Challenges in Future Short Range Wireless Systems Abstract: Introduction

Transcription

1 Challenges in Future Short Range Wireless Systems Gerhard Fettweis, Ernesto Zimmermann, TU Dresden Volker Jungnickel, Fraunhofer Heinrich-Hertz Institute for Telecommunications Eduard A. Jorswieck, Royal Institute of Technology (KTH) Abstract: As RF and baseband engineers strive to satisfy the demand for ever higher data rates in next generation wireless systems, they are faced with three challenging requirements: both spectral efficiency and bandwidth have to be increased, and the cost per bit has to be kept low. A combination of MIMO, OFDM and TDD is a promising candidate technology to meet these objectives. However, realizing the potential gains of this approach requires tackling a number of new challenges: real MIMO channels, real - Dirty - RF and tough real-time constraints. Introduction The past decade has been marked by two parallel trends that radically changed the way people work and live the advent of the Internet and the widespread introduction of personal mobile communications. It is widely anticipated that these two digital industries converge in the next decade. Seamless interoperation of the available communication infrastructure wireless as well as cable based will provide users with the desired information anywhere at any time. Example applications are the access to , intranet and Internet, and the distribution of multimedia content. Such applications require an air interface which offers high peak data rates, makes the best possible use of the available spectrum, and still enables low cost terminals. By using multiple antennas at both transmitter (Tx) and receiver (Rx) side, a multiple-input multiple-output (MIMO) radio channel is set up, enabling a higher spectral efficiency than with single antenna systems. Data transmission at high data rates is such facilitated in a spectrum which is limited by regulation and other factors. At the same time, with increased bandwidth in future radio systems, more and more channel echoes are resolved, calling for efficient equalization techniques. Orthogonal frequency-division multiplexing (OFDM) is a very attractive option, as it is not only spectrally efficient but also transforms the multi-path channel into parallel flat fading channels, for which well-known MIMO detection schemes can be used thus substantially reducing the complexity of the spatiotemporal processing [1]. The plethora of diversity available in broadband MIMO channels can be exploited by using appropriate space-frequency codes [30] which might however require relatively complex detection algorithms at the receiver. PHOTODISC /06/$ IEEE IEEE VEHICULAR TECHNOLOGY MAGAZINE JUNE 2006

2 Water-filling and related methods, based on channel state information (CSI) at the transmitter, are another promising option. CSI at the transmitter provides the flexibility to shift the signal processing effort to wherever it is desired for example to the base station in the up- and down-link in the infrastructure mode, or one can alternatively share the effort between two mobile terminals in the ad-hoc mode. This principle is in fact the key to realizing the above stated requirement of keeping the cost per bit low while providing very high data rates. The key challenge for such techniques is to make CSI of sufficient quality instantaneously available at the transmitter. In the frequency-division duplex (FDD) mode, this can be achieved by sending direct channel feedback [2] over the reverse link. The overhead required for such feedback scales with the product of the numbers of Tx and Rx antennas. The time-division duplex (TDD) mode offers a more efficient option (see Figure 1). Orthogonal training sequences are transmitted in the up-link (UL) direction from each terminal (for which the overhead scales with the number of Tx antennas only) before the data transmission in the down-link (DL) takes place. Due to channel reciprocity, the CSI can be used to pre-process the transmitted data and to control the scheduling of multiple users signals in the space-frequency domain (see Figure 1). Channel variations between the UL and the DL phase must of course be negligible in order for this concept to work. Fortunately, this requirement is not much stricter than for conventional wireless systems which use CSI only at the receiver. Combining MIMO, OFDM and TDD thus bears a lot of synergy effects which should be exploited in next generation wireless systems. MIMO Channels: Theory vs. Reality The mean capacity of an independent and identically distributed (i.i.d.) Rayleigh fading MIMO channel is well known to scale linearly with the minimum of the number of transmit and receive antennas. This is confirmed by measurements for indoor non-line-of-sight (NLOS) scenarios (cf. Figure 2 [3]). With line-of-sight (LOS) present, a minor degradation is observed at large numbers of antennas. The LOS component is normally not dominant, compared to the scattered signal at least in typical indoor scenarios. This can be verified in the lab with two omni-directional