Beamforming in Combination with Space-Time Diversity for Broadband OFDM Systems

Transcription

1 Beamforming in Combination with Space-Time Diversity for Broadband OFDM Systems Armin Dammann, Ronald Raulefs and Stefan Kaiser German Aerospace Center (DLR), Institute of Communications and Navigation Research Group for Mobile Radio Transmission Oberpfaffenhofen, Germany Abstract In this paper, we investigate broadband OFDM systems which apply beamforming in combination with different space time diversity techniques. Various beamforming scenarios with transmitter and/or receiver sided beamforming are considered. Space time diversity is obtained by cyclic delay diversity (CDD) in order to artificially shape the spectrum of the received signal. Thus, an advantageous distribution of the errors before a Viterbi channel decoder is obtained. Simulation results for the bit error rate performance are presented and compared for OFDM systems applying different beamforming scenarios and CDD in a Rayleigh fading channel. Maximum ratio combining (MRC) of the signals received on multiple beams/antennas is also taken into account in the performance analysis. I. INTRODUCTION ULTIPATH transmission in wireless digital systems causes constructive and destructive superposition of the signal at the receiver. The resulting fading leads to a quality loss in wireless communications, which could destroy an existing link, or even prevent it altogether. Several well-known state-of-the-art techniques exist to reduce fading. The first technique is channel coding [] to correct transmission errors by using redundant data. The redundant data decreases the spectral efficiency of the system. Current broadcasting systems, such as DAB or DVB T, and digital cellular mobile systems, such as GSM or the future UMTS, exhibit losses of up to 50%. Power Control [2] increases the transmission power on request, in case fading is too strong for a connection. The increased power need of one connection increases interference for all other connections. In general, it is a disadvantage to spend transmission power for a wireless radio channel that could be used for other channels. In a balanced system, all components should be optimized. Very effective methods to deal with fading are diversity techniques. The use of multiple transmitter and/or multiple receiver antennas allows detecting the data of independently jammed signals at the receiver correctly. However, the wellknown diversity techniques [], [3], [4] do not transmit data power effectively. Data is transmitted via isotropic, or at best sectored, antennas, and is not targeted to the receiver directly. Space-time coding [5], [6] adds spatial redundancy. Multiple antennas transmit differently coded signals via the wireless channel, and are received by one or multiple antennas. Tarokh et al. [5] describe space-time coding in detail, where at least two isotropic transmit antennas, and one or several receiver antennas are used. Only applying space-time coding does not allow to target transmit power spatially. If the receiver is using a single isotropic antenna, then only a superposition of the transmitted signal is possible. Smart antennas [7], [8] combine multiple signals to receive or transmit with multiple antenna elements in an intelligent way, using an adaptive antenna processor. The transmitted signals are sent using an antenna beam aimed at the best known direction for the receiver. The transmission power used is multiplexed ideally, and the interference of the digital cellular mobile system is minimized. The antenna beams of the smart antenna focus to the desired direction, and therefore suppress the interference. However, the signal of the antenna beam spreads dispersively, and therefore the signal is attenuated. This paper presents a novel approach to carefully direct the transmission power to the desired receiver by using the topographical scenarios of the wireless channel. The presented diversity methods are designed for orthogonal frequency division multiplexing (OFDM) systems [9], like HIPERLAN/2 or IEEE802.a [2]. The proposed technique modifies the transmission signal in a way that the received signal can be detected more reliable by the receiver than in conventional techniques. The negative impact of fading is minimized and therefore the needed transmission power is reduced, implicitly minimizing the cell interference in a wireless digital cellular system as well. This paper is organized as follows. Section II covers novel beamforming concepts. The proposed diversity techniques and its features are sketched in Section III, followed by Section IV where an exemplary application is presented. The simulation environment and detailed results are presented in Section V. II. BEAMFORMING CONCEPTS In this section we introduce the basic ideas behind the new technique. Multiple beams of one or more smart transmission antennas are aimed at the receiver, where each beam is modified by a different process. Each of the beams reaches the receiver by using the topographical scenarios of the wireless channel. We assume that the wireless channels are not corellated to each other. The transmission signal can be mod-

