New SRRC receiver filter design with reduced number of filter taps for wireless communication systems

Transcription

1 IET Communcatons Research Artcle ew SRRC recever flter desgn wth reduced number of flter taps for wreless communcaton systems ISS Receved on 6th July 07 Revsed 3rd January 08 Accepted on 8th February 08 E-Frst on 3rd ay 08 do: 0.049/et-com Hoon Kang Jong-Seon o Department of Electrcal and Computer Engneerng IC Seoul atonal Unversty Seoul 0886 Republc of Korea E-mal: jsno@snu.ac.kr Abstract: In wreless communcaton systems t s well known that nter-symbol nterference (ISI) can be avoded by usng a par of matched square-root-rased-cosne (SRRC) flters n the transmtter and recever. In an effort to fnd methods whch mnmse the number of flter taps n the matched flter numerous studes have been done. However n practse when the communcaton specfcaton s fxed by the standard t s not possble to change the coeffcents of the transmt flter. In ths study the authors propose a new SRRC flter desgn wth the reduced number of flter taps for a recever of a wreless communcaton system. The proposed desgn utlses a recursve steepest-descent algorthm when the flter coeffcents of the transmtter are fxed. That s relaxng the ISI crteron whle mantanng the stopband attenuaton the proposed recever flter has fewer flter taps than that n the conventonal case wthout undergong bt error rate performance degradaton. The proposed recever flter desgn wth the reduced number of flter taps reduces the computatonal complexty and the detecton delay n the recever. Introducton In wreless communcaton systems the receved sgnal s often dstorted by the nter-symbol nterference (ISI) due to the narrowband bandpass sgnallng. In order to realse an ISI-free system the recever must have a square-root-rased-cosne (SRRC) flter dentcal to that of the transmtter known as the matched flter desgn []. In wreless communcaton systems t s also mportant to ensure that the magntude response of the SRRC recever flter s desrable n the frequency doman because one of the man purposes of the SRRC flter n the recever s to remove adjacent channel nterference (ACI). That s most of recever flter desgn algorthms attempt to mnmse the ISI and meet the target magntude response under the matched-flter constrant. There are three dfferent desgn methods for the SRRC flters as follows: () Optmse the magntude response of the SRRC flter wth zero ISI [ 8]. () Optmse the magntude response of the SRRC flter wth mnmum ISI [9 4]. () Optmse the SRRC flter through a jont cost functon of the ISI and the magntude response [5 9]. In fact when the communcaton specfcaton s fxed by a standard there s no way to modfy the recever flter n the conventonal systems because the matched-flter constrant should also be satsfed by the recever. However several studes modfed the recever flter by relaxng the matched-flter constrant wth no degradaton of the ISI whch shows hgh potental for new recever flter desgns [0 ]. A smplfed system model of a wreless communcaton system s llustrated n Fg.. odulated data passes through the narrowband SRRC transmtter flter and dgtal-to-analogue converter (DAC) to make a band-lmted analogue sgnal. The converted analogue sgnal s transmtted through the narrowband channel whch s typcally a mult-path fadng channel n wreless moble communcaton systems. In the recever sde ACI and addtve whte Gaussan nose (AWG) are added to the receved sgnal. After convertng the receved analogue sgnal to a dgtal sgnal by an analogue-to-dgtal converter (ADC) the dgtsed receved sgnal s fltered by the SRRC recever flter and demodulated. Even though the mult-path fadng and ACI are the most mportant channel dstortons n the wreless communcaton systems we wll focus on ISI and ACI for the desgn of the SRRC recever flter n the AWG channel. In ths paper we propose a new desgn of an SRRC flter for the recever n a wreless communcaton system whch uses a recursve steepest-descent algorthm whle the SRRC flter of the transmtter s fxed. By relaxng the ISI crteron whle mantanng the stopband attenuaton the proposed SRRC flter of the recever has fewer flter taps than the conventonal SRRC matched flter wthout any degradaton of the bt error rate (BER) performance n a wreless communcaton system. The reduced number of flter taps of the modfed SRRC flter of the recever results n low computatonal complexty and the low detecton delay n the recever both of whch are mportant factors for the moble statons n the cellular communcaton systems. The remanng of the paper s organsed as follows. In Secton ISI and stopband attenuaton are brefly revewed as the flter desgn crtera and these are derved n the matrx form for the proposed SRRC flter desgn algorthm. In Secton 3 the conventonal SRRC flter desgn algorthm s ntroduced and a new SRRC recever flter desgn algorthm based on the steepestdescent method s proposed. In Secton 4 the performance assessment of the proposed SRRC flter n varous envronments s provded through a numercal analyss. Fnally conclusons are gven n Secton 5. Fg. Smplfed system model of wreless communcaton system IET Commun. 08 Vol. Iss. 9 pp The Insttuton of Engneerng and Technology 08 8

