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IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 11, NO. 2, SECOND QUARTER 2009 87 Multiple-Antenna Techniques for Wireless Communications – A Comprehensive Literature Survey Jan Mietzner, Member, IEEE, Robert Schober, Senior Member, IEEE, Lutz Lampe, Senior Member, IEEE, Wolfgang H. Gerstacker, Member, IEEE, and Peter A. Hoeher, Senior Member, IEEE Abstract—The use of multiple antennas for wireless commu- nication systems has gained overwhelming interest during the last decade - both in academia and industry. Multiple antennas can be utilized in order to accomplish a multiplexing gain, a diversity gain, or an antenna gain, thus enhancing the bit rate, the error performance, or the signal-to-noise-plus-interference ratio of wireless systems, respectively. With an enormous amount of yearly publications, the ﬁeld of multiple-antenna systems, often called multiple-input multiple-output (MIMO) systems, has evolved rapidly. To date, there are numerous papers on the per- formance limits of MIMO systems, and an abundance of trans- mitter and receiver concepts has been proposed. The objective of this literature survey is to provide non-specialists working in the general area of digital communications with a comprehensive overview of this exciting research ﬁeld. To this end, the last ten years of research efforts are recapitulated, with focus on spatial multiplexing and spatial diversity techniques. In particular, topics such as transmitter and receiver structures, channel coding, MIMO techniques for frequency-selective fading channels, di- versity reception and space-time coding techniques, differential and non-coherent schemes, beamforming techniques and closed- loop MIMO techniques, cooperative diversity schemes, as well as practical aspects inﬂuencing the performance of multiple-antenna systems are addressed. Although the list of references is certainly not intended to be exhaustive, the publications cited will serve as a good starting point for further reading. Index Terms—Wireless communications, multiple-antenna sys- tems, spatial multiplexing, space-time coding, beamforming. I. INTRODUCTION H OW IS IT possible to design reliable high-speed wireless communication systems? Wireless communication is based on radio signals. Traditionally, wireless applications were voice-centric and demanded only moderate data rates, while most high-rate applications such as ﬁle transfer or video streaming were wireline applications. In recent years, however, there has been a shift to wireless multimedia applications, Manuscript received 20 February 2007; revised 29 October 2007. This work was partly supported by a postdoctoral fellowship from the German Academic Exchange Service (DAAD). Jan Mietzner, Robert Schober, and Lutz Lampe are with the Communication Theory Group, Dept. of Elec. & Comp. Engineering, The University of British Columbia, 2332 Main Mall, Vancouver, BC, V6T 1Z4, Canada (e- mail: {janm,rschober,lampe}@ece.ubc.ca). Wolfgang H. Gerstacker is with the Institute for Mobile Communications, Faculty of Engineering Sciences, University of Erlangen-Nuremberg, Cauer- str. 7, D-91058 Erlangen, Germany (e-mail: gersta@LNT.de). which is reﬂected in the convergence of digital wireless networks and the Internet. For example, cell phones with integrated digital cameras are ubiquitous already today. One can take a photo, email it to a friend – and make a phone call, of course. In order to guarantee a certain quality of service, not only high bit rates are required, but also a good error performance. However, the disruptive characteristics of wireless channels, mainly caused by multipath signal propagation (due to reﬂec- tions and diffraction) and fading effects, make it challenging to accomplish both of these goals at the same time. In particular, given a ﬁxed bandwidth, there is always a fundamental trade- off between bandwidth efﬁciency (high bit rates) and power efﬁciency (small error rates). Conventional single-antenna transmission techniques aim- ing at an optimal wireless system performance operate in the time domain and/or in the frequency domain. In particular, channel coding is typically employed, so as to overcome the detrimental effects of multipath fading. However, with regard to the ever-growing demands of wireless services, the time is now ripe for evolving the antenna part of the radio system. In fact, when utilizing multiple antennas, the previously un- used spatial domain can be exploited. The great potential of using multiple antennas for wireless communications has only become apparent during the last decade. In particular, at the end of the 1990s multiple-antenna techniques were shown to provide a novel means to achieve both higher bit rates and smaller error rates.1 In addition to this, multiple antennas can also be utilized in order to mitigate co-channel interference, which is another major source of disruption in (cellular) wireless communication systems. Altogether, multiple-antenna techniques thus constitute a key technology for modern wire- less communications. The beneﬁts of multiple antennas for wireless communication systems are summarized in Fig. 1. In the sequel, they are characterized in more detail. A. Higher Bit Rates with Spatial Multiplexing Spatial multiplexing techniques simultaneously transmit in- dependent information sequences, often called layers, over multiple antennas. Using M transmit antennas, the overall bit rate compared to a single-antenna system is thus enhanced Peter A. Hoeher is with the Information and Coding Theory Lab, Faculty of Engineering, University of Kiel, Kaiserstr. 2, D-24143 Kiel, Germany (e-mail: ph@tf.uni-kiel.de). Digital Object Identiﬁer 10.1109/SURV.2009.090207. 1Interestingly, the advantages of multiple-antenna techniques rely on the same multipath fading effect that is typically considered detrimental in single- antenna systems. 1553-877X/09/$25.00 c 2009 IEEE

