mplemented. Ths SCM scheme assumes that the subcarrer wth the hghest SNR from the frst hop should be mapped to the subcarrer wth the lowest SNR on the second hop etc. Ergodc capacty performance of OFDM AF FG relay system wth SCM has been analyzed through dfferent approaches n [6] and [7] whle ts BER performance has been evaluated n [7] and []. However the level of capacty enhancement and BER performance mprovement acheved through mplementaton of SCM at the R staton n OFDM AF VG relay system has not been examned yet. Thus n ths paper we perform analytcal and smulaton evaluaton of the performance benefts attaned wth ths new soluton for the OFDM based relay systems. The paper s organzed as follows: Secton II descrbes the analyzed OFDM AF VG relay system wth SCM and the consdered scenaro. The analytcal dervaton of the probablty densty functon (PDF) and moment generaton
Kocan and Pejanovc-Djursc: OFDM AF Varable Gan Relay System 5 functon (MGF) of the SNR at D s gven n Secton III. Ths Secton also contans an analytcal approach for dervaton of the BER expresson for DPSK (Dfferentally Phase Shft Keyng) modulated consdered system as well as dervaton of the upper bound of the ergodc capacty. Secton IV presents the analytcally and smulaton obtaned BER and ergodc capacty results. Secton V concludes the paper. II. SYSTEM MODEL We consder an OFDM dual-hop relay system wth a source termnal S a half-duplex relay termnal R and a destnaton one D each equpped wth a sngle antenna. A scenaro wthout the possblty of drect communcaton between S and D s assumed. Orthogonalty of the S-R and R-D channels s acheved by dvdng a communcaton process nto two tme slots. The R termnal has FFT (Fast Fourer Transformaton) and IFFT (Inverse Fast Fourer Transformaton) blocs for OFDM demodulaton and OFDM modulaton respectvely. It s assumed that R has perfect channel nowledge of both S-R and R-D channels. Usng that R performs varable gan relayng where the sgnal that reaches the relay on the -th subcarrer s amplfed by a gan G =/H wth H beng the -th subcarrer channel transfer functon. Furthermore R has a bloc that performs subcarrer mappng (SCM) mappng subcarrers from the frst hop to subcarrers on the second hop n accordance wth ther nstantaneous SNRs. In order to perform sgnal demodulaton t s necessary that D nows the permutaton functon performed at R. Fg. presents the smplfed bloc scheme of the relay staton n OFDM varable gan relay system wth SCM. Fg.. OFDM AF VG relay staton wth SCM. The post-fft sgnal on the -th subcarrer receved at the relay staton s gven by: YR = XH N M () where M s the total number of subcarrers and X s a data symbol sent by source on the -th subcarrer. N represents an addtve whte Gausssan nose on the -th subcarrer wth varance E( N )=N E( ) denotng the expectaton operator. Assumng that the SCM functon ν() performs mappng of the -th subcarrer from the frst hop to the -th subcarrer on the second hop the frequency doman sgnal at D can be wrtten as: YD = GH YR ν ( ) N () = GH H X GH N N M wth H denotng the -th subcarrer channel transfer functon on the second hop. N s an addtve whte Gaussan nose on the -th subcarrer at the destnaton havng varance E( N ) =N. Fadngs n the S-R and R- D channels are assumed to be ndependent and dentcally dstrbuted (..d.) wth the Raylegh dstrbuton resultng n the exponental form of PDF of SNR on both channels. Usng () and the descrbed gan G appled at the subcarrer level at R the nstantaneous SNR on the -th subcarrer at D can be presented as: SR end = (3) SR where SR and denote nstantaneous SNR on the -th subcarrer of the S-R ln and on the -th subcarrer of the R-D ln respectvely. III. PERFORMANCE ANALYSIS In order to attan performance analyss of OFDM AF VG relay system mplementng SCM t s necessary to now PDF of the SNR per subcarrer at D. A. PDF of SNR The PDF of SNR for the -th weaest subcarrer meanng that t has the -th lowest SNR out of the M total ones on the S-R ln for the assumed Raylegh fadng s gven n [7] as: w SRx f ( x) = λ α e βλ (4) SR = where λsr = / and SR SR denotes the average SNR on the S-R ln. The coeffcents α and β have the values: M α = ( ) M β = M (5) wth (:) representng the bnomal coeffcent. The PDF of SNR for the -th strongest subcarrer on the R-D ln meanng that t has the -th hghest SNR out of the M total ones can be wrtten as n [7]: M s x f ( x) = λ α e βλ. (6) = Here λ = / wth representng the average SNR on the R-D ln. The ntroduced coeffcents are equal to: M M δ = ( ) M ; ε =. (7) Assumng that the random varable SR denotes the nstantaneous SNR of the -th weaest subcarrer on the S- R ln and the nstantaneous SNR of the -th strongest subcarrer on the R-D ln the harmonc mean of these two random varables can be wrtten as SR. (8) μh ( SR ) = = = end SR SR Usng (4) and (6) and followng the same steps as n [] for dervng the PDF of the harmonc mean of two exponentally dstrbuted random varables we derved the PDF of μ H ( SR ) and through ths the PDF of SNR for the -th subcarrer at D n the case of BTW SCM:
6 Telfor Journal Vol. 4 No.. β j ε M αδ x BTW j SR β j SRε f ( ) end x = xe j= = SR SR εβ (9) j βε j βε j K x K x SR SR where K ( ) and K ( ) are zero and frst order modfed Bessel functons of the second nd defned n [ eqs. (9.6.) (9.6.)]. The PDF of SNR for the -th subcarrer at D n the case of BTB SCM scheme mplemented can be obtaned followng the same dervaton steps as the ones for the BTW SCM but assumng that subcarrers n both hops are ncreasngly ordered accordng to ther nstantaneous SNRs. The fnal expresson s then derved n the form: β j β αα x BTB j SR β j SRβ f ( ) end x = xe j= = SR SR ββ () j ββ j ββ j K x K x. SR SR B. BER Performance Analyss We used the moment generatng functon (MGF) based approach for the BER performance analyss of the DPSK modulated OFDM AF VG relay system employng SCM at R staton. Usng the nown PDF of SNR the MGF of SNR for the -th subcarrer at D n the consdered relay system s derved usng [3 eq. (6.6.3)]: end s ( e ) () s = E = M 6 j 3 j= = SR ( s Lj Bj ) 4L 3 5 s L B j j j F 3 ; ; s L j B j s Lj B j 3 5 s L B 3 ; ;. j j F s Lj Bj αδ () In () F ( ) s the Gaussan hypergeometrc functon defned n [ eq. (9.)] whle the ntroduced coeffcents are equal to L j = β j/ SR ε / and B j = β jε / SR. For the OFDM AF VG relay system mplementng BTB SCM the MGF of SNR for the -th subcarrer at D s obtaned n the form: end () s = αα 6 j 3 j= = SR ( s I j Aj ) 4I 3 5 s I A j j j F 3 ; ; s I j Aj s I j Aj 3 5 s I A j j F 3 ; ; s I j Aj wth I j = β j/ SR β/ and Aj = ββ j / SR. () Havng the closed form soluton for the MGF of SNR for the -th subcarrer at D n both BTB and BTW SCM schemes the average BER for the DPSK modulated OFDM AF relay system wth the SCM can be evaluated as: M Pb = (). (3) end M = C. Ergodc Capacty Analyss As t s proven that the BTB SCM scheme acheves the hghest capacty among all the other possble SCM schemes n ths part we analyze the ergodc capacty bound of the OFDM AF VG relay system employng BTB SCM. The ergodc capacty normalzed to a unt bandwdth for the -th subcarrer at D n the consdered relay system can be calculated usng the obtaned PDF of SNR for the -th subcarrer at D: BTB C = E ( log ( ) ) = log ( ) f ( ) d. (4) end The factor / comes due to transmsson over two tmeslots. Havng BTB f ( ) as n () precludes fndng a end closed-form soluton for the ntegral n (4). However the ergodc capacty can be upper bounded usng Jensen s nequalty [7] and notng that log( ) s a concave functon yeldng: C log ( ( )) E. (5) The expectaton of the -th subcarrer SNR at D s determned as: BTB E( ) = f ( ) d = j ( ) α α (6) end SR j= = where and denote the ntegrals: I j I j = e K ( Aj ) d (7) A j.5 I j = j ( ) e K A d. (8) Usng the ntegral soluton gven n [3 eq. (6.6.3)] the closed-form expressons for and n (7) and (8) respectvely are found thus obtanng: 8 αα j 3I j E( ) = 3 5SR j= = I I j A j A j j (9) ( ) 3 7 I A 7 I A 4 ; ; 3 ; ;. j j j j F F I j Aj I j Aj Substtutng (9) nto (5) an upper bound for the -th subcarer ergodc capacty n OFDM AF VG relay system wth BTB SCM s derved. Average ergodc capacty per subcarrer s then obtaned through averagng over all M subcarrers of the consdered system: M C M = C =. ()
