Transmitter Antenna Diversity and Adaptive Signaling Using Long Range Prediction for Fast Fading DS/CDMA Mobile Radio Channels 1

Transcription

1 Transmitter Antenna Diversity and Adative Signaling Using ong Range Prediction for Fast Fading DS/CDMA Mobile Radio Channels 1 Shengquan Hu, Tugay Eyceoz, Alexandra Duel-Hallen North Carolina State University Det. of Electrical and Comuter Engineering Center for Advanced Comuting and Communication Box 7914, Raleigh, NC {shu, teyceoz, sasha}@eos.ncsu.edu, Hans Hallen North Carolina State University Physics Deartment Box 8202, Raleigh, NC Hans_Hallen@ncsu.edu Abstract -- Recently, the authors introduced a novel algorithm for long range rediction of flat fading channels that can reliably redict future fading coefficients far beyond the coherence time. This rediction caability rovides enabling technology for ower and bandwidth efficient adative modulation and coding methods. In this aer, we extend our results to the Direct Sequence Code Division Multile Access (DS/CDMA) channels. It is demonstrated that frequency selective channels encountered in CDMA can also be redicted far ahead, and that the roosed rediction methods can be combined with RAKE receivers. In addition, we utilize rediction to imrove erformance of the selective transmitter diversity system roosed for the third generation CDMA. 1. INTRODUCTION DS/CDMA technology is attractive for wireless access because of its numerous advantages over other multile access techniques. The Wideband DS/CDMA (WCDMA) has been develoed as a redominant radio access technology for the next generation global wireless standard [1,2]. One of the novel features of WCDMA is suort for transmitter antenna diversity for the downlink [3,4,5]. Some of the roosed transmitter antenna diversity schemes are Orthogonal Transmitter Diversity (OTD), Transmitter Adative Array (TxAA), Selective Transmitter Diversity (STD), and Sace Time Transmitter Diversity (STTD). TxAA and STD can result in better erformance than OTD and STTD, but require feedback of channel state information (CSI) from the mobile to the base station. In ractice, the erformance of these schemes can be degraded due to imerfect and delayed CSI. In articular, even small delay can result in significant degradation due to the time varying nature of the fading channel. In this aer, we roose to utilize the long range rediction method [6-9] to imrove the erformance of transmitter diversity systems. In articular, we focus on Selective Transmitter Diversity. Accurate rior knowledge of the channel for the entire duration of the next frame or slot rovided by long-term rediction would enable more efficient antenna switching at the transmitter. In the next section, we review the CDMA channel and analyze an ideal STD+RAKE system. In Section 3, the long range rediction method is summarized. A comarison of the mean square errors for three aroaches to long range total ower rediction for multiath channels (required for STD imlementation) is carried out in Section 4. In Section 5, the Bit Error Rate (BER) gain achieved by long term rediction for an STD+RAKE system is demonstrated. 2. CDMA SYSTEM MODE AND STD The WCDMA channel is often frequency-selective due to large transmission bandwidth [1,2,10]. As a result, large diversity gain can be realized using the RAKE receiver. This gain can be further enhanced by utilized antenna (diversity) arrays. In ractice, the mobile is often limited to a single antenna, whereas the base station can emloy several antennas. Thus, transmitter antenna diversity techniques for down link signaling have been recently investigated by many researchers (e.g., [3-5].) We consider a combined Selective Transmitter Diversity and RAKE receiver (STD+RAKE) system shown in Figure 1 for two antennas (it can be easily extended to a greater number of antennas). When the signal of the desired user is transmitted either from antenna A or from antenna B, the channel is characterized as frequencyselective Rayleigh fading with aths. All aths are i.i.d. and each channel has unit average ower, i.e., E{ c A k 2 } = E{ c B k 2 } = 1/,,,. The total instantaneous owers associated with the channels of antennas A and B are: Ω A = c A k 2, and Ω B = c B k 2, resectively. Both Ω A and Ω B are Chi-Square distributed with 2 degrees of freedom. For an STD system, the transmission antenna is selected based on the ower comarison between Ω A and Ω B. The antenna that results in a stronger signal at the receiver will be used as the transmission antenna. Thus, assuming erfect CSI at the transmitter, the channel ower of the STD system is Ω S, and the selected multiath fading channel comonents are {c s 1, c s 2,, c s }, where s = argmax A or B {ΩA, Ω B }. The robability density function (df) of Ω S is: -1 f Ω s(x) = 2 (-1)! x-1 e -x (1-e -x (x) k 1 k! ) (1) k=0 Thus, the received signal of the desired user is modeled as r(t)= c s i (t)s(t-kt-it c )b k + z(t) (2) k=0 i=1 where b k is the binary hase shift keying (BPSK) data sequence, T is the symbol interval, s(t) is the signature sequence, T c is the chi duration, and z(t) is a comlexvalued zero-mean white Gaussian noise rocess with variance 1 This research was suorted by NSF grants CCR and NCR

2 A B c 1 A c 1 B c2 B c 2 A c A c B channel ower redictior RAKE receiver Figure 1. Configuration of combined STD+RAKE system N 0 /2. The noise term in this aer models multiuser and intersymbol interference and thermal noise. We also assume that the multiath-delayed versions of the signature waveform s(t) are orthogonal to each other. The RAKE receiver with maximal ratio combining collects the owers of the multiath comonents at the receiver [10]. The instantaneous SNR er bit is given by: γ s b = E b N 0 c s k 2 =γ c Ω S (3) E where E b is the transmitted energy er bit, γ c = b. The df N 0 s of γ b, fγ s b (x), can be determined from (1) and (3). Then the BER of the STD+RAKE system can be obtained as: P b = Q( 2x) fγ s b (x)dx (4) 0 For =2, the closed form of P b is: P b =2(2+µ)( 1-µ 2 )2-1 2 (2+µ')(1-µ 2 )2 1 2 ((1-µ' 2 )3 ( (1+µ') + 3 (1+µ')2)) (5) 2 γ where µ= c γ, and µ'= c. (6) 1+γ c 2+γ c Eq. (5) is the lower bound on the BER of STD+RAKE, since the derivation above assumes erfect CSI at the transmitter and the receiver. In ractice, the roagation delay, fading channel variation, feedback channel errors and receiver channel estimation errors degrade CSI. In the following two sections, we discuss the utilization of the long term rediction in overcoming CSI inaccuracies at the transmitter associated with the roagation delay and fading. 3. ONG RANGE PREDICTION OF THE FADING CHANNE The long range rediction caability for the comlex valued fading channel was demonstrated in [6-9] and references therein. In revious work, we concentrated on flat fading signals. Our linear rediction (P) method is based on the AR channel modeling. Assume that the equivalent comlex Rayleigh fading rocess c(t) is samled at the rate f s = 1/T s, where f s is at least twice the maximum Doler shift, f dm [11]. et c j = c(jt s ). The linear MMSE rediction of the future channel samle c^ n based on reviously observed channel samles c n-1., c n-2,, c n- is ^ c n = d j c n-j (7) where d j's are the coefficients of the P filter. The otimal coefficients d j 's are comuted as d = R -1 r (8) where d = (d 1 d ). R is the autocorrelation matrix ( ) with coefficients R ij = E[c n-i c * n-j] and r is the autocorrelation vector ( 1) with coefficients r j = E[c n c * n+j]. Therefore, the resulting MMSE is given by E[ e n 2 ] = E[ c n - c^ n 2 ] = r 0 - d j r j (9) The P can be generalized to redict any time τ ahead, where τ is the rediction range [7]. In (7), the rediction is one ste ahead, i.e. τ = T s. In ractical imlementation, we iterate this one-ste rediction to forecast the channel further than one samling interval ahead by utilizing reviously redicted samles instead of the observations. It was shown in [6,7] that the key to the long range rediction is the sufficiently long memory san achieved for moderate model order by selecting low samling rate, f s (much lower than the data rate). Interolation is used to erform rediction at the data rate. Furthermore, an