88 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 11, NO. 2, SECOND QUARTER 2009 Multiple- antenna techniques Tx Rx Spatial multiplexing techniques Spatial diversity techniques (Space- time coding & diversity reception) Smart antennas (Beamforming) Trade-off Trade-off Multiplexing gain Diversity gain Coding gain Antenna gain Interference suppression Higher bit rates Smaller error rates Higher bit rates/ Smaller error rates Fig. 1. Beneﬁts of multiple-antenna techniques for wireless communications. by a factor of M without requiring extra bandwidth or extra transmission power.2 Channel coding is often employed, in order to guarantee a certain error performance. Since the individual layers are superimposed during transmission, they have to be separated at the receiver using an interference- cancellation type of algorithm (typically in conjunction with multiple receive antennas). A well-known spatial multiplexing scheme is the Bell-Labs Layered Space-Time Architecture (BLAST) [1]. The achieved gain in terms of bit rate (with respect to a single-antenna system) is called multiplexing gain in the literature. time domain. Correspondingly, a diversity gain3 and a coding gain can be achieved without lowering the effective bit rate compared to single-antenna transmission. Well-known spatial diversity techniques for systems with multiple transmit antennas are, for example, Alamouti’s trans- mit diversity scheme [2] as well as space-time trellis codes [3] invented by Tarokh, Seshadri, and Calderbank. For systems, where multiple antennas are available only at the receiver, there are well-established linear diversity combining tech- niques dating back to the 1950’s [4]. C. Improved Interference Mitigation Using Smart Antennas Signal-to-Noise Ratios and Co-Channel- B. Smaller Error Rates through Spatial Diversity Similar to channel coding, multiple antennas can also be used to improve the error rate of a system, by transmitting and/or receiving redundant signals representing the same in- formation sequence. By means of two-dimensional coding in time and space, commonly referred to as space-time coding, the information sequence is spread out over multiple transmit antennas. At the receiver, an appropriate combining of the redundant signals has to be performed. Optionally, multiple receive antennas can be used, in order to further improve the error performance (diversity reception). The advantage over conventional channel coding is that redundancy can be accommodated in the spatial domain, rather than in the 2In other words, compared to a single-antenna system the transmit power per transmit antenna is lowered by a factor of 1/M. In addition to higher bit rates and smaller error rates, multiple-antenna techniques can also be utilized to improve the signal-to-noise ratio (SNR) at the receiver and to suppress co- channel interference in a multiuser scenario. This is achieved by means of adaptive antenna arrays [5], also called smart antennas or software antennas in the literature. Using beam- forming techniques, the beam patterns of the transmit and re- ceive antenna array can be steered in certain desired directions, whereas undesired directions (e.g., directions of signiﬁcant interference) can be suppressed (‘nulled’). Beamforming can be interpreted as linear ﬁltering in the spatial domain. The SNR gains achieved by means of beamforming are often called antenna gains or array gains. The concept of antenna arrays 3If the antenna spacings at transmitter and receiver are sufﬁciently large, the multipath fading of the individual transmission links can be regarded as statistically independent. Correspondingly, the probability that all links are degraded at the same time is signiﬁcantly smaller than that for a single link, thus leading to an improved error performance.

MIETZNER et al.: MULTIPLE-ANTENNA TECHNIQUES FOR WIRELESS COMMUNICATIONS – A COMPREHENSIVE LITERATURE SURVEY 89 with adaptive beam patterns is not new and has its origins in the ﬁeld of radar (e.g., for target tracking) and aerospace technology. However, intensive research on smart antennas for wireless communication systems started only in the 1990’s. D. Combined Techniques The above families of multiple-antenna techniques are, in fact, quite different. Spatial multiplexing is closely related to the ﬁeld of multiuser communications and aims predominantly at a multiplexing gain compared to a single-antenna system. Space-time coding is more in the ﬁeld of modulation and channel coding and aims at a (coding and) diversity gain. Finally, smart antennas and beamforming techniques belong more in the area of signal processing and ﬁltering and aim at an antenna gain, i.e., at an improved SNR or an improved signal-to-interference-plus-noise ratio (SINR). There are also composite transmission schemes that aim at a combination of the different gains mentioned above. However, given a ﬁxed number of antennas, there are certain trade-offs [6] between multiplexing gain, diversity gain, and SNR gain. In fact, a strict distinction between the above three types of multiple-antenna techniques is sometimes difﬁcult. For example, spatial multiplexing techniques can also accomplish a diversity gain, e.g., if an optimum receiver in the sense of maximum-likelihood (ML) detection is employed. Similarly, spatial diversity techniques can also be used to increase the bit rate of a system, when employed in conjunction with an adaptive modulation/channel coding scheme.4 E. Development of the Field Extensive research on multiple-antenna systems for wireless communications, often called multiple-input multiple-output (MIMO) systems, started less than ten years ago. The great interest was mainly fueled by the pioneering works of Telatar [7], Foschini and Gans [1], [8], Alamouti [2], and Tarokh, Seshadri, and Calderbank [3] at the end of the 1990’s. On the one hand, the theoretical results in [7], [8] promised signif- icantly higher bit rates compared to single-antenna systems. Speciﬁcally, it was shown that the (ergodic or outage) capacity, i.e., the maximum bit rate at which error-free transmission is theoretically possible, of a MIMO system with M transmit and N receive antennas grows (approximately) linearly with the minimum of M and N .5 On the other hand, the work in [1]-[3] suggested design rules for practical systems. In [1] the BLAST spatial multiplexing scheme was introduced that accomplished bit rates approaching those promised by theory (at non-zero error rates). In [2], Alamouti proposed his simple transmit diversity scheme for systems with two transmit antennas, and in [3] design criteria for space-time trellis codes were derived. The invention of space-time trellis 4If the error rate accomplished by means of spatial diversity is smaller than desired, one can switch to a higher-order modulation scheme or to a channel coding scheme with less redundancy. By this means, it is possible to trade error performance for a higher effective bit rate (since higher-order modulation schemes typically come with a loss in power efﬁciency). In fact, adaptive modulation and channel coding schemes are employed in most state- of-the-art wireless communication systems. 5Again, the underlying assumption is that the individual transmission links are subject to statistically independent fading. codes was like an ignition spark. With an enormous amount of yearly publications, the ﬁeld of MIMO systems started to evolve rapidly. To date, there are numerous papers on the performance limits of MIMO systems, and an abundance of transmitter and receiver concepts has been proposed.6 Interestingly, although the period of intensive research ac- tivities has been relatively short, multiple-antenna techniques have already entered standards for third-generation (3G) and fourth-generation (4G) wireless communication systems.7 For example, some 3G code-division multiple access (CDMA) systems use Alamouti’s transmit diversity scheme for cer- tain transmission modes [10]. MIMO transmission is also employed in the IEEE 802.11n wireless local area network (WLAN) standard (see [11] for an overview). Further ex- amples include the IEEE 802.20 mobile broadband wireless access system [12] and the 3GPP Long Term Evolution (LTE) of wideband CDMA (W-CDMA) [13]. F. Drawbacks of Multiple-Antenna Systems Clearly, the various beneﬁts offered by multiple-antenna techniques do not come for free. For example, multiple parallel transmitter/receiver chains are required, leading to increased hardware costs. Moreover, multiple-antenna techniques might entail increased power consumptions and can be more sen- sitive to certain detrimental effects encountered in practice. Finally, real-time implementations of near-optimum multiple- antenna techniques can be challenging. On the other hand, (real-time) testbed trials have demonstrated that remarkable performance improvements over single-antenna systems can be achieved in practice, even if rather low-cost hardware components are used [14]. G. Focus and Outline of the Survey The objective of this literature survey is to recapitulate the last ten years of research efforts, so as to provide a comprehensive overview of this exciting research ﬁeld. Fo- cus will be on spatial multiplexing techniques (Section II) and spatial diversity techniques (Section III). Smart antenna techniques will brieﬂy be outlined in Section IV. Finally, alternative categorizations of the available multiple-antenna techniques will be discussed in Section V, and the beneﬁts and requirements of various schemes discussed will be highlighted. Some conclusions are offered in Section VI. Although the list of references is not intended to be exhaus- tive, the cited papers (as well as the references therein) will serve as a good starting point for further reading. In particular, there are various tutorial-style articles, e.g., [5], [15]-[21], all of which have quite a different focus. II. SPATIAL MULTIPLEXING TECHNIQUES As discussed in the Introduction, three types of fundamental gains can be obtained by using multiple antennas in a wireless 6In April 2008, a search with IEEE Xplore R for papers in the general ﬁeld of multiple-antenna communication systems yielded a total number of more than 14,600 documents. 7In fact, the authors of [9] predict that multiple-antenna techniques will become crucial for system operators to secure the ﬁnancial viability of their business.

