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487
Towards an Information Theory of Large Networks: An Achievable Rate Region
 IEEE Trans. Inform. Theory
, 2003
"... Abstract — We study communication networks of arbitrary size and topology and communicating over a general vector discrete memoryless channel. We propose an informationtheoretic constructive scheme for obtaining an achievable rate region in such networks. Many wellknown capacitydefining achievabl ..."
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Cited by 204 (12 self)
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Abstract — We study communication networks of arbitrary size and topology and communicating over a general vector discrete memoryless channel. We propose an informationtheoretic constructive scheme for obtaining an achievable rate region in such networks. Many wellknown capacitydefining achievable rate regions can be derived as special cases of the proposed scheme. A few such examples are the physically degraded and reverselydegraded relay channels, the Gaussian multipleaccess channel, and the Gaussian broadcast channel. The proposed scheme also leads to inner bounds for the multicast and allcast capacities. Applying the proposed scheme to a specific wireless network of nodes located in a region of unit area, we show that a transport capacity of ¡£ ¢ bitmeters/sec is feasible in a certain family of networks, as compared to the best possible transport capacity ¡£¢§ ¦ ¨ ¤ of bitmeters/sec in [16] where the receiver capabilities were limited. Even though the improvement is shown for a specific class of networks, a clear implication is that designing and employing more sophisticated multiuser coding schemes can provide sizable gains in at least some large wireless networks. Index Terms — Discrete memoryless channels, Gaussian channels, multiuser communications, network information theory,
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.
Optimal Designs for SpaceTime Linear Precoders and Decoders
 IEEE Trans. Signal Processing
, 2001
"... In this paper we introduce a new paradigm for the design of transmitter spacetime coding that we refer to as linear precoding. It leads to simple closed form solutions for transmission over frequency selective multipleinput multipleoutput (MIMO) channels, which are scalable with respect to the nu ..."
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Cited by 188 (6 self)
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In this paper we introduce a new paradigm for the design of transmitter spacetime coding that we refer to as linear precoding. It leads to simple closed form solutions for transmission over frequency selective multipleinput multipleoutput (MIMO) channels, which are scalable with respect to the number of antennas, size of the coding block and transmit average/peak power. The scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension. The specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses, under average and peak power constraints. The solutions are shown to convert the MIMO channel with memory into a set of parallel flat fading subchannels, regardless of the design criterion, while appropriate power/bits loading on the subchannels is the specific signature of the different designs. The proposed designs are compared in terms of various performance measures such as information rate, BER and symbol mean square error.
On the capacity of OFDMbased spatial multiplexing systems
 IEEE Trans.Commun
, 2002
"... Abstract—This paper deals with the capacity behavior of wireless orthogonal frequencydivision multiplexing (OFDM)based spatial multiplexing systems in broadband fading environments for the case where the channel is unknown at the transmitter and perfectly known at the receiver. Introducing a phy ..."
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Cited by 167 (15 self)
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Abstract—This paper deals with the capacity behavior of wireless orthogonal frequencydivision multiplexing (OFDM)based spatial multiplexing systems in broadband fading environments for the case where the channel is unknown at the transmitter and perfectly known at the receiver. Introducing a physically motivated multipleinput multipleoutput (MIMO) broadband fading channel model, we study the influence of physical parameters such as the amount of delay spread, cluster angle spread, and total angle spread, and system parameters such as the number of antennas and antenna spacing on ergodic capacity and outage capacity. We find that, in the MIMO case, unlike the singleinput singleoutput (SISO) case, delay spread channels may provide advantages over flat fading channels not only in terms of outage capacity but also in terms of ergodic capacity. Therefore, MIMO delay spread channels will in general provide both higher diversity gain and
An Overview of MIMO Communications: A Key to Gigabit Wireless
 Proc. IEEE
, 2004
"... High data rate wireless communications, nearing 1 Gigabit/second (Gbps) transmission rates, is of interest in emerging Wireless Local Area Networks (WLANs) and home Audio/Visual (A/V) networks. Designing very high speed wireless links that offer good QualityofService (QoS) and range capability in ..."
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Cited by 165 (0 self)
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High data rate wireless communications, nearing 1 Gigabit/second (Gbps) transmission rates, is of interest in emerging Wireless Local Area Networks (WLANs) and home Audio/Visual (A/V) networks. Designing very high speed wireless links that offer good QualityofService (QoS) and range capability in NonLineofSight (NLOS) environments constitutes a significant research and engineering challenge. Ignoring fading in NLOS environments, we can, in principle, meet the 1Gbps data rate requirement with a singletransmit singlereceive antenna wireless system if the product of bandwidth (measured in Hz) and spectral efficiency (measured in bps/Hz) is equal to 10 9. As we shall outline in this paper, a variety of cost, technology and regulatory constraints make such a brute force solution unattractive if not impossible. The use of multiple antennas at transmitter and receiver, popularly known as multipleinput multipleoutput (MIMO) wireless is an emerging costeffective technology that offers substantial leverages in making 1Gbps wireless links a reality. This paper provides an overview of MIMO wireless technology covering channel models, performance limits, coding, and transceiver design.
