WHILE the demand for higher and higher data rates

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1 Transmit Diversity for Frequency Selective Channels in UMTS-TDD Uwe Ringel, Ralf Irmer and Gerhard Fettweis Dresden University of Technology, Mommsenstrasse 3, 6 Dresden, Germany {ringel,irmer,fettweis}@ifnettu-dresdende Abstract Multipath propagation and fading are typical characteristics of wireless communication channels Simultaneously, they are also the most limiting factors for high speed data rates This paper investigates the performance of systems using multiple transmit antennas (MISO - multiple input single output) in frequency-selective channels, which combat fading and exploit multipath propagation The system considered in this paper is UMTS-TDD The investigations focus on different antenna configurations and on correlated propagation channels The impact of Doppler-spread due to the velocity of the mobile user is considered The problem of asymmetrical data-rates on up- and downlink is addressed Keywords transmit diversity, frequency selective channels, MISO-transmission, UMTS-TDD, Doppler spread, channel correlation, variable switching point configuration I INTRODUCTION WHILE the demand for higher and higher data rates in wireless communication systems is continuously growing, also the importance of effectively mitigating or even exploiting typical characteristics of wireless channels, such as multipath propagation and fading increases Currently, several extensions of the 3G systems or proposals for 4G are discussed The possibility of applying multiple antennas in the transmitter is discussed in this paper Diversity measures, conventionally used at the receiver, concentrate on exploiting either the temporal domain (multipath propagation), eg by Rake-receivers, or the spatial domain, eg by antenna arrays Recently, research more and more focuses on transmit diversity techniques [3] [4] [5] [] The reason is that data rates of future wireless applications are expected to be asymmetric in up- and downlink, with the main data portion in the downlink direction Thus, the downlink needs to be especially robust At the same time, the receiver terminals, ie the handhelds, have to be kept as simple as possible due to cost reasons Therefore, transmit diversity schemes are primarily intended to be employed at base stations where computing and power resources are sufficiently available However, approaches for employing transmit diversity techniques at the handset exist as well [] Subsequently, it is assumed that base stations are equipped with an antenna array and the mobile receiver solely has a single antenna available (MISO, multiple input - single output) All techniques assume an a priori knowledge of the channel impulse response (CIR) at the transmitter In the Time Divison Duplex (TDD) mode of UMTS, the same channel is used for up- and downlink Thus, the CIR required for subsequent downlink transmission can be obtained by uplink channel estimation In a Frequency Division Duplex (FDD) system, the CIRs have to be relayed back from the receiver to the transmitter through a separate feedback channel Then, additional aspects as for example the feedback amount and latency issues must be considered Important issue of all these methods is the robustness in realworld environments Therefore, spatial correlation of the antennas due to insufficient antenna spacing has to be considered Imperfect channel estimation in the transmitter and receiver due to the mobile user velocity and due to asymmetrical duplex rates in UMTS-TDD are further topics of this paper This paper is organized as follows In section II and III, the channel and the systems are modelled and the investigated transmit diversity systems are described Section IV presents simulation results for idealized conditions and for more realistic environments, including correlated antennas and imperfect channel estimation Finally, conclusions are drawn in section V A Notation II SYSTEM AND CHANNEL MODEL In this paper, lower case bold letters are used for vectors, capital bold letters for matrices, T, and H for transposed, conjugate and Hermitian, respectively Convolution is denoted by The indices T x, Ch and Rx stand for transmitter, channel and