Effect of Pulse Shaping on BER Performance of QAM Modulated OFDM Signal

Transcription

1 Eect o Plse Shapng on BER Perormance o QAM Modlated OFDM Sgnal D.K. Sharma, A. Mshra and Rajv Saxena Ujjan Engneerng College, Ujjan, MP, Inda Madhav Insttte o Technology & Scence, walor, MP, Inda Jaypee Insttte o Engneerng & Technology, na, MP, Inda E-mal: dlp_sharma7@yahoo.com; drabhaymshra@yahoo.com; rajv.saxena@jet.ac.n Abstract Plse shapng o a sgnal at base-band orms a more mportant tool n controllng and analyzng the parameters lke ISI, the modlated sgnal envelope normty, the phase contnty as these parameters lead to the ecent spectral connement o a bnary sgnal whch s a tre and nowadays a major mportant aspect n the desgn o a wreless celllar commncaton system. In ths paper, erent tme-lmted waveorm are dscssed whch are bascally avalable as wndows nctons and comparng the perormance o Rectanglar, Rased ne and BT and prove that the BT plse s spposed to be a batter plse shapng or OFDM n terms o obtanng better BER perormance and proposed two plse shapes whch are gvng better E[ ] n respectve cases whch n trn provdes better BER as compared to BT whch was consdered as one o the best plse shape. Keywords: Inter Symbol Intererence, Inter Channel Intererence, Sgnal to Nose Rato, Bt Error Rate. Introdcton A lnear lter channel dstorts the transmtted sgnal and the parameter lke ISI s an ndesred overlap o the neghborng symbols both n tme and n phase. The channel dstortons reslts n ISI at the otpt o the demodlator whch leads to an ncrease n ISI at the otpt o the demodlator and leads to an ncrease n the probablty o error at the detector and hence BER perormance s degraded. reater ISI allows the spectrm to be more compact, makng demodlator more complex, hence, spectral compactness s the prmary trade-o n gong rom one type o plse shapng to other type.e. the plse shapng can take care o the BER perormance o the OFDM system and can be a major tool to redce the ISI and ICI eects ecently n an OFDM system [, ]. The premodlaton low pass lter (LPF mst have a narrow Bandwdth wth sharp cto reqency and very lttle overshoot n ts mplse response. In ths paper, erent tme-lmted waveorm are dscssed whch are bascally avalable as wndows nctons. The synthess o wndow ncton s an mportant technqe or plse shapng [], [] and the plse shapng gves a consderable perormance mprovement o OFDM systems n mltpath rado channels as compared to the conventonal OFDM. Thereore, wndowng nds a wde and large area o applcatons extendng rom spectrm estmaton, dgtal lterng, speech processng, srace acostc wave (SAW lter desgn [], [5] and many other elds o commncaton and sgnal processng. An exhastve revew o many plses shapng nctons or tme lmted waveorm s done on the bass o ther applcaton and characterstcs n [] wth a conclson that the Comparng the perormance o Rectanglar, Rased ne and BT, the BT gves smaller eqvalent nose power and hence lower BER vales. Thereore, the BT plse s spposed to be a batter plse shapng or OFDM n terms o obtanng better BER perormance [6]. There ater a good nmber o wndows have been proposed by varos athors wth some perormng better n the reqency doman and some n the tme doman. A concse comparatve stdy has also been perormed n erent way [7]. The man crteron or the selecton o a wndow s applcaton orented, means that whether the applcaton reqres better spectral perormances or the better tme doman perormances [8] and t can be conclded that the two proposed plses are gvng better E[ ] n respectve cases whch n trn provdes better BER as compared to BT whch was consdered as one o the best plse shape [6]. ICI IN OFDM The plse shapng plays a major role n mprovsng the Bt Error Rate (BER perormance o modlated OFDM system [9], [7], snce the BER s related to the sgnal to nose rato (SNR o a sgnal where sgnal power s spposed to be the second moment o the ampltde o the plse shapng sgnal, where t can be observed that the role o actor s present n the second moment o ampltde whch ndcates that the role o actor s responsble or the perormance o BER o the sgnal. Ths ndcates that a play n the role o actor or a partclar plse shapng can mprove the BER perormance. Snce, ICI power s the nothng bt the mean sqare vale o an ICI term present n an OFDM transmtted sgnal and s dependent on the ampltde or magntde o the weghtng ncton whch s otherwse also known as plse shapng ncton. Ths, t s evdent that the play n the role o actor o a plse shape wll aect the ICI power also o the transmtted OFDM sgnal. [Page No. 66]