antennas and a network analyzer in a span of more than 100 MHz. For antenna separations exceeding one meter, the fading holes characteristic for the NLOS component are always present. On the other hand, the role of the LOS component is enhanced when going from indoor to outdoor deployment. In Figure 3, the statistics of the ordered singular values (SVs amplitude gains of the spatially multiplexed streams) for a NLOS (top) and LOS scenario (center) are shown. Measurements were done at 5.2 GHz with 10 Tx and 16 Rx antennas in the campus of the TU Berlin at distances of 84 m and 108 m and Rx antenna heights of 40 m and 26 m above ground, respectively. The transmitter is moved along a 10 m track in each scenario, to get sufficient statistics. The random matrix theory predicts an almost equal spacing between the mean SVs, which is a good prediction for the NLOS case, and observed in about 40% of the 22 outdoor scenarios investigated. In other scenarios, the LOS is free or slightly shaded by leaves on trees. This results in a singular value distribution similar to the center graph in Figure 3. The two channels with higher SVs are attributed to the polarization. It offers two independent spatial channels even in a pure LOS scenario. FIGURE 1 In the TDD mode, channel state information for the down-link can be made available at the transmitter by using the reciprocal channel information from the up-link, and vice versa. FIGURE 2 Measured indoor MIMO capacities. JUNE 2006 IEEE VEHICULAR TECHNOLOGY MAGAZINE 25

3 power over a reduced number of spatial streams. The (open-loop) capacity can be approached with reduced feedback information using bit-loading techniques [4] [6]. FIGURE 3 Singular value distributions for outdoor LOS (top) and NLOS (center) scenarios. Capacity distribution with normalized SNR (bottom). FIGURE 4 Optimal power allocation in MIMO OFDM with three users. The mean capacity is thus reduced when the LOS component is dominant (cf. Figure 3, bottom; it is of course higher when the SNR is not normalized). In the NLOS case, multi-path diversity increases the steepness of the capacity distribution compared to the narrow-band case, i.e., even in shadowed areas, broadband MIMO links exploiting frequency-selective fading may be similarly robust as a wired link. Particularly in the LOS scenario, the singular values are often close to zero for one or more spatial channels. However, reliable data transmission is possible even over such illconditioned MIMO channels, provided that CSI is available at the transmitter: Optimal water-filling then disperses the Capacity Optimization Under perfect CSI at the transmitters as well as the receivers, the duality theory connects the capacity region of the MIMO multiple access channel (MAC) and the MIMO broadcast channel (BC). A popular system performance measure is the sum capacity, which describes the total throughput. For the single-antenna multiuser case the optimal strategy is to allocate power only to the user with the best channel quality [29] simple TDMA. The more users are available, the higher is the probability that the best user has good channel conditions. This fact coined the term multiuser diversity. However, if only partial CSI is available, or if multiple antennas are applied, it is in general necessary to support more than one user at a time to achieve the sum capacity [7], [8]. The important point to note here is that MAC schemes that are optimal for single-antenna systems can be highly inefficient in multiple antenna scenarios. Figure 4 shows that the spatial dimension allows placing users simultaneously on the same time-frequency bin. The higher the SNR, the more users are active. There has also been some effort to analyze the complete performance region of the MIMO MAC and BC [9] and its relation to the stability region of an overlayed queuing system [10]. The above results underline the importance of making CSI of high quality available at the transmitter. Some of the RF imperfections discussed in the following section turn this issue into a significant challenge. Dirty RF Traditionally, wireless system design tried to keep the domains of baseband and RF processing separate, i.e., baseband engineers essentially assumed the RF to be perfect RF imperfections were kept to such low a level that they did not have any deteriorating effect on the system performance. However, with ever higher integration, deep sub-micron technology and the associated dirt effects are becoming more and more relevant for wireless system design, and particularly for the presented systems based on MIMO-OFDM and channel reciprocity. The following sections highlight some of the core Dirty RF [11] issues and how they can be overcome. Non-Linearities The time-domain signal in an OFDM system is the superposition of the signals of a large number of sub-carriers, resulting in an approximately Gaussian distribution of the complex base-band signal. Consequently, OFDM systems require transmit and receive signal processing blocks with a high dynamic range. This requires not only a higher resolution of DA and AD converters, the high power 26 IEEE VEHICULAR TECHNOLOGY MAGAZINE JUNE 2006