2 Characteristic Characteristic Characteristic (a) Receiver diversity (b) Transmitter diversity (c) Diversity at both ends Fig.. Diversity at the transmitter and/or at the receiver Data Signal Transmitter Beam # Beam #2 Beam #N Processor s Processor Receiver Beam # Beam #2 Beam #M Signal ified by several methods introduced in Section III. The antenna beams are aimed at the receiver by using several different paths to direct the available power more precisely, improving the receiver quality by using several different channels. If one channel is subject to strong fading, the possibility that another channel has sufficient transmission quality is high enough to keep the transmission alive. Fig. depicts exemplary scenarios for applications of smart antennas at the transmitter and/or at the receiver. The scenario in Fig. (a) shows an isotropic antenna as transmitter and smart antennas at the receiver. Our technique prevents the superposition of single propagation paths. It compensates for the delay difference between paths, e.g. between path and path 2, and cancels the transmitted signal on path 3. The scenario in Fig. (b) shows smart antennas at the transmitter and an isotropic antenna at the receiver. It uses known transmitting channel parameters in an ideal way. As in scenario Fig. (a), it is possible to compensate the delay difference between the transmission paths. Additionally, the delay/phase difference introduced in Section III-A. causes frequency selective fading which enhances the performance as explained later. The scenario in Fig. (c) shows how to unite the properties of both cases. The spatial selectivity at the transmitter and at the receiver offers independent channels. Therefore, the transmitting power and the transmitted data can be allocated along information theoretical principles. Multipath transmission allows to combine signal processing with adaptive antennas in a very flexible way. The targeted spatial orientation of the adaptive antenna admits a spatial distribution of the transmission power and the transmitted data. The receiver antenna characteristic allows a selected sample of spatial transmission paths. Both characteristics of an adaptive antenna at the transmitter and at the receiver allow the separation of the signal. Fig. 2 shows the scheme of the combination of signal processing and smart antennas in more detail. The signal processing unit forms signal streams handled by the antenna processor. The antenna processor controls the adaptive an- Fig. 2. Block scheme of the combination of the signal processing unit and the adaptive antenna processor (AAP) at the transmitter and the receiver. tenna group so that signal streams are transmitted according to the propagation scenarios in several different spatial directions. At the receiver the antenna processor modifies the antenna characteristics so that all signal streams are optimally received, and finally all signal streams are formed back. III. BEAMFORMING WITH SPACE TIME DIVERSITY The proposed antenna beamforming scheme which exploits additional diversity due to specific modifications of the signal at the individual beams can be realized with different techniques and results in different, advantageous system properties. The various diversity techniques are realized in the signal processing block shown in Fig. 2, and are especially designed for multicarrier modulated systems like HIPERLAN/2 or IEEE802.a [2], applying orthogonal frequency division multiplexing (OFDM) [9]. A. Space Time Diversity Techniques A. Delay Diversity, Phase Diversity and Cyclic Delay Diversity The signals at the individual beams can be transmitted delayed to each other according to the principle of delay diversity (DD) presented in [3]. This can be considered as an artificial spread of the signal in time direction, increasing the frequency selectivity of the resulting signal spectrum at the receiver antenna. Thus, a flat fading channel can be transformed in a frequency selective channel which has benefits Data

3 A W F with respect to the error distribution when e.g. a subsequent Viterbi decoder is applied. I.e., we can avoid scenarios where the total signal spectrum is in a deep fade and significant disturbances at the receiver up to a total system failure would occur. However, beamforming with DD introduces artificial intersymbol interference (ISI) or reduces the effective guard interval used in OFDM systems. To overcome this drawback, the signals at the individual beams can be shifted against each other in phase according to the principle of phase diversity (PD) [3] or cyclic delay diversity (CDD) [4]. It can be shown that PD and CDD have the same performance, whereby CDD has some implementation advantages. This section will briefly introduce delay diversity (DD). The OFDM modulated signal is transmitted simultaneously over beams, whereas the particular signals only differ in a beam specific delay. Before shifting, an additional cyclic prefix