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103
Capacity Limits of MIMO Channels
 IEEE J. SELECT. AREAS COMMUN
, 2003
"... We provide an overview of the extensive recent results on the Shannon capacity of singleuser and multiuser multipleinput multipleoutput (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about t ..."
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Cited by 411 (17 self)
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We provide an overview of the extensive recent results on the Shannon capacity of singleuser and multiuser multipleinput multipleoutput (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about the underlying timevarying channel model and how well it can be tracked at the receiver, as well as at the transmitter. More realistic assumptions can dramatically impact the potential capacity gains of MIMO techniques. For timevarying MIMO channels there are multiple Shannon theoretic capacity definitions and, for each definition, different correlation models and channel information assumptions that we consider. We first provide a comprehensive summary of ergodic and capacity versus outage results for singleuser MIMO channels. These results indicate that the capacity gain obtained from multiple antennas heavily depends
A VectorPerturbation technique for NearCapacity . . .
 IEEE TRANS. COMMUN
, 2005
"... Recent theoretical results describing the sum capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity. We introduce a simple encoding algorithm that achi ..."
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Cited by 326 (10 self)
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Recent theoretical results describing the sum capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity. We introduce a simple encoding algorithm that achieves nearcapacity at sum rates of tens of bits/channel use. The algorithm is a variation on channel inversion that regularizes the inverse and uses a “sphere encoder ” to perturb the data to reduce the power of the transmitted signal. This paper is comprised of two parts. In this first part, we show that while the sum capacity grows linearly with the minimum of the number of antennas and users, the sum rate of channel inversion does not. This poor performance is due to the large spread in the singular values of the channel matrix. We introduce regularization to improve the condition of the inverse and maximize the signaltointerferenceplusnoise ratio at the receivers. Regularization enables linear growth and works especially well at low signaltonoise ratios (SNRs), but as we show in the second part, an additional step is needed to achieve nearcapacity performance at all SNRs.
MultiCell MIMO Cooperative Networks: A New Look at Interference
 J. Selec. Areas in Commun. (JSAC
, 2010
"... Abstract—This paper presents an overview of the theory and currently known techniques for multicell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacitylimiting factor, multicell cooperation can dramatically improv ..."
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Cited by 250 (39 self)
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Abstract—This paper presents an overview of the theory and currently known techniques for multicell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacitylimiting factor, multicell cooperation can dramatically improve the system performance. Remarkably, such techniques literally exploit intercell interference by allowing the user data to be jointly processed by several interfering base stations, thus mimicking the benefits of a large virtual MIMO array. Multicell MIMO cooperation concepts are examined from different perspectives, including an examination of the fundamental informationtheoretic limits, a review of the coding and signal processing algorithmic developments, and, going beyond that, consideration of very practical issues related to scalability and systemlevel integration. A few promising and quite fundamental research avenues are also suggested. Index Terms—Cooperation, MIMO, cellular networks, relays, interference, beamforming, coordination, multicell, distributed.
On the duality of Gaussian multipleaccess and broadcast channels
 IEEE Trans. Inf. Theory
, 2004
"... Abstract—We define a duality between Gaussian multipleaccess channels (MACs) and Gaussian broadcast channels (BCs). The dual channels we consider have the same channel gains and the same noise power at all receivers. We show that the capacity region of the BC (both constant and fading) can be writt ..."
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Cited by 116 (14 self)
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Abstract—We define a duality between Gaussian multipleaccess channels (MACs) and Gaussian broadcast channels (BCs). The dual channels we consider have the same channel gains and the same noise power at all receivers. We show that the capacity region of the BC (both constant and fading) can be written in terms of the capacity region of the dual MAC, and vice versa. We can use this result to find the capacity region of the MAC if the capacity region of only the BC is known, and vice versa. For fading channels we show duality under ergodic capacity, but duality also holds for different capacity definitions for fading channels such as outage capacity and minimumrate capacity. Using duality, many results known for only one of the two channels can be extended to the dual channel as well. Index Terms—Broadcast channel (BC), channel capacity, duality, fading channels, multipleinput multipleoutput (MIMO) systems, multipleaccess channel (MAC). I.
Duality between channel capacity and rate distortion with twosided state information
 IEEE TRANS. INFORM. THEORY
, 2002
"... We show that the duality between channel capacity and data compression is retained when state information is available to the sender, to the receiver, to both, or to neither. We present a unified theory for eight special cases of channel capacity and rate distortion with state information, which al ..."
