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269
How Much Training is Needed in MultipleAntenna Wireless Links?
 IEEE Trans. Inform. Theory
, 2000
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HighRate Codes that are Linear in Space and Time
 IEEE Trans. Inform. Theory
, 2000
"... Multipleantenna systems that operate at high rates require simple yet effective spacetime transmission schemes to handle the large traffic volume in real time. At rates of tens of bits/sec/Hz, VBLAST, where every antenna transmits its own independent substream of data, has been shown to have good ..."
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Cited by 422 (13 self)
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Multipleantenna systems that operate at high rates require simple yet effective spacetime transmission schemes to handle the large traffic volume in real time. At rates of tens of bits/sec/Hz, VBLAST, where every antenna transmits its own independent substream of data, has been shown to have good performance and simple encoding and decoding. Yet VBLAST suffers from its inability to work with fewer receive antennas than transmit antennasthis deficiency is especially important for modern cellular systems where a basestation typically has more antennas than the mobile handsets. Furthermore, because VBLAST transmits independent data streams on its antennas there is no builtin spatial coding to guard against deep fades from any given transmit antenna. On the other hand, there are many previouslyproposed spacetime codes that have good fading resistance and simple decoding, but these codes generally have poor performance at high data rates or with many antennas. We propose a highrate coding scheme that can handle any...
From theory to practice: an overview of MIMO spacetime coded wireless systems
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2003
"... This paper presents an overview of recent progress in the area of multipleinput–multipleoutput (MIMO) space–time coded wireless systems. After some background on the research leading to the discovery of the enormous potential of MIMO wireless links, we highlight the different classes of technique ..."
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Cited by 371 (6 self)
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This paper presents an overview of recent progress in the area of multipleinput–multipleoutput (MIMO) space–time coded wireless systems. After some background on the research leading to the discovery of the enormous potential of MIMO wireless links, we highlight the different classes of techniques and algorithms proposed which attempt to realize the various benefits of MIMO including spatial multiplexing and space–time coding schemes. These algorithms are often derived and analyzed under ideal independent fading conditions. We present the state of the art in channel modeling and measurements, leading to a better understanding of actual MIMO gains. Finally, the paper addresses current questions regarding the integration of MIMO links in practical wireless systems and standards.
Distributed spacetime coding in wireless relay networks,”IEEE Trans.
 on Wireless Communications,
, 2006
"... Abstract In this paper, we present a coding strategy for half duplex wireless relay networks, where we assume no channel knowledge at any of the transmitter, receiver or relays. The coding scheme uses distributed spacetime coding, that is, the relay nodes cooperate to encode the transmitted signal ..."
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Cited by 225 (16 self)
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Abstract In this paper, we present a coding strategy for half duplex wireless relay networks, where we assume no channel knowledge at any of the transmitter, receiver or relays. The coding scheme uses distributed spacetime coding, that is, the relay nodes cooperate to encode the transmitted signal so that the receiver senses a spacetime codeword. It is inspired by noncoherent differential techniques. The proposed strategy is available for any number of relays nodes. It is analyzed, and shown to yield a diversity linear in the number of relays. We also study the resistance of the scheme to relay node failures, and show that a network with R relay nodes and d of them down behaves, as far as diversity is concerned, as a network with R − d nodes. Finally, our construction can be easily generalized to the case where the transmitter and receiver nodes have several antennas.
Universal SpaceTime Coding
 IEEE Trans. Inform. Theory
, 2003
"... A universal framework is developed for constructing fullrate and fulldiversity coherent spacetime codes for systems with arbitrary numbers of transmit and receive antennas. The proposed framework combines spacetime layering concepts with algebraic component codes optimized for singleinputsi ..."
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Cited by 143 (7 self)
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A universal framework is developed for constructing fullrate and fulldiversity coherent spacetime codes for systems with arbitrary numbers of transmit and receive antennas. The proposed framework combines spacetime layering concepts with algebraic component codes optimized for singleinputsingleoutput (SISO) channels. Each component code is assigned to a "thread" in the spacetime matrix, allowing it thus full access to the channel spatial diversity in the absence of the other threads. Diophantine approximation theory is then used in order to make the different threads "transparent" to each other. Within this framework, a special class of signals which uses algebraic numbertheoretic constellations as component codes is thoroughly investigated. The lattice structure of the proposed numbertheoretic codes along with their minimal delay allow for polynomial complexity maximumlikelihood (ML) decoding using algorithms from lattice theory. Combining the design framework with the Cayley transform allows to construct full diversity differential and noncoherent spacetime codes. The proposed framework subsumes many of the existing codes in the literature, extends naturally to timeselective and frequency selective channels, and allows for more flexibility in the tradeoff between power efficiency, bandwidth efficiency, and receiver complexity. Simulation results that demonstrate the significant gains offered by the proposed codes are presented in certain representative scenarios.
MIMO Capacity with Interference
 IEEE J. Select. Areas Commun
, 2002
"... System capacity is considered for a group of interfering users employing single user detection and multiple transmit and receive antennas for flat Rayleigh fading channels with independent fading coefficients for each path. The focus is on the case where there is no channel state information at the ..."
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Cited by 129 (3 self)
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System capacity is considered for a group of interfering users employing single user detection and multiple transmit and receive antennas for flat Rayleigh fading channels with independent fading coefficients for each path. The focus is on the case where there is no channel state information at the transmitter, but channel state information is assumed at the receiver. It is shown that the optimum signaling is sometimes different from cases where the users do not interfere with each other. In particular, the optimum signaling will sometimes put all power into a single transmitting antenna, rather than divide power equally between independent streams from the different antennas. If the interference is either sufficiently weak or sufficiently strong, we show that either the optimum interferencefree approach, which puts equal power into each antenna, or the approach that puts all power into a single antenna is optimum and we show how to find the regions where each approach is best.