receiver A is the number of transmit antennas and M is the number of chips per block, ie per slot B Signal Spreading In a Multiple-Input Single-Output (MISO) system, the transmitter has A Tx-antennas and the receiver has one Rxantenna, as shown in Fig In contrast to space-time blockcoding (STBC), the same spread signal is transmitted from all Tx-antennas, which is however individually pre-filtered by an FIR filter at each antenna Due to the slot-structure of TDD-systems the signals are transmitted burst-by-burst Therefore, vector-matrix notation is used In UMTS-TDD, the digital modulation format is QPSK The burst of information symbols d {,, j, j} is organized in a column vector d of length N The short complex spreading code is denoted by c with spreading gain G and nor- G malized power i= c(i) = The spread signal of the desired user is represented by a vector s of size M = N G chips s = Cd, () with the (N M) spreading matrix C = blockdiag{c} C Channel Model The channel of the a th Tx antenna is modeled as a length L tapped-delay line with equidistant chip-spaced taps, h Ch,a = [h Ch,a (), h Ch,a (),, h Ch,a (L )] T ()

2 data symbols spreader n RAKE MRC-FIR despreader data symbols d c A- A- h Rx c* ^ d h Tx h Ch Fig MISO System Model with Transmit-Filters, Channels and Rake-Receiver The (M M) block channel matrix is H Ch,a = h Ch,a () h Ch,a () h Ch,a (L ) h Ch,a (), (3) and H Ch,a is the size (L L) upper left submatrix of H Ch,a The length M signal at the receiver is r a = H Ch,a s + n, (4) where n denotes the vector containing the AWGN-samples of variance σ Note that, for simplicity reasons the received signal vector r a has the same length as the transmit signal vector s Therefore, the last symbol of s is incompletely received, and thus, performance considerations are exclusively valid under the constraint that M L Migrating from the aforementioned described SISO-model to the MISO-model, the channel vector has A diversity branches h Ch = h T Ch,, h T Ch,,, h T T Ch,A (5) Then, the size (M M A) and (L L A) channel matrices are H Ch = [H Ch,,, H Ch,A ] H Ch = H Ch,,, H Ch,A With that, the length M signal at the receiver is given as (6) r = H Ch s + n, (7) where the multiple Tx-antenna transmit signal vector s is defined according to equation (9) D Transmitter Each of the A transmit antennas has its own transmit FIR filter with impulse response h T x,a of length L T x and filter matrix H T x,a defined as in (3) Without loss of generality it is assumed that L T x = L This assumption is valid because h T x,a can be made arbitrary long by zero-padding The length (L T x A) MISO transmitter pre-filter vector and size (M A M) pre-filter matrix are h T x = h T T x,, h T T x,,, h T T x,a H T x = H T T x,,, H T T x,a The length (M A) spread signal vector T T (8) s = H T xs = H T xcd (9) is the concatenation of the signals transmitted at the A antennas The length (L ) effective impulse response of channel and pre-filter is given by E Receiver h a = h T x,a h Ch,a, h = A a= h a () In this paper two receiver structures are considered The first structure employs a Rake-filter at the receiver as displayed in Fig The length (L ) impulse response of the Rake-filter is h Rx = Th with the size (L L ) swapping matrix T = () With that, the receiver-filter is matched to the combination of transmit-filter and CIR The second structure is just a code-matched filter It can be seen as a Rake-filter using a single filter-tap only, eg h Rx =, which requires less hardware effort III TRANSMIT DIVERSITY SYSTEMS Subsequently, the investigated Tx-diversity systems are introduced Their performances are compared by means of the SNR s at the receiver Basis of the investigation is the decision variable ˆd, which is given for a general transmit diversity system in Fig by ˆd = C H H RxH Ch H T xcd + C H H Rxn, () with matrices built according to (3) A Space-Time (ST) Pre-Rake The employs an FIR-filter (Pre-Rake combiner) in each transmit antenna branch, whereas the receiver uses only a code matched filter [4] [5] [9] This code-matched

