Internationa Journa of Appied Engineering Research ISSN 973-456 Voume 3, Number 5 (8) pp. 77-83 Research India Pubications. http://www.ripubication.com Effect of Estimation Error on Adaptive -MRC Receiver over Nakagami-m Fading Channes Bhargabjyoti Saikia,*, Rupaban Subadar, Department of Eectronics and Communication Engineering, Nor Eastern Hi University, Meghaaya, India. Abstract One of e key chaenges in wireess communication is to deiver high speed data, using a imited bandwid, among a arge group of user. Adaptive diversity receiver is a very popuar potentia soution in wireess system design, to achieve is goa. However, e idea estimation technique which is considered to optimize e performance of a diversity receiver is difficut to impement. Hence, in a practica scenario, e system performance of a diversity receiver is consideraby degraded. In is paper e expression for average bit error rate (ABER) and outage probabiity has been derived and studied for an arbitrary branch maximum ratio combiner (-MRC) system for different moduation techniques over Nakagami-m fading channes considering estimation error. Keywords: Adaptive MRC receiver, Estimation Error, Nakagami-m fading, ABER, Outage Probabiity, SNR, QAM, PS INTRODUCTION Diversity technique is one of e very effective techniques to reduce e adverse effect of fading at e receiver. Though ere are numbers of diversity techniques are ere, among ese, e maximum ratio combining (MRC) is considered to be best for its optima potentia. Adaptive techniques furer increase e performance of a receiver. Here e transmitter power and e rate of data transmission can be adapted depending on e channe information from e receiver. Therefore, eoreticay for optima outcome, e receiver shoud have e perfect estimation of e phase and e enveope information of e received signa []. However, in practice, e perfect estimation of phase or enveop is quite arduous and so e design of an optima receiver is aso chaenging [4]. In is study, e effect of phase and enveop estimation error has been anayzed in terms of ABER and outage probabiity for an arbitrary branch MRC receiver (- MRC), considering different moduation schemes over Nakagami-m fading channes. From e anaysis, it can be distinguished at, for different moduation schemes, ere is a very remarkabe effect of phase and enveop estimation error, on e receiver performance. In [] a study on capacity anaysis has been carried out for an -MRC receiver over Nakagami-m fading channes for different power and rate adaptation schemes. In [3] e capacity anaysis of an adaptive singe antenna receiver has been shown over Nakagami-m fading distribution. Then cosed-form expressions has been evauated for e outage probabiity, spectra efficiency and average bit-error-rate (ABER) assuming perfect channe estimation and negigibe time deay between channe estimation and signa set adaptation. The impact of time deay on e BER of an adaptive M-QAM aso has been presented in is paper. The effective receiver output SNR statistics and outage probabiity have been presented for an MRC receiver, over Rician fading channes wi channe estimation error in [4]. In [5], e performance anaysis of a generaized seection combining (GSC) and an equa gain combining (EGC) receiver has been given, considering Gaussian weighting errors over Rayeigh, Rician, Nakagami-m and Nakagami-q fading channes. In [6] different fading channes incuding Nakagami-m and different system have been described and anayzed. Capacity anaysis for an adaptive SC and MRC receiver has been done considering correated Hoyt fading distribution in [8]. Performance anaysis of a dua MRC receiver has been presented over correated Hoyt fading channes is presented in [9]. Maematica expression of e SNR PDF of e receiver, outage probabiity and ABER has been evauated in e paper wi a perfect channe estimation. In [] e performance of an -independent branch and dua correated branch, SC receivers are anayzed over Hoyt fading channes. A new bit error probabiity expression for m-ary phase-shift keying (M- PSK) has been presented for bo additive white Gaussian noise (AWGN) and fading channes in []. In [] e outage probabiity and ABER of arbitrary branches of an arbitrary branch MRC receiver over TWDP fading channe has been discussed. Capacity anaysis