90 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 11, NO. 2, SECOND QUARTER 2009 communication system: A multiplexing gain, a diversity gain, and an antenna gain (cf. Fig. 1). In this section, we will mainly focus on the multiplexing gain. The fact that the capacity of a MIMO system with M transmit and N receive antennas grows (approximately) lin- early with the minimum of M and N (without requiring extra bandwidth or extra transmission power) [7], [8] is an intriguing result. For single-antenna systems it is well known that given a ﬁxed bandwidth, capacity can only be increased logarithmically with the SNR, by increasing the transmit power. In [1], the theoretical capacity results for MIMO systems were complemented by the proposal of the BLAST scheme, which was shown to achieve bit rates approaching 90% of outage capacity. Similar to the theoretical capacity results, the bit rates of the BLAST scheme were characterized by a linear growth when increasing the number of antenna elements. The ﬁrst real-time BLAST demonstrator [22] was equipped with M = 8 transmit and N = 12 receive antennas. In a rich-scattering indoor environment, it accomplished bit rates as high as 40 bit/s per Hertz bandwidth (corresponding to about 30% of capacity) at realistic SNRs. Wireless spectral efﬁciencies of this magnitude were unprecedented and can not be achieved by any single-antenna system. A. Transmitter and Receiver Structure The idea of spatial multiplexing was ﬁrst published in [23]. The basic principle of all spatial multiplexing schemes is as follows. At the transmitter, the information bit sequence is split into M sub-sequences (demultiplexing), that are modulated and transmitted simultaneously over the transmit antennas using the same frequency band. At the receiver, the trans- mitted sequences are separated by employing an interference- cancellation type of algorithm. The basic structure of a spatial multiplexing scheme is illustrated in Fig. 2. In the case of frequency-ﬂat fading, there are several options for the detection algorithm at the receiver, which are characterized by different trade-offs between performance and complexity. A low-complexity choice is to use a linear receiver, e.g., based on the zero-forcing (ZF) or the minimum- mean-squared-error (MMSE) criterion. However, the error per- formance is typically poor, especially when the ZF approach is used (unless a favorable channel is given or the number of receive antennas signiﬁcantly exceeds the number of transmit antennas). Moreover, at least as many receive antennas as transmit antennas are required (N ≥ M ), otherwise the system is inherently rank-deﬁcient. If the number of receive antennas exceeds the number of transmit antennas, a spatial diversity gain is accomplished. The optimum receiver in the sense of the maximum- likelihood (ML) criterion performs a brute-force search over all possible combinations of transmitted bits and selects the most likely one (based on the received signals). The ML detector achieves full spatial diversity with regard to the number of receive antennas, irrespective of the number of transmit antennas used. In principle, the use of multiple receive antennas is optional. Yet, substantial performance improvements compared to a single-antenna system are only achieved when multiple receive antennas are employed. The major drawback of the ML detector is its complexity. It grows exponentially with the number of transmit antennas and the number of bits per symbol of the employed modulation scheme. Due to this, the complexity of the ML detector is often prohibitive in a practical system. However, it can be reduced by means of more advanced detection concepts, such as sphere decoding. For the BLAST scheme, an alternative detection strategy known as nulling and canceling was proposed. The BLAST detector was originally designed for frequency-ﬂat fading channels and provides a good trade-off between complexity and performance. In contrast to the ML detector, the estimation of the M sub-sequences, called layers in the terminology of BLAST, is not performed jointly, but successively layer by layer. Starting from the result of the linear ZF receiver (nulling step) or the linear MMSE receiver, the BLAST detector ﬁrst selects the layer with the largest SNR and estimates the transmitted bits of that layer, while treating all other layers as interference. Then, the inﬂuence of the detected layer is subtracted from the received signals (canceling step). Based on the modiﬁed received signals, nulling is performed once again, and the layer with the second largest SNR is selected. This procedure is repeated, until the bits of all M layers are detected. Due to the nulling operations, the number of receive antennas must at least be equal to the number of transmit antennas (as in the case of the linear receivers), otherwise the overall error performance degrades signiﬁcantly.8 The error performance resulting for the individual layers is typically dif- ferent. In fact, it depends on the overall received SNR, which layer is best. In the case of a low SNR, error propagation effects from previously detected layers dominate. Correspond- ingly, the layer detected ﬁrst has the best performance. At the same time, layers that are detected later have a larger diversity advantage, because less interfering signals have to be nulled. Therefore, in the high SNR regime, where the effect of error propagation is negligible, the layer detected last offers the best performance [24]. A detailed performance analysis of the BLAST detector was, for example, presented in [25]. The BLAST detection algorithm is very similar to suc- cessive interference cancellation (SIC), which was originally proposed for multiuser detection in CDMA systems. Sev- eral papers have proposed complexity-reduced versions of the BLAST detector, e.g. [26]. Similarly, many papers have suggested variations of the BLAST detector with an improved error performance, e.g. [27]. An interesting approach to im- prove the performance of the BLAST scheme was presented in [28]. Prior to the BLAST detection algorithm, the given MIMO system is transformed into an equivalent system with a better conditioned channel matrix, based on a so-called lattice reduction. The performance of the BLAST detector is signiﬁcantly improved by this means and approaches that of the ML detector, while the additional complexity due to the lattice reduction is rather small. B. Channel Coding In order to guarantee a certain error performance for spatial multiplexing schemes, channel coding techniques are usually 8Note that this is a crucial requirement when a simple receiver is desired.