2 Eect o Plse Shapng on BER Perormance o QAM Modlated OFDM Sgnal Ths, n order to analyze varos plse shapes n the lght o BER perormance rstly the ampltde moment o each o them has to be calclated, the ICI o an OFDM sgnal s calclated as per eqaton (. where, mperect carrer oset (ICI Ν Ν Ν [ k] g( kτ a l, Cl m a a C ( k k m l k k m k km and the eqvalent nose E[ ] n geometrcal progresson (. P. s derved as- Ν ( ak ( Ck m k [ ] ( C k m ( k [ ] g ( kτ dτ g ( t replacng the actor (- Kt - τ by t as- [ ] g ( t dt ( k ( whch s nothng bt the Parseval s Theorem. Types o Plse Shapes n OFDM As lot o plse shapng nctons have been desgned, optmzed and appled or varos applcatons, wth a reslt some perormng better n tme doman whereas some n reqency doman. In ths secton some most commonly sed plse shapng nctons whch dene a class o modlaton technqes are nclded [, -, & ]. Case-I: The Rectanglar Plse ( rect ( Case-II: Rased Cosne ( Plse (, or (, or ( (, otherwse (5 where, the alpha ( s known as the plse shapng actor les. dt Case-III: Better than Rased Cosne (BT Plse (, or log ( e, or log ( ( e, or, otherwse (6 Ths, the BT plse shape has a small BER n presence o ISI and symbol tmng error n an OFDM or base band system n comparson to the rectanglar and rased ne plse modlated system and a BT modlated sgnal represents a better eye dagram wth respect to that o the Rectanglar and Rased ne modlaton [6]. Case-IV: Proposed-I Plse Shapes (, or ( / ( ( /, or, otherwse (7 where, s role o actor les n between zero and one and s the weghtng coecent o proposed-i sch that. Case-V: Proposed-II Plse Shape (, or ( (, or, otherwse (8 where, ( s the weghtng coecent o proposed-ii plse shape and s roll o actor o proposed-ii plse shapes. These above sad plse shapes are expected to provde better BER perormance than the other plse shapes dened earler n ths secton. Eect o Plse Shapng on BER Perormance n OFDM Case-I: Eect o Rectanglar Plse Shapng on BER Consderng the spectrm o a rectanglar plse rom eqaton ( and sng eqaton ( the second moment or power contaned n ths type o plse can be evalated as- [Page No. 67]

3 5 th IEEE Internatonal Conerence on Advanced Comptng & Commncaton Technologes [ICACCT-] ISBN [Page No. 68] (9 Case-II: Eect o Plse Shapng on BER Consder the spectrm o plse rom eqaton (5 and sng the eqaton ( or evalatng the second moment as- d d d ( Case-III: Eect o BT Plse Shapng on BER Consder the spectrm o BT plse rom eqaton (6 sng the eqaton ( or evalaton o second moment or ths type o plse as- log exp log exp log 8 log log 8 log ( Case-IV: Eect o Proposed-I Plse Shapng on BER Consder the spectrm o Proposed-I plse rom eqaton (7 sng the eqaton ( or evalaton o second moment or ths type o plse as- at /, above eqaton becomes as ( Case-V: Eect o Proposed-II Plse Shapng on BER Consder the spectrm o Proposed-II plse rom eqaton (8 sng the eqaton ( or evalaton o second moment or ths type o plse as- at, /, above eqaton becomes as- / ( / 8 / /

