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302
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 420 (12 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...
Achieving nearcapacity on a multipleantenna channel
 IEEE Trans. Commun
, 2003
"... Recent advancements in iterative processing of channel codes and the development of turbo codes have allowed the communications industry to achieve nearcapacity on a singleantenna Gaussian or fading channel with low complexity. We show how these iterative techniques can also be used to achieve nea ..."
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Cited by 391 (2 self)
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Recent advancements in iterative processing of channel codes and the development of turbo codes have allowed the communications industry to achieve nearcapacity on a singleantenna Gaussian or fading channel with low complexity. We show how these iterative techniques can also be used to achieve nearcapacity on a multipleantenna system where the receiver knows the channel. Combining iterative processing with multipleantenna channels is particularly challenging because the channel capacities can be a factor of ten or more higher than their singleantenna counterparts. Using a “list ” version of the sphere decoder, we provide a simple method to iteratively detect and decode any linear spacetime mapping combined with any channel code that can be decoded using socalled “soft ” inputs and outputs. We exemplify our technique by directly transmitting symbols that are coded with a channel code; we show that iterative processing with even this simple scheme can achieve nearcapacity. We consider both simple convolutional and powerful turbo channel codes and show that excellent performance at very high data rates can be attained with either. We compare our simulation results with Shannon capacity limits for ergodic multipleantenna channel. Index Terms—Wireless communications, BLAST, turbo codes, transmit diversity, receive diversity, fading channels, sphere decoding, softin/softout, concatenated codes 1
Communication on the Grassmann Manifold: A Geometric Approach to the Noncoherent MultipleAntenna Channel
 IEEE Trans. Inform. Theory
, 2002
"... In this paper, we study the capacity of multipleantenna fading channels. We focus on the scenario where the fading coefficients vary quickly; thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver. We use a noncoherent block fading model ..."
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Cited by 271 (8 self)
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In this paper, we study the capacity of multipleantenna fading channels. We focus on the scenario where the fading coefficients vary quickly; thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver. We use a noncoherent block fading model proposed by Marzetta and Hochwald. The model does not assume any channel side information at the receiver or at the transmitter, but assumes that the coefficients remain constant for a coherence interval of length symbol periods. We compute the asymptotic capacity of this channel at high signaltonoise ratio (SNR) in terms of the coherence time , the number of transmit antennas , and the number of receive antennas . While the capacity gain of the coherent multiple antenna channel is min bits per second per hertz for every 3dB increase in SNR, the corresponding gain for the noncoherent channel turns out to be (1 ) bits per second per herz, where = min 2 . The capacity expression has a geometric interpretation as sphere packing in the Grassmann manifold.
On Beamforming with Finite Rate Feedback in Multiple Antenna Systems
, 2003
"... In this paper, we study a multiple antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any f ..."
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Cited by 271 (14 self)
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In this paper, we study a multiple antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any finite set of beamformers. The universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel. Using the bound, it is shown that finite information systems approach the perfect information case as (t 1)2 , where B is the number of feedback bits and t is the number of transmit antennas. The geometrical bounding technique, used in the proof of the lower bound, also leads to a design criterion for good beamformers, whose outage performance approaches the lower bound. The design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook, and is equivalent to the problem of designing unitary space time codes under certain conditions. Finally, we show that good beamformers are good packings of 2dimensional subspaces in a 2tdimensional real Grassmannian manifold with chordal distance as the metric.
Differential spacetime modulation
 IEEE Trans. Inform. Theory
, 2000
"... Abstract—Space–time coding and modulation exploit the presence of multiple transmit antennas to improve performance on multipath radio channels. Thus far, most work on space–time coding has assumed that perfect channel estimates are available at the receiver. In certain situations, however, it may b ..."
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Cited by 262 (1 self)
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Abstract—Space–time coding and modulation exploit the presence of multiple transmit antennas to improve performance on multipath radio channels. Thus far, most work on space–time coding has assumed that perfect channel estimates are available at the receiver. In certain situations, however, it may be difficult or costly to estimate the channel accurately, in which case it is natural to consider the design of modulation techniques that do not require channel estimates at the transmitter or receiver. We propose a general approach to differential modulation for multiple transmit antennas based on group codes. This approach can be applied to any number of transmit and receive antennas, and any signal constellation. We also derive lowcomplexity differential receivers, error bounds, and modulator design criteria, which we use to construct optimal differential modulation schemes for two transmit antennas. These schemes can be demodulated with or without channel estimates. This permits the receiver to exploit channel estimates when they are available. Performance degrades by approximately 3 dB when estimates are not available. Index Terms—Differential modulation, group codes, multipath channels, noncoherent communication, space–time coding, transmit diversity. I.
