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1 Reduced Cmpleity Diversity Cmbining and Adaptive Equalizatin Using Interplated Channel Estimates with Applicatins t Cellular Mbile Radi Channels. Tugay Eycez and Aleandra Duel-Hallen Dept. f Electrical & Cmputer Engineering, Nrth Carlina State University, B 7911, Raleigh, NC teycez@es.ncsu.edu, sasha@es.ncsu.edu Abstract{In this paper, we investigate an antenna diversity cmbiner-equalizer receiver structure t cmbat multipath fading in Cellular Mbile Radi (CMR) cmmunicatins. Our system specicatins are cmpatible with the U.S. digital cellular system. The technique utilizes blck adaptatin and linear r decisin feedback equalizatin. The receiver ers cmpleity reductin relative t previusly prpsed blck adaptatin methds [1, 2] withut sacricing perfrmance. I Intrductin The main bjective in the design f digital cmmunicatin systems is t achieve the highest pssible transmissin rate with acceptable level f reliability. In CMR cmmunicatins the basic prblem is the time dispersin intrduced by the Rayleigh fading multipath channel. Thus, the signal dispersin caused by frequency selective multipath fading and the time-varying signal prpagatin resulting frm vehicular mtin intrduce intersymbl interference (ISI) and randm dppler fading [3, 4, 5, 6]. In rder t cmbat intersymbl interference (ISI) and rapid time variatins in CMR cmmunicatins ccurring ver frequency selective fading multipath channels, we investigated a diversity cmbiner-adaptive equalizer receiver structure. Specically, we used diversity receptin, knwn t cmbat fast fading, alng with adaptive equalizatin, knwn fr mitigating the eects f ISI, fr ur receiver structure. As a diversity receptin technique we used space diversity with multiple antennas, spaced suciently far apart s that their received signals fade independently. It is imprtant t cnsider channel fading in the design f an adaptive equalizer. In CMR cmmunicatins where the channel is fast fading, cmbiner equalizer parameters can be calculated peridically based n channel estimates r updated using an adaptive equalizatin algrithm. We used the frmer apprach. Specically, blck adaptatin using knwn training sequences is used fr ur CMR cmmunicatins system. In cntrast t cntinuus adaptatin, a blck adaptatin algrithm cmputes and changes the receiver parameters at the beginning f each data frame. The start f each data frame cntains a knwn training sequence which is used t estimate the channel impulse respnse (CIR). Hwever, fr a fast fading channel, the CIR estimate btained frm training at the beginning f a data frame shuld be updated several times during the data frame. This time-varying CIR is determined by interplating a set f estimated CIR This research was supprted by NSF grant NCR values. Then the cmbiner-equalizer parameters are adaptively cmputed using interplated channel estimates frm each f the L diversity channels, yielding the ptimum perfrmance in the MMSE sense. In [2], L et al. used the same blck-adaptive strategy. Hwever, their receiver structure was dierent. They used an individual fractinally spaced feedfrward lter fr each diversity path and ne cmmn symbl spaced feedback lter. On the ther hand, in [7], Balaban and Salz derived a symbl spaced Minimum Mean Square Errr (MMSE) ptimum receiver structure. They als cmbined diversity receptin with adaptive equalizatin int a single receiver. Implementing this receiver requires knwledge f actual channel characteristics, since this receiver features a set f matched lters fr each diversity path. The additinal parts f their ptimum receiver structure cnsist f tapped-delay line lters used fr prcessing the sum f the utput samples frm the matched lters prir t detectin. We cmbined blckadaptive strategy apprach with the receiver structure similar t that f Balaban and Salz. Our receiver has fractinally spaced matched lter fr each diversity branch fllwed by a single symbl spaced Linear Equalizer () r Decisin Feedback Equalizer (). This receiver structure has lwer cmputatinal cmpleity than that f L et al., and des nt require prir knwledge f channel parameters