3 filter is tuned to the strongest path of the combined transmitfilter-channel impulse response The Pre-RAKE impulse response h T x,a = α ath Ch,a (3) is matched to the channel The normalization constant α a is due to the transmit power constraint h H T xh T x =, (4) which requires the total transmitted power of the Tx-system to be equal to the transmit power of a conventional single antenna system One possible solution for the power constraint is to normalize the Tx-filter coefficients according to the maximal-ratio principle in both temporal and spatial domains, denoted with Maximal-Ratio Transmission (MRT) The normalization factor is α a = (5) h H Ch h Ch Since the concept uses a less complex receiver structure than the system shown in Fig, formula () reduces to ˆd = C H H Ch H T xcd + C H n (6) The receive-snr of the is found as SNR ST P rerake = B Space-Time Pre-Post-Rake A h H Ch,ah Ch,a a= σ = hh Chh Ch σ (7) The is an extension of the concept by utilizing an additional Rake-filter at the receiver With that, this system is identical to the block diagram of Fig A SISO-based version of this concept can be found in [3] The receiver filter (Post-Rake) impulse response is already given in conjunction with formula () It is matched to the combination of transmit filter impulse response in equation (3) and the CIR Rewriting the decision variable in () leads to ˆd = C H H H T xh H ChH Ch H T xcd + C H H H T xh H Chn (8) Then, the receive-snr of the is found as SNR ST P rep ostrake = hh T x R hh H H Ch H Ch h T x σ (9) with h T x as defined in equations (3) and (8), and R hh as the channel correlation matrix C Space-Time Eigenprecoder The it not optimum yet with respect to receive-snr In [], a MISO system is proposed using optimized transmit and receive filter coefficients For that, the receive-snr SNR = hh T xr hh h T x σ, () is maximized subject to the transmit power constraint in (4) The mathematical problem is h T x,opt = arg max h T x h H T xr hh h T x σ st h H T xh T x = () The optimization problem is an Eigenvalue-problem Therefore, the optimum filter coefficients vector h T x,opt is the one that belongs to the largest Eigenvalue λ max of the channel correlation matrix R hh The SNR at the receiver becomes SNR = λmax(r hh) σ () The largest Eigenvalue together with the corresponding Eigenvector can be computed using the Power method D Selection Eigenprecoder To save computational complexity, the Selection Eigenprecoder transmitter does not use all A antennas for downlink transmission but selects the antennas having the strongest propagation paths In [8], the Generalized Selection Combining Eigenprecoder is treated in more detail There, transmit and receive filter optimization for reduced complexity transmitters and receivers is proposed In this paper, the Selection Eigenprecoder selects only one Tx-antenna IV SIMULATIONS The simulation parameters follow the 3GPP specifications for UMTS-TDD These specifications are detailed laid out in [] [] [6] The used channel model corresponds to case 3 of these specifications For convenience, key simulation parameters are listed below in Table I and the UMTS-TDD frame/slot-structure is reviewed in Fig The channels are chip rate TABLE I SIMULATION PARAMETERS slot duration 384MHz 56 chips spreading gain 6 spreading code real OVSF scrambling code complex (code-nr 5) modulation format fading type QPSK Rayleigh number of multipaths 4 multipath power profile multipath delays db, -3dB,-6dB,-9dB chip each Monte Carlo trials assumed to be uncorrelated and constant for at least one slot duration (zero Doppler-spread) The mean channel power for each antenna branch is E h H Ch,ah Ch,a = 56 chips frame Slot Slot Slot 3 Slot 4 Slot 5 Data Burst Midamble Data Burst GP Fig Frame/Slot-Structure of UMTS-TDD A Number of Tx-Antennas The first simulations investigate the impact of the number of Tx-antennas on the performance of the transmit diversity systems introduced in section III Figure 3 shows the BER s depending on the transmit-snr For comparison, the BER of a SISO Pre-Rake transmitter, ie SISO Rake-receiver, is also shown The first observation that can be made in Fig 3 is that the performance increases considerably with an increase of the number of Tx-antennas The second observation refers to the relative performances of the algorithms The higher the