adative decision-directed longrange rediction method allows to reduce the effect of noise and to kee u with the channel variations. In addition to the theoretical analysis and simulations for the Rayleigh fading and the Jakes model [11], we verified the erformance of long range rediction for realistic hysical channel models and measured data [8, 9]. Our revious investigations of the long range rediction for the fading channel focused on the case when the comlex valued flat-fading coefficients were redicted and observed. However, deending on the alication, a different rediction roblem might be of interest. For examle, in the decision directed channel estimation, hase ambiguity requires differential encoding, and absolute hases are not available. This makes rediction of future hases roblematic. But this is not a serious limitation, since imlementation of many roosed adative coding methods, e.g. [12-14], deends on the knowledge of future ower only, and hase rediction is not necessary. Thus, it is desirable to examine long range rediction of the fading channel ower using observed ower samles (see also [8]). In the STD+RAKE systems for WCDMA, it is of interest to determine the future total ower for each antenna to aid the antenna selection. However, in contrast to the channels with hase ambiguity, in the roosed 3 rd generation WCDMA systems, coherent channel estimates are available at the receiver since the ilot channel is used. Therefore, comlex fading coefficients associated with different multiath comonents and transmitter antennas (see Section 2) can serve as observations. As we show below, several aroaches to future ower rediction can be exloited deending on the erformance/comlexity requirements.

3 4. STD WITH PREDICTION IN WCDMA SYSTEMS One of the key features that makes WCDMA feasible globally is its high carrier frequency of 2 GHz. However, this high carrier frequency results in very large Doler shifts at moderate vehicular seeds (e.g. 65 mi/h corresonds to f dm = 200 Hz.) These high Doler shifts result in significant variations of the fading channel coefficient over short time eriods. Thus, outdated channel estimates fed back to the transmitter become less useful for adative signaling alication, and long-term fading rediction caability becomes more imortant. Using accurately redicted future channel ower, the transmitter can aroriately select the signaling method for the future frame even when channel varies raidly due to fast fading. In this section, we analyze three aroaches to long-range rediction of the down link channel ower for each transmitter antenna given a sequence of channel observations associated with that antenna. This information about future channel ower allows the mobile to make a suitable selection of the base station antenna for the next transmission interval. In this analysis, we assume that resent and ast samles of the i.i.d. Rayleigh fading coefficients c k for aths (,, ) are observed at the mobile for each transmitter antenna (i.e. samles of c A k (t) and c B k (t) as in section 2 are observed, but we suress the antenna (A or B) and time indices in the sequel). This analysis can be extended to include noise resent in the observations (e.g. noisy ilot symbols). In this aer, we restrict the derivation to the noiseless case to show the otential of long-term ower rediction for the ideal Rayleigh fading channel, and the noisy case is examined through simulation. In the derivations, (7-9) are generalized to include different observation rocesses and arbitrary rediction range τ. Case 1: In this aroach, each future comlex Gaussian fading coefficient c k (t) is redicted searately for each ath and each antenna as in (7), and the total redicted ower for each antenna is calculated using these estimates. These future redicted samles are denoted as c^ 1, c^ 2,, c^. The autocorrelation function of each comonent is [15]: r j = (1/)(Ω 0 /2)J 0 (2πf dm jt s ) (10) where E[ c i 2 ] = Ω 0 /. The rediction MMSE er comonent is ξ i = E[ e i 2 ], where e i = c i - c^ i. By the orthogonality rincile, E[ c^ i 2 ] = E[c i c^ i * ] = E[c * i c^ i] = E[ c i 2 ] - ξ i (11) Since each c i has comlex Gaussian distribution, the estimate c^ i and the error e i are also comlex Gaussian (see (7)). Thus, E[ c^ i 4 ] = 2(E[ c i 2 ] - ξ i ) 2 = 2(Ω 0 /- ξ i ) 2 (12) The total ower rediction mean squared error is ξ T = E[ ( c i 2 - c^ i 2 ) 2 ] = E[ e i ' 2 ] + E[e k 'e j '] (13) i=1 i=1 k j where e i ' = c i 2 - c^ i 2. Exress ξ i ' = E[ e i ' 2 ] = E[ c i 4 ] + E[ c^ i 4 ]-2E[ c i 2 c^ i 2 ] (14) where E[ c i 2 c^ i 2 ] = E[ c i 4 ] - ξ i '. Thus, ξ i ' = E[ c i 4 ]- E[ c^ i 4 2 ] = 4 (Ω 0 /)ξ i 2ξ i (15) Using (15), the fact that e k ' are i.i.d., and E[e k ']=ξ i, we find the total mean squared error for Case 1 as: ξ T = 4 Ω 0 ξ i + ( 2 2-3) ξ i (16) Since ξ i = ξ flat /, where ξ flat is the MMSE of the comlex fading coefficient rediction for =1, the ξ T is given as ξ T = (4 Ω 0 /) ξ flat + ( 2-3)/ 2 2 ξ flat (17) Case 2: In this case, we aly linear MMSE rediction directly to the observations of owers Ω 1,, Ω 2,,, Ω, where Ω i = c i 2 reresents the ower of the fading channel associated with the i-th multiath comonent for a given antenna. The total redicted ower will be comuted using these individual estimates Ω^ i. This Case (and Case 3) are articularly useful to investigate for channels with hase ambiguity since they do not require the knowledge of the hases of the fading coefficients. Each Ω i has the autocorrelation function [15]: r(τ) = (Ω 0 /) 2 J 2 0 (2πf dm τ)+(ω 0 /) 2 (18) The total rediction MSE is ξ T = E[ (Ω i - Ω^ I) 2 ]. i=1 Similarly to Case 1, the total MSE can be exressed as ξ T = ξ i +(-1)(Ω 0 /) 2 (1- d j ) 2 (19) where ξ i = E[ Ω i - Ω^ i 2 ], and d j are the P coefficients for the MMSE ower rediction calculated as in (8) using the autocorrelation function r(τ) (18). Also, from (18), ξ i = (Ω 0 /) 2 (1- d j ) + (Ω 0 /) 2 (1 - d j J 2 0 (2πf dm jts)). Therefore the total MSE for Case 2 is given as: ξ T = Ω 2 0 (1- d j ) 2 + (Ω 2 0 /)(1- d j )( d j ) + Ω 2 0 /(1- d j J 2 0 (2πf dm jts)) (20) Case 3: In this aroach, we form the linear MMSE rediction of the total ower of the fading channel for each antenna using revious total ower samles observed at the receiver. The total ower is given as Ω T = Ω 1 + Ω Ω. It can be shown that the autocorrelation function of Ω T is r T (τ) = (Ω 0 /) 2 J 2 0 (2πf dm τ)+ω 2 0, (21) and the MMSE E[ Ω T - Ω^ T 2 ] for Case 3 can be exressed as ξ T = Ω 2 0 (1- d j ) + Ω 2 0 /(1- d j J 2 0 (2πf dm jts)) (22) Performance Comarisons of 3 Cases: We comare the MSEs of the three aroaches derived above for the noiseless case. In our analysis, the total channel ower for each antenna is normalized to 1. To make system arameters consistent with the third-generation WCDMA system, we assume the carrier frequency is 2 GHz and f dm=200 Hz. In the theoretical calculation of the model coefficients, it is required to invert the autocorrelation matrices obtained from samling (10), (18) and (21) for Cases 1, 2, and 3, resectively. We found that higher samling rates f s (e.g., 1.6KHz) cause matrix singularities when the model is large. This is due to oversamling the channel relative to the Nyquist rate of 400Hz. If the samling rate is chosen closer to 400Hz, the

4 MMSE MMSE =50,f s =500Hz, theoretical =50,f s =500Hz, simulation =15,f s =1000Hz, theoretical =1 = Number of aths, Figure 2. Prediction MSE of total multiath channel ower. Prediction range τ=2ms. matrix does not become singular for large. In ractice, additive noise and the finite observation interval result in a non-singular matrix. In this comarison of the ideal noiseless MSEs, we concentrate on cases when the matrix is not singular. This is assured by choosing sufficiently low f s for a given value of. In Figure 2, we fix the rediction range τ=2ms, and examine two choices of rediction arameters. The first selection (=50, f s =500 Hz) corresonds to much larger memory san /f s than the second set (=15, f s =1 KHz). Nevertheless, the second selection results in much lower MSE for Case 1, suggesting that it is beneficial to samle recent observation at sufficiently high rate (of