Effect of Channel Estimation Errors on the Performance of a M-MRC Receiver over TWDP Fading Channels

Transcription

1 Internatona Journa of Apped Engneerng Reearch ISSN Voume 3, Number 8 (8) pp Reearch Inda Pubcaton. Effect of Channe Etmaton Error on the Performance of a -RC Recever over TWDP Fadng Channe hargabyot Saka and Dr. Rupaban Subadar Reearch Schoar, Aocate Profeor,, North-Eatern H Unverty (NEHU), Shong, eghaaya. Abtract To meet the demand hgh-peed data requrement mutantenna (dverty) ytem are we-accepted technque. Thee type of communcaton recever ue etmator to optmze the performance. However, an dea etmator chaengng to obtan whch ead degradaton of the expected performance of the dverty ytem. Th paper anayze the outage and average bt error rate (AER) performance of an arbtrary branch maxma rato combnng (RC) recever over two wave dffue power (TWDP) fadng channe wth error n the etmator. The anay of the obtaned reut how that the etmaton error a gnfcant component of the degn apect and can t be negected. Keyword: Etmaton error, AER, RC recever, Coherrent moduaton, TWDP fadng. INTRODUCTION To mtgate the advere reut of the fadng, dverty technque popuary empoyed n the wree recever degn. Among the prmary dverty combnng technque, maxma rato combnng (RC) dever optma performance. However, the performance hghy depended on the channe etmator. The optmum reut theoretcay etabhed conderng perfect phae and an enveope etmaton of the channe []. However, n practce, both phae and the enveope etmaton error are typca, and o the optma recever degn a omewhat chaengng tak []. In th paper the performance degradaton of the RC recever by phae and enveop etmaton error ha been anayzed, n term of outage probabty and AER. From the anay, t can be een that the recever performance affected everey by the enveope etmaton error than the phae etmaton error. Two wave dffued power (TWDP) dtrbuted fadng mode a new mode propoed n the year [3]. It cont of two domnant path aong wth the dffuey propagatng wave component and atfactory agree wth the practcay obtaned data. A a partcuar cae the other we-accepted fadng mode Rayegh, Rcan, One wave fadng mode can be derved from th. In a propagaton cenaro ke narrow band recever operaton, wdeband gna, drectona antenna, etc. TWDP may be oberved [4]. The coed form expreon of th fadng mode not avaabe, however; a uffcenty good approxmate coedform expreon ha been gven n [4] for dfferent vaue of K and. The performance anay of varou dverty recever over TWDP fadng channe wth perfect channe etmaton avaabe n the terature [5]-[]. The performance anay done for bnary hft keyng (PSK) pre detecton RC recever over TWDP fadng n [5]. In [6] foowng a moment generatng functon the average bt error rate of the RC recever over TWDP fadng channe ha been carred out. The capacty anay of arbtrary branche of eecton combnng (SC) recever ha been ntroduced n [7]. The ymbo error rate of an SC recever ha been preented n [8] for -ary phae hft keyng and quadrature amptude moduaton (QA) over TWDP fadng channe. The performance of arbtrary branche of SC recever ha been tuded n [9]. In [] the outage probabty and average bt error rate of arbtrary branche of an RC recever over TWDP fadng channe have been preented. After carefu npecton of the terature reated to the TWDP fadng channe wth dverty recever, we found that the etmaton error ha not been condered anywhere. Th paper preent the performance of an arbtrary branch RC recever over TWDP fadng channe, conderng both phae and enveope etmaton error. CHANNELS AND SYSTE ODEL Fgure : Sytem ode 3737

2 Internatona Journa of Apped Engneerng Reearch ISSN Voume 3, Number 8 (8) pp Reearch Inda Pubcaton. The ytem condered to receve mut-path gna ha an - RC ytem wth arbtrary no of antenna to mprove the gna quaty a demontrated n Fg.. The channe n th mode aumed to be ow and frequency non-eectve wth TWDP dtrbuton. The receved gna over th bt duraton can be gven a, where, y n () the tranmtted ymbo n th nterva, wth E energy E[ ] and noe vector,,..., T n n n n n, the compex Gauan noe havng zero mean and two ded power pectra denty N. In the condered mode,,,..., n T the channe coeffcent vector for branche and t eement are TWDP dtrbuted. The enveop pdf of a TWDP dtrbuted receve gna gven by [4], L r f exp k a D ; k, C () σ σ σ π( ) where, =Δco C L, D x; k, C expck I x k( C ) exp Ck I x k ( C ) K= Specuar power Dffued power, Peak Specuar Power Convenent parameter and Average Specuar Power L the order k. T L Conderng,...,, a the etmated channe vector at the recever de, the channe etmaton error at each branch can be condered a,{ e. A gven n [], a verate mode for channe etmaton error of any arbtrary near channe etmaton can be repreented a, z (3) f, f, f, where, =,, 3,.., L, f the dffued component and the error z f, L are the d equvaent etmaton error term wth zero mean and varance z. In (3) denoted a the normazed etmaton correaton coeffcent between and where, and can be wrtten a, e the phae offet of. In cae of ICE or both may are, whch degrade the recever or performance []. A. Effectve Output SNR of RC recever wth ICE Conderng ICE to detect the tranmtted ymbo () at the RC recever we have to take the hep of compex decon varabe (DV), whch gven a, r D []. Appyng the haf pane decon method [3] the compex DV D w be rotated wth a pane ange to obtan a new DV a, D De (4) where, and N the conteaton ze. N However, for PSK (=). So conderng the haf pane decon method for a DV D, the effectve output SNR of a RC recever gven a [], RC (5) ICE where, a functon of and gven by, co, N. 3738