as that f Balaban and Salz. In the fllwing sectins we describe ur CMR cmmunicatin mdel and discuss simulatin results. II CMR System Descriptin A blck diagram f the CMR cmmunicatins system is presented in Figure 1. Our system specicatins are cmpatible with the U.S. digital cellular system. A narrwband time divisin multiple access (TDMA) channel access methd accmmdates three users in a band f 30 khz in each directin, with 8 kbits/s user. The =4-shifted DQPSK mdulatin methd is used. The transmit and receive lters have square rt raised csine frequency respnse characteristics with a 35% rll factr. In this paper a discrete-time representatin is used which crrespnds t sampling all signals at T =2, where T is a symbl interval. At the l th diversity branch, the received signal is V l (t) = S(t) h l (t) + N l (t) = X k S(kT )h l (t? kt ) + N l (t) (1)

2 data surce Gray Encde and map t pi/4-dqpsk g(kt/2) transmit filter c 1 (kt/2) c L (kt/2) diversity channels N 1 (kt/2) AWGN N L (kt/2) g 1 * (kt/2) g L * (kt/2) receive filter h 1 (kt/2) h L (kt/2) channel etimatrs f 1 (kt/2) f L (kt/2) channel interplatrs h 1 * (kt/2) hl * (kt/2) T T T U k ptimum cmbiner / equalizer Figure 1: CMR cmmunicatins system with linear blck adaptive equalizatin where S(kT ) is the =4-shifted DQPSK data sequence at time kt, N l (t) is the AWGN with the variance f 2 n, and h l (t) is the channel impulse respnse (CIR) which als includes the transmit and received lter respnses. Channel Mdel Fr each diversity branch, the CMR channel is mdeled in cmple baseband representatin as an FIR lter in the frm f a T/2-spaced tapped-delay-line (TDL) as shwn in Figure 2. The TDL cnsists f three cmple tap cecients, c i l (kt ) i=1,2,3, each representing a distinct multipath. The multipath pwer delay prle (MPDP) f the channel is specied with a three-paths "muntainus terrain" mdel with relative rms pwers f 0, -5, and -15 db. Each channel tap cecient having Rayleigh fading characteristics is simulated with the "mdied Jakes mdel" [3, 8] using siteen sinusids with distinct Dppler frequencies up t a maimum Dppler frequency, fdm f 100 Hz. Furthermre, cmple additive white gaussian nise (AWGN) with variance n 2 is added t the transmitted signal at the utput f each diversity channel. These nise cmpnents are independent. input X(kT) T/2 X(kT-T/2) T/2 X(kT-T) Since CIR estimates are updated at the beginning f each data frame, this type f peridic training imprves the adaptatin prblem. Hwever, it intrduces sme system verhead, which is dened as the percentage data thrughput: %T = 100N d % = 100N d % (3) N d + N t This signaling strategy is simpler than prpsed narrwband TDMA signaling frmat. Fr eample, sme signaling infrmatin such as synchrnizatin, guard and ramp times, and ther cntrl signals are nt included in ur time slt. Therefre, we ignre this verhead in ur analysis. Blck Adaptatin-Channel Estimatin and Interplatin In this sectin, we describe the channel estimatin prcedure which is perfrmed fr each diversity branch. We mit the branch inde t simplify ntatin. T estimate the channel impulse respnse (CIR), blck adaptatin using a knwn training sequence is emplyed [2]. This technique is ptimum under the assumptin that the CIR is ed during the training perid. In ur system, the verall CIR length, N c, is ed t si symbl perids f which ve symbl perids are due t transmit and receive lter impulse respnses, and ne symbl perid is due t the actual CIR f the CMR channel. The training sequence is 15 symbls lng as suggested in [2]. During a training sequence, the verall CIR estimate, h, is btained frm the Blck Least Squares (BLS) slutin described in [2]. The channel estimate is timevarying and changes during the data frame. After training, blck-adaptive strategy cmputes the time-varying CIR by interplating a set f estimated CIR values [2]. The relative psitins f the estimated and interplated CIR samples within the TDMA time slt are illustrated in Fig 3. training sequence data sequence time slt data frame T D T D T D T D c l 1 (kt) c l 2 (kt) c l 3 (kt) T s T s Σ AWGN N l (kt) Y l (kt) Figure 2: T =2-spaced TDL with three-paths "muntainus terrain" channel mdel at l th diversity branch Signaling Frmat The signaling frmat f alternating training and data sequences within a lng TDMA time slt is used. Each data frame cnsists f a training sequence f length N t symbls fllwed by an uncrrelated data sequence f length N d symbls. Therefre, the number f symbls in each transmitted frame is = N d + N t (2) Figure 3: CIR interplatin within a TDMA time slt. ''- estimated CIR sample at the end f a training sequence, Q=4, ''-interplated CIR in the middle data frame, R = T s =T 0 s = 4 T satisfy Nyquist's sampling criterin, the sampling rate f the CIR estimates is required t be f s 2f dm (4) where f dm is the maimum Dppler frequency. This indicates that CIR estimates have t be calculated at least as ften as 2f dm. Furthermre, the nrmalized sampling rate f the CIR estimates is dened as f = f s 2f dm = 1 2f dm T 1 (5)

3 i.e., fr the maimum Dppler frequency f f dm = 100 Hz and symbl rate f 1 T = 24 ksps, the required frame length shuld be = N t + N d 120 symbls. This blck adaptatin strategy was previusly published [2], but its utilizatin in the receiver structure is new as described belw. Receiver Structures We used interplated CIR estimates, h l, frm each f the L diversity channels t cmpute the receiver parameters yielding the ptimum perfrmance in the MMSE sense. The ptimal receivers are derived under the assumptin that the channel respnse h l (t) can be estimated perfectly, i.e., h l (t) is given by the actual respnse h l (t). V 1 (t) V 2 (t) V L (t) h * 1 (-t)... h * 2 (-t) h * L (-t) T T T T T T U 0 U k Figure 4: Optimum diversity cmbiner linear equalizer structure V 1 (t) V 2 (t) V L (t) h * 1 (-t)... h * 2 (-t) h * L (-t) T T T T Decisins T T U q 1 q k 0 Figure 5: Optimum diversity cmbiner decisin feedback equalizer structure It was shwn in [7] that rst step in the implementatin f the ptimum linear r decisin feedback equalizer is t pass the received signal V (t) thrugh a matched lter assciated with the l th diversity channel. The utputs f the matched lters are then summed and prcessed using a symbl-spaced decisin structure. The ptimal cnguratins are depicted in Figures 4 and 5 fr the linear and the decisin feedback Received V l (kt+t/2) V l (kt) V l (kt-t/2) signal T/2 T/2 T/2 T/2 T/2 T/2 h * l ((N c -1)T/2) h * l (T/2) h * l (0) h * l (-T/2) h * l (-N c T/2) Figure 6: Fractinally spaced Matched Filter fr the l th diversity branch fr equalizers, respectively. Mrever, the tap cecients f these equalizers are derived as in [7]. In [7], knwn channel respnses are assumed. Hwever, in the adaptive implementatin, channel respnses need t be estimated t determine respnses f the matched lters fr each branch. We implemented these matched lters as fractinally spaced (specically T =2 spaced), transversal lters as seen in Figure 6. The lter tap cecients are determined by the current channel estimates btained as described in the previus subsectin. The verall length f the matched lter is si symbl perids which is the length f the CIR estimate. The cmputatinal cmpleity reductin f the new structure results frm emplying a single equalizer fllwing a diversity cmbiner. Previusly prpsed adaptive receivers featured separate fractinally spaced equalizers assciated with each diversity branch. Calculatin f the equalizer cecients is signicantly simplied. The cmputatinal cmpleity is independent f the number f antenna elements as ppsed t linear dependence in previus implementatins [1, 2]. III Simulatin Results The CMR cmmunicatin system is mdeled with equivalent cmple baseband signals and simulated thrugh etensive use f Mnte Carl apprach. Optimum diversity cmbiner linear equalizer with N = 5 taps is dented as OD- C(5,0), and ptimum diversity cmbiner decisin feedback equalizer with N f = 3 taps in the frward lter and N b = 2 taps in the feedback lter is dented as ODC(3,2). Numerical results illustrate several perfrmance characteristics f the prpsed receivers. System perfrmance imprves with mre frequent CIR training while reducing the system thrughput. Fr ODC(5,0) the average perfrmance as a functin f the nrmalized sampling rate, f, fr dierent values f the maimum Dppler frequency is illustrated in Figure 7 fr the case f SN R = 20 db and L = 1. We see frm this gure that the average mntnically decreases fr increasing values f f fr high Dppler frequencies. Hwever, when is used instead f, we bserve the decreasing fr all Dppler frequencies as seen in Figure 7 fr ODC(3,2). is superir t fr all Dppler shifts since is mre apprpriate fr channels with spectral nulls and it des nt suer frm nise enhancement. The average perfrmance as a functin f the nr-