4 amplifier must also be linear over the full range. Clipping can occur both at DA/AD converters and the amplifier. In order to avoid this clipping, the power amplifier has to work with a large input power back-off (IBO) making it far less power-efficient than in previous generations of mobile systems using constant-envelope signals [12]. There are two approaches to reduce this problem: one can either avoid large Peak to Average Power Ratios (PAPR reduction [13]) or live with the clipping effects. However, most PAPR reduction schemes lack flexibility and/or cause a reduction in user data rate. The impact of clipping is twofold if the clipping occurs in the high power amplifier after most filters have already been passed, there is out-ofband emission. Since restrictions for out-of-band emissions are quite high, this effect has to be avoided by deliberately clipping the signal in the digital domain. On the other hand, a clipped pulse has a white spectrum leading to an increased bit error rate on all sub-carriers. The resulting loss in channel capacity, however, is not very severe [14]. To appropriately detect the distorted signal at the receiver, digital base-band compensation can be employed [15]. A combination of digital clipping at the transmitter and appropriate signal processing at the receiver can hence be used to tackle the challenges due to high PAPR in multicarrier systems such as OFDM. Phase Noise The performance of an OFDM system can be substantially degraded by the presence of random phase noise in oscillators. The higher the carrier frequencies and modulation formats and the smaller the sub-carrier spacing, the more critical is the impact of phase noise, which causes constellation rotation (common phase error, CPE), as well as inter-carrier interference (ICI). However, several methods have been proposed to compensate both effects [16], [17]. Phase noise has to be taken into account especially when designing MIMO systems, as hybrid designs with common low-frequency reference but separate PLLs suffer from independent phase noise. This might be desirable if we do not try to compensate the phase noise. For compensation algorithms, a contrary strategy has to be followed. As it is evidently beneficial to only have to track a single phase noise process, the parallel RF chains of the different antennas should use the same oscillator split. I/Q Imbalance The I/Q mismatch must not be overlooked when implementing OFDM systems, as it is often critical for the performance. I/Q imbalance is a typical Dirty RF effect in low-cost direct conversion transceivers, where the 90 phase shift of the local oscillator may not be perfect and amplitude mismatches occur as well. The phase imbalance originates from imprecise placement of the in-phase and quadrature mixers on the printed circuit board (PCB), while the amplitude imbalance is due to different mixer efficiencies and baseband gains. Both effects are normally narrow-band in their nature. In very broadband designs, however, a difference in the two paths towards the summation point after the I- and Q- mixers could make the I/Q imbalance frequency selective. The best is to integrate the entire I/Q modulator on the same chip. This keeps path and hence phase differences small. There are several ways of dealing with I/Q imbalance. An example digital compensation method is calibration and correction. With OFDM, this requires the use of orthogonal training symbols at positive and negative subcarrier indices [18]. The imbalance is estimated in the frequency domain but modeled and corrected in the time domain. But training sequences designed for I/Q imbalance compensation are typically not available in standards. A blind estimation of the parameters of the I/Q mismatch is therefore useful and has been presented in [19]. The effects of I/Q imbalance can in principle be avoided with digital up- and down-conversion. Straightforward approaches result in a high sampling frequency of the IF signal at the transmitter since sideband suppression is required in the RF domain. An alternative is a low IF design using single-sideband modulation at the transmitter and digital image rejection at the receiver. In this way, the cross-talk between image carriers is removed completely but the interference is converted to out-of-band emission for which restrictions exist as described above. RF Non-Reciprocity Channel reciprocity holds at the antennas but usually gets lost in the baseband. This becomes obvious from Figure 5 (left). Typically, different I/Q mixers, amplifiers and path lengths are used in the separate RF chains at the transmitter and at the receiver. The major challenge of TDD is hence to provide channel reciprocity at the baseband inputs and outputs of the communication system as well. The requirements on the residual nonreciprocity of transceivers have been studied in [20]. The non-reciprocity is modeled as a random error of the channel coefficients. The allowable error vector magnitude (EVM) between forward and reverse channel