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187
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 386 (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
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 235 (36 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.
Space–time transmit precoding with imperfect channel feedback
 IEEE Trans. Inform. Theory
, 2001
"... Abstract—The use of channel feedback from receiver to transmitter is standard in wireline communications. While knowledge of the channel at the transmitter would produce similar benefits for wireless communications as well, the generation of reliable channel feedback is complicated by the rapid time ..."
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Cited by 192 (7 self)
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Abstract—The use of channel feedback from receiver to transmitter is standard in wireline communications. While knowledge of the channel at the transmitter would produce similar benefits for wireless communications as well, the generation of reliable channel feedback is complicated by the rapid time variations of the channel for mobile applications. The purpose of this correspondence is to provide an information–theoretic perspective on optimum transmitter strategies, and the gains obtained by employing them, for systems with transmit antenna arrays and imperfect channel feedback. The spatial channel, given the feedback, is modeled as a complex Gaussian random vector. Two extreme cases are considered: mean feedback, in which the channel side information resides in the mean of the distribution, with the covariance modeled as white, and covariance feedback, in which the channel is assumed to be varying too rapidly to track its mean, so that the mean is set to zero, and the information regarding the relative geometry of the propagation paths is captured by a nonwhite covariance matrix. In both cases, the optimum transmission strategies, maximizing the information transfer rate, are determined as a solution to simple numerical optimization problems. For both feedback models, our numerical results indicate that, when there is a moderate disparity between the strengths of different paths from the transmitter to the receiver, it is nearly optimal to employ the simple beamforming strategy of transmitting all available power in the direction which the feedback indicates is the strongest. Index Terms—Antenna arrays, fading channels, feedback communication, space–time codes, spatial diversity, transmit beamforming, wireless communication. I.
Transmitter Optimization for the MultiAntenna Downlink with PerAntenna Power Constraints
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2007
"... This paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the basestation. In contrast to the conventional sumpower constraint on the transmit antennas, this paper adopts a more realistic perantenna power constraint, because in ..."
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Cited by 127 (7 self)
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This paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the basestation. In contrast to the conventional sumpower constraint on the transmit antennas, this paper adopts a more realistic perantenna power constraint, because in practical implementations each antenna is equipped with its own power amplifier and is limited individually by the linearity of the amplifier. Assuming perfect channel knowledge at the transmitter, this paper investigates two different transmission schemes under the perantenna power constraint: a minimumpower beamforming design for downlink channels with a single antenna at each remote user and a capacityachieving transmitter design for downlink channels with multiple antennas at each remote user. It is shown that in both cases, the perantenna downlink transmitter optimization problem may be transformed into a dual uplink problem with an uncertain noise. This generalizes previous uplink–downlink duality results and transforms the perantenna transmitter optimization problem into an equivalent minimax optimization problem. Further, it is shown that various notions of uplink–downlink duality may be unified under a Lagrangian duality framework. This new interpretation of duality gives rise to efficient numerical optimization techniques for solving the downlink perantenna transmitter optimization problem.
Coordinated beamforming for the multicell multiantenna wireless system
 IEEE Trans. Wireless Commun
"... Abstract—In a conventional wireless cellular system, signal processing is