course 1KHz is still much lower than the data rate). We find that the total MSEs for all 3 cases decrease as grows and aroach the saturation values that can be determined from (17), (20), and (22). The theoretical MSEs of cases 2 and 3 for both choices are close enough to be considered as same. In general, these cases erform much oorer than Case 1 for realistic rediction ranges and number of aths. However, Case 3 requires only one redictor er antenna, so its comlexity is lower than that of Cases 1 and 2, which require redictors for each antenna. Of course, in the resence of hase ambiguity Case 1 is not feasible, and Case 3 is the better choice. In Figure 2, we also show simulation results for the noiseless case for the lower f s. They were imlemented using 2000 observation samles for the Jakes model with 100 oscillators. Due to the channel mismatch [7], simulations do not closely match theoretical results, but erformance trends are the same. In Figure 3, we consider the MSE erformance versus the rediction range for the samling rate, f s = 1.6 KHz, and =10. Observe that Cases 2 and 3 outerform Case 1 for sufficiently large rediction range. We also found that as increases and f s decreases, this cross-over occurs for a lower value of the rediction range. Thus, when rediction far ahead is desired, Case 1 is not always the best choice, considering its high comlexity. However, for most ractical alications Case 1 would result in the best erformance. We also examined erformance of our rediction method with noisy observations by simulation (not shown). It was Prediction range τ (ms) Figure 3. Theoretical rediction MSE vs. rediction range. found that MSE erformance degrades greatly for low SNR (all three cases erform above MSE of 10-1 for SNR=10dB). Therefore, it is imortant to reduce the effect of noise. This can be accomlished in ractice by combining rediction with adative tracking [7-9]. 5. BIT ERROR RATE OF STD+RAKE We resent the BER simulation results of the long range channel rediction algorithm for STD+RAKE system shown in Figure 1. Jakes model with nine oscillators was used to generate the fading channels. We samle the channel at the rate of 1.6 khz, which corresonds to the ower control rate in the WCDMA system [1]. Assume the transmission data rate is 80 kbs and f dm =200Hz. First, for a flat fading channel, we investigate STD with different switching frequencies corresonding to one slot (1.6KHz), four slots (400Hz) and one frame (160Hz) of the WCDMA system. Assume that antenna selection bit is chosen based on the ower comarison at the receiver and sent to the transmitter. This selection is made during the slot that recedes the antenna switching. When no rediction is erformed, the outdated channel estimates are used to make this selection, since fading conditions during revious slot determine which antenna is going to be chosen. This feedback delay is given by the duration of one slot. When rediction is utilized (we assume noiseless observations and use Case 1), revious channel samles collected at the rate of 1.6KHz are used to redict the channel ower during the next switching interval. The most recent samle is delayed by ms with resect to the beginning of the switching interval same delay as when rediction is not emloyed. Antenna switching is based on the average of interolated channel samles at the data rate. These interolated data rate samles are comuted using redicted lower rate (1.6 KHz) channel samles. Multi-ste rediction is erformed to forecast sufficient number of samles. To reduce comlexity, we can avoid interolation by averaging the oints redicted at the lower samling rate without significantly degrading the BER erformance. The rediction technique emloyed in this aer does not utilize adative tracking. Adatation would further imrove rediction

