On Channel Estimation of OFDM-BPSK and -QPSK over Generalized Alpha-Mu Fading Distribution

Transcription

1 Int. J. Communcatons, Network and System Scences, 010, 3, do:10.436/jcns Publshed Onlne Aprl 010 ( On Channel Estmaton of OFDM-BPSK and -QPSK over Generalzed Alpha-Mu Fadng Dstrbuton Abstract Neetu Sood, Ajay K. Sharma, Mon Uddn Natonal Insttute of Technology, Jalandhar, Inda Emal: Receved January 9, 010; revsed February 11, 010; accepted March 18, 010 Ths paper evaluates the performance of OFDM-BPSK and -QPSK system n -µ dstrbuton. A fadng model whch s based on the non-lnearty present n the propagaton medum s utlzed here for generaton of -µ varants. Dfferent combnatons of and µ provdes varous fadng dstrbutons, one of whch s Webull fadng. Investgatons of channel estmaton schemes gave an dea of further reducng the as to mprove the performance of OFDM based systems. In flat fadng envronment, channel estmaton s done usng phase estmaton of the transmtted sgnal wth the help of traned symbols. Fnal results show the mprovement n. However, the amount of results mproved depends upon the amount of traned symbols. The more traned symbols wll result nto more mproved. Keywords: OFDM, Fadng Dstrbuton, Webull Fadng, Nakagam Fadng, Channel Estmaton, Tranng Symbols 1. Introducton In recent years, OFDM have been studed very wdely and deeply n wreless communcaton systems because of bandwdth effcency and ts robustness to channel fadng and Inter Symbol Interference (ISI). OFDM system s capable of mtgatng a frequency selectve channel to a set of parallel fadng channels, whch need relatvely smple processes for channel equalzaton. There exsts a large number of dstrbuton schemes to descrbe the statstcs of moble rado sgnal. A key assumpton n the theoretcal explanaton of the Raylegh, Rcan, Nakagam and Webull dstrbuton was that the statstcs of the channel do not change over the small (local) area under consderaton. However, to descrbe the long-term sgnal varatons lognormal dstrbuton s beng used [1]. These dstrbutons are helpful n precse desgnng of wreless systems to make the systems more robust to nose. Raylegh and Rcan fadng channels have already been studed and employed n OFDM systems n frequency selectve and flat fadng envronment. Nakagamm dstrbuton s another useful and mportant model to characterze the fadng model. A threshold value of m s calculated for both frequency and flat fadng envronment n []. There exst many other fadng models n lterature, whch have been proposed for better fttng of data whle amng at non-lnearty of channel. So our motvaton behnd ths paper to explore the non-lnear fadng envronment. One of the nterestng models that we could fnd n lterature s μ dstrbuton [3], whch provdes the generalzed model for fadng dstrbuton. Dependng upon the value of and μ, ths model can be utlzed for the generaton of Nakagam-m and Webull varants. However, t also treats One-Sded Gaussan, Raylegh and Negatve Exponental dstrbutons as ts specal cases. The generalzed fadng model usng three parameter generalzed gamma dstrbuton descrbng all forms of multpath fadng and shadowng n wreless systems s analyzed n [4]. Ths paper s organzed as follows: In Secton, OFDM system model s dscussed. Secton 3, descrbes the generalzed model of μ dstrbuton. Flat fadng channel model to use n OFDM systems s descrbed n Secton 4. In Secton 5, channel estmaton technque s dscussed. The analyss of OFDM system wthout estmaton has been done n Secton 6, whle results wth estmaton have been presented n Secton 7. Fnally Secton 8 concludes the paper.. OFDM Model A Complex base band OFDM sgnal wth N sub-carrers, Copyrght 010 ScRes.