MIETZNER et al.: MULTIPLE-ANTENNA TECHNIQUES FOR WIRELESS COMMUNICATIONS – A COMPREHENSIVE LITERATURE SURVEY 91 Transmitter Receiver Information bit sequence i l g n x e p i t l u m e D 1 M 1 2 N Detection Algorithm Estimated bit sequenc e Fig. 2. Basic principle of spatial multiplexing. M sub-sequences required. Most spatial multiplexing schemes employ a channel coding structure that is composed of one-dimensional encoders and decoders operating solely in the time domain. This is in contrast to space-time coding techniques like [2], [3], where two-dimensional coding is performed in time and space, i.e., across the individual transmit antennas. In principle, three different types of (one-dimensional) channel coding schemes can be used in conjunction with spatial multiplexing: Hor- izontal coding, vertical coding, or a combination of both. Horizontal coding means that channel encoding is performed after the demultiplexer (cf. Fig. 2), i.e., separately for each of the M layers. The assignment between the encoded layers and the transmit antennas remains ﬁxed, i.e., all code bits associated with a certain information bit are transmitted over the same antenna. At the receiver, channel decoding can thus be performed individually for each layer (after applying one of the above receiver structures). In the case of vertical coding, however, channel encoding is performed before the demultiplexer, and the encoded bits are spread among the individual transmit antennas. Compared to horizontal coding, vertical coding thus offers an additional spatial diversity gain. However, the drawback of vertical coding is an increased detector complexity, because at the receiver all layers have to be decoded jointly. For the BLAST scheme, a combination of horizontal and vertical encoding was proposed, called diagonal coding [1]. Correspondingly, the original BLAST scheme is also known as Diagonal BLAST (D-BLAST). As in horizontal coding, channel encoding is performed separately for each layer. Subsequently, a spatial block interleaver is employed. For a certain time period, the assignment between the encoded layers and the transmit antennas remains ﬁxed, and is then changed in a modulo-M fashion. Thus, the overall coding scheme has a diagonal structure in time and space. In principle, diagonal coding offers the same spatial diversity advantage as vertical coding, while retaining the small receiver complexity of horizontal coding. A comparative performance study of horizontal, vertical, and diagonal coding was presented in [29]. Moreover, several improved channel coding schemes for BLAST can be found in the literature, e.g. [30]. The ﬁrst BLAST demonstrator [22], coined Vertical BLAST (V- BLAST), was in fact realized without any channel cod- ing scheme. C. Channels with Intersymbol Interference The receiver concepts discussed in Section II-A were de- signed for frequency-ﬂat fading channels, i.e., for channels without intersymbol interference (ISI). However, depending on the delay spread of the physical channel (due to multipath signal propagation), the employed transmit and receive ﬁlter, and the symbol duration, this assumption might not be valid in a practical system. If no counter measures are employed, ISI can cause signiﬁcant performance degradations (see, for example, [31] where the BLAST scheme was studied in the presence of ISI). One approach to circumvent the problem of ISI is to use a multicarrier transmission scheme and multiplex data symbols onto parallel narrow sub-bands that are quasi-ﬂat. Transmission schemes developed for frequency-ﬂat fading channels can then be applied within each sub-band. A popular multicarrier scheme is orthogonal frequency-division multi- plexing (OFDM) which uses an inverse fast Fourier transform (IFFT) at the transmitter and a fast Fourier transform (FFT) at the receiver, making it simple to implement. Speciﬁcally, it is straightforward to combine OFDM with multiple antennas (MIMO-OFDM) [32]. The combination of (an improved ver- sion of) the BLAST scheme with OFDM was, for example, considered in [33]. Alternatively, one can also use a single-carrier approach and employ suitable techniques for mitigating ISI. Generally, there are two main classes of techniques, namely transmitter- sided predistortion and receiver-sided equalization techniques. Predistortion techniques require channel knowledge at the transmitter side, e.g., based on feedback information from the receiver. Predistortion for frequency-selective MIMO channels is a rather new research topic, and not much work has yet been reported [34]. In contrast to this, there are many equalization schemes for MIMO systems, most of which are generalizations of existing techniques for single-antenna systems. For exam- ple, a low-complexity option is to use a linear equalizer (LE) or a decision-feedback equalizer (DFE) in time domain. In the case of a single-antenna system, these equalizers are usually realized by means of ﬁnite-impulse-response (FIR) ﬁlters with real-valued or complex-valued ﬁlter coefﬁcients. Generalized linear and decision-feedback equalizers for MIMO systems (MIMO-LEs/DFEs) can be obtained by replacing the scalar ﬁlter coefﬁcients by appropriate matrix ﬁlter coefﬁcients, see e.g. [24], [35]. An alternative to time-domain equalization is