5 Bit Error Rate 10-3 STD theoretical without rediction with rediction switch at 1600 Hz switch at 400 Hz switch at 160 Hz Rayleigh Average SNR er channel (db) Figure 4. BER erformance of STD over flat Rayleigh fading channel with and without rediction for various antenna switching rates. accuracy by reducing the effect of the finite observation interval. Figure 4 also contains the BER of the Rayleigh fading channel [ 10] and the ideal erformance of the STD (5). We conclude that significant erformance gains (2dB or greater) are achieved for fast vehicle seeds when long range rediction is used. Now, we consider the BER erformance of STD+RAKE system shown in Figure 1 for =2. Theoretical BER erformance is given by (5). In the simulation, we adatively select the antenna at the rate of 1.6 KHz. The BERs of STD+RAKE system obtained using simulations with three different ower rediction aroaches roosed in Section 3 are lotted in Figure 5. As exected, Case 1 gives the best erformance. However, the gain with resect Case2 and 3 is not very significant. This is because STD is not as sensitive to the rediction error as adative ower control schemes (e.g. truncated channel inversion [6]), since only the information on the ranking of channel owers is required. Finally, the BER of STD with 1-slot delayed channel state information (without rediction) was also investigated by simulations. As in the flat fading case, our ower rediction method achieves significant erformance gains over the delayed channel estimation. As the number of aths increases, the ideal erformance of STD+RAKE given by (5) imroves, although saturation occurs for large. ong range rediction hels to realize the gains for this romising downlink diversity technique for raidly varying multiath fading channels. 6. CONCUSION We evaluated erformance of the transmitter selection diversity technique for multiath fading CDMA channels aided by long range ower rediction algorithms. Suitable choice of rediction arameters results in accurate rediction that makes STD feasible even for high vehicle seeds. Bit Error Rate 10-3 theoretical without rediction with rediction Average SNR er channel (db) Figure 5. BER erformance comarison of STD+RAKE (switching frequency 1.6KHz, =2) without rediction and for three ower rediction methods. ACKNOWEDGMENT The authors would like to thank Secin Guncavdi and Dr. Dimitrios Efstathiou for helful discussions. REFERENCES [1] E. Dahlman et al., "WCDMA The Radio interface for Future Mobile Multimedia Communications", IEEE Trans. on Vehicular Tech.., vol. 47, No. 4, , Nov [2] F. Adachi, M. Sawahashi, and H. Suda, "Wideband DS-CDMA for Next Generation Mobile Communications Systems", IEEE Comm. Mag., , Set [3] W. M. DeSevilla and E. Sousa, "Fading Resistant Transmission from Several Antennas", Proc. IEEE PIMRC'95, , [4] T. Heikkinen and A. Hottinen, "On Downlink Power Control and Caacity with Multi-Antenna Transmission", Proc. Conf. Inf. Sci. and Syst. (CISS'98), Princeton, , March [5] A. Hottinen and R. Wichman, "Transmit Diversity by Antenna Selection in CDMA Downlink", Proc. of IEEE 5 th Int. Sym. on Sread Sec. Tech. and Al., , Set [6] T. Eyceoz, A. Duel-Hallen, and H. Hallen, Deterministic Channel Modeling and ong Range Prediction of Fast Fading Mobile radio Channels, IEEE Comm. etters, Vol. 2, No. 9, , Set [7] T. Eyceoz, S. Hu, and A. Duel-Hallen, "Performance Analysis of ong Range Prediction for Fast Fading Channels", Proc. of CISS'99. [8] S. Hu, H. Hallen and A. Duel-Hallen, "Physical Channel Modeling, Adative Prediction and Transmitter Diversity for Flat Fading Mobile Channels," Proceedings of SPAWC'99. [9] S. Hu, H. Hallen and A. Duel-Hallen, "Adative Power Control Using ong Range Prediction for Realistic Fast Fading Channel Models and Measured Data", to aear in Proceedings of ISCTA'99 [10] J. G. Proakis, Digital Communications, McGraw-Hill, New York,1995. [11] W. C. Jakes, Microwave Mobile Communications, IEEE Press, [12] A. J. Goldsmith and S. G. Chua, Adative Coded Modulation for Fading Channels, IEEE Trans. on Comm., vol. 46, No. 5, , May [13] D.. Goeckel, Adative Coding for Fading Channels using Outdated Channel Estimates, Proceedings of VTC, May [14] E. Biglieri, G. Cairo, and G. Taricco, Coding and Modulation under Power Constraints, IEEE Personal Communications, , June [15] G.. Stuber, Princiles of Mobile Communications, Kluwer, 1996