as guard interval may be inserted. Note, that in case of DD, denote simple time shifts. Because of linearity, it is also possible to implement DD at the receiver side. To avoid intersymbol interference (ISI) the time delays must hold the following condition: () Where is the guard interval length and denotes the multipath channel delay spread. For tight dimensioned guard intervals, where is only slightly larger than!, () strongly restricts the choice of the time delays!. In the next section CDD is introduced, which overcomes this problem. Fig. 3 illustrates the difference between DD and CDD in the time domain and shows the transmission of two consecutive OFDM symbols with their cyclic prefixes as guard intervals. For clarity, the #"%$ subcarrier is plotted as a sine wave. The reference signal is not delayed and transmitted (resp. received) for both DD and CDD. In the case of DD it can be seen, that the DD signal is a simple copy of the reference signal, delayed by. It is also observable, that OFDM symbols of the DD signal partly overlap the guard interval of the subsequent OFDM symbol in the reference signal by. This results in the above mentioned restriction in the choice of (see ()). In the case of CDD one can see, that there is no overlapping of CDD signal OFDM symbols with reference signal OFDM symbols, whereas the phase of the subcarriers are equal to that of the DD signal. This makes the performance of CDD equal to DD while () restricts DD. Further it can be seen, that the OFDM symbols of the CDD signal can be generated from the reference signal OFDM symbols just by a cyclic time shift of!&%'. Fig. 4 shows the block diagram of an -beam OFDM system with CDD at the transmitter. The OFDM modulated signal is transmitted over beams, whereas the particular signals only differ in a beam specific cyclic shift. After cyclic Reference Signal DD Signal CDD Signal cyclic extension cyclic extension cyclic extension OFDM-Symbol OFDM-Symbol OFDM-Symbol max g Time Section for OFDM Demodulation ISI Fig. 3. OFDM time signals at the receiver cy Time shifting, the guard interval is inserted. Note, that in case of CDD, &%'#(, )* +, denote cyclic shifts. Due to linearity CDD can be implemented at the receiver as well. OFDM cycl cycl N- to beam # to beam #2 to beam #N Fig. 4. OFDM system with transmitter sided cyclic delay diversity Because of simple time shifts for DD and cyclic shifts for CDD, respectively, these techniques are implementable with low complexity as long as the delays,!- and,.%/#0 - are chosen to be multiples of the system sampling time. Otherwise some kind of time domain interpolation has to be done, which increases complexity. The next section introduces phase diversity (PD), which is done in the frequency domain and allows implicitly the choice of arbitrary delays. The equivalence between PD and CDD is a property of the Discrete Fourier Transformation (DFT) and can directly be seen from the length IDFT definition 2O3U3V5XW,.%/ 7ZY\[^] 7 _ `a b c@ded)fhgji -4kml : ; 8 : ; <>=@? 3IH7KJ L MONQP R BTS BCEDGF <>=@? A L = M NQP R\n B n oqpsr J 3IHt7 BCED _ `a b u dfqgvi -kml 3IHt7 denote the discrete time, frequency and the complex-valued signals in time- and frequency- where 5, H, 2O3V57 and F domain respectively with 5xwTH8 :zy y y W (2) J L M NQP R\n B n S :.,#.%/ stands for a cyclic time shift in samples. Note, that in time domain for,.%/ actually the choice of any integer value is possible, but due to the characteristics 3,!.%/ { HJ 7ZY\[^] 8,.%/ and L M NIP R~}jo p6r B n < 8L M NIP R o p6r, the range of values for,#.%/ can reasonably be restricted to,#.%/ 8 ƒ yy y :. As it can be seen

4 from (2), a cyclic delay #&%' in the time domain corresponds to a (phase) factor of O t 4ˆQ ŠŒ qž6 in the frequency domain. But in the frequency domain, there is no more need for &%' to be an integer value. So reasonably &%' may be within the interval t ). Furthermore PD is not only restricted to linearly incremented phases. It is also possible to choose phase factors T 4, where Qšt is an arbitrary function of the discrete frequency š. As it can be seen from (2), the operation for PD has to be done before OFDM modulation. So for an -beams PD system, OFDM transformations have to be done and therefore the implementation of PD is more complex compared to CDD. CDD and PD are independent of the existence of a cyclic prefix (guard interval) and are capable to increase the channel frequency selectivity without increasing the overall channel delay spread because these operations are done before guard interval insertion and are restricted to the OFDM symbol itself. In order to achieve any diversity effects, i.e. to get constructive and destructive interference within the OFDM signal bandwidth, the delays have to fulfill ž œ A.2 Subcarrier Diversity 4 (3) Another opportunity to increase the diversity gain with beamforming in OFDM systems would be to split the subcarriers of an OFDM symbol in subsets, where each subset of subcarriers is transmitted on a different beam. Thus, if the subset of subcarriers from one beam is located