2 N. SOOD ET AL. 381 s expressed as 1 0 () N j πkf t st De 0 t T (1) k 0 For each OFDM symbol, the modulated data sequences are denoted by D(0), D(1),... D( N 1). Here, f 0 denote the sub-carrers spacng and s set to f 1 0, the condton of orthogonalty. After IFFT, the T tme-doman OFDM sgnal can be expressed as: 1 S(n) N N 1 k 0 j πkf0n N De () After IFFT, the modulated sgnal s up-converted to carrer frequency f C and then the followng sgnal s produced and transmtted through channel: xt () Re N 1 j πk( f0 fc ) t De k 0 0 t T (3) x() t represents the fnal OFDM sgnal n whch sub-carrers shall undergo a flat fadng channel. 3. The μ Dstrbuton The μ dstrbuton s a general fadng dstrbuton that can be used to represent varous fadng model. Ths dstrbuton deals wth non-lnearty of propagaton medum [5]. Fadng sgnal wth envelope r, an arbtrary constant parameter 0 and a root mean value rˆ E r shall have ts probablty densty functon pr (), whch s wrtten as: μ μ1 μ r r pr ( ) exp( μ ) μ rˆ ( μ) rˆ Webull and Nakagam-m dstrbuton can be easly derved from μ dstrbuton as ts specal cases. By settng μ 1, Equaton (4) shall reduce to Webull probablty dstrbuton functon as: (4) 1 pr ( ) βr exp( βr ) (5) where β rˆ. Here, by varyng the value of dfferent curves of pdf can be plotted. From Webull dstrbuton by settng, the Raylegh dstrbuton can be obtaned as: r r pr () exp( ) γ γ (6) where γ rˆ /. Now, f we put 1 n Webull dstrbuton, t shall reduce to Negatve exponental dstrbuton represented as: pr () δexp( δr ) (7) where δ r ˆ1 So by keepng the value of μ 1 and varyng the value of t has generated Raylegh and Negatve exponental dstrbuton. Whereas f we keep and vary the value of μ, we shall be able to represent ths μ dstrbuton as Nakagam-m dstrbuton In such a case μ μ1 μ r r pr () exp( μ ) μ ( μ) By settng μ 1/, one-sded Gaussan dstrbuton can be obtaned as: However, for be wrtten as: pr () exp( r ) πrˆ ˆr (8) (9) μ dstrbuton the envelope r can 1 N r x y (10) 1 where, x and y are n-phase and quadrature elements of multpath components represented by symbol. It was nterestng to fnd that n Equaton (10) shall reduce to the envelope equaton of Raylegh fadng dstrbuton [6] descrbed as: r x y N 1 (11) Same concept has been shown n Equatons (5) and (6) that by puttng, Webull dstrbuton converts to Raylegh dstrbuton, hence ntroducng the non-lnearty nto propagaton medum. However, at dfferent values of dfferent fades can be generated. 4. Channel Model In ths paper, the sub-channel spacng s equal to nverse of tme perod, so that the produced parallel fadng subchannels have flat fadng characterstcs. Here μ dstrbuton has been utlzed for generaton of Webull dstrbuton by settng μ 1 and varyng the value of. Copyrght 010 ScRes.

3 38 N. SOOD ET AL. In flat fadng envronment, the base-band sgnal at the nput of recever yt () s as descrbed as follows: yt () xt ()*() rt nt () (1) where, x() t denotes the base-band transmtted sgnal, s the Webull dstrbuted channel envelope and nt () the addtve whte Gaussan nose wth zero mean. 5. Channel Estmaton rt () Channel estmaton n frequency selectve has dfferent approach then compared wth flat fadng envronment. A comparatve study usng Mnmum Mean Squared Error (MMSE) and Least square (LS) estmator n frequency selectve fadng envronment has been presented n [7]. The channel estmaton based on comb type plot arrangement s studed usng dfferent algorthms by baha et al. [8]. A novel channel estmaton scheme for OF- DMA uplnk packet transmssons over doubly selectve channels was suggested n [9]. The proposed method uses rregular samplng technques n order to allow flexble resource allocaton and plot arrangement. In flat fadng envronment, estmaton of the channel usng traned sequence of data has been studed and mplemented n [10]. He presented the channel estmaton n flat fadng envronment usng some traned data. Channel phase was estmated durng each coherence tme. Then plot data of some requred percentage of data length (referred as tranng percentage n smulaton) s nserted nto the source data. It s used to estmate the random phase shft of the fadng channel and tran the decson to adjust the receved sgnal wth phase recover. The results obtaned showed the great varaton n for wth and wthout estmaton curves. It s clear from lterature revewed that phase estmaton usng tranng symbol can be mplemented n flat fadng envronment to mprove the performance of system. In ths paper, we have mplemented the above descrbed phase estmaton technque n flat fadng for Webull fadng dstrbuton on OFDM system. 6. Results wthout Estmaton OFDM-BPSK and -QPSK sgnal s smulated n MAT- LAB envronment by choosng total number of sub-carrers 400, IFFT length 104 by usng guard nterval of length 56. The results presented n Fgures 1 and are smulated by varyng the value of and keepng μ 1. Here, the values have been obtaned for varyng over a range of 1 to 7, however, mprovement n was not sgnfcant for hgher values of, So range has been s kept from 1 to 7, both for OFDM-BPSK and -QPSK system. From the smulatons, t has been verfed that the results for are same that are obtaned by usng Raylegh fadng dstrbuton. It has been observed that f we plot curves by changng the value of μ there s no change n these curves. Ths s because of fact that n the envelope Equaton 10, the varable parameter s whch vares the fadng varants and μ has no role to change ths fadng envelope and hence no change n values vs. Vs.SNR Usng Webull channel for for BPSK alpha=1 alpha=1.5 alpha=1.85 alpha= alpha=.5 alpha=3 alpha=3.5 alpha=4 alpha=4.5 alpha=5 alpha=6 alpha= Fgure 1. vs. SNR for OFDM-BPSK system vs. Vs.SNR Usng Webull channel for for QPSK QPSK alpha=1 alpha=1.5 alpha=1.85 alpha= alpha=.5 alpha=3 alpha=3.5 alpha=4 alpha=4.5 alpha=5 alpha=6 alpha= Fgure. vs. SNR for OFDM-QPSK system. Copyrght 010 ScRes.