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Cited by 96 (3 self)
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We show that the duality between channel capacity and data compression is retained when state information is available to the sender, to the receiver, to both, or to neither. We present a unified theory for eight special cases of channel capacity and rate distortion with state information, which also extends existing results to arbitrary pairs of independent and identically distributed (i.i.d.) correlated state information @ I PA available at the sender and at the receiver, respectively. In particular, the resulting general formula for channel capacity a �— � @ A ‘ @ Y P A @ Y IA “ assumes the same form as the generalized Wyner–Ziv rate distortion function @ A a �� � @ A @ ” A ‘ @ Y I A @ Y PA“.
Capacity bounds for twoway relay channels
 in International Zurich Seminar on Communications (IZS 2008
, 2008
"... Abstract—We provide achievable rate regions for twoway relay channels (TRC). At first, for a binary TRC, we show that the subspacesharing of linear codes can achieve the capacity region. And, for a Gaussian TRC, we propose the subsetsharing of lattice codes. In some cases, the proposed lattice co ..."
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Cited by 63 (5 self)
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Abstract—We provide achievable rate regions for twoway relay channels (TRC). At first, for a binary TRC, we show that the subspacesharing of linear codes can achieve the capacity region. And, for a Gaussian TRC, we propose the subsetsharing of lattice codes. In some cases, the proposed lattice coding scheme can achieve within 1/2bit the capacity and is asymptotically optimal at high signaltonoise ratio (SNR) regimes. I.
Trellis Precoding for the Broadcast Channel
"... This paper considers the vector Gaussian broadcast channel where a single transmitter with multiple antennas sends independent information to multiple receivers. An achievable rate region is derived by decomposing the broadcast channel into a series of singleuser channels with noncausal side infor ..."
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Cited by 62 (1 self)
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This paper considers the vector Gaussian broadcast channel where a single transmitter with multiple antennas sends independent information to multiple receivers. An achievable rate region is derived by decomposing the broadcast channel into a series of singleuser channels with noncausal side information. The side information may be completely presubtracted using precoding techniques. A practical trellis precoding method is presented. Trellis precoding can be viewed as a generalization of the TomlinsonHarashima precoder. By taking into account the entire noncausal sideinformation sequence, a trellis precoder gives an additional shaping gain up to 1.53dB compared to a Tomlinson precoder. I.
Lattice strategies for the dirty multiple access channel
 in Proceedings of IEEE International Symposium on Information Theory
, 2007
"... A generalization of the Gaussian dirtypaper problem to a multiple access setup is considered. There are two additive interference signals, one known to each transmitter but none to the receiver. The rates achievable using Costa’s strategies (i.e. by a random binning scheme induced by Costa’s auxili ..."
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Cited by 59 (10 self)
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A generalization of the Gaussian dirtypaper problem to a multiple access setup is considered. There are two additive interference signals, one known to each transmitter but none to the receiver. The rates achievable using Costa’s strategies (i.e. by a random binning scheme induced by Costa’s auxiliary random variables) vanish in the limit when the interference signals are strong. In contrast, it is shown that lattice strategies (“lattice precoding”) can achieve positive rates independent of the interferences, and in fact in some cases which depend on the noise variance and power constraints they are optimal. In particular, lattice strategies are optimal in the limit of high SNR. It is also shown that the gap between the achievable rate region and the capacity region is at most 0.167 bit. Thus, the dirty MAC is another instance of a network setup, like the KornerMarton modulotwo sum problem, where linear coding is potentially better than random binning. Lattice transmission schemes and conditions for optimality for the asymmetric case, where there is only one interference which is known to one of the users (who serves as a “helper ” to the other user), and for the “common interference ” case are also derived. In the former case the gap between the helper achievable rate and its capacity is at most 0.085 bit.
SpaceTime Multiple Access: Linear Growth in the Sum Rate
 in Proc. 40th Annual Allerton Conf. Communications, Control and Computing
, 2002
"... It is known that some of the spectacular capacity gains of using multiple antennas on a pointtopoint rich scattering channel, namely linear growth with the number of antennas, can also be obtained in a multiuser environment. We give the constant of proportionality of linear growth in the sumcapa ..."
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Cited by 57 (9 self)
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It is known that some of the spectacular capacity gains of using multiple antennas on a pointtopoint rich scattering channel, namely linear growth with the number of antennas, can also be obtained in a multiuser environment. We give the constant of proportionality of linear growth in the sumcapacity when the number of users and antennas grow simultaneously, but with fewer users than antennas. We assume that the transmitter and receivers know the channel. Because of the linear growth in sumcapacity, we can accommodate more users simply by adding more antennas, without increasing total transmitted power or bandwidth or lowering the rate to existing users. We dub any scheme that can achieve linear growth in this fashion a spacetime multiple access scheme. Channelhardening arguments show that a "channelinversion" technique used in pointtopoint multipleantenna links achieves a large fraction of this linear growth in a multiuser environment without excessive transmitter power. Thus, multipleantennas offer a tremendous advantage in designing scheduling, networking, and multipleaccess protocols in rich scattering environments.