coefficients is in the order of 15 db with a simple zero-forcing joint transmission scheme with 4 Tx and 2 Rx and QPSK modulation to achieve an uncoded bit error rate (BER) below The use of 4 Rx antennas requires an EVM below 30 db for the same BER. Of course, higher order modulations require even smaller EVMs. There are several proposals to realize reciprocity by calibration. In [21] one antenna is used as a reference, and a test signal transmitted over the air is measured at the other antennas. In general, over-the-air calibration is more difficult than over cable, due to fading effects of the wireless channel. Multiple references are preferable to stabilize the estimated component parameters. The self-calibration of front-ends is proposed in [22] using a JUNE 2006 IEEE VEHICULAR TECHNOLOGY MAGAZINE 27

5 FIGURE 5 Standard transceivers lose the reciprocity in the baseband (left). A new concept makes the transceiver reciprocal by its architecture (right). FIGURE 6 Measured error vector magnitudes of the residual nonreciprocity. FIGURE 7 Structure of an adaptive MIMO-OFDM link. noise source as a reference, while the antenna is disconnected from the transceiver. However, perfect switches and directional couplers are required for this approach, which increases the RF costs. To our knowledge, no measurement data on the achievable EVMs has so far been published. Recently, a transceiver structure has been proposed which is close to reciprocal already by design (cf. Figure 5, right [23]). In principle, the I/Q mixer as well as the amplifiers can be reused since in the TDD mode a terminal (or AP) never transmits and receives simultaneously. By using an RF transfer switch, the link direction of the low-noise and power amplifiers arranged in line is reversed. The I/Q mixer is used both as a modulator and a demodulator. For this reciprocal transceiver, we present EVM measurement results here see Figure 6. With a commercial broadband mixer, the EVM is in the order of 30 db in 100 MHz, already without calibration. An EVM below 45 db is achieved after a narrow-band calibration which basically removes IQ imbalance effects. These results indicate that the problems in the TDD transceiver chains can be solved already without any calibration using the reciprocal transceiver architecture and a well-designed I/Q mixer. There may be additional sources of non-reciprocity. One point is that input and output impedances of the LNA and HPA are switched in parallel to the antenna in the Rx and the Tx mode, respectively, such that the base impedance could possibly be changed. But it must be the same according to the reciprocity theorem in electromagnetics. Measurements in a metal box with reproducible scattering indicated that the calibration functions are similar but not identical if the impedance is either artificially modified or kept equal while switching from Tx to Rx mode. These findings are similar to [24], where, despite the calibration, deviations from the reciprocity have been observed using a prototype UMTS TDD transceiver. A possible reason for this is that the radiation patterns of the antenna might be slightly modified if the base impedance is changed. The fading is then modified and this effect cannot be corrected by calibration. Hence, LNAs and HPAs must have wellmatching in- and output impedances, respectively. For our reciprocal transceivers, the return loss is better than 10 db at both amplifiers and such pattern effects were not noticeable in our over-the-air measurements. Reciprocity in low-cost radios is still in its infancy. It needs a concerted action of RF, signal processing and systems engineers to bring this promising concept into application. Real-Time Implementation Our MIMO-OFDM transmission concept is based on full CSI at the transmitter. For moving terminals, the channel can change rapidly and we need to readjust the entire signal processing chain to the current channel at 28 IEEE VEHICULAR TECHNOLOGY MAGAZINE JUNE 2006

6 a relatively high rate (some few Hz up to some khz). As a general statement, this adaptation to the channel must take place in a fraction of the channel coherence time. But there are other issues to be considered. Typical adaptation times for Wireless LANs and cellular systems are both in the order of a few ms, even though a much higher mobility is required for cell phones. This is due to the SNR at which these systems operate. After an initial estimate of the channel, the time variation causes an interference rising with a slope of 20 db per decade in time. Once this interference becomes comparable to the noise, a new estimate is needed. Wireless LANs operate at much higher SNR (and lower noise) than cellular systems, and so the time constant of adaptation can be the same even if the mobility requirements are different. Another issue is the diversity realized in the temporal, frequency and spatial domains. Diversity renders the wireless link more robust against any sort of interference, and thus also against the interference due to time-variant fading. With more diversity we can consequently realize a higher