Representation Theory for HighRate MultipleAntenna Code Design
 IEEE Trans. Inform. Theory
, 2000
"... this paper, we show how to design signal matrices satisfying these requirements. As shown in [1], the design problem for unitary space time constellations is the following: let ..."
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Cited by 119 (15 self)
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this paper, we show how to design signal matrices satisfying these requirements. As shown in [1], the design problem for unitary space time constellations is the following: let
Signal constellations for quasiorthogonal spacetime block codes with full diversity
 IEEE Trans. Inform. Theory
, 2004
"... Abstract—Space–time block codes (STBCs) from orthogonal designs proposed by Alamouti, and Tarokh–Jafarkhani–Calderbank have attracted considerable attention lately due to their fast maximumlikelihood (ML) decoding and full diversity. However, the maximum symbol transmission rate of an STBC from com ..."
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Cited by 109 (10 self)
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Abstract—Space–time block codes (STBCs) from orthogonal designs proposed by Alamouti, and Tarokh–Jafarkhani–Calderbank have attracted considerable attention lately due to their fast maximumlikelihood (ML) decoding and full diversity. However, the maximum symbol transmission rate of an STBC from complex orthogonal designs for complex signals is only Q R for three and four transmit antennas, and it is difficult to construct complex orthogonal designs with rate higher than I P for more than four transmit antennas. Recently, Jafarkhani, Tirkkonen–Boariu–Hottinen, and Papadias–Foschini proposed STBCs from quasiorthogonal designs, where the orthogonality is relaxed to provide higher symbol transmission rates. With the quasiorthogonal structure, the quasiorthogonal STBCs still have a fast ML decoding, but do not have the full diversity. The performance of these codes is better than that of the codes from orthogonal designs at low signaltonoise ratio (SNR), but worse at high SNR. This is due to the fact that the slope of the performance curve depends on the diversity. It is desired to have the quasiorthogonal STBCs with full diversity to ensure good performance at high SNR. In this paper, we achieve this goal by properly choosing the signal constellations. Specifically, we propose that half of the symbols in a quasiorthogonal design are chosen from a signal constellation set and the other half of them are chosen from a rotated constellation. The resulting STBCs can guarantee both full diversity and fast ML decoding. Moreover, we obtain the optimum selections of the rotation angles for some commonly used signal constellations. Simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high SNRs. Index Terms—Diversity, multiple antennas, orthogonal designs, quasiorthogonal designs, space–time block codes (STBC), wireless communications. I.
Cayley differential unitary space–time codes
 IEEE Trans. Inform. Theory
, 2002
"... One method for communicating with multiple antennas is to encode the transmitted data differentially using unitary matrices at the transmitter, and to decode differentially without knowing the channel coefficients at the receiver. Since channel knowledge is not required at the receiver, differential ..."
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Cited by 80 (8 self)
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One method for communicating with multiple antennas is to encode the transmitted data differentially using unitary matrices at the transmitter, and to decode differentially without knowing the channel coefficients at the receiver. Since channel knowledge is not required at the receiver, differential schemes are ideal for use on wireless links where channel tracking is undesirable or infeasible, either because of rapid changes in the channel characteristics or because of limited system resources. Although this basic principle is well understood, it is not known how to generate goodperforming constellations of unitary matrices, for any number of transmit and receive antennas and for any rate. This is especially true at high rates where the constellations must be rapidly encoded and decoded. We propose a class of Cayley codes that works with any number of antennas, and has efficient encoding and decoding at any rate. The codes are named for their use of the Cayley transform, which maps the highly nonlinear Stiefel manifold of unitary matrices to the linear space of skewHermitian matrices. This transformation leads to a simple linear constellation structure in the Cayley transform domain and to an informationtheoretic design criterion based on emulating a Cauchy random matrix. Moreover, the resulting Cayley codes allow polynomialtime nearmaximumlikelihood decoding based on either successive nulling/cancelling or sphere decoding. Simulations show that the Cayley codes allow efficient and effective highrate data transmission in multiantenna communication systems without knowing the channel.
Asymptotic Error Probability Analysis of Quadratic Receivers in RayleighFading Channels With Applications to a Unified Analysis of Coherent and Noncoherent SpaceTime Receivers
, 2001
"... A general, asymptotic (high signaltonoise (SNR)) error analysis is introduced for quadratic receivers in frequency flat and multipath Rayleighfading channels with multiple transmit and receive antennas. Asymptotically tight expressions for the pairwise error probabilities are obtained for cohere ..."
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Cited by 66 (14 self)
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A general, asymptotic (high signaltonoise (SNR)) error analysis is introduced for quadratic receivers in frequency flat and multipath Rayleighfading channels with multiple transmit and receive antennas. Asymptotically tight expressions for the pairwise error probabilities are obtained for coherent, noncoherent, and differentially coherent spacetime receivers. Not only is our unified analysis applicable to more general modulation schemes and/or channel models than previously considered, but it also reveals a hitherto unrecognized eigenvalue structure that is common to all of these problems. In addition to providing an easy recipe for computing the asymptotic pairwise error rates, we make some conclusions regarding criteria for the design of signal constellations and codes such as a) the same design criteria apply for both correlated and independent and identically distributed (i.i.d.) fading processes and b) for noncoherent communications, unitary signals are optimal in the sense that they minimize the asymptotic union bound.