in a deep fade, the subsets of subcarriers from the other beams can still be received with sufficient power and by using interleaving and channel decoding, the errors due to the lost subset can be corrected. The advantage of subcarrier diversity is the reduced peak-to-average power ratio per beam. However, the performance of this method is slightly worse compared to DD, PD and CDD [3]. A.3 Space Time Coding Moreover, the proposed beamforming concept can apply space time coding in order to introduce redundancy not only in time and/or frequency direction, but also in space direction. A.4 Maximum Ratio Combining At the receiver, the compensation of the delays and phase rotations between the signals on the different beams of the receiver can easily be realized. If the channel parameters like attenuation, phase shift and delay for the individual propagation paths, i.e., beams, are available at the transmitter, a precompensation can be applied within a point-to-point transmission. In the case of the use of multiple beams at the receiver, where the transmitted signals can be modified by DD, PD or CDD, the signals at the individual beams can be combined by maximum ratio combining (MRC) at the receiver. B. System Properties If beamforming is carried out at the transmitter and receiver side, the modification of the signals at the individual beams can be carried out such that groups of transmit and receive antennas are assigned to each other, each group creating one data channel. Within each group CDD or other diversity techniques can be applied. With this modification, multiple data channels are provided at the same time in the same frequency band between two radio stations, increasing the total available data rate. The data rate can be adapted to the requirements of the system, where data channels can flexibly be switched on and off. The combination of transmitter and receiver beamforming also offers new opportunities for the handover in a cellular scenario. A mobile terminal can transmit and receive its data not only to/from one base station but to/from multiple beams from different base stations. Each transmitter/receiver can apply CDD or other diversity techniques. Moreover, this feature simplifies the soft handover procedure, where the mobile terminal changes the base station. The mobile can establish a link to the new base station over one or several beams, before the link to the old base station is released over one or several other beams. IV. APPLICATION In this section we introduce the transmitter and receiver system models, which are used for simulations. In general, we apply CDD at the transmitter side of a convolutionally coded OFDM system. At the receiver side adaptive antenna processing (AAP) is used at the front end of a MRC-OFDM receiver. A. Transmitter For the implementation of CDD at the OFDM transmitter, only a second signal path after OFDM-modulation has to be added. Fig. 5 shows the transmitter sided inner part with transmitter CDD. After channel coding and interleaving, the bit-stream is mapped to complex-valued QAM-symbols. The functional block Frame Adaption is responsible for QAMsymbol interleaving, pilot insertion and transmission parameter signaling (TPS). The resulting symbol-stream is OFDMmodulated. Then the signal is split, the antenna specific cyclic delays are inserted and the guard intervals are built. Finally, the signals are fed into an AAP unit and are transmitted. It is important to note that the signals at the transmit antennas are normalized by the number of transmit antennas. I.e. signal splitting does not increase the overall transmission power.

5 " ± Coding B. Receiver Interleaving QAM Mapping Frame Adaption Pilot & TPS Signals OFDM cy Fig. 5. OFDM transmitter with CDD and AAP We use AAP in front of a MRC-OFDM receiver as shown in Fig. 6. The AAP unit forms an antenna characteristic for each desired signal propagation path and additionally corrects its path delay. It is assumed that only one propagation path is received per antenna characteristic, i.e. all other paths are faded out due to this characteristic. It is also supposed that the directions of arrival for each signal propagation path can be resolved. If propagation paths are desired to be received, the signal streams, resulting from different antenna characteristics, are fed into a receiver. Remove Remove IOFDM IOFDM Equalization CSI MRC, QAM Demodulation Equalization Symbol Deinterl. -branch MRC-OFDM Deinterl. Fig. 6. MRC-OFDM receiver with AAP frontend Decoding After guard interval removal, the received signal is OFDM-demodulated and equalized using zero forcing. For our investigations we assume perfect knowledge of the channel state information (CSI). The complex-valued symbolstreams are combined and soft-out QAM demodulated before symbol- and bit-deinterleaving is done. Finally the bit stream is soft-decision-maximum-likelihood (SDML) decoded. V. SIMULATIONS In this section we present simulation results for some specific scenarios, which were introduced in Section II. First, the channel models and system