Kocan and Pejanovc-Djursc: OFDM AF Varable Gan Relay System 7 IV. RESULTS The subsequent analytcal and smulaton results assume a perfectly synchronzed OFDM AF VG relay system wth the mplemented SCM at R staton. The OFDM system has M=3 subcarrers whch n a real scenaro can be consdered as 3 chuns wth uncorrelated transfer functons from chun to chun [8]. It s also assumed that nose varances at R and D are the same N =N. We used Monte Carlo smulatons of the consdered OFDM relay system where we have modeled ts part that belongs to frequency doman. Ths can be consdered as an adequate approach as we have assumed perfect tme and frequency synchronzaton among S R and D. In smulatons ndependent and dentcally dstrbuted subcarrers were generated as complex random Gaussan varables havng zero mean value and varance / thus modelng the Raylegh fadng dstrbuton where each subcarrer has ts power normalzed to one. Fg. gves the analytcally obtaned as well as smulated BER performances of the consdered OFDM AF VG relay system wth SCM. In order to get an nsght nto the level of BER performance mprovement acheved through the mplementaton of SCM at R staton the BER of the OFDM AF VG relay system wth no SCM s presented. A scenaro wth the equal average SNRs on both hops s assumed. BER - - BTW SCM (analytcally) BTB SCM (analytcally) no SCM (analytcally) Smulaton results -3 4 6 8 4 6 8 Average SNR per hop [db] Fg.. BER performance of DPSK modulated OFDM AF VG relay system wth SCM. The BER values gven n Fg. clearly show that all the analytcally obtaned results are completely verfed by smulatons. In other words t can be concluded that the algorthms ntroduced for the end-to-end SNR statstcs (PDF and MGF) determnaton can be consdered as vald. Further on t s obvous that the SCM mplementaton does not offer sgnfcant BER performance enhancements for ths type of relay systems when compared wth the mprovements acheved n the OFDM AF FG relay systems [7]. Addtonally for the relay system wth a varable gan the best BER values are attaned wth the BTB SCM scheme when average SNR per hop s below 3dB whle above ths SNR value the advantage s on the sde of the BTW SCM. However the level of BER performance mprovement acheved through BTW SCM at hgh average SNR values per hop s very small compared to the system wth no SCM. Thus from the pont of vew of the acheved BER performance mprovement only the mplementaton of the BTB SCM scheme can justfy the ncreased system complexty. The system wth BTB SCM has the best BER performance n the range of low average SNR values.e. when the channel propagaton condtons can be consdered as unfavorable for the deployment of the system wth no SCM. For example the SNR gan acheved wth BTB SCM s equal to db for the BER value of - when compared wth the system wth no SCM. Moreover the BTB SCM scheme s nown as the one that maxmzes the achevable capacty. The analytcally obtaned ergodc capacty values are also compared wth the smulaton results for the sae of verfcaton. Smulatons nclude generaton of ndependent Raylegh fadng channel transfer functons for each subcarrer on the S-R ln ( H ) and on the R-D ln ( H ) and for each channel realzaton where n denotes the n-th channel realzaton ( n n tot ). The value of the ergodc capacty for the -th subcarrer at the system recevng end for the consdered n-th smulaton realzaton s defned as: ( ) ( G ) H H X n C = log. () ( G ) H N N G (n) represents the gan factor ntroduced at the R staton whch corresponds to the n-th S-R ln channel realzaton. The average ergodc capacty for the -th subcarrer at the recevng end of the consdered relay system s then found by averagng over n tot smulaton repettons: C n tot n tot n= = C () whle the average ergodc capacty per subcarrer s then obtaned through averagng over all M subcarrers. Plots gven n Fg. 3 represent the analytcal and smulaton results for the average capacty per subcarrer of the consdered OFDM AF VG relay system wth BTB SCM n the scenaro assumng equal average SNR on both hops. In order to gan an nsght nto the level of Average ergodc capacty per subcarrer [b/s/hz].5.5.5 BTB SCM (smulaton) BTB SCM (upper bound) no SCM (smulaton) 4 6 8 4 6 8 Average SNR per hop [db] Fg. 3. Ergodc capacty per subcarrer of OFDM AF VG relay system wth and wthout SCM.