4 - BER's for ST Algorithms; Antennas:,4,8,6; Ns=5; Trials: Rake/Pre-Rake Sel Eigenprecoder Tx-SNR Degradation for BER=e-3 vsspatial Correlation Level Sel Eigenprecoder BER - -3 Antennas -4 4 Antennas 8 Antennas 6 Antennas Eb Tx /N,Bit in db Fig 3 The Number of Tx-Antennas as Parameter Spatial Correlation Level Fig 4 Tx-SNR Degradation Profiles vs Level of Spatial Correlation number of Tx-antennas is, the smaller is the performance difference of the algorithms The reason is that the gain obtained by multiple Tx-antennas exceeds the performance gain due to exploitation of the multipath diversity Thus, if many Txantennas are available then a less hardware demanding system, as for example the, achieves a BER similar to the BER s of the more complex structures Additionally it is worth noting that each antenna doubling gains more than 3 db of transmit-snr at a certain BER for all systems except for the Selection Eigenprecoder The gain of these systems consists of the gain from independently fading propagation channels (diversity gain in the classical sense) and the gain from coherent signal addition at the receiver since all Tx-antennas are simultaneously used to transmit the same signal, whereas the noise does not add coherently In contrast to that, the diversity gain of the Selection Eigenprecoder consists solely of the diversity gain in the classical sense with the result of a less significant performance improvement B Spatially Correlated Antennas Even though base-stations have enough space for an antenna array, the antenna elements are typically separated by a few tens of centimeters only With that, spatial correlation of the propagation paths from different antenna elements can not be completely excluded Therefore, the spatial diversity may be reduced leading to a possible performance degradation The results shown in Fig 3 assume no correlation between the antenna elements Following, the impact of spatial correlation between the antenna elements is investigated in terms of Tx-SNR degradation profiles Fig 4 shows the required increase in Tx-SNR to achieve a target-ber of 3 for different levels of spatial correlation In the simulations, the number of Tx-antennas is four It can be observed that spatial correlation levels up to 7 cause only slight Tx-SNR degradations for all considered systems Therefore, they require insignificantly more transmit power compared to uncorrelated propagation paths It is concluded that spatial correlation harms the BER s of the systems, but does not cause the transmit diversity algorithms to fail Techniques using multiple antennas simultaneously for transmission are superior to the selection-based scheme because of the coherency gain Similar results are observed in simulation environments that include Doppler-spread, though those results are not reported here due to the limited extend of this paper C Impact of Mobile Velocity The former simulations assumed a static propagation environment with no relative motion between transmitter and receiver However, the major advantage of wireless communication systems is the mobility of the users Therefore, it is inevitable to investigate the introduced Tx-diversity systems regarding relative motion between transmitter and receiver, or in other words, with respect to Doppler-spread In Fig 5, Tx- SNR degradation profiles to achieve BER= 3 are shown for 4 Tx-antennas Systems employing a Post-Rake perform 5 5 Tx-SNR Degradation for BER=e-3 vs Relative Speed Sel Eigenprecoder Relative Speed in Km/h Fig 5 Tx-SNR Degradation Profiles vs Relative Speed generally better than the which does not use a Post-Rake filter The reason is that the Post-Rake computes its filter coefficients based upon a more up-to-date channel estimate, namely performed in the midamble of the downlink slot, in contrast to the transmitter-filter which depends on the channel estimate made in the midamble of the previous uplink slot The shows a slightly better performance than the This is in contrast to the expectations of section II A possible explanation is that the ST Eigenprecoder maximizes the receive-snr, yet does not take into account the self-interference which might be significant The copes better with the self-interference by accumulating the signal energy in a single path Generally, it is observed that relative speeds up to 4 Km/h only insignificantly require an increase in transmit power to achieve the target-ber