parameters are introduced. Finally, the simulation results are presented. A. Channel Models For simulations we use a 3-path channel with wide sense stationary uncorrelated scatterers (WSSUS). Table I shows the main channel properties of the 3-path model. The maximum Doppler frequency for each Rayleigh fading signal propagation path is Ÿ. This corresponds to a mobile velocity of #Ÿ (Ÿx ). Because AAP is assumed to resolve the signal propagation paths for multipath channels, we also use a Rayleigh fading channel for simulations with AAP. The properties for this channel are equivalent to path of Table I. The overall noise is divided into two parts as described in [0]: interfering noise from a discrete source impinging at the antenna group is responsible for 80% of the noise power. spreaded noise homogeneously over the whole area of incidence is responsible for 20% of the noise power. Hence, the signal-to-interference-noise ratio (SINR) is defined as SINR >ª«(4) where represents the homogeneous noise and the discrete interferer noise power. Path Path- Delay ] TABLE I MAIN CHANNEL PROPERTIES rel. avg. Power [ 4 ] Fading- Char. max. Doppler [ ] Doppler Spectr. Form 0 0 Rayleigh 50 Jakes Rayleigh 50 Jakes Rayleigh 50 Jakes B. System Parameters The simulation system is an OFDM system with an ² channel. The duration of the OFDM symbol is ³@ µµ and the number of used carriers is ¹ OŸ. This yields a subcarrier spacing of º ³Z» 4¼ 4 and a spacing between the spectrum edge carriers of Ĩ! Tº ³Z ¹½ ¼t# ². Beside these basic parameters, there are additional transmission parameters regarding modulation, guard interval length and channel coding as depicted in Table II. C. Results TABLE II OFDM SYSTEM PARAMETERS FOR SIMULATIONS Code Rate /2 Signal Constellation 4-QAM Guard In this section we present simulation results for some scenarios that are described in Section II. C. AAP at the Receiver This scenario is closely related to Fig. (a). We use an isotropic antenna at the transmitter side, i.e. the AAP unit in Fig. 5 produces an isotropic antenna characteristic. This can be achieved, if only one element of the antenna array is used for transmission. Therefore the AAP unit at the transmitter would simply look like the one, shown in Fig. 7. Where ¾ and ¾t \ for the -transmit-antenna (TX) simulations

6 a 0 a Fig. 7. AAP unit for transmitter of Fig. 5 À¾ Á  for the 2TX (CDD) simulations. Note and ¾ that due to this factors, the overall transmitted power is equal for all simulations. For the 2TX simulations, a cyclic delay is chosen. Bit Error Rate TX/RX 3-Path-Channel TX/3RX 3-Path-Channel 2TX/3RX, CDD, 3-Path-Channel TX, 3-Path AAP-Receiver 2TX, 3-Path AAP-Receiver, CDD isotropic reference system about O 4 at a BER of µ ƽ È ÈÇ. It must be pointed out that the noise signals, which are fed from the AAP unit into the MRC-OFDM receiver are not uncorrelated. So the results for the AAP systems are a lower bound for the BER performance. C.2 AAP at the Transmitter In this section we focus on different transmitter concepts, and therefore only one isotropic receiver antenna without any diversity is applied. Fig. (b) shows an AAP implemented only at the transmitter and not at the receiver. By using an AAP at the transmitter all three paths can be correctly delayed according to the known channel delay. This opens new advantages and disadvantages in a cellular network. On the one hand the data rate could be increased, by minimizing the guard interval. On the other hand the three path channel is seen as one Rayleigh channel at the receiver. Therefore multipath diversity is lost, but additionally we can effectively adopt CDD to combat the diversity loss and still have a higher data rate. Using AAPs at all transmitters within a cellular network, lowers the directional interference at the receiver despite the fact that it is impossible to cancel them at the receiver. However this is not guaranteed and depends on the traffic behavior within the cellular network. Fig. 9 shows the lowest ÒÑÓ¾4Ô and the highest Õ 4 possible yield for an AAP at the transmitter SINR [db] Fig. 8. BER vs. SINR for receiver AAP Path AAP-TX, I = max. 3-Path AAP-TX, I = 0 3-Path AAP-TX, CDD, I = max. 3-Path AAP-TX, CDD, I = 0 Fig. 8 first shows reference results for MRC-OFDM receivers with isotropic antennas (TX/RX, TX/3RX and 2TX/3RX) in a 3-path channel model, which was described in Sec. V-A. It has to be emphasized that the received power is not normalized to the number of receiver antennas. In case of TX/3RX and 2TX/3RX the 3-fold signal power is received compared to the TX/RX system. As it can be seen, about ÅŸxŌ can be gained at a BER of µeæq ÈÇ for additional CDD (2TX/3RX) compared to a single transmit antenna system (TX/3RX). For the AAP-receivers we assume independent Rayleigh channels for each propagation path. Again, if we compare the TX system with the 2TX CDD system, a SINR gain of ɹŌ at a BER of µ>æ! t ÈÇ can be observed. However, the more interesting comparison is done between the 2TX system with 3-path AAP and the 2TX/3RX reference system. The realized