3 Internatona Journa of Apped Engneerng Reearch ISSN Voume 3, Number 8 (8) pp Reearch Inda Pubcaton. OUTPUT SNR PDF OF TWDP WITH ESTIATION ERROR RC a technque where the receved gna are co-phaed and weghted a per ther SNR vaue to optmze the quaty of the output gna and expreon of the output SNR gven a [], E b RC... N (6) Where, ndex ued to repreent the th recevng antenna and we aume the average nput SNR etmaton error n a branche of RC recever, PDF of SNR for th branch can be gven a [], f a e I p L { } ( ) p (7). Conderng equa K ( ) where, the etmaton error of the recever and, p K ( ) Co L and the actua receved gna SNR. A per the (6) the output SNR of the -RC recever can be evauated by addng a the SNR of ndvdua branche. Foowng a charactertc functon baed approach, th output SNR can be derved a hown beow. The charactertc functon of the (7) can be derved a, ( ) 4 p L p 4( ) (8) ( ) a e e Snce we have condered the ndependent branche, therefore the ont charactertc functon of nput SNR can be obtaned by takng the product of each charactertc functon a, p L p ( t )... (,..., ) ae e t ( t ) (9) Repacng... n (9) and then wrtng the expreon n the ere form expreon one exponenta term n nfnte ere the charactertc functon of output SNR can be expreed a, (,..., )... p t t t a e p t t L L t t t......!( ) () The PDF of the output SNR of the -RC recever can be obtaned, takng the nvere Fourer tranform of the () ung [[6],3.38.7]a, L L p f ( ) mrc mrc e e ()! a p t t t t t t t t 3739

4 Internatona Journa of Apped Engneerng Reearch ISSN Voume 3, Number 8 (8) pp Reearch Inda Pubcaton. Expreng the above equaton n term of Hypergeometrc functon the coed form equaton of the PDF of the output SNR of the -RC recever wth etmaton error can be obtaned a, p t t t L L a e e t ( t ) ; ; t t t f F p () where, F a z the confuent hypergeometrc functon and. ; ; the gamma functon. IV.AER expreon for RC recever wth ICE In th ecton we have derved the AER expreon ung () and the genera formua of bt error rate gven n [4], P P e f d (3) e Where, Pe a condtona ER. For coherent bnary moduaton cheme P e Q a (4) Pe gven a [5], where, a= for PSK and a=.5 for FSK. Subttutng () and (4) n (3) and ovng the ntegra ung [[6],6.455()], the fna AER expreon can be wrtten a, P e, coh p t t t a ae p t t L L t t t......! b ( ) F, ; ; b b ( ) (5) Smpfyng eq.(5 ) the expreon can be rewrte a, P e, coh L L p t t t a ae t p t t t t! b( ) ( ) b b F, ; ; (6) 374

5 Internatona Journa of Apped Engneerng Reearch ISSN Voume 3, Number 8 (8) pp Reearch Inda Pubcaton. OUTAGE PROAILITY ANALYSIS FOR -RC RECEIVER WITH ICE When the ntantaneou error probabty exceed a pecfed vaue, or the output SNR, fa beow a partcuar threhod vaue th [] then t known a outage probabty. The outage probabty can be derved from the equaton,a gven n [], th P f d (7) out where, th the threhod SNR vaue. Now,ubttutng () n (7) and ovng the equaton ung [[6],3.38.] the fna expreon can be expreed for -RC ytem wth channe etmaton error a, p t t t a e p t t L L t t t......, th Pout g! (8) where g(.) the ower order ncompete Gamma functon. NUERICAL RESULTS AND ANALYSIS: Fgure : AER v SNR wth Enveope etmaton error 374