92 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 11, NO. 2, SECOND QUARTER 2009 frequency-domain equalization (FDE), which is quite similar to OFDM. The major difference is that the FFT and the IFFT operations are both performed at the receiver side. This allows for equalization in the frequency domain by leveling the quasi- ﬂat sub-bands. Like OFDM, FDE can readily be combined with multiple antennas. For example, a combination of the BLAST scheme with FDE was considered in [36]. A high complexity option for mitigating ISI at the receiver is to perform an optimal sequence or symbol-by-symbol estimation, e.g., by means of a trellis-based equalizer. For example, maximum-likelihood sequence estimation (MLSE) can be performed by means of a vector version of the well- known Viterbi algorithm. Alternatively, a generalized version of the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm can be used to perform symbol-by-symbol maximum a-posteriori (MAP) detection. The complexity of MLSE and symbol-by- symbol MAP detection grows exponentially with the number of transmit antennas and the number of bits per modulation symbol. Additionally, it also grows exponentially with the effective memory length of the channel. The use of multiple receive antennas is (in principle) again optional. Similar to the case without ISI, the complexity of MLSE can be reduced signiﬁcantly by means of a sphere decoding approach [37]. Finally, several papers have proposed direct generalizations of the BLAST detection algorithm to ISI channels, e.g. [38]. In essence, the nulling operation is replaced by a set of generalized decision-feedback equalizers for MIMO systems. An iterative extension of [38] was later proposed in [24]. D. Alternative Transmitter and Receiver Concepts More recently, an alternative receiver concept has been proposed for spatial multiplexing systems (without ISI) [39], which is based on the concept of probabilistic data association (PDA). PDA has its origins in target tracking and has been adopted in many different areas, for example, in multiuser communication systems based on CDMA. The key idea is to use an iterative receiver, which detects the individual layers (or, in a multiuser system, the bit sequences of the individual users) by regarding the other, interfering layers as Gaussian noise (Gaussian assumption). Within each iteration, the mean and the variance of the assumed Gaussian noise are adjusted by exploiting knowledge about already detected bits. When a sufﬁciently large number of layers is used (and a modulation scheme with moderate cardinality) the Gaussian assumption ﬁts well, and a near-optimum error performance is achieved.9 The principle of the PDA detector can also be applied for mitigating ISI. A PDA-based equalizer for MIMO systems was, for example, presented in [41]. Further stochastic detection algorithms for spatial multiplexing systems without ISI were proposed in [42]. These are based on the concept of particle ﬁltering and achieve near-ML performance at a reasonable complexity. There are many connections between spatial multiplexing schemes and multiuser communication systems. Hence the idea to adopt multiple-access techniques for spatial multiplex- ing is quite obvious. For example, one could use orthogonal spreading codes (also called signature sequences) to separate the individual layers, just as in a direct-sequence (DS) CDMA system. However, if perfect mutual orthogonality between all layers is desired, the maximum possible bit rate is the same as in a single-antenna system, i.e., the advantage of using multiple transmit antennas is sacriﬁced. On the other hand, relaxing the strict orthogonality constraint causes additional noise within the system (overloaded system). Yet, the use of spreading codes can be beneﬁcial in the case of an unfavorable channel, so as to allow for a separation between a few critical layers [43] (possibly, at the expense of a moderate loss in bit rate). A promising alternative to DS-CDMA is interleave-division multiple access (IDMA). In contrast to a DS-CDMA system, the orthogonality constraint is completely dropped in IDMA, and hence no spreading code design is required. The individual users or layers are separated solely on the basis of different, quasi-random interleaver patterns. At the transmitter, the infor- mation bits are ﬁrst encoded using a simple low-rate repetition code. Alternatively, a more advanced low-rate channel code may be used. Afterwards, the coded bits (called chips) are permuted using a layer-speciﬁc quasi-random block interleaver over multiple code words. In order to separate the individual layers at the receiver, the powerful turbo principle is used. The iterative IDMA receiver uses a Gaussian assumption for the interference stemming from other layers (similar to the PDA detector) and is thus able to efﬁciently separate the individual layers, even in the case of a signiﬁcantly overloaded system. In [44], the idea of IDMA was transferred to (single-user) multiple-antenna systems. The ST-IDM scheme in [44] offers an overall bit rate of 1 bit per channel use and is therefore rather a space-time coding scheme. However, by overloading the system the overall bit rate can be increased, so that a multiplexing gain is achieved (‘multilayer ST-IDM’).10 Such an (overloaded) ST-IDM system has two major advantages when compared to the conventional BLAST system. First, the number of receive antennas can be smaller than the number of transmit antennas, which is particularly attractive for the downlink of a cellular system, where a simple mobile receiver is desired. Even with a single receive antenna, an overall transmission rate of up to 4 bits per channel use can be achieved with an error performance close to the capacity limit. Second, the ST-IDM scheme is inherently robust to ISI, making it suitable for a large range of wireless applications. An alternative approach for spatial multiplexing with less receive antennas than transmit antennas was proposed in [45]. It is based on group MAP detection and is applicable for channels without ISI. In [46], a spatial multiplexing scheme called Turbo-BLAST was proposed, which is similar to the (overloaded) ST-IDM scheme. It also uses quasi-random in- terleaving in conjunction with an iterative receiver structure, so as to separate the individual layers. As in ST-IDM, the number of receive antennas can be smaller than the number of transmit antennas. Moreover, a generalization of Turbo-BLAST to frequency-selective MIMO channels is straightforward. Spatial multiplexing in the presence of ISI with less re- 9As shown in [40], four layers are already sufﬁcient to achieve a near- optimum performance with 4-ary modulation and an outer rate-1/2 turbo code. 10In order to accomplish a good error performance, an optimized transmit power allocation strategy is required, however.

