Application of Zero-Forcing Adaptive Equalization in Compensation of Fading Effect of Two-hop Wireless Link

Transcription

1 IACSI International Journal of Engineering and echnology Vol. 3 o. 6 Deceber Application of Zero-Forcing Adaptive Equalization in Copensation of Fading Effect of wo-hop Wireless in Abu Sayed d. ostafizur Rahaan d. Idadul Isla and. R. Ain eber IEEE Abstract Wireless lin in obile cellular counication syste is experienced by large and sall scale fading. Since the lin is non line of sight (OS) therefore severely affected by ultipath fading. In a two-hop wireless lins each lin is affected by fading and noise degrades the overall perforance of the counication syste. In this paper perforance of two- hop lins is analyzed under Rayleigh and aagai- fading environents separately for QPSK and 8-PSK odulation schees. In this paper zero-forcing adaptive equalizer is used on two-hop wireless lins to enhance the perforance of the syste. ere we find that zero-forcing adaptive equalizer wors better for QPSK schee and aagai- fading channel copared to 8-PSK schee and the Rayleigh fading channel. Index ers Probability of sybol error OS aagai- and Rayleigh fading Coherent deodulator SE and Gaussian Q function. I. IRODUCIO he electroagnetic (E) radio wave in wireless channel ay be reflected refracted and scattered by surrounding objects which results in ultipath propagation of signals. herefore ultiple copies of the sae signal arrive at the receiving end and creates delay spread. When separation between the transitter and the receiver is very large then ean signal strength is considered at the receiver (nown as large scale propagation odel) but when separation between the transitter and the receiver is low (less than 5 ) usually in an urban or suburban area then rapid variation of the signal strength within short distance or short duration is considered (nown as sall scale propagation odel). Under a ultipath propagation environent the aplitude and phase of a coposite odulated sybol very widely and rapidly a phenoenon nown as fading. wo ost iportant paraeters of a fading channel are the coherence tie and the coherence bandwidth as described in [][]. A lot of paraeters lie: sybol period ultipath delay spread Doppler spread coherence tie/ bandwidth tie variant or invariant property channel gain etc. plays vital role on the perforance of a wireless lin as suarized in []-[3]. A channel ay be tie selective or frequency selective anuscript received August 3 ; revised oveber 6. Abu Sayed d. ostafizur Rahaan and d. Idadul Isla are with the Departent of Coputer Science and Engineering Jahangirnagar University Dhaa 34 Bangladesh. d. Idadul Isla wors also as an adjunct professor of Electronics and Counications Engineering Departent at East West University 43 ohahali Dhaa Bangladesh (e-ail: idad@juniv.edu).. R. Ain is with the Electronics and Counications Engineering Departent East West University 43 ohahali Dhaa Bangladesh (e-ail: rain@ewubd.edu). depending on the tie-varying nature of the ipulse response of the channel. Fro the autocorrelation of the channel ipulse response the channel ay be classified as wide-sense stationary (WSS) uncorrelated scattering (US) or wide-sense stationary uncorrelated scattering (WSSUS) channel. he coplex envelope of a odulated wave is a rando variable (RV) and ay follow Rayleigh Ricean or aagai- distribution depending on the condition of the channel. For exaple if there is a strong line-of-sight (OS) between the transitter and the receiver along with ultipath fading the distribution follows Ricean probability density function (PDF) instead of Rayleigh PDF. Dual-hop wireless lin has gained uch interest in recent years because of its application in co-operative wireless networs [4]-[6]. In [7] end-to-end perforance of dual-hop relaying systes is evaluated considering bea foring over aagai- fading channels. he source and destination uses t and r nuber of antennas while the relay station uses only one antenna. Siilar analysis is done in [8] and [9] for aply-and-forward (AF) and iperfect channel case. Both the papers plot the outage probability and bit error rate (BER) against signal-to-noise ratio (SR). In [] a nuber of relay nodes are placed randoly and the best relay is selected to observe the outage probability and the BER. he cobination of Rayleigh and Riccian fading is considered in [] for two-hop AF case. In [] the perforance of dual-hop relay lin is deterined for coherent and non-coherent binary odulation schees when the relay strea is only for AF purpose. he paper considers both average power scaling and instantaneous power scaling constraints over aagai- fading channel. In this paper adaptive equalizer is added at relay and receiving end to iprove the perforance of the dual-hop wireless lin. he paper considers 8-PSK and QPSK schees under Rayleigh and aagai- fading environents. he paper is organized as follows. Section II gives soe review wor on the theoretical analysis of adaptive equalization and then describes the odel of the two-hop wireless lin under fading environent. Section III gives the results and finally Sec. IV concludes the entire analysis. II. SYSE ODE A. Adaptive Equalizer et us consider that the transitted signal of an wireless counication syste is s( ( cos(π ft + φ( ) the received signal of an -ultipath channel can be written as [3-4]: α ( ) ( )cos( + ( ) + ( )) n n t t πft φ t θn t 68