2 h r k h t k = 0 R ISI can be rewrtten as + k = R ISI = h r T Hh r. () Fg. agntude response and ts stopband attenuaton of the recever flter Recever flter desgn crtera There are three flter desgn crtera to be consdered: the mpulse response magntude response and phase response. In ths paper the desgn of a fnte mpulse response (FIR) SRRC flter s consdered where the phase response s gnored because a symmetrc FIR flter has a lnear phase characterstcs [3]. Thus we concentrate only on the mpulse response and magntude response for the desgn of the recever flter. ISI s the most mportant channel dstorton when estmatng the performance of the mpulse response because ISI s drectly related to the receved sgnal qualty. The magntude response of the recever flter s also used to estmate the stopband attenuaton where removng the ACI s requred n the moble communcaton systems. atrx forms of ISI and the stopband attenuaton are derved for the proposed SRRC flter desgn algorthm.. Inter-symbol nterference The sample of the desred symbol at the samplng tme should be located at the zero crossng pont of the adjacent symbols. ISI occurs from the adjacent symbols n the tme doman where zero crossngs of the adjacent symbols at the samplng tme of the desred symbols are broken; that s the sampled symbols contan the non-zero meanngful nterferences from the adjacent symbols. Suppose that the receved sgnal s oversampled by V tmes. If the samples of the adjacent symbols are non-zero at each samplng pont these wll work as addtve nose to the desred sampled symbol. Let and denote the number of transmtter and recever flter taps respectvely. Then the squared power rato of the ISI to the desred sgnal s then expressed as R ISI = m 0 k = 0 h r k h t k = 0 h r k h t + + mv k () + k where h t k and h r k are the kth flter coeffcents of the transmtter and the recever flters respectvely. Let h t = h t ( ) h t ( ) h t (0) T and h r = h r (0) h r () h r ( ) T where T denotes the transpose and let H be an matrx whose k n element s expressed as h k n = + V m = + V m 0 h t h t + + mv k Then the matrx form of () s expressed as R ISI = + + mv n. h T r Hh r. k = 0 h r k h t + k If we normalse the flter coeffcents h t k and h r k such that IET Commun. 08 Vol. Iss. 9 pp The Insttuton of Engneerng and Technology 08. Stopband attenuaton The stopband attenuaton of the low-pass flter s determned by the magntude response of the hgher frequency band above the sgnal bandwdth. The recever flter removes the ACI dependng on ts stopband attenuaton. As depcted n Fg. we can calculate the stopband attenuaton accordng to the dscrete Fourer transform (DFT) output of the recever flter where the frequency ndex k s the ndex of the DFT output. The stopband attenuaton A SB can be expressed as A SB = + α V k = + α V H r k (3) where H r k s the kth frequency component of the recever flter n DFT output and α s the roll-off factor of the orgnal SRRC flter wth 0 α. Clearly / s the last frequency ndex and (( + α)/v) s the frst frequency ndex of the stopband. / (( + α)/v) n the rght-hand sde of (3) represents the number of frequency ndces n the stopband whch s used for the normalsaton of (3). The kth component power H r (k) n the summaton s computed as H r k = h r n e ( jπnk)/ n = 0 = h r n e (jπnk)/ h r m e (( jπmk)/) n = 0 m = 0 = h r n e (( jπ m n k)/) h r m. n = 0 m = 0 Smlar to the ISI case the stopband attenuaton s also changed to the matrx form as A SB = h r T Wh r where the matrx W s the DFT operator and ts (m n) element W m n s gven as W m n = + α V k = + α V e (( jπ m n k)/). Let W be an matrx whose element W m n s expressed as W m n = + α V k = + α V cos π m n k Snce W s a Hermtan matrx A SB can be rewrtten as A SB = h r T Wh r. (4) 3 Proposed SRRC recever flter desgn In ths secton the conventonal SRRC flter desgn s revewed and the SRRC recever flter s modfed by reducng the number of the recever flter taps based on jont optmsaton by usng a. 9