4 10 0 fdm = 75 Hz fdm = 50 Hz fdm = 25 Hz fdm = 0 Hz 10 0 L = 1 L = 2 L = Nrmalized sampling rate, fs/2fdm Figure 7: Average as a functin f nrmalized sampling rate, f, and the maimum Dppler frequency, f dm fr ODC(5,0) and ODC(3,2) 10 6 Nrmalized sampling rate, fs/2fdm Figure 8: Average as a functin f nrmalized sampling rate, f, and diversity fr bth ODC(5,0) and OD- C(3,2) with SN R = 20 db and f dm = 100 Hz malized sampling rate, f, fr the number f diversity channels, L, is illustrated in Figure 8 fr the case f SN R = 20 db and the maimum Dppler frequency, f dm = 100 Hz. It can be seen frm the gure that the system perfrmance imprves with increasing f and L. Hwever, fr all diversity cases, the system perfrmance at the Nyquist sampling rate (i.e., f = 1) is lw. This pr perfrmance is caused by insuciently frequent training and by the severe aliasing distrtin due t the interplatin lter which leads t pr tracking f the fast fading channel at each diversity branch. The system perfrmance gains tend t atten ut at high sampling rates. The average imprvement in Figures 7 and 8 is due t mre frequent training as we increased the nrmalized sampling rate, f. The perfrmance imprvement with increasing f results in an verhead f reduced system thrughput, %T (see Eq.3). Specically, at f = 1:0, the system thrughput, %T, is 87:5% and the prcessing delay, D t, is 15 ms while at f = 3:0, %T is 62:5% and D t is 5 ms. Therefre, ne can select the suitable nrmalized sampling rate by cnsidering the trade- between the system perfrmance and the thrughput/delay requirements. Our results fr varius Dppler frequencies and the number f diversity channels shw that a value f f = 2:0 (i.e., twice the Nyquist sampling rate), with an assciated %T = 75% and D t = 7:5 ms, is a reasnable design chice fr ur CMR cmmunicatins system. Net, we discuss the system perfrmance as a functin f the average channel SNR. The nrmalized sampling rate is chsen t be f = 2:0 fr the rest f the simulatins. The average perfrmance as a functin f the average channel SNR fr the number f diversity channels, L, and maimum Dppler frequency, f dm, is illustrated in Figure 9 fr ODC(5,0) and ODC(3,2). The high channel nise is the dminant reasn fr the pr system perfrmance at lw SNR values. Althugh the system perfrmance imprves with increasing SNR, an irreducible was fund t ccur at high values f SNR 20 db. This is due t receiver limitatins in estimatin and tracking the rapid time variatins in the fading channel. The use f diversity channels imprves the system perfrmance. Althugh it des nt eliminate the errr r, it des reduce the level f the irreducible. Althugh innite number f equalizer taps is needed t cancel all ISI, we have t cnsider cmputatinal cmpleity invlved in the calculatin f the equalizer cecients. Therefre, we searched fr ptimum equalizer length fr ur CMR cmmunicatins system [1]. Our results indicate that the linear equalizer size f 5 symbl perids is ptimum in terms f cancelling ISI fr L = 1. In additin, fr diversity channels, L = 2 and L = 4, there is nly less than 2 db dierence between the equalizer size f 5 and the innite tap equalizer. Therefre, cnsidering the cmputatinal cmpleity invlved in calculatin f the equalizer cecients, the equalizer size f 5 symbl perids is a very gd chice fr ur ptimum diversity cmbiner and equalizer structure. Mrever, the equalizer length f 1 means nly diversity is emplyed. We als nte that when equalizer length is 1, the system perfrmance is severely degraded [1]. Hence, it is necessary t use an equalizer in additin t diversity cmbining t achieve