2 IACSI International Journal of Engineering and echnology Vol. 3 o. 6 Deceber α n ( is the attenuation and θn ( is the phase rotation of the n-th reflected path. In ost of the cases the ipulse response of the channel is found tie selective i.e. the channel is better at soe selected ties than other ties. o neutralize the delay spread of the wireless channel adaptive equalizer is used in the passband signal [3]-[5]. In this study a zero-forcing adaptive equalizer circuit is used at receiver end to neutralize the fading effect. ere QPSK and 8-PSK odulation schees are selected to copare the sybol error probability for the case of with and without equalization. Counication Equalizer eq (f) x ( Channel c (f) yt () Fig.. Equalizer in cascade with the channel. If any signal x ( is ultiplied by a constant or delayed by an aount t d then the resultant signal becoes t t d ). Such distortion is called linear distortion and linear distortion is curable in counication syste. For a linear distortion channel of Fig. y( t t d ). aing Fourier transfor we have jω t Y( f ) / X ( f ) e d ( f ). In presence of distorting channel of transfer function c (f) received signal can be ade distortionless incorporating a equalizer at the receiving end as shown in Fig. the overall transfer jωt function of the syste becoes ( ) ( ) d c f eq f e (f) is called the aplitude response which is needed to be constant over the entire bandwidth (BW) of the input signal and θ ( f ) is the phase response and needed to be a linear function of frequency over the entire BW of the input signal for recovery of the transitted sybol [5]-[7]. et us consider the tapped delay finite ipulse response (FIR) filter of Fig. the output signal is [8][9]: y( C t ( + ) ). () aing Fourier transfor of Eq. ( ) we have Y ( f ) j( + ) C e X ( f ) fro which we obtain Y( f ) eq ( f ) X ( f ) e j Ce j( + ) C e j If the relation j ω t d c ( f ) eq ( f ) e can be satisfied by adjusting the nuber of delay blocs and weighting factors of Eq. () then the distortion at the receiving end can be copletely eliinated. B. Zero-Forcing Equalizer aing inverse Fourier transfor of ( ) j j eq f e C e We obtain j h eq ( e Cnδ ( t n ). n For the distorted input signal the equalized output is j y ( heq ( e Cn t n ) (3) n aing absolute value of the output signal y( we have y ( Cn t n ). n. () t- ) t-) t- ) C - C -+ C -+ C C Σ y( Fig.. apped delay equalizer. In zero-forcing condition y( is sapled at t and a condition y( ) Cn n ) n (4) ; δ ( ) ; ± ±... ±. aing y ( ) Cn. (5) n We ay expressed the relation of {y()} {)} and {C n } in the following atrix for: ) ) x ) + ) ) ) ) ) ) ) yxc ) 3) ) ) ) K O O + ) ) + ) + ) ) ) ) ) + ) ) he diension of the above vector x is (+) (+) and that of vectors [ ] c [ c c ] c y y ( ) y() y( ) and are (4+) and (+) 69