3 Table Proposed SRRC recever flter desgn examples 49 taps 4 taps 33 taps 5 taps 7 taps h r (0) h r ( ) h r () h r ( ) h r () h r ( 3) h r (3) h r ( 4) h r (4) h r ( 5) h r (5) h r ( 6) h r (6) h r ( 7) h r (7) h r ( 8) h r (8) h r ( 9) h r (9) h r ( 0) h r (0) h r ( ) h r () h r ( ) h r () h r ( 3) h r (3) h r ( 4) h r (4) h r ( 5) h r (5) h r ( 6) h r (6) h r ( 7) h r (7) h r ( 8) h r (8) h r ( 9) h r (9) h r ( 0) h r (0) h r ( ) h r () h r ( ) h r () h r ( 3) h r (3) h r ( 4) h r (4) steepest-descent method wth no degradaton of the BER performance at the recever. 3. Conventonal SRRC flter desgn In the wreless communcaton systems the specfcaton of the SRRC transmtter flter s gven as a standard []. When we use the same flter n the recever sde t makes a matched flter whch s known to have the best BER performance. Ths s the most popular desgn rule for the SRRC flters of the recevers n the wreless communcaton systems. The conventonal desgn method for the SRRC transmtter flter s to generate ts flter coeffcents by the nverse DFT (IDFT) of the followng frequency response: H t f = f < α V 0 + cos πv α f α V α V f + α V + α V < f < V. The tme-doman response of the SRRC flter s gven as sn π t V α + 4α t V cos π t ( + α) V h t t = π t V 4a t (5) V whch s also used as the recever flter response as noted earler [4]. 3. ew desgn algorthm of the SRRC recever flter The proposed SRRC recever flter desgn algorthm reduces the number of FIR recever flter taps by relaxng the restrcton of the ISI crteron whle mantanng the stopband attenuaton wthout degradng the BER performance. By reducng the number of recever flter taps the computatonal complexty and the detecton delay of the recever can be reduced. In ths subsecton we wll combne the ISI R ISI and the stopband attenuaton A SB to make one cost functon as C hr = γ R ISI + γ A SB where γ 0 < γ < s the weghtng factor for the lnear combnaton of the ISI and the stopband attenuaton. The gradent of the lnearly combned C hr s gven as hr C hr = γ Hh r + γ Wh r. (6) Subsequently we can determne the optmum flter coeffcents by applyng the steepest-descent algorthm to (6) as follows: Step : We set the ntal flter coeffcent vector h 0 r of the recever by choosng coeffcents dentcal to those of the transmtter whch s generated by (5). The error vector h r 0 s set to 0. We calculate recever flter coeffcents by teratng the followng three steps from Step to Step 4 for =... ter where ter s the number of allowed teratons. Step : Calculate h r at the th teraton as h r = h r h t T h r h t. Step 3: Calculate the gradent hr C hr at the th teraton as hr C hr = γ Hh r + ( γ) Wh r whch s derved from (6). Step 4: Calculate the error vector h r for next teraton as h r = h r μ hr C hr where μ s the step sze of the steepest-descent algorthm for optmsaton. any researches have been done to fnd the optmal step sze for fast acquston and to mnmse the jtter after the acquston step [ 5 6]. Because optmsaton can be done n the preprocessng stage to fnd the flter coeffcents we set the step sze to a very small number such as wth a very large teraton number of Thus we can fnd the globally optmal soluton because t s a quadratc problem. 3.3 Desgn example In ths subsecton an example of the proposed SRRC recever flter desgn s gven. We set the parameters as follows. The oversamplng rate s V = 4 the weghtng factor γ = 0.9 and the roll-off factor α = 0. all of whch are sourced from the thrdgeneraton partnershp project wdeband code dvson multple access standard [4] where a conventonal FIR SRRC recever flter wth 49 flter taps was used. Then the proposed SRRC flter coeffcents wth number of and 49 taps are desgned n Table. The BER performance of the recever wll be evaluated by a numercal analyss for the proposed number of the SRRC recever flter taps n the followng secton. 4 Performance evaluaton In ths secton we wll show the performance of the proposed SRRC recever flter wth the reduced number of flter taps. Frst the performances of ISI and stopband attenuaton for the proposed SRRC recever flter are evaluated. The BER performance of the 30 IET Commun. 08 Vol. Iss. 9 pp The Insttuton of Engneerng and Technology 08

4 orgnal SRRC flter and the proposed flter do not affect the phase ampltude and delay. Ths means that those flters have almost the same BER performance n the wreless moble channel f they have the same performance n the AWG channel. 4. Performance of ISI and stopband attenuaton Fg. 3 ISI of the proposed SRRC recever flter and the conventonal SRRC flter In order to derve the relatonshps between γ and ISI and between γ and the stopband attenuaton for the proposed recever flter and compare these results wth those for the conventonal SRRC flter varous numercal analyses are conducted as shown n Fg. 3 whch shows that the ISI s reduced as γ and the number of flter taps ncrease. There exsts a floor of the ISI for γ = 0.9 and larger than 4 flter taps. The ISI of the proposed SRRC recever flter s lower than that of the conventonal SRRC recever flter when γ 0.5. The stopband attenuatons for the proposed SRRC recever flter and the conventonal SRRC flter are presented n Fg. 4 whch shows that the stopband attenuaton decreases as γ decreases or as the number of flter taps ncreases. ote that the stopband attenuaton of the proposed recever flter s better than that of the conventonal SRRC flter. 