4 Eect o Plse Shapng on BER Perormance o QAM Modlated OFDM Sgnal [ ] 9 ( Reslt and Dscsson: Ths, the overall plse shapng perormance n OFDM QAM based system as dscssed n case o Rectanglar, Rased Cosne, BT, Proposed-I and Proposed-II plse shapes can be smmarzed and comparsons between the mean sqare vale o ICI terms n all ve cases s presented n Table-. Table-: The vale o E[ ] or erent types o plse shapes n OFDM wth QAM. Types o Plse Shapes Rectanglar Plse Plse BT Plse Proposed-I Plse Proposed-II Plse Second Moment [ ] R [ ] BT BT[ ] log 57 Pr Pr oposed I [ ] 6 9 Pr Pr oposedii [ ] oposed I oposedii In order to mantan the same BER perormance, t s mandatory that the eqvalent nose power mst be eqvalent to each other,.e. [ ] [ ] Hence, BT. 69 BT BT or log ( Bt, t s clear rom eqaton ( and ( that BT plse has lower eqvalent nose power; thereore t wll have better BER perormance as compared to Rectanglar and plses. The second moment o Intererence I completely descrbed the assan dstrbton and ts varance dened as- Var [] Ι [ Ι ] Ω L Ρ [ ] Ι σ ICI (5 The vale o E[ ] s derved n eqatons (9- or erent types o plse shapes n OFDM wth QAM. The total eqvalent nose power s dened as- σ Var Ι (6 t [] Hence, average BER, condton on R s, s dened by- Q Ρ s r σ t Ρ b R r s s s (7 - E[ ] Var[I] - σ t P b (BER (8 eq. (5 to 9 - eq. (-eq. (-eq. ( (9 Conclson It s observed that the BER perormance obtaned rom the assan Approxmaton depends only on total ntererence sgnal power as per eqaton (5. It s also observed that larger vale o gves smaller vale or mean sqare vale {E[ ]} and hence smaller vales or Var[I] and σ t, as rom eqaton (7, t s clear that the BER wll also be correspondngly redced. Thereore, rom the assan Approxmaton eqaton (7, t s clear that the vale o excess bandwdth provdes a tradeo between spectral ecency and detecton perormance n an OFDM system. Comparng the perormance o Rectanglar, Rased ne and BT orm eqaton (9 to (, the BT gves smaller eqvalent nose power and hence lower BER vales. Thereore, the BT plse s spposed to be a batter plse shapng or OFDM n terms o obtanng better BER perormance [6]. It can be conclded that the two proposed plses are gvng better E[ ] n respectve cases whch n trn provdes better BER as compared to BT whch was consdered as one o the best plse shape [6]. Reerences [] A. Mshra, R. Saxena and Y. M. pta, Sgnalng Technqes n CPM, Indan Jornal o Telecommncatons, vol. 5, no., pp. 9-9, Jly- Agst. [] H.. Ry, C. X. Wang and S. B. Ry, Nonlnear Dstorton Redcton or the Improvement o the BER Perormance n OFDM Commncaton Systems, IEEE Proceedngs o Internatonal Symposm on Commncatons and Inormaton Technologes, pp. 66-7, 7. [] J. K. atam, A. Kmar and R. Saxena, WINDOWS: A Tool n Sgnal Processng, IETE Techncal Revew, vol., no., pp. 7-6, May-Jne 995. [] A. Vallavaraj, B.. Stewart and D. K. Harrson, An evalaton o moed µ-law compandng to redce the PAPR o OFDM systems, Internatonal Jornal o Electroncs and Commncatons (AEU, vol. 6, pp ,. [5] R. Saxena and K. Sngh, Fractonal Forer Transorm: A Novel Tool For Sgnal Processng, Jornal o the Indan Insttte o Scence, vol. 85, no., pp. -6, Jan.-Feb. 5. [6] P. Tan and N. C. Beale, Redced ICI n OFDM systems sng the better than rased-ne plse, IEEE Commncaton Letters, vol. 8, pp. 5-7, Mar.. [7] P. Tan and N. C. Beale, Improved BER perormance n OFDM system wth reqency oset [Page No. 69]

5 5 th IEEE Internatonal Conerence on Advanced Comptng & Commncaton Technologes [ICACCT-] ISBN by novel plse-shapng, IEEE Commncatons Socety, lobecom, pp. -6,. [8] R. Sood and H. Xao, Root Nyqst Plses wth an Energy Crteron, IEEE Commncatons Socety the ICC 7 proceedngs, pp. 7-76, Jne 6, 9. [9] P. K. Vtthaladevn, M. S. Alon and J. C. Keer, Exact BER comptaton or cross QAM constellatons, IEEE Transactons on Wreless Commncatons, vol., no. 6, pp. 9-5, November 5. [] J. K. atam, A. Kmar and R. Saxena, Correcton to and Comments on-mnmm Bas Wndow or Hgh Resolton Spectral Estmates, IEEE Transacton on Inormaton Theory, vol., no., pp., May 996. [] J. K. atam, A. Kmar and R. Saxena, On the Moed Bartlett-Hannng Wndows (Famly, IEEE Transacton on Sgnal Processng, vol., no. 8, pp. 98-, Agst 996. [] N. C. Beale and P. Tan, On the Eects o Recever Wndowng on OFDM Perormance n the Presence o Carrer Freqency Oset, IEEE Transactons on Wreless Commncatons, vol. 6, no., pp. -9, Janary 7. [] R. U. Mahesh and A. K. Chatrved, Closed Form BER Expressons or BPSK OFDM Systems wth Freqency Oset, IEEE Commncatons Letters, vol., no. 8, pp. 7-7, Agst. Fg. : Tme doman o Proposed-I Plse or erent vale o,.5 & Tme doman waveorm o rased ne plse shapng lters.8 rc alpha. rc alpha btrc alpha. btrc alpha am pltde, g(t Fg. : Tmes doman Representaton o Proposed-II Plse Shape or erent vale o tme, t Fg. : and BT plotted n tme doman or erent vale o [Page No. 7]