6 Internatona Journa of Apped Engneerng Reearch ISSN Voume 3, Number 8 (8) pp Reearch Inda Pubcaton. Fgure 3: AER v SNR wth Phae etmaton error Fgure 4: Outage v SNR wth Phae and Enveop etmaton error The reut obtaned n the prevou ecton ha been numercay evauated and potted to mnutey oberve the behavor of the ytem aong wth the etmaton error. In Fg. -4 AER and outage probabty have been found wth enveope ( ) and phae ( ) etmaton error for dfferent dverty order wth varyng channe condton. In Fg. effect of enveope etmaton error have been hown on coherent AER for varou dverty order. It ha been noted that for an error of % n the etmaton to mantan a bt error rate of -4 approxmatey extra 8 d power needed wth dua dverty. Same may ao be oberved n hgher order dverty branch. Smary, n Fg.3 the AER v. SNR hown for varou phae error n coherent PSK moduaton. Fg.4 how the outage probabty anay wth both phae and enveope error. From th anay, we oberved that the expected beneft of dverty mght not be achevabe f the etmator ue are not perfect. 374

7 Internatona Journa of Apped Engneerng Reearch ISSN Voume 3, Number 8 (8) pp Reearch Inda Pubcaton. CONCLUSION In th paper the anay of an - RC recever wth etmaton error ha been preented n term of AER and outage probabty over TWDP fadng channe. An output SNR PDF expreon of an -RC recever wth ICE ha been cacuated foowed by a CF baed approach. From the cacuated SNR PDF the AER and outage probabty expreon wth ICE ha been obtaned and potted. From the tudy t can be concuded that, nce an -RC recever requre the etmator to optmze the performance; o f the etmate are not perfect, then f the SNR degraded conderaby, the practca appcaton of -RC neffcent. However, ncreang the no of antenna at the recever de the recever performance can be ncreaed. REFERENCES [] Smon K, Aoun S, "A unfed approach to the performance anay of dgta communcaton over generazed fadng channe" Proc IEEE 998; 86(September(9)); [] Y. a, R Schober and S Paupathy, "Effect of channe etmaton error on RC Dverty n Rcan Fadng Channe" IEEE Tran.on Vehcuar Tech.5; 54(November); [3] G.D. Durgn, T.S. Rappaport, New Anaytca ode and Probabty Denty Functon for Fadng n Wree Communcaton, IEEE Tranecton on Communcaton; 5 (6); ();5-5. [4] Frok J,"A cae for conderng Hyper-Rayegh fadng channe" IEEE Tranacton Wree communcaton 7; 6(Apr); [5] Oh SH, L KH and Lee WS,"Performance of PSK pre-detecton RC ytem over two-wave wth dffue power fadng channe", IEEETran.Wree Communcaton;7; 6(Augut); [6] Lu Y. Yang N.,"Symbo error probabty of QA wth RC dverty n two wave wth dffued power fadng channe" IEEE Communcaton Letter ; 5(January;-. [7] Sng AD, Subadar R.,"Capacty anay of -SC recever over TWDP fadng channe" Int. J Eectron Communcaton (AEU) 4;68(February); [8] Tan S,L KH, Teh KC,"Symbo error rate of eecton combnng over Two Wave Dffued Power fadng" IEEE ICSPCS. [9] Subadar R.,Sng AD," Performance of SC recever over TWDP fadng channe" IEEE WCL 3; (June);67-7. [] Subadar R.,Sng AD," Performance of -RC recever over TWDP fadng channe" Int. J of Eectron.Commun.(AEU);4; 68(January); [] Y. a, Schober.R.and Paupathy S.,"Effect of channe etmaton error on RC Dverty n Rcan Fadng Channe" IEEE Tran. on Vehcuar Tech. 5; 54(November); pp [] Y. a, Schober.R.and S. Paupathy,"Performance of -PSK wth GSC and EGC wth gauan weghtng error" IEEE Tran. on Vehcuar Tech. 5; 54(January ); pp [3] Jeong Woon, Lee Jaeyoon, and Yoon Dongweon, "New ER Expreon of PSK"IEEE Tran. on Vehcuar Technoogy ; 6(4(ay)); pp [4]. K. Smon and.s. Aoun, "Dgta Communcaton over Fadng Channe" John Wey and Son Inc.; 5. [5] Aao V. A., "Performance of maxma-rato dverty ytem n a correated Nakagam-fadng envronment" IEEE Tran. on Commun.995; 43(8(Augut)); pp [6] I.S. Gradhteyn and I.. Ryzhk "Tabe of Integra, Sere And Product," Eever Inc,