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24
Opportunistic Beamforming Using Dumb Antennas
 IEEE Transactions on Information Theory
, 2002
"... Multiuser diversity is a form of diversity inherent in a wireless network, provided by independent timevarying channels across the different users. The diversity benefit is exploited by tracking the channel fluctuations of the users and scheduling transmissions to users when their instantaneous cha ..."
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Cited by 654 (1 self)
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Multiuser diversity is a form of diversity inherent in a wireless network, provided by independent timevarying channels across the different users. The diversity benefit is exploited by tracking the channel fluctuations of the users and scheduling transmissions to users when their instantaneous channel quality is near the peak. The diversity gain increases with the dynamic range of the fluctuations and is thus limited in environments with little scattering and/or slow fading. In such environments, we propose the use of multiple transmit antennas to induce large and fast channel fluctuations so that multiuser diversity can still be exploited. The scheme can be interpreted as opportunistic beamforming and we show that true beamforming gains can be achieved when there are sufficient users, even though very limited channel feedback is needed. Furthermore, in a cellular system, the scheme plays an additional role of opportunistic nulling of the interference created on users of adjacent cells. We discuss the design implications of implementing this scheme in a complete wireless system.
Duality, achievable rates, and sumrate capacity of Gaussian MIMO broadcast channels
 IEEE TRANS. INFORM. THEORY
, 2003
"... We consider a multiuser multipleinput multipleoutput (MIMO) Gaussian broadcast channel (BC), where the transmitter and receivers have multiple antennas. Since the MIMO BC is in general a nondegraded BC, its capacity region remains an unsolved problem. In this paper, we establish a duality between ..."
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Cited by 271 (20 self)
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We consider a multiuser multipleinput multipleoutput (MIMO) Gaussian broadcast channel (BC), where the transmitter and receivers have multiple antennas. Since the MIMO BC is in general a nondegraded BC, its capacity region remains an unsolved problem. In this paper, we establish a duality between what is termed the “dirty paper” achievable region (the Caire–Shamai achievable region) for the MIMO BC and the capacity region of the MIMO multipleaccess channel (MAC), which is easy to compute. Using this duality, we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the MIMO BC. We also show that the dirty paper achievable region achieves the sumrate capacity of the MIMO BC by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the MIMO BC.
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 99 (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.
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 58 (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.
Capacity of adhoc networks with node cooperation
 IEEE Int. Symp. Inform. Theory
, 2004
"... Abstract — This paper examines communication between a cluster of closelypacked nodes with another cluster of closelypacked nodes. The nodes within each cluster are separated by small distances, relative to the distance between the two clusters. The effect on capacity of cooperation between nodes ..."
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Cited by 44 (9 self)
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Abstract — This paper examines communication between a cluster of closelypacked nodes with another cluster of closelypacked nodes. The nodes within each cluster are separated by small distances, relative to the distance between the two clusters. The effect on capacity of cooperation between nodes in the transmitting cluster and cooperation between nodes in the receiving cluster is investigated. I. System Model Consider a system with two transmitters and two receivers, as shown in Fig. 1. TX 1 wishes to communicate to RX 1, and TX 2 wishes to communicate to RX 2. It is assumed that the distance between each of the four transmitterreceiver pairs is the same, and each channel gain is normalized to have amplitude one. Thus, the channels between each transmitterreceiver pair are identical, except for a random uniformly distributed phase. The channel can be written as: jθ1 y1 x1 n1 e e
On the Capacity of Multiple Input Multiple Output Broadcast Channels
 In Proceedings of Int. Conf. Commun
, 2002
"... We consider a twouser multiple input multiple output (MIMO) Gaussian broadcast channel (BC), where the transmitter has t transmit antennas and receivers have r1 ; r2 antennas respectively. Since the MIMO broadcast channel is in general a nondegraded broadcast channel, its capacity region remains a ..."