simulations take into account discrete interfering noise signals. An isotropic receiver antenna is unable to cancel discrete interfering signals. Therefore the AAP works in a system that has Ð an advanced system performance of about ¹ Ō Ê QË eìjí4î Ï Рª # U. It can be seen that the 2TX AAP system outperforms the 2TX/3RX Bit Error Rate SINR [db] Fig. 9. BER vs. SINR for transmitter AAP C.3 AAP at both Transmitter and Receiver In this section we use AAP at both transmitter and receiver to divide the considered multipath propagation channel scenario spatially into independent radio links with Rayleigh fading characteristics. Hence, different data can be transmitted over these links, i.e. the data rate is improved. Because of the independence of the data links, we consider one data

7 link in the simulations. In the case of multiple data links, the transmission power has to be normalized according to the number of data links. Fig. 0 first shows the BER performance of AAP at the transmitter and receiver. It can be observed that a BER of µ ÆO t ÖÇ is reached at a SINR of about ŸxŌ. This poor performance can be improved significantly by applying CDD. Bit Error Rate AAP AAP + Transmitter CDD SINR [db] Fig. 0. BER vs. SINR for both transmitter and receiver AAP VI. CONCLUSIONS This paper presents a novel approach using advanced signal processing and adaptive antennas to modify the transmission signal that improves the reliability of the detection of the signal at the receiver. For an isotropic transmitter antenna system and an adaptive antenna processor (AAP) system at the receiver, our results show the SINR gain is about ¹½ÅŸxŌ at a BER of µøæ! ^ ÈÇ in the best case compared to the basic system. This is due to the effects of cyclic delay diversity (CDD), adaptive antenna gain and maximum-ratio-combining at the receiver. The AAP allows to cancel interfering signals, and therefore increases the signal-to-interference-noise ratio significantly. In case of an AAP at the transmitter and an isotropic receiver antenna, it is general possible to minimize the directional interference within the cellular network. The maximum gain in the introduced traffic scenario is ¹x 4. Additionally the data rate can be increased by minimizing the guard interval and applying CDD at the expense of multipath diversity. Using an AAP at both ends of the wireless channel offers to modify the transmitting signal, to use the topographical scenarios for several propagation paths and to transmit in parallel different data signals. The results show that with the help of CDD the needed SINR for a given BER decreases dramatically. Using CDD and AAP at both ends, the proposed technique offers to adaptively switch on or off the data channels, depending on the application. enables an enhanced detection at the receiver by orienting multiple transmission beams at the receiver along multiple propagation paths. implies optimized power control by only transmitting to the desired receiver, and minimizes interference in the entire system. In comparison to conventional schemes with adaptive antennas the novel approach alters the spectrum and the error distribution at the receiver, and therefore performs much better for the used OFDM system. REFERENCES [] John G. Proakis, Digital Communications, McGraw-Hill, 3rd edition, 995. [2] Richard van Nee and Ramjee Prasad, OFDM for Wireless Multimedia Communications, Artec House Publishers, Boston, London, [3] Stefan Kaiser, Spatial transmit diversity techniques for broadband OFDM systems, in Proceedings IEEE Global Telecommunications Conference (GLOBECOM 2000), San Francisco, USA, November 2000, pp [4] Armin Dammann and Stefan Kaiser, Standard conformable antenna diversity techniques for OFDM and its application to the DVB-T system, in Proceedings IEEE Global Telecommunications Conference (GLOBECOM 200), November 200, pp [5] Vahid Tarokh, Nambi Seshadri, and A. Robert Calderbank, Spacetime codes for high data rate wireless communication: Performance criterion and code construction, IEEE Transactions on Information Theory, vol. 44, no. 2, pp , March 998. [6] Siavash M. Alamouti, A simple transmit diversity technique for wireless communications, IEEE Journal on Selected Areas in Communications, vol. 6, no. 8, pp , October 998. [7] L. C. Godara, Application of antenna arrays to mobile communications. Part I: Performance improvement, feasibility, and system considerations, Proceedings of the IEEE, vol. 85, no. 7, pp , July 997. [8] L. C. Godara, Application of antenna arrays to mobile communications. Part II: Beam-forming and direction-of-arrival considerations, Proceedings of the IEEE, vol. 85, no. 8, pp , August 997. [9] S. B. Weinstein and P. M. Ebert, Data transmission by frequency division multiplexing using the discrete fourier transform, IEEE Transactions on Communications, vol. COM-9, no. 5, pp , October 97. [0] P.W. Baier, C.A. Jötten, and T. Weber, Review of TD-CDMA, in Proceedings of the ÙÚhÛ International Workshop on Commercial Radio Sensors amd Communication Techniques, Linz, Austria, August 200, pp. 20.