mobility [26]. The central challenge in the reciprocal TDD system is that any algorithm used must be strictly real-time proof, while still performing close to the optimum. The signal processing for MIMO can be decomposed into two fundamental parts (cf. Figure 7): the symbol-rate processing (marked with grey background in Figure 7) which is a huge data pipeline operated at 100 MHz (or 10 ns clock cycle) in the experimental system. Beside this, various processing functions in the pipeline are controlled by the link adaptation (marked with blue background) operating at the channel update rate. A new adjustment of all transmission parameters is typically generated every few microseconds. In general, the combination of MIMO and OFDM has a significant potential of parallel and pipelined processing [27], [28]. The symbol-rate processing pipeline contains many well known parts similar to standard OFDM transmission chains: the channel encoder and decoder, the modulation and FFT/IFFT units and the FIR filters to remove aliasing effects. The synchronization unit can be widely reused, but the spatial diversity inherent in the MIMO system should be exploited to improve timing and frequency offset estimates [25] and phase tracking as well. Only a few parts are new: The adaptive flow control unit distributes the data in the space-frequency domain, the space-frequency pre-processing couples the data streams optimally into the eigenmodes of the channel. There is also a completely revised channel estimation unit [27]. The space-frequency post-processing unit is similar to the pre-processing. The MIMO-OFDM post-processing is performed after the FFTs at the receiver (Figure 8). A pipelined matrix-vector multiplication unit is used as a space-frequency filter which separates the four antenna signals arriving at the inputs (cf. Figure 8 left) into the four data streams at the outputs (cf. FIGURE 8 Principle of the space-frequency processing unit. FIGURE 9 Parallelized channel-rate processing for MIMO-OFDM using a DSP star. Figure 8 bottom). The weights for each subcarrier are written into a dual port RAM each few microseconds by the DSP and a new weight is read out each 10 ns for each new subcarrier (corresponding to the 100 MHz clock). The channel rate processing involves the calculation of the weight matrices for each sub-carrier. It is realized with a floating point DSP. For higher numbers of subcarriers or higher mobility, a DSP star is useful (see Figure 9) where each DSP is responsible for a fraction of the subcarriers. JUNE 2006 IEEE VEHICULAR TECHNOLOGY MAGAZINE 29

7 The integrated system is depicted in Figure 10 and has been shown at the 3GSM World Congress in February 2005 where data has been transmitted over the air at 1 Gbit/s, using a 3 Tx and 5 Rx antenna configuration in a bandwidth of 100 MHz. In this case, CSI was exploited at the Rx side only and a linear MMSE detector was used. Recently, we have integrated the adaptive modulation on each sub-carrier and each antenna, which has been demonstrated at the CeBIT, Hannover, in Spring 2005, including over the air synchronization. Experiments have verified that Gbit transmission is feasible with antenna elements spaced as closely as 0.2 wavelengths in indoors, consistent with previous measurements [31]. Use cases The potential application scenarios for the proposed MIMO-OFDM TDD approach span from wireless personal area networks (WPAN) to even cellular applications however, the implementation is in very different stages. In WPAN based on ultra-wideband (UWB) technology, the use of MIMO is currently under investigation, but link reciprocity may turn out to be out of reach since calibration is a critical issue at ultra-high bandwidth. In wireless local area networks (WLAN), the current IEEE draft standard n already uses MIMO-OFDM with TDD, and contains optional transmission modes exploiting reciprocity. However, while calibration tools are defined in the standard, they have hardly been tested in practice so far some time will pass before WLANs will be able to fully realize potential of the MIMO-OFDM TDD system concept presented here. The same holds for wireless metropolitan area networks (WMAN) such as the (mobile) WiMAX standard e which is based on OFDM and TDD and also features MIMO modes based on reciprocity. MIMO-OFDM in combination with TDD (as an option besides FDD) is currently also discussed for cellular systems, in the framework of 3GPP long-term evolution (LTE). In this scenario, the reduced range in the TDD mode, compared to FDD, is an important issue as it may lead to increased infrastructure cost. Moreover, interference issues require a synchronized switching between uplink and downlink at adjacent base stations. FIGURE 10 Top: MIMO-OFDM Tx (left) and Rx (right). Bottom: The Tx spectrum in a 100 MHz span (left), and the reconstructed 64-QAM constellation of the first antenna (right). Conclusions We have shown that a combination of MIMO, OFDM and TDD can fulfill the requirements of next generation wireless systems: high data rates, high quality of service and lowcost terminals. The