gd system perfrmance. In [2], L et al. used a dierent technique t calculate the receiver cecients. Instead f using a matched lter fr each diversity path, they used an individual fractinally spaced feedfrward lter fr each diversity path and ne cmmn symbl spaced feedback lter. The authrs f [2] slved matri equatins with the rder f (LN f +N b )(LN f +N b ) t calculate their equalizer cecients, where N f and N b are the number f frward and feedback taps respectively. Thus, the dimensins f the matri depends n L. Hwever, in ur receiver structure, we slve matri equatins with the rder f N N fr the and (N f + N b ) (N f + N b ) fr

5 L=1 fdm = 10 Hz L s receiver Our receiver, ODC(3,2) fdm = 75 Hz fdm = 50 Hz fdm = 25 Hz fdm = 0 Hz L= SNR Figure 9: Average as a functin f channel SNR, diversity and Dppler fading fr ODC(5,0) and ODC(3,2) the. Fr eample, L et al. chse N f = 3 and N b = 2. Fr the diversity rder f L = 4, they slved a matri equatin. Hwever, with the same number f taps (this number is als ptimum fr ur system), we slve a 55 matri equatins regardless f diversity. Hence, cmputatinal cmpleity invlved in calculatin f the ptimum diversity cmbiner and equalizer structure is cnsiderably reduced as the number f diversity channels increases. In Figure 10, the average perfrmance as a functin f the nrmalized sampling rate, f, fr dierent values f the maimum Dppler frequency is illustrated fr ur ODC(3,2) and L's receiver fr the case f SN R = 20 db and L = 1. We see frm the gure that ur receiver structure is slightly better than L's mdel fr high maimum Dppler frequencies and the nrmalized sampling rate less than 2, ( f < 2). Fr lw Dppler frequencies and f 2, the receiver structures perfrm almst identically. We als bserve the similar eect as we increase the number f diversity channels. The main reasn fr this imprvement is the use f the fractinally spaced matched lter fr each diversity branch. Since the matched lter spans the whle CIR, we maimize the pwer f the current symbl. IV Cnclusins A simplied antenna diversity cmbiner-equalizer structure was prpsed and analyzed fr CMR channel. This receiver is preferable t previusly prpsed appraches when CIR estimatin rather than adaptive equalizatin is perfrmed. Further research issues include "phase alignment" prblem [11] which arises in CIR estimatin fr dierentially encded data and receiver design fr systems with errr cntrl cding. References [1] T. Eycez, "Reduced Cmpleity Optimal Diversity Cmbining and Adaptive Equalizatin Using Interplated Channel Estimates with Applicatins t Cellular Nrmalized sampling rate, fs/2fdm Figure 10: Perfrmance cmparisn f ur receiver structure and L's receiver structure as a functin f the nrmalized sampling rate, f, and the maimum Dppler frequency, f dm with SN R = 20 db and L = 1 Mbile Radi Channels", Master's thesis, Nrth Carlina State Univ., Nvember [2] N. W. K. L, D. D. Falcner, and A. U. H. Sheikh, "Adaptive Equalizatin and Diversity Cmbining fr a Mbile Radi Channel using Interplated Channel Estimates", IEEE Transactins n Vehicular Technlgy, 40(3):636{645, August [3] W. C. Jakes, Micrwave Mbile Cmmunicatins, Jhn Wiley and Sns, New Yrk, [4] W. C. Y. Lee, Mbile Cmmunicatins Engineering, McGraw-Hill, New Yrk, [5] J. G. Prakis, Digital Cmmunicatins, McGraw-Hill, New Yrk, [6] S. Stein, "Fading Channel Issues in System Engineering", IEEE Jurnal n Selected Areas in Cmmunicatins, 5(2):68{89, February [7] P. Balaban and J. Salz, "Optimum Diversity Cmbining and Equalizatin in digital Data Transmissin with Applicatins t Cellular Mbile Radi-Part I: Theretical Cnsideratins", IEEE Transactins n Cmmunicatins, 40(5):885{894, May [8] P. Dent, G. E. Bttmley, and T. Crft, "Jakes Fading Mdel Revisited", Electrnics Letters, 29(13):1162{ 1163, June [9] J. Salz, "Optimum Mean-Square Decisin Feedback Equalizatin", Bell Systems Technical Jurnal, 52(8):1341{1373, Octber [10] S. U. H. Qureshi, "Adaptive Equalizatin", Prceedings f the IEEE, 73(9):1349{1387, September [11] R. D. Kilpillai, S. Chennakeshu, and R. L. Ty, "Lw Cmpleity Equalizers fr U.S. Digital Cellular System", Prceedings f VTC, 744{747, May 1992.