MIETZNER et al.: MULTIPLE-ANTENNA TECHNIQUES FOR WIRELESS COMMUNICATIONS – A COMPREHENSIVE LITERATURE SURVEY 93 ceive than transmit antennas can also be performed using a complexity-reduced version of joint detection, e.g., based on the (trellis-based) vector Viterbi algorithm. For example, a (space-time) channel shortening ﬁlter can be employed prior to the vector Viterbi algorithm, in order to reduce the effective memory length of the MIMO channel, e.g. [47]. A similar receiver structure has previously been applied in the related ﬁeld of (single-antenna) co-channel interference (CCI) cancellation, see [48]. III. SPATIAL DIVERSITY TECHNIQUES In contrast to spatial multiplexing techniques, where the main objective is to provide higher bit rates compared to a single-antenna system, spatial diversity techniques predom- inantly aim at an improved error performance. This is ac- complished on the basis of a diversity gain and a coding gain. Indirectly, spatial diversity techniques can also be used to enhance bit rates, when employed in conjunction with an adaptive modulation/channel coding scheme. There are two types of spatial diversity, referred to as macroscopic and microscopic diversity. Macroscopic (large- scale) diversity is associated with shadowing effects in wire- less communication scenarios, due to major obstacles between transmitter and receiver (such as walls or large buildings). Macroscopic diversity can be gained if there are multiple transmit or receive antennas, that are spatially separated on a large scale. In this case, the probability that all links are simultaneously obstructed is smaller than that for a single link. Microscopic (small-scale) diversity is available in rich- scattering environments with multipath fading. Microscopic diversity can be gained by employing multiple co-located antennas. Typically, antenna spacings of less than a wavelength are sufﬁcient, in order to obtain links that fade more or less independently.11 Similar to macroscopic diversity, the diversity gains are due to the fact that the probability of all links being simultaneously in a deep fade decreases with the number of antennas used. A comprehensive survey of the value of spatial diversity for wireless communication systems can be found in [20]. The idea to utilize macroscopic diversity in wireless com- munication systems is not new. It dates back to the 1970’s [49]. Even more so, the use of multiple receive antennas for gaining microscopic diversity (diversity reception) has been well established since the 1950’s, e.g. [4]. However, it took until the 1990’s before transmit diversity techniques were developed [2]. A. Diversity Reception Diversity reception techniques are applied in systems with a single transmit antenna and multiple receive antennas. They perform a (linear) combining of the individual received sig- nals, in order to provide a microscopic diversity gain. In the case of frequency-ﬂat fading, the optimum combining strategy in terms of maximizing the SNR at the combiner output is maximum ratio combining (MRC), which requires 11Due to this, the term microscopic diversity was chosen for this type of spatial diversity. This does not imply that the associated performance gains are small. In fact, they can be quite substantial. perfect channel knowledge at the receiver. Several suboptimal combining strategies have been proposed in the literature, such as equal gain combining (EGC), where the received signals are (co-phased and) added up, or selection diversity (SD), where the received signal with the maximum instantaneous SNR is selected (antenna selection), whereas all other received signals are discarded. All three combining techniques achieve full diversity with regard to the number of receive antennas. Optimal combining techniques for frequency-selective fading channels were, for example, considered in [50]. B. Transmit Diversity and Space-Time Codes The main idea of transmit diversity is to provide a diversity and/or coding gain by sending redundant signals over multiple transmit antennas (in contrast to spatial multiplexing, where independent bit sequences are transmitted). To allow for coherent detection at the receiver, an adequate preprocessing of the signals is performed prior to transmission, typically without channel knowledge at the transmitter. With transmit diversity, multiple antennas are only required at the transmitter side, whereas multiple receive antennas are optional. However, they can be utilized to further improve performance. In cellular networks, for example, the predominant fraction of the overall data trafﬁc typically occurs in the downlink.12 In order to enhance the crucial downlink it is therefore very attractive to employ transmit diversity techniques, because then multiple antennas are required only at the base station. With regard to cost, size, and weight of mobile terminals this is a major advantage over diversity reception techniques. An early beginning of transmit diversity schemes was made with two papers that independently proposed a simple technique called delay diversity [51], [52].13 Another early publication on transmit diversity can be found, e.g. in [54]. However, the value of transmit diversity was only recognized in 1998, when Alamouti proposed a simple technique for two transmit antennas [2]. In the same year, Tarokh, Seshadri, and Calderbank presented their space-time trellis codes (STTCs) [3], which are two-dimensional coding schemes for systems with multiple transmit antennas. While delay diversity and Alamouti’s transmit diversity scheme provide solely a diversity gain (more precisely, full diversity with regard to the number of transmit and receive antennas), STTCs yield both a diversity gain and an additional coding gain. Within the scope of this survey, we will use the generic term space-timecodingscheme for all transmitter-sided spa- tial diversity techniques, irrespective of the presence of any additional coding gain. The basic structure of a space-time coding scheme is illustrated in Fig. 3. The preprocessing of the redundant transmission signals is performed by the space-time encoder, which depends very much on the speciﬁc scheme under consideration. At the receiver, the corresponding detection/decoding process is carried out by the space-time de- 12Comparatively large amounts of data may be downloaded from the base station to a single mobile terminal, whereas in the uplink typically little data trafﬁc is required to initiate the download. 13Prior to this, there were already publications on transmit diversity schemes that used different modulation parameters at the individual transmit antennas (‘modulation diversity’), e.g. [53].