8 Telfor Journal Vol. 4 No.. capacty enhancement acheved through the BTB SCM mplementaton at R the average ergodc capacty for the OFDM AF VG relay system wthout SCM obtaned through smulatons s also presented. From the plots gven n Fg. 3 t can be seen that a very tght upper bound of the ergodc capacty has been derved whch confrms the accuracy of the undertaen analytcal approach. Namely the obtaned analytcal results dffer less than.5% from the smulaton results for all analyzed SNR values on both hops (Table ) thus approvng that they can be used for the ergodc capacty analyses. The comparatve analyss of the average ergodc capacty of OFDM AF VG relay system mplementng BTB SCM wth the ergodc capacty of the system wthout SCM gven n Table shows the level of the capacty enhancement acheved through SCM at R staton. It s very mportant that the greatest capacty enhancement s attaned n the regon of small average SNRs on both hops.e. when the channel condtons are bad and t may happen that the system wth no SCM cannot meet the requred qualty of servce. Thus for example the system wth BTB SCM has 4.8% hgher capacty than the system wthout SCM for the average SNR per hop value of 4dB whle the capacty enhancement acheved through BTB SCM s equal to 7.8% for the average SNR per hop value of db. TABLE : ERGODIC CAPACITY OF OFDM AF VG SYSTEM Average SNR per hop [db] 4 no SCM [b/s/hz] (smul).387.9.54 BTB SCM [b/s/hz] (smul.).483.5.43 BTB SCM [b/s/hz] (up. bou.).49.65.464 Capacty enhancement 4.8% 6.6% 7.8% Snce n moble cellular systems the R staton wll be placed n such a poston that channel varatons between the base staton (representng S n the downln communcaton process) and R staton wll be small then t s nterestng to analyze the ergodc capacty performance as a functon of the average SNR on the R-D ln. The plots gven n Fg. 4 assume ths nd of scenaro and they confrm the prevously conducted conclusons about the sgnfcance of the mplementaton of BTB SCM for the capacty enhancement especally n the regon of small SNRs on both hops. The gven plots show that for SR = 5dB and = db the relay system wth BTB SCM acheves 3% hgher capacty than the system wthout SCM whle for the case when SR = 5dB and = db the capacty enhancement s equal to 8%. V. CONCLUSIONS BER and ergodc capacty performance evaluaton of the OFDM AF VG relay system mplementng SCM at the R staton has been conducted. Closed form BER expressons are derved for the DPSK modulated consdered system mplementng BTB SCM and BTW SCM. The obtaned results are completely verfed by Average ergodc capacty per subcarrer [b/s/hz].8.6.4..8.6 SR =5dB SR =5dB no SCM (smulaton).4 BTB SCM (smulaton) BTB SCM (upper bound). 4 6 8 4 6 8 Average SNR on R-D ln [db] Fg. 4. Ergodc capacty per subcarrer of OFDM AF VG relay system wth and wthout SCM. smulatons. They have shown that n order to mprove BER performances the BTB SCM scheme should be mplemented n the regon of small and medum average SNRs on both hops whle for the hgher average SNRs SCM should not be mplemented. Ergodc capacty analyss of the consdered system wth BTB SCM has resulted n dervaton of the very tght upper bound of acheved ergodc capacty whch dffers less than.5% from the smulaton results for all SNR values on both hops. Comparatve analyss has shown that very sgnfcant capacty enhancement can be acheved through the mplementaton of BTB SCM at the R staton especally n the regon of small SNRs on both hops (up to 3%). Ths s partcularly mportant as t means that the BTB SCM scheme enables the hghest BER performance mprovement and capacty enhancement n the worst case scenaro. The obtaned results have confrmed that the consdered OFDM AF VG relay system mplementng SCM at the R staton can be consdered as an nterestng soluton for the next generaton moble cellular networs. REFERENCES [] A. Nosratna T. E. Hunter and A. Hedayat Cooperatve communcaton n wreless networs IEEE Communcaton Magazne Vol. 4 no. pp. 74-8 Oct 4. [] K. Loa and C-C. Wu et al IMT-Advanced Relay Standards IEEE Communcaton Magazne Vol. 48 no. 8 pp. 4-48 Aug.. [3] Y. Yang H. HU J. Xu and G. Mao Relay Technologes for WMAX and LTE-Advanced Moble Systems IEEE Commun. Magazne pp. -5 October 9. [4] A. Hottnen and T. Henen Subchannel assgnment n OFDM relay nodes n Proc. of 4th Annual Conf. on Informaton Scences and Systems 6. [5] I. Hammerstrom and A. Wttneb Jont power allocaton for nonregeneratve MIMO-OFDM relay lns n Proc. of IEEE Internatonal Conference on Acoustc Speech and Sgnal Processng May 6. [6] C. R. N. Athaudage M. Sato and J. Evans Performance analyss of dual-hop OFDM relay systems wth subcarrer mappng n Proc. of IEEE ICC 8 Bejng Chna 8. [7] E. Kocan M. Pejanovc Djursc D. S. Mchalopoulos and G. K. Karagannds Performance evaluaton of OFDM Amplfy-and- Forward Relay System wth Subcarrer Permutaton IEICE Trans. on Commun. Vol.E93-B no.5 pp. 6-3 May. [8] M. Herdn A chun based OFDM amplfy-and-forward relayng scheme for 4G moble rado systems n Proc. of the IEEE ICC 6 Istanbul Turey 6.
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