4 N. SOOD ET AL. 383 To explore the other sde of μ, by keepng the value of fxed and varyng the value of μ, we are able to have curves for other dstrbutons. In Fgure 3, Negatve exponental dstrbuton has been plotted as specal case where 1 and μ can vary. Here, t has been plotted for fxed value of 1. Raylegh dstrbuton s havng and μ can vary. Here, t has been plotted wth μ 1.One sded dstrbuton has been plotted wth and μ 1/. vares n the range of to for OFDM- BPSK and -QPSK for SNR of 0 to 5 db. In case of OFDM-BPSK the value of s obtaned at SNR of 10dB. However, for -QPSK case the of s obtaned at SNR of 0 db. Comparson between Negatve exponental value, Raylegh and one sded dstrbuton results clearly reveals the fact that n μ dstrbuton the varaton n value of can change the value of, however by changng the value of μ, there s no mpact upon the. Results obtaned wthout estmaton technque has been presented n [11]. 7. Results wth Estmaton Traned symbols are added to source sgnal as dscussed n Secton 5. The percentage of such symbol may be vared dependng upon the system response to the traned sequence. We have analyzed the results for varous percentage values of traned sequence. We have plotted new graphs wth value of 7 and varyng value of tranng sequence over the range from 10% to 50%. Results for OFDM-BPSK and -QPSK have plotted n Fgures 4 and 5 respectvely. In depth analyss of these graphs shows that decreases, f the tranng percentage s ncreased. In Fgure 5, f we evaluate the readng obtaned at SNR = 10 db, has decreased from to for tranng percentage of 10 to 50. Ths means, for the same value of SNR and, dfferent tranng percentage has resulted nto dfferent values of. More traned sequence wll results nto lesser errors. The same has been depcted from Fgure Vs.SNR vs. Usng Webull channel for BPSK wth Channel estmaton ctg=10% ctg=5% ctg=50% Channel SNR (db) (db) Fgure 4. vs. SNR for OFDM-BPSK wth channel estmaton. vs. Vs.SNR Usng Usng dffrent dstrbuton for BPSK -ve exponental Raylegh one sded dstrbuton Vs.SNR vs. Usng Webull channel for QPSK wth Channel estmaton ctg=10% ctg=5% ctg=50% Fgure 3. vs. SNR for negatve, raylegh and exponental dstrbutons Fgure 5. vs. SNR for OFDM-QPSK wth channel estmaton. Copyrght 010 ScRes.

5 384 N. SOOD ET AL. 8. Conclusons Ths paper, presents performance analyss of OFDM system wth generalzed fadng model of μ dstrbuton wth and wthout estmaton. The non-lnearty added n propagaton medum has been clearly shown n smulated results, snce the has sgnfcantly reduced by varyng from 1 to 7. However, hgher values of can be used for further reductons n. It s clear from the smulatons that the result shows sgnfcant mprovement by applyng the phase estmaton usng traned symbols. 9. References [1] H. Hashem, The Indoor Rado Propagaton, proceedngs of IEEE, Vol. 81, No. 7, July 1993, pp [] D. Zheng, J. L. Cheng and N. C. Beauleu, Accurate Error Rate Performance Analyss of OFDM on Frequency Selectve Nakagam-m Fadng Channels, IEEE Transacton on Communcatons, Vol. 54, No., February 006, pp [3] Mechel Daoud Yacoub, The -µ Dstrbuton: A General Fadng Dstrbuton, 00, pp [4] J. Malhotra, A. K. Sharma and R. S. Kaler, On the Performance Analyss of Wreless Recever Usng Gene- Ralzed-Gamma Fadng Model, Annals of Telecommuncaton Annals Des Telecommuncatons, Internatonal Journal, Sprnger, Vol. 64, No. 1-, November 008, pp [5] M. D. Yacoub, The -µ Dstrbuton: A Physcal Fadng Model for the Stacy Dstrbuton, IEEE Transactons on Vehcular Technology, Vol. 56, No. 1, Janurary 007, pp [6] G. S. Prabhu and P. M. Shankar, Smulaton of Flat Fadng Usng MATLAB for Classroom Instructon, IEEE Transacton on Educaton, Vol. 45, No. 1, February 00, pp [7] J.-J. van de Beek, O. Edfors, M. Sandell, S. K. Wlson and P. O. B. Rjesson, On Channel Estmaton n OFDM Systems, Proceedngs of Vehcular Technology Conference (VTC Ô95), Chcago, USA, Vol., September 1995, pp [8] S. Coler, M. Ergen, A. Pur and A. Baha, A Study of Channel Estmaton n OFDM Systems, IEEE VTC, Vancouver, Canada, September 00. [9] P. Fertl and G. Matz, Mult-User Channel Estmaton n OFDMA Uplnk Systems Based on Irregular Samplng and Reduced Plot Overhead, IEEE ICASSP, Vol. 3, 007. [10] Z. F. Chen, Performance Analyss of Channel Estmaton and Adaptve Equalzaton n Slow Fadng Channel, Unversty of Florda. [11] N. Sood, A. K. Sharma and M. uddn, Performance of OFDM-BPSK and -QPSK over Generalzed Alpha-Mu Fadng Dstrbuton, IEEE Internatonal Advance Computng Conference (IACC-009), Patala, Inda, 6-7 March 009, pp Copyrght 010 ScRes.