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Cited by 44 (12 self)
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We consider a twouser multiple input multiple output (MIMO) Gaussian broadcast channel (BC), where the transmitter has t transmit antennas and receivers have r1 ; r2 antennas respectively. Since the MIMO broadcast channel is in general a nondegraded broadcast channel, its capacity region remains an unsolved problem. In this paper, we establish a duality between what is termed the \dirty paper" region (or the CostaCaireShamaiYu achievable region) [5, 7] for the MIMO broadcast channel and the capacity region of the the MIMO multipleaccess channel (MAC), which is easy to compute. Using this duality, we greatly reduce the computation complexity required for obtaining the dirty paper achievable region for the MIMO BC. The duality also enables us to translate previously known results for the MIMO MAC (like iterative waterlling [7]) to the MIMO BC. We show that the dirty paper achievable region achieves the sumrate capacity of the MIMO BC by establishing that the sumrate point in this region equals an upperbound on the sum rate of the MIMO BC. I.
A Dual Decomposition Approach to the Sum Power Gaussian Vector Multiple Access Channel Sum Capacity Problem
 in Proc. 37th Annual Conf. on Information Sciences and Systems (CISS
, 2003
"... Abstract — The Gaussian vector multiple access channel with a sumpower constraint across all users, rather than the usual individual power constraint on each user, has recently been shown to be the dual of a Gaussian vector broadcast channel [1] [2]. Further, a numerical algorithm for the sum capac ..."
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Cited by 32 (3 self)
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Abstract — The Gaussian vector multiple access channel with a sumpower constraint across all users, rather than the usual individual power constraint on each user, has recently been shown to be the dual of a Gaussian vector broadcast channel [1] [2]. Further, a numerical algorithm for the sum capacity under the sum power constraint has been proposed in [3]. This paper proposes a different algorithm for this problem based on a dual decomposition approach. The proposed algorithm works in the Lagrangian dual domain; it is based on a modified iterative waterfilling algorithm for the multiple access channel; and it is guaranteed to converge to the sum capacity in all cases. This spectrum optimization problem for the sumpower multiple access channel is also applicable to the optimal power allocation problem for an OFDM system with correlated noise. I.
Rate scheduling in multiple antenna downlink scheduling systems
 IEEE Trans. Commun
, 2005
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Practical Costa precoding for the multiple antenna broadcast channel
 IEEE Glob. Telecom. Conf
, 2004
"... Abstract — For a multiple antenna broadcast channel, the sumrate capacity achieving transmit strategy requires the centralized transmitter to simultaneously communicate with multiple receivers. The objective of this paper is to design an implementable sumrate capacity achieving transmit strategy th ..."
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Cited by 14 (2 self)
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Abstract — For a multiple antenna broadcast channel, the sumrate capacity achieving transmit strategy requires the centralized transmitter to simultaneously communicate with multiple receivers. The objective of this paper is to design an implementable sumrate capacity achieving transmit strategy that uses a combination of beamforming and coding for known interference. For a twouser Gaussian broadcast channel, results indicate that in the context of typical QAM constellations, with Mt = 2 and Mr = 1, there is significant gain in sumrate capacity over an approach that uses only beamforming. 1 I.
Input optimization for multiantenna broadcast channels and perantenna power constraints
 in Proc. IEEE GLOBECOM
, 2004
"... Abstract — This paper considers a Gaussian multiantenna broadcast channel with individual power constraints on each antenna, rather than the usual sum power constraint over all antennas. Perantenna power constraints are more realistic because in practical implementations each antenna has its own p ..."
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Cited by 10 (0 self)
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Abstract — This paper considers a Gaussian multiantenna broadcast channel with individual power constraints on each antenna, rather than the usual sum power constraint over all antennas. Perantenna power constraints are more realistic because in practical implementations each antenna has its own power amplifier. The main contribution of this paper is a new derivation of the duality result for this class of broadcast channels that allows the input optimization problem to be solved efficiently. Specifically, we show that uplinkdownlink duality is equivalent to Lagrangian duality in minimax optimization, and the dual multipleaccess problem has a much lower computational complexity than the original problem. This duality applies to the entire capacity region. Further, we derive a novel application of Newton’s method for the dual minimax problem that finds an optimal search direction for both the minimization and the maximization problems at the same time. This new computational method is much more efficient than the previous iterative waterfillingbased algorithms and it is applicable to the entire capacity region. Finally, we show that the previous QRbased precoding method can be easily modified to accommodate the perantenna constraint. I.