94 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 11, NO. 2, SECOND QUARTER 2009 coder.14 In the delay diversity scheme [51], [52], for example, identical signals are transmitted via the individual antennas, using different delays. This causes artiﬁcial ISI, which can be resolved at the receiver by means of standard equalization techniques available for single-antenna systems. In contrast to this, Alamouti’s transmit diversity scheme [2] performs an orthogonal space-time transmission, which allows for ML detection at the receiver by means of simple linear processing. STTCs [3] may be interpreted as a generalization of trellis- coded modulation to multiple transmit antennas. Optimum decoding in the sense of MLSE can be performed using the Viterbi algorithm. On the basis of simulation results, it was shown in [3] that STTCs offer an excellent performance that is within 2-3 dB of the outage capacity limit. However, this performance comes at the expense of a comparatively high decoding complexity. Motivated by the simple receiver structure of [2], orthogonal space-time block codes (OSTBCs) were introduced in [55], which constitute a generalization of Alamouti’s scheme to more than two transmit antennas. OSTBCs are designed to achieve full diversity with regard to the number of transmit and receive antennas. In contrast to STTCs, OSTBCs do not offer any additional coding gain. STTCs and OSTBCs can be combined with different diver- sity reception techniques at the receiver side. For example, the performance of STTCs and OSTBCs combined with antenna (subset) selection techniques at the receiver was examined in [56] and [57], respectively. C. Optimized STTCs and OSTBCs In [3], general design criteria were derived for STTCs that guarantee a maximum diversity advantage and allow for an optimization of the coding gain (both for high SNR values). These design criteria depend on the number of transmit and receive antennas as well as on the cardinality of the employed modulation scheme. Unfortunately, ‘good’ STTCs can not be constructed analytically, but have to be found by means of a computer search. An efﬁcient design procedure for STTCs, which is based on simple lower and upper bounds on the coding gain, was presented in [58]. In [3], some examples of optimized STTCs were stated, for certain modulation schemes and certain numbers of transmit antennas.15 Further examples of optimized STTCs, sometimes based on (slightly) modiﬁed design criteria, can be found, e.g., in [58]-[60]. A tight bound on the error performance of STTCs was presented in [61]. OSTBCs are based on the mathematical theory of (gener- alized) orthogonal designs, which dates back to the 1890s. Orthogonal designs are a special class of orthogonal matrices. In general, the use of OSTBCs causes a rate loss when compared to an uncoded single-antenna system. For the case of a real-valued modulation scheme, full-rate (and delay- optimal) OSTBCs for systems with two to eight transmit antennas could be established in [55] (partly based on general- ized orthogonal designs). Given a complex-valued modulation scheme, however, the only full-rate OSTBC is Alamouti’s 14All space-time coding schemes discussed in the sequel were designed for frequency-ﬂat fading. 15The STTCs constructed in [3] provide the best trade-off between data rate, diversity advantage, and trellis complexity. Speciﬁcally, the codes do not cause any rate loss compared to an uncoded single-antenna system. transmit diversity scheme [2] for two transmit antennas. In [55] it was shown that half-rate OSTBCs for complex-valued modulation schemes can be constructed for any number of transmit antennas. However, to ﬁnd OSTBCs with higher rates (and moderate decoding delay) is, in general, not a trivial task. A systematic design method for high-rate OSTBCs was presented in [62], for complex-valued modulation schemes and arbitrary numbers of transmit antennas. Further examples of optimized OSTBCs for different numbers of transmit antennas can be found in [63], [64]. A performance analysis of OSTBCs based on channel capacity and the resulting average symbol error rate can be found in [65] and [66], respectively. D. Other Families of Space-Time Codes Since the advent of STTCs and OSTBCs in 1998, various other families of space-time codes have been proposed in the literature. In [67] the family of square-matrix embeddable STBCs was introduced, which includes some of the OST- BCs proposed in [55] as special cases. Similar to OSTBCs, square-matrix embeddable STBCs allow for ML detection at the receiver by means of (generalized) linear processing. A family of non-orthogonal full-rate linear STBCs, called diagonal algebraic STBCs, was constructed in [68]. Diagonal algebraic STBCs provide full transmit diversity and allow for efﬁcient ML detection by means of the sphere decoding approach. Another non-orthogonal full-rate STBC for two transmit antennas, constructed based on number theory, was presented in [69]. For more than one receive antenna, this STBC provides an improved coding gain compared to Alam- outi’s transmit diversity scheme [2]. In [70], STBCs based on linear constellation precoding were proposed, which provide full rate and full diversity for any number of transmit antennas and perform superior to OSTBCs. For decoding, a sphere decoding approach as well as suboptimal alternatives were considered in [70]. An alternative idea for constructing full- rate STBCs for complex modulation schemes and more than two antennas was pursued in [71]. Here the strict constraint of perfect orthogonality was relaxed in favor of a higher data rate. The resulting STBCs are therefore referred to as quasi-orthogonal STBCs. Due to the relaxed orthogonality constraint, however, quasi-orthogonal STBCs typically offer reduced diversity gains compared to OSTBCs. In addition to the above examples, many other families of STBCs can be found in the literature, some of which were presented in [72]- [74]. In [75] recursive STTCs were considered. In particular, the parallel concatenation of two identical recursive STTCs was studied. Here the encoder structure was inspired by the original turbo code proposed by Berrou, Glavieux, and Thitimajshima in 1993.16 Further examples of concatenated space-time codes can be found, e.g., in [76], [77]. Recursive STTCs are also well suited for a serial concatenation with an outer channel code (with iterative detection at the receiver). In [78], the family of super-orthogonal STTCs was introduced and was later extended in [79] to a larger set of modulation schemes. 16Turbo codes, also called parallel concatenated codes (PCCs), are among the most powerful channel codes for additive-white-Gaussian-noise (AWGN) channels.

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