On the capacity of spatially correlated MIMO Rayleighfading channels
 IEEE Trans. Inform. Theory
, 2003
"... Abstract—In this paper, we investigate the capacity distribution of spatially correlated, multipleinput–multipleoutput (MIMO) channels. In particular, we derive a concise closedform expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the tran ..."
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Cited by 134 (15 self)
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Abstract—In this paper, we investigate the capacity distribution of spatially correlated, multipleinput–multipleoutput (MIMO) channels. In particular, we derive a concise closedform expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequencyflat Rayleighfading environments. Using the exact expression of the c.f., the probability density function (pdf) and the cumulative distribution function (CDF) can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels. Our results are valid for scenarios with the number of transmitting antennas greater than or equal to that of receiving antennas with arbitrary correlation among them. Moreover, the results are valid for an arbitrary number of transmitting and receiving antennas in uncorrelated MIMO channels. It is shown that the capacity loss is negligible even with a correlation coefficient between two adjacent antennas as large as 0 5 for exponential correlation model. Finally, we derive an exact expression for the mean value of the capacity for arbitrary correlation matrices. Index Terms—Eigenvalues distribution, multiple input–multiple output (MIMO), multiple antennas, Rayleighfading channels, Shannon capacity, Wishart matrices. I.
Limited feedback unitary precoding for spatial multiplexing systems
 IEEE Trans. Info. Theory
, 2005
"... Abstract—Multipleinput multipleoutput (MIMO) wireless systems use antenna arrays at both the transmitter and receiver to provide communication links with substantial diversity and capacity. Spatial multiplexing is a common space–time modulation technique for MIMO communication systems where indepe ..."
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Cited by 125 (21 self)
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Abstract—Multipleinput multipleoutput (MIMO) wireless systems use antenna arrays at both the transmitter and receiver to provide communication links with substantial diversity and capacity. Spatial multiplexing is a common space–time modulation technique for MIMO communication systems where independent information streams are sent over different transmit antennas. Unfortunately, spatial multiplexing is sensitive to illconditioning of the channel matrix. Precoding can improve the resilience of spatial multiplexing at the expense of full channel knowledge at the transmitter—which is often not realistic. This correspondence proposes a quantized precoding system where the optimal precoder is chosen from a finite codebook known to both receiver and transmitter. The index of the optimal precoder is conveyed from the receiver to the transmitter over a lowdelay feedback link. Criteria are presented for selecting the optimal precoding matrix based on the error rate and mutual information for different receiver designs. Codebook design criteria are proposed for each selection criterion by minimizing a bound on the average distortion assuming a Rayleighfading matrix channel. The design criteria are shown to be equivalent to packing subspaces in the Grassmann manifold using the projection twonorm and Fubini–Study distances. Simulation results showthat the proposed system outperforms antenna subset selection and performs close to optimal unitary precoding with a minimal amount of feedback. Index Terms—Diversity methods, Grassmannian subspace packing, multipleinput multipleoutput (MIMO) systems, quantized precoding, Rayleigh channels, spatial multiplexing, vertical Bell Labs layered space– time (VBLAST) architecture. I.
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 118 (14 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
BLAST Training: Estimating Channel Characteristics for High Capacity SpaceTime Wireless
 Proc. 37th Annual Allerton Conference on Communications, Control, and Computing
, 1999
"... BLAST (Bell Labs Layered SpaceTime) is a multipleantenna communication scheme whose outage capacity in a Rayleigh flat fading environment grows linearly with the minimum of the number of transmit and receive antennas, with no increase in bandwidth or transmitted power. Based on its knowledge of th ..."
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Cited by 111 (6 self)
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BLAST (Bell Labs Layered SpaceTime) is a multipleantenna communication scheme whose outage capacity in a Rayleigh flat fading environment grows linearly with the minimum of the number of transmit and receive antennas, with no increase in bandwidth or transmitted power. Based on its knowledge of the matrix of propagation coefficients, the receiver performs two critical operations: nulling and cancellation, that in effect create independent virtual subchannels. Assume that the receiver estimates the propagation matrix from a known set of transmitted training signals, and then uses the estimate as though it were correct for nulling and cancellation. How much training is needed for satisfactory operation? The optimal training signals are orthogonal with respect to time among the transmit antennas, and each transmit antenna is fed equal energy. Errors in estimating the propagation matrix manifest themselves as crosstalk among the virtual subchannels. If its magnitude is too large, the cro...
Bandwidth Scaling for Fading Multipath Channels
, 1999
"... We show that very large bandwidths on fading multipath channels cannot be effectively utilized by spread spectrum systems that (in a particular sense) spread the available power uniformly over both time and frequency. The approach is to express the input process as an expansion in an orthonormal set ..."
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Cited by 108 (12 self)
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We show that very large bandwidths on fading multipath channels cannot be effectively utilized by spread spectrum systems that (in a particular sense) spread the available power uniformly over both time and frequency. The approach is to express the input process as an expansion in an orthonormal set of functions each localized in time and frequency. The fourth moment of each coefficient in this expansion is then uniformly constrained. We show that such a constraint forces the mutual information to 0 inversely with increasing bandwidth. Simply constraining the second moment of these coefficients does not achieve this effect. The results suggest strongly that conventional direct sequence CDMA systems do not scale well to extremely large bandwidths. To illustrate how the interplay between channel estimation and symbol detection affects capacity, we present results for a specific channel and CDMA signaling scheme.