3 IACSI International Journal of Engineering and echnology Vol. 3 o. 6 Deceber respectively. he sae job can be done using adaptive algorith of iniu ean square error (SE). In this case the weighting vector c R xx R xy (6) R xx x x and is called autocorrelation atrix and R xy x y is called the cross-correlation vector. C. wo-op Wireless in In a dual-hop wireless counication syste the sender node S counicates with the detector node D through the relay station R as shown in Fig. 3. et us first concentrate on the analytical solution of the probability of sybol error Ps under additive white Gaussian noise (AWG) channel in a fading environent. In PSK odulation schee the received signal vector of coherent deodulator on Φ( - Φ ( plane is and r r r r i ( θ i + n { S + n( } Φ ( dt E cos r { Si ( + n( } Φ ( dt E sinθ i + n. he signal S i ( is the i-th odulated wave in the region t (+) E is the energy of a sybol n and n are the noise of the in-phase and quadrature coponent of the received signal respectively. S aing r Fig. 3 wo-hop wireless lin. ρ cos ˆ θ i and i r ρ ˆ sinθ the joint PDF of ρ and θˆ i (given S i ( is transitted) is [3]: p{ ρ ˆ θi Si ( is transitte d} (7) exp { cos( ˆ ρ + E ρ E θi θi )}. π Integrating both side of Eq. (7) with respect to ρ and taing ϕ ˆ θ i θ i [ π π ] p{ ϕ S ( is transitted} i Rayleigh/ aaga i- fading E / e πe + π the PDF of ϕ becoes ( ) ( / cosϕ e E ) ( ) E G ϕ + erf cosϕ. R Rayleigh/ aagai - fading D cos ϕ G ( ϕ) (8) he probability of sybol error then can be written as [3] [3]: π / Ps p{ ϕ Si ( is transitted} dϕ π /.5erf > 4. π E π sin π E / sin e y π erf y cot dy If E / >> then Eq. (9) can be approxiated to E π P s Q sin. () et us now consider the generalized for of the sybol error probability of different odulation schees using Gaussian Q function Q ( g ) g is a constant and depends on the odulation schee and detection technique (for exaple g for BPSK g for QPSK). In a slow fading channel the instantaneous SR per bit E / is a tie invariant RV with PDF f Γ ( ) which depends on the particular fading environent. he average probability of error can be found for a fading channel as [] []: X( e s Γ ) (9) P P ( ) f ( d. () C( Wireless channel R( B( Fig. 4. Equalizer in z-doain. Equalizer Y( In this paper we consider Rayleigh and aagai- fading channels their PDFs are: / avg fγ ( ) Rayleigh e avg () / avg fγ ( ) aagai e avg Γ( ) is the aagai- fading paraeter which ranges fro ½ to. et the transfer function of the wireless channel and the equalizer to be C( and B( respectively as shown in Fig. 4. he z-transfor of the received signal is then Y( X(C(B( fro which we obtain the overall transfer function Y( ( C( B(. (3) X ( o eliinate intersybol interference (ISI) we need to ipose the following requireent [8][9]: Y ( X( that is ( C( B( which iplies that c( b( δ ( 63

4 IACSI International Journal of Engineering and echnology Vol. 3 o. 6 Deceber or n b( ) c( n. (4) et the ipulse response of the channel be c( a δ ( t ). he z-transfor of c( gives C( a z. (5) he transfer function of the equalizer is ( C( B( thus we obtain B( C( a z (6) b + b z + b z In the presence of additional noise n n at the end of n-th sybol interval at the effective channel output the variance of noise will be σ ( ) v b nn (7) ( b ). herefore the probability of bit error is Eb P b Q. (8) σ v If the transit power at sender and repeater stations are P and P with fading aplitudes h SR and h RD respectively then SR of S-R and R-D lins are[]-[3] []: h SR P and h RD P / is the two-sided power spectral density (psd) of the AWG. he equivalent SR of the two-hop lin is eq (9) + + c c for exact value of and c for approxiate value of at higher SR. III. RESUS et us consider an adaptive equalizer of 7 taps and a received distorted set of pulse saples: {)} [ ]. We will find the weighting vector of the zero-frocing adaptive equalizer. For 7 taped filter the diension of atrix x is and is given as x Applying AAB 9.x we get the auto-correlation atrix R xx he cross-correlation vector R xy he weighting vector is W Fig.5 shows the 7 saples at both input and output of the filer the interfering coponents at output is found negligible. aing the co-efficients of the ipulses of the channel a.5 a.34 a.75 a 3.3 a 4. we get the transfer function of the equalizer as ( z z z z -4. herefore the variance of the noise is 3 4 σ v b b b b b he probability of bit error of both 8-PSK and QPSK schees under Rayleigh and aagai- fading is plotted in Fig. 6 for two-hop wireless lin. he Fig. 6 copares the perforance of the two-hop lin with and without zero-forcing equalization. We now that the BER of a single-hop lin is always better than that of two-hop lin case for any type of odulation schee because of low SR experienced by the equivalent lin of two-hop syste. In this section we only consider the coparison of two-hop wireless lin under two odulation schees viz. QPSK and 8-PSK and inclusion of zero-forcing equalizer at the repeater and receiving end. We observe fro Fig. 6 that the BER of QPSK odulation is found uch lower than that of 8-PSK case because of the signal space of the constellation diagra. Finally the BER of the aagai- fading is found better than that of Rayleigh fading case for both type of the odulation schees. In aagai- fading the paraeter is related to the nuber 63