Distributed spacetime coding in wireless relay networks
, 2006
"... We apply the idea of spacetime coding devised for multipleantenna systems to the problem of communications over a wireless relay network with Rayleigh fading channels. We use a twostage protocol, where in one stage the transmitter sends information and in the other, the relays encode their rece ..."
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Cited by 223 (15 self)
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We apply the idea of spacetime coding devised for multipleantenna systems to the problem of communications over a wireless relay network with Rayleigh fading channels. We use a twostage protocol, where in one stage the transmitter sends information and in the other, the relays encode their received signals into a “distributed ” linear dispersion (LD) code, and then transmit the coded signals to the receive node. We show that for high SNR, the pairwise error probability (PEP) behaves as (log P/P) min{T,R} , with T the coherence interval, that is, the number of symbol periods during which the channels keep constant, R the number of relay nodes, and P the total transmit power. Thus, apart from the log P factor, the system has the same diversity as a multipleantenna system with R transmit antennas, which is the same as assuming that the R relays can fully cooperate and have full knowledge of the transmitted signal. We further show that for a network with a large number of relays and a fixed total transmit power across the entire network, the optimal power allocation is for the transmitter to expend half the power and for the relays to collectively expend the other half. We also show that at low and high SNR, the coding gain is the same as that of a multipleantenna system with R antennas. However, at intermediate SNR, it can be quite different, which has implications for the design of distributed spacetime codes.
A differential detection scheme for transmit diversity
 IEEE J. Select. Areas Commun
, 2000
"... Abstract—We present a transmission scheme for exploiting diversity given by two transmit antennas when neither the transmitter nor the receiver has access to channel state information. The new detection scheme can use equal energy constellations and encoding is simple. At the receiver, decoding is a ..."
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Cited by 212 (7 self)
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Abstract—We present a transmission scheme for exploiting diversity given by two transmit antennas when neither the transmitter nor the receiver has access to channel state information. The new detection scheme can use equal energy constellations and encoding is simple. At the receiver, decoding is achieved with low decoding complexity. The transmission provides full spatial diversity and requires no channel state side information at the receiver. The scheme can be considered as the extension of differential detection schemes to two transmit antennas. Index Terms—Antenna arrays, differential detection, spacetime codes, transmitter diversity. I.
Systematic design of unitary spacetime constellations
 IEEE TRANS. INFORM. THEORY
, 2000
"... We propose a systematic method for creating constellations of unitary space–time signals for multipleantenna communication links. Unitary space–time signals, which are orthonormal in time across the antennas, have been shown to be welltailored to a Rayleigh fading channel where neither the transm ..."
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Cited by 198 (11 self)
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We propose a systematic method for creating constellations of unitary space–time signals for multipleantenna communication links. Unitary space–time signals, which are orthonormal in time across the antennas, have been shown to be welltailored to a Rayleigh fading channel where neither the transmitter nor the receiver knows the fading coefficients. The signals can achieve low probability of error by exploiting multipleantenna diversity. Because the fading coefficients are not known, the criterion for creating and evaluating the constellation is nonstandard and differs markedly from the familiar maximumEuclideandistance norm. Our construction begins with the first signal in the constellation—an oblong complexvalued matrix whose columns are orthonormal—and systematically produces the remaining signals by successively rotating this signal in a highdimensional complex space. This construction easily produces large constellations of highdimensional signals. We demonstrate its efficacy through examples involving one, two, and three transmitter antennas.
On the spheredecoding algorithm I. Expected complexity
 IEEE Trans. Sig. Proc
, 2005
"... Abstract—The problem of finding the leastsquares solution to a system of linear equations where the unknown vector is comprised of integers, but the matrix coefficient and given vector are comprised of real numbers, arises in many applications: communications, cryptography, GPS, to name a few. The ..."
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Cited by 128 (7 self)
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Abstract—The problem of finding the leastsquares solution to a system of linear equations where the unknown vector is comprised of integers, but the matrix coefficient and given vector are comprised of real numbers, arises in many applications: communications, cryptography, GPS, to name a few. The problem is equivalent to finding the closest lattice point to a given point and is known to be NPhard. In communications applications, however, the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known. Therefore, in this paper, rather than dwell on the worstcase complexity of the integer leastsquares problem, we study its expected complexity, averaged over the noise and over the lattice. For the “sphere decoding” algorithm of Fincke and Pohst, we find a closedform expression for the expected complexity, both for the infinite and finite lattice.