broadband MIMO channel promises wirelike quality of service over the wireless link. The optimal multiple access scheme with MIMO must definitely include the spatial domain. Various problems need to be solved for OFDM in general: non-linearity, phase noise, I/Q imbalance. One topic which is important not only for MIMO but is still in its infancy: to realize channel reciprocity in the base-band. The challenge of the entire concept is the strict real-time constraint due to the channel-aware transmission. Most functions have already been implemented, but further effort is required to finalize the system integration. With increasing progress during this work, we feel that the proposed MIMO-OFDM TDD system concept can eventually be realized. Acknowledgments Many people have contributed to this work: D. Petrovic, M. Windisch, and P. Zillmann from TU Dresden, H. Boche, A. Forck, H. Gaebler, T. Haustein, C. von Helmolt, U. Krüger from HHI, S. Jaeckel from FH Telekom in Leipzig, C. Juchems, M. Luhn and M. Pollock from IAF GmbH in Braunschweig, J. Eichinger, M. Lampe, E. Schulz and W. Zirwas from SIEMENS Munich. The authors wish to thank the German Ministry of Education and Research (BMBF) as well as SIEMENS for financial support in the projects HyEff, 3GeT and WIGWAM and the European Commission for support in the IST project WINNER. Author Information Gerhard Fettweis studied electrical engineering at the Aachen University of Technololgy (RWTH) in Germany where he earned his Ph.D. degree in From 1990 to 1991, he was Visiting Scientist at the IBM Almaden Research Center in San Jose, CA, developing signal processing innovations for IBM s disk drive products. From 1991 to 1994, he was a Scientist with TCSI Inc., Berkeley, CA, responsible for signal processor development projects for mobile phone chip-sets. Since September 1994 he holds the Vodafone Chair at the Technische Universität in Dresden, Germany. In addition he cofounded Systemonic as CTO in 1999, which was successfully acquired by Philips Semiconductor in December Now he is Chief Scientist of Philips Semiconductors BL-C. In 2000, a second start-up was spun-out of the Vodafone 30 IEEE VEHICULAR TECHNOLOGY MAGAZINE JUNE 2006

8 Chair: Radioplan delivers products and professional services related to 2.5G, 3G and 4G network development, planning and optimization. In 2003 a third startup was spun out: Signalion provides leading edge consulting, engineering & prototype development for signal processing and communications systems. The forth startup, InCircuit (2004) delivers custom electronic circuit solutions for signal processing products. The fifth startup, Dresden Silicon (2005), delivers media codec circuits and solutions for mobile devices. Gerhard Fettweis research at the Vodafone Chair focuses on new wireless communications systems for cellular and short range networks, and their hardware/software implementation. Ernesto Zimmermann received his Dipl.-Ing. degree from Technische Universität Dresden in April 2003, after studies at TU Dresden, UPC Barcelona, and ENSTB Rennes. He gained practical experience during internships at IBM, BMW, and McKinsey. He joined the Vodafone Chair at TU Dresden in June 2003, where he is currently pursuing his Ph.D. degree. His research interests lie in information theory, channel coding, iterative MIMO receivers, and cooperative relaying. Volker Jungnickel received the Dipl.-Phys. (M.S.) and Dr. rer. nat. (Ph.D.) degrees in experimental physics, both from Humboldt University in Berlin, Germany, in 1992 and 1995, respectively. He has worked on photoluminescence of semiconductor quantum dots and minimal-invasive laser-surgery before joining the Fraunhofer Institute for Telecommunications (Heinrich-Hertz-Institut) in After completing a 155 Mbit/s wireless indoor communications link based on infrared his research is focussed on broadband multiple-input multiple-output (MIMO) systems. He has recently completed a 1 Gbit/s MIMO-OFDM radio link in real time. His current research is concerned with nextgeneration cellular systems. Volker is a lecturer at the Technical University in Berlin and a member of the IEEE. Eduard A. Jorswiek received his Diplom-Ingenieur (M.S.) degree and Doktor-Ingenieur (Ph.D.) degree, both in electrical engineering and computer science from the Technische Universität Berlin, Germany, in 2000 and 2004, respectively. He has been with the Fraunhofer Institute for Telecommunications, Heinrich-Hertz-Institut (HHI) Berlin, in the Broadband Mobile Communication Networks Department since Since 2005, he is lecturer at the Technical University in Berlin. He joined the Department of Signals, Sensors and Systems at the Royal Institute of Technology (KTH) in 2006 as post-doc. His research activities comprise performance and capacity analysis of wireless systems and optimal transmission strategies for single- and multi-user multiple antenna systems. References [1] G.G. Raleigh and J.M. Cioffi, Spatio-temporal coding for wireless communications, IEEE Trans. Commun., vol. 46, no. 3, Mar [2] T.A. 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