5 D Variable Switching Point Configuration in UMTS-TDD Due to the variable switching point configuration, UMTS- TDD is able to support variable data rates on up- and downlink For multimedia services, a higher data-rate is required in the downlink Fig 6 shows an example of two different switching point configurations Following, the capability Fig 6 Variable Switching Point Configurations DL/UL-Symmetry DL/UL-Ratio 3: of the Tx-diversity systems to support different data-rates on up- and downlink for typical urban speeds (5Km/h) is investigated Fig 7 shows the Tx-SNR degradations for different downlink(dl)-uplink(ul)-ratios β compared to symmetrical transmission with β = The speed is 5 km/h, 4 Tx-antennas are used, and the target-ber is 3 The Tx Tx-SNR Degradation for BER=e-3 vs DL/UL-Ratio, v=5km/h Sel Eigenprecoder DL/UL-Ratio Fig 7 Tx-SNR Degradations for different DL-UL-Ratios β and Urban Speed SNR of the degrades quickly such that β = 4 already requires twice the transmit power compared to DL- UL-symmetry The reason is that the filter coefficients depend solely on the channel estimate made in the uplink slot and then kept constant during downlink transmission Thus, its coefficients do not match the actual channel parameters at the end of the downlink phase The degradations of systems with Post-Rake and multiple Tx-antennas are significantly lower, for the same reasons as in Sec IV-C The performance of the is dominant Since a relative velocity of 5Km/h requires only insignificantly more Tx-power compared to zero speed (Fig 5) and a DL-UL-ratio of β = 7 requires about twice the power compared to DL-ULsymmetry, it is concluded that this ratio of 7: is feasible for urban velocities It is shown that for urban speeds variable data-rates are feasible with the introduced Tx-diversity schemes, although the possible asymmetry is limited, and thus, the maximal possible DL-UL-ratio can not be achieved REFERENCES [] 3GPP: TS 5 Radio Transmission and Reception (TDD), 3GPP Technical Specification Group Radio Access Network, [] 3GPP: TS 5 Physical layer-general description, 3GPP Technical Specification Group Radio Access Network, [3] Barreto, AN; Fettweis, G: Performance Improvement in DS-Spread Spectrum CDMA Systems using a Pre- and a Post-Rake, Proc of Int Zurich Seminar on Broadband Communications, p39-46, Zurich (Switzerland), February [4] Choi, R; Khaled, B; Letaief, K; Murch, R-D: CDMA Pre-Rake Diversity System with Base Station Transmit Diversity, IEEE VTC Proceedings, vol, p95-955, Tokio (Japan), Spring [5] Esmailzadeh, R; Nakagawa, M: Pre-Rake Diversity Combination for Direct Sequence Spread Spectrum Mobile Communications Systems, IEICE Trans on Comm, vole76-b(8), p8-5, August 993 [6] Haardt, M; Klein, A; Oestrich, S; Purat, M; Sommer, V; Ulrich, T: The Physical Layer of UTRA TDD, IEEE VTC Proceedings, vol, p75-8, Tokio (Japan), Spring [7] Irmer, R; Noll-Barreto, A; Fettweis, G: Transmitter Precoding for Spread-Spectrum Signals in Frequency- Selective Fading Channels, Proc 3G Wireless, San Francisco, May [8] Irmer, R; Fettweis, G: MISO Concepts for Frequency- Selective Channels, Proc International Zurich Seminar (IZS), p4/-4/6, Zurich, Switzerland February [9] Jeong, I; Nakagawa, M: A Novel Transmission Diversity System in TDD-CDMA, IEICE Trans on Comm, vol E8-B(7), p49-46, July 998 [] Mostafa, R; Tikku, A; Ringel, U; Reed J-H: Transmit Diversity at the Handset in a Flat-Fading Wireless Channel, submitted to ICC for publication [] Wang, J-B; Ming, Z; Zhou, S-D; Yao, Y: A Novel Multipath Transmission Diversity Scheme in TDD- CDMA Systems, IEICE Transactions on Communications, vole8-b(), p76-79, October 999 V CONCLUSIONS Different transmit diversity systems that exploit multipath propagation have been investigated by means of analysis and simulation The simulations have shown that multiple transmit antennas can considerably reduce the BER It is found that correlated channels harm the BER s of the Tx-diversity systems, but do not cause them to fail Furthermore, it is observed that Doppler-spreads corresponding to relative velocities up to 4Km/h practically do not impact the BER s Systems having a Post-Rake are more stable with respect to Doppler-spread