4. BER performance n the AWG channel Fg. 4 Stopband attenuaton of the proposed SRRC recever flter and the conventonal SRRC flter The BER performance of the recever wth the proposed SRRC recever flter s numercally analysed for QPSK 6QA and 64QA wth γ = and wth and 49 flter taps as gven n Fg. 5 whch shows that the BER performance of the proposed SRRC recever flter wth 5 flter taps when γ = 0.9 s nearly dentcal to that of the conventonal SRRC flters wth 49 flter taps even though the ISI and stopband attenuaton of the proposed SRRC recever flters are deterorated compared to the conventonal case. The computatonal complexty of the proposed SRRC recever flter s reduced compared to the conventonal recever flter whch reduces the computatonal complexty and the detecton delay. 4.3 BER performance n hgh ISI envronment In order to check the effect of ISI the BER performance of the proposed SRRC recever flter s evaluated wth phase offset 0V 3 4 0V 0V 0V 5 and 0V for QPSK 6QA and 64QA whch s compared wth the conventonal SRRC recever flter as presented n Fg. 6. To evaluate the BER performance 5 flter taps SRRC recever flter s used whch comes from the prevous subsecton. In Fg. 6 Conv. means the conventonal SRRC flter Prop. means the proposed SRRC flter and PO means phase offset. As the ISI ncreases the BER performance of the conventonal SRRC flter and the proposed SRRC flter deterorates n the same manner. From the smulaton results the conventonal SRRC flter and the proposed SRRC flter have almost the same BER performance under ISI. 4.4 BER performance wth ACI Fg. 5 BER performance of the proposed and the conventonal SRRC recever flters wth QPSK 6QA and 64QA n AWG channel (a) γ = 0. (b) γ = 0.9 recever wth the proposed SRRC recever flter s also numercally analysed n the AWG channel hgh ISI envronment and hgh ACI envronment respectvely whch s then compared wth the conventonal SRRC recever flter wth the reduced number of flter taps. In the wreless moble channel the transmtted sgnal s dstorted n phase ampltude and delay by mult-path fadng. The IET Commun. 08 Vol. Iss. 9 pp The Insttuton of Engneerng and Technology 08 When fewer flter taps are chosen the proposed recever flter has lower stopband attenuaton performance as shown n Fg. 4. However t s challengng to fnd an ACI tolerance gap between cases wth small and large numbers of flter taps whch causes the stopband attenuaton performance dfference between these cases. For example when γ = 0.5 the stopband attenuaton gap between the cases wth 7 and 49 flter taps s approxmately 0 db whch does not mean that there s a 0 db BER performance gap between them. The BER performance of the proposed SRRC recever flter s evaluated for QPSK 6QA and 64QA wth γ = 0.9 and and 49 flter taps as shown n Fg. 7 whch shows that the BER performance of the recever of the proposed SRRC recever flter wth 5 flter taps for γ = 0.9 s almost the same as that of the conventonal SRRC flters wth 49 flter taps and the proposed recever flter wth 33 flter taps has better performance than that of the conventonal SRRC flters wth 49 flter taps. 3

5 proposed SRRC recever flter desgn algorthm effcently reduces the number of flter taps wthout BER performance degradaton n the AWG channel where the proposed recever flter desgn algorthm can reduce the number of flter taps to 7 for QPSK and 6QA and 5 for 64QA wthout BER performance degradaton compared to the conventonal SRRC flter wth 49 flter taps. In hgh ISI envronment the proposed SRRC recever flter wth 5 flter taps for QPSK 6QA and 64QA have almost the same BER performance as the conventonal SRRC recever flter wth 49 flter taps. In hgh ACI envronment the proposed recever flter wth 5 flter taps has almost the same BER performance as the conventonal SRRC flter wth 49 flter taps. Fg. 6 BER performance of the proposed and the conventonal SRRC recever flters wth QPSK 6QA and 64QA n hgh ISI envronment 6 [] [] [3] [4] [5] [6] [7] [8] [9] [0] [] [] [3] [4] [5] [6] [7] Fg. 7 BER performance of the proposed and the conventonal SRRC recever flters wth QPSK 6QA and 64QA n ACI envronment [8] (a) 5 tap flter (b) 33 tap flter [9] 5 Concluson In ths paper a new recever flter desgn algorthm for the wreless communcaton systems s proposed by reducng the number of flter taps whch s based on the steepest-descent method wth a jont cost functon of ISI and stopband attenuaton. Reducton of the recever flter taps reduces the computatonal complexty and the detecton delay n the recever. The ISI and stopband attenuaton were modfed nto the matrx forms to make the jont cost functon for the steepest-descent method. From the numercal analyss t s shown that ISI and stopband attenuaton are degraded by reducng the number of flter taps. The 3 [0] [] [] [3] [4] [5] References Proaks J.G. 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