5 IACSI International Journal of Engineering and echnology Vol. 3 o. 6 Deceber of OS paths as in Rayleigh fading case there is no strong OS path hence perforance of aagai- fading is better than the Rayleigh fading channel as is easily seen fro Fig. 6. Sybol error probability (Ps) )y() output of the equalizer input of the equalizer Fig. 5. Copensation of ultipath affect on wireless lin Average SR (db) QPSK Rayleigh fading two hop QPSK Rayleigh fading two hop with equalizer QPSK aagai- fading two hop QPSK aagai- fading two hop with equalizer 8-PSK Rayleigh fading two hop 8-PSK Rayleigh fading two hop with equalizer 8-PSK aagai- fading two hop 8-PSK aagai- fading two hop with equalizer Fig. 6. Coparison of BER of two-hoped wireless lin under zero forcing adaptive equalizer. he BER of both the odulation schees is iproved with incorporation of the zero-forcing adaptive equalizer as is visualized fro Fig. 6. he ipact of zero-forcing equalizer is uch ore proinent for the QPSK schee than that of 8-PSK schee at the sae tie the zero-forcing equalizer perfors well at higher SR. Finally the equalizer wors better for the aagai- fading channel copared to that of the Rayleigh fading channel. IV. COCUSIO In this paper we have incorporated zero-forcing adaptive equalizer at the repeater and the receiving end to enhance perforance of the two-hop wireless lins. Zero-forcing adaptive equalizer iproves perforance of the two-hop lins for both QPSK and 8-PSK odulation schees under the Rayleigh and aagai- fading environents. It has also been observed that the perforance of the aagai- odel is better than that of the Rayleigh fading odel. In this study a single antenna schee is used at the sender the repeater and the receiving end. We have the scope to consider the ultiple-input single-output (ISO) lin between the transitter and the repeater and single-input ultiple-output (SIO) between the repeater and the receiving end. It should be further entioned here that the adaptive equalizer can be incorporated also with orthogonal space diversity at stage- and axial ratio cobining (RC) at stage- to observe the perforance of ultiple antenna at the sender and the receiver with single antenna at the repeater. he wor along this line is in progress and will be reported else. APPEDIX A he output of the equalizer at a discrete instant of tie n is y ( w. he error signal is defined as e( z( y(. he ean square error is ζ E[ e( e ( ] E e( E z( w E z( w E[ z ( ] w x ( z( + w wi E x n x [ ( ) ( n i)] i σ z w p( ) w p ( ) + w wi ( i ) i ( i ) E[ x ( n i)] p( ) E[ z ( ] p ( ) E[ z( ]. We also have ζ σ W P P W W z + RW R Rxx P Rnz ζ p + W R W R P Rxx Rnz β. REFERECES [] hrodore S. Rapaport Wireless counications principles and practice Pearson Education nd edition. [] Sion ayin ichael oher odern Wireless Counications Pearson Education 5. 63

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Abu Sayed d. ostafizur Rahaan received his B.Sc. degree in Electronics and Coputer Science fro Jahangirnagar University Savar Dhaa Bangladesh in 3 and.sc. degree fro Stuttgart University at Stuttgart Gerany in Inforation echnology (IFOEC) in the branch of Ebedded Syste Engineering in 9. Since 4 he is a woring as an assistant professor at the Departent of Coputer Science and Engineering of Jahangirnagar University Savar Dhaa Bangladesh. e is currently pursuing his Ph.D. at the departent of Coputer Science and Engineering Jahangirnagar University Dhaa. Currently his research focuses on telecounication ebedded and parallel systes reconfigurable coputing ulticore architecture and software engineering. d. Idadul Isla has copleted his B.Sc. and.sc Engineering in Electrical and Electronic Engineering fro Bangladesh University of Engineering and echnology Dhaa Bangladesh in 993 and 998 respectively and has copleted his Ph.D degree fro the Departent of Coputer Science and Engineering Jahangirnagar University Dhaa Bangladesh in the field of networ traffic engineering in. e is now woring as a Professor at the Departent of Coputer Science and Engineering Jahangirnagar University Savar Dhaa Bangladesh. Previously he wored as an Assistant Engineer in Sheba eleco (Pvt.) D (A joint venture copany between Bangladesh and alaysia for obile cellular and W) fro Sept.994 to July 996. e has a very good field experience in installation of Radio Base Stations and Switching Centers for W. is research field is networ traffic wireless counications wavelet transfor OFDA WCDA adaptive filter theory AFIS and array antenna systes. e has ore than hundred research papers in national and international journals and conference proceedings.. R. Ain received his B.S. and.s. degrees in Physics fro Jahangirnagar University Dhaa Bangladesh in 984 and 986 respectively and his Ph.D. degree in Plasa Physics fro the University of St. Andrews U. K. in 99. e is a Professor of Electronics and Counications Engineering at East West University Dhaa Bangladesh. e served as a Post-Doctoral Research Associate in Electrical Engineering at the University of Alberta Canada during e was an Alexander von uboldt Research Fellow at the ax-planc Institute for Extraterrestrial Physics at Garching/unich Gerany during e was awarded the Coonwealth Postdoctoral Fellowship in 997. Besides these he has also received several awards for his research including the Bangladesh Acadey of Science Young Scientist Award for the year 996 and the University Grants Coission Young Scientist Award for 996. is current research fields are wireless counications and networs and also nonlinear plasa dynaics. e is a eber of the IEEE. 633