of a dua-mrc system for e adaptive schemes, optimum rate adaptation (ORA) and channe information wi fixed rate (CIFR) schemes has been studied in [3], over correated Nakagami-m fading channes wi non-identica fading parameters. In [4] an optima power aocation scheme has been studied for spectrum sharing between transmitter and receiver wi estimation error over Rayeigh fading channe. Two asymptotic cosed form bit error rate (BER) formuas have been presented in [5] considering a TWDP fading channe. Though a few works on imperfect channe estimation are avaiabe in iterature sti more investigation is required for * Corresponding auor. E-mai address: bhargab.8@gmai.com 77
Internationa Journa of Appied Engineering Research ISSN 973-456 Voume 3, Number 5 (8) pp. 77-83 Research India Pubications. http://www.ripubication.com different scenarios. This generates a motive to derive e unknown ABER and outage probabiity performance measures of a arbitrary branch MRC receiver over Nakagamim fading mode. The rest of e paper is organized as foows. In section channe and system mode is discussed. ABER for e considered system has been evauated in section 3. In section 4 outage probabiity of e system is evauated. The resut and anaysis are presented in section 5. Finay e paper is concuded in section 6. CHANNES AND SYSTEM MODE Figure : System mode for imperfect channe estimation The mentioned wireess system in Figure is an -MRC system wi arbitrary number of antennas wi a feedback pa from e receiver to e transmitter. In is considered mode, receiver estimates e channe condition depends on e received mutipa signas and sends e estimated information to e transmitter. From e estimated channe information transmitter adjust its transmitted signa power and rate of data transmission []. In our anaysis e channe is treated as sow and frequency non seective wi Nakagami-m distribution which is e best fit for e muti custer channes. For e channe, e received signa over i bit duration can be represented as [], j y i e x i n i () where x(i) is e transmitted symbo in i interva, wi energy E x = E[ x(i) ] and noise vector n(i) = [n (i), n (i),, n (i)] T, is e compex Gaussian noise having zero mean and two sided power spectra density N. In e considered mode, is e phase and represents e Nakagami-m distributed fading ampitude. The enveop pdf ( Nakagami-m distributed received signa is given by [6], m m m m exp ; m m ) of a where, E is e mean square vaue of a random variabe (RV) is and m is e Nakagami fading parameter ( m ). For imperfect channe estimation (ICE), if e channe vector at e receiver side is denoted as i i,..., i ˆ ˆ ˆ T (), e estimation error at each branch can be represented as, e i i i. A fexie mode for such estimation error, of an arbitrary inear channe estimation is presented in [4] as, i ˆ i z i (3) f, f, f, where, =,, 3,..,, f is e diffused component and e errors z f, i are e iid (independent identicay distributed) equivaent estimation error terms wi zero mean (=) and variance. In e equation, is symboized as z e standardized estimation correation coefficient between e enveope i i, and can be represented as and j e, where ˆ is e phase offset of. In case or or of imperfect channe estimation, bo, which degrades e receiver performance [4]. Effective Output SNR wi ICE In presence of estimation error, to detect e transmitted symbo xi at e MRC receiver, e hep of e compex decision variabe (DV) have to take, which is given as, D ˆ ir i ˆ [5]. Now appying e haf pane decision meod as given in [], e compex DV D wi be rotated wi a pane ange to obtain a new DV as, D De j (4) 78
Internationa Journa of Appied Engineering Research ISSN 973-456 Voume 3, Number 5 (8) pp. 77-83 Research India Pubications. http://www.ripubication.com where,, N is e consteation size. So N considering e haf pane decision meod for a DV D, e effective output SNR of a MRC receiver is given as [4], MRC B ˆ (5) ICE where, B is a function of and given by, B cos og N, ˆ ˆ N. og N PDF of -MRC receiver output SNR, over Nakagami-m fading channe, wi error estimation To diminish e uncompimentary effect of fading in an MRC scheme, non-identica, attenuated and time deayed mutipa components are weighted adequatey and co-phased before combining. The expression of e output SNR of an branch MRC system can be represented as [], MRC ICE (6) The SNR pdf for branch of e MRC system can be expressed as [], m m m m exp m where, instantaneous SNR per symbo is given by E N, e average SNR per symbo is s s E N,. (7) is a Gamma function and Es is e energy per symbo. From (7), doing some maematica cacuation, foowed by a random variabe transformation a cosed-form expression of SNR PDF for Nakagami-m distribution of MRC receiver is given by [], m m m exp m m In is anaysis, it has been considered at e variation in e combiner output SNR is not tracked perfecty by e receiver and is variation has been sent back to e transmitter via a time varying feedback pa. So eq.(8) can be expressed in terms of imperfect channe estimation considering e random variabe mutipication wi error parameter B as per e equation given in eq.(5). Then e modified SNR pdf for Nakagami-m fading wi estimation error can be represented as, ˆ ˆ m m m m B ˆ B ˆ expm B m ABER OF -MRC RECEIVER OVER NAKAGAMI-M FADING WITH ESTIMATION ERROR ABER expression for an -MRC receiver can be derived by substituting eq.(9) in e foowing eq. as given in [6], ˆ (8) (9) P P e ˆ ˆ d ˆ () e a ˆ ˆ ˆ b, for different coherent moduation. Vaues of a and b are given in Tabe:. where, Pe aq b Substituting eq. (9) and e vaues of Pe ˆ in eq. () it can be represented as, m mb ˆ m m ˆ a m b P ˆ, exp ˆ e B d B m () Now soving e integra as given in [7; 6.455() ], e ABER expression for Nakagami-m fading wi m-array coherent moduation can be expressed as, b m m m ab m mb Pe F, m, m, Bm m mb b mb b m () 79
Internationa Journa of Appied Engineering Research ISSN 973-456 Voume 3, Number 5 (8) pp. 77-83 Research India Pubications. http://www.ripubication.com b Tabe : Vaues of a and b for considered coherent m-ary moduations a -.5 4(M-)/M BFSK - - - BPSK - sin (/M) - M-PSK - 3/(M-) - - M-QAM OUTAGE PROBABIITY OF -MRC RECEIVER OVER NAKAGAMI-M FADING WITH ESTIMATION ERROR Outage probabiity can be defined as e instantaneous error probabiity which exceeds a specified vaue or equivaenty, e output SNR, ˆ,fas beow a particuar reshod vaue. The outage probabiity can be expressed from e equation,as given in [9], Pout ˆ ˆ d ˆ (3) Now substituting eq.(9) in eq.(3) and soving e integra using [7, 3.38()], e fina outage probabiity expression for Nakagami-m fading wi estimation error can be derived as, P out m m m m B mb mb g m, B m (4) Eq. (4) furer can be simpified as, P out mb g m, m (5) RESUTS AND ANAYSIS Figure : ABER anaysis wi ICE for different QAM schemes 8
Internationa Journa of Appied Engineering Research ISSN 973-456 Voume 3, Number 5 (8) pp. 77-83 Research India Pubications. http://www.ripubication.com The obtained resuts in e above sections has been numericay evauated and potted to anayze e behavior of e -MRC adaptive receiver wi estimation error over Nakagami-m fading channes. From fig: to fig:4 e ABER anaysis has been presented. In fig: for a constant m (m=.5), fixed number of receiver branch (=) and different M-QAM, ABER anaysis has been performed for various enveop ( ) and phase estimation error ( ). In is fig it can be ceary observed at, wi estimation error ( =.999 and = ) e ABER is remarkaby increased an e perfect channe estimation ( = and = ). The ABER furer increases, if bo enveop and phase estimation errors = 5 have been considered ( =.999 and rad ). On e oer hand, wi e increase of consteation size e ABER is aso increased. In fig:3, for m= and m=.5 e effect of ICE has been anayzed in terms of ABER for arbitrary number of antennas. From e fig: 3 it can be observed at for a constant m parameter (m= or m=.5) and estimation error, e ABER is decreased wi e increase of e number of antennas at e receiver (In is case when - =3). But for a particuar receiver (= or =3), e increase of m parameter indicates e decrease of ABER vaues accordingy. The effect of M-QAM and M-PSK moduation on ABER wi ICE has been presented in fig:4, for a constant enveop error ( =.98) and m parameter (m=3) considering a dua MRC receiver. Here it can be observed at, in bo moduation schemes e ABER is consideraby increased wi increase of consteation size. However in case of M-PSK e ABER is comparativey ow an e M-QAM scheme. Therefore ABER becomes quite ow when we consider BPSK (-PSK) moduation. In fig:5 outage probabiity anaysis for a -MRC receiver has been presented considering estimation error at e receiver. From e figure it can be observed at, ike ABER wi e increase of consteation size e outage probabiity of e receiver is aso increased. On e oer hand considering enveop estimation error or phase estimation error or considering bo, e outage probabiity increased remarkaby an e perfect channe estimation (when = and = ). However from e figure it is aso ceary observabe at, irrespective of moduation scheme, e effect of enveop error is very high an e effect of phase error on e system. In fig:5, for 8- QAM moduation, for a considered SNR, e difference between e outage probabiity for =.999 and =.98 (wi no phase error) is higher an e outage probabiity where = 3 and 7 (wi no enveop error). Figure 3: ABER anaysis wi ICE for different M-QAM schemes & m parameters considering =,3 8
Internationa Journa of Appied Engineering Research ISSN 973-456 Voume 3, Number 5 (8) pp. 77-83 Research India Pubications. http://www.ripubication.com Figure 4: Effect of M-QAM & M-PSK moduation schemes on ABER wi ICE Figure 5: Outage probabiity anaysis wi ICE for a -MRC receiver (=3) CONCUSION In is paper wi ICE e expressions of ABER and outage probabiity of an -MRC receiver has been derived over Nakagami-m fading channes for different coherent m-ary moduation schemes. The ABER and outage probabiity expression has been obtained, using SNR PDF and conditiona error probabiity of coherent moduation schemes. From e anaysis, it can be concuded at, e estimation error has a very strong impact on e wireess system performance. On e oer hand e used moduation scheme has a remarkabe impact on it. The obtained resuts are verified wi Monte Caro simuation. 8
Internationa Journa of Appied Engineering Research ISSN 973-456 Voume 3, Number 5 (8) pp. 77-83 Research India Pubications. http://www.ripubication.com REFERENCES [] M.K. Simon and M.S Aouini, A unified approach to e performance anaysis of digita communication over generaized fading channe, IProc IEEE, Vo. 86, pp.56 64, September 998 [] M.S. Aouini and A.Godsmi,"Capacity of Nakagami mutipa fading channes," IEEE Vehicuar Technoogy Conference, vo, pp 358-36, May 997 [3] Mohamed-Sim Aouini and Andrea J. Godsmi, Adaptive Moduation over Nakagami Fading Channes, Wireess Persona Communications, Voume 3, Issue, pp 9 43, May [4] Y. Ma, R. Schober and S. Pasupay, Effect of channe estimation error on MRC diversity in Rician fading channes, IEEE Trans. on Vehicuar Tech., Vo. 54, pp. 37 4, November 5 [5] Y. Ma, R. Schober and S. Pasupay, "Performance of M-PSK wi GSC and EGC wi gaussian weighting errors," IEEE Trans. on Vehicuar Tech., vo. 54, pp. 49-6, January 5 [6] M.K. Simon and M.S. Aouini, Digita Communication over Fading Channes, John Wiey and Sons Inc., USA [7] I.S. Gradshteyn and I.M. Ryzhik Tabes of Integras, Series and Products, Esevier Inc., 7 [8] R. Subadar, P.R. Sahu, Capacity anaysis of dua- SC and MRC system over correated Hoyt fading channe," IEEE TECON, pp-5, January 9 [9] R. Subadar and P. R. Sahu, Performance Anaysis of Dua-MRC Receiver in Correated Hoyt Fading Channe, IEEE Communication etters, Vo 3 (6), pp 45-47, June 9. [] R. Subadar P.R. Sahu,"Perfromance of - independent and Dua Correated Seection Combiners in Hoyt Fading Channes," IEEE Transaction on Communications, Vo 59, No 4, pp 93-99, Apri [] Jeong Woojin, ee Jaeyoon and Yoon Dongweon,"New BER Expression of MPSK," IEEE Trans. on Vehicuar Technoogy, Vo. 6.No 4, pp 96-94, May. [] R. Subadar and A.D. Sing, Performance of M-MRC receivers over TWDP fading channes, Int. J of Eectron. Commun. (AEU), Vo. 68, pp.569 57, June 4 [3] P.B. Devi, A. Yengkhom, M. I. Hasan and G. Chandwani, Capacity of dua branch MRC system over correated Nakagami-m fading channe wi nonidentica fading parameters and imbaanced average SNRS, Internationa Journa of Wireess and Mobie Computing, Vo. 3, No., pp.5 63, September 7 [4] S. Pandit and G. Sing, Capacity imits over fading environment wi imperfect channe state information for cognitive radio networks, Spectrum Sharing in Cognitive Radio Networks, pp.77 99, Apri 7 [5] D. Kim, H. ee and J. Kang, Comprehensive anaysis of e impact of TWDP fading on e achievabe error rate performance of BPSK signaing, IEICE Transaction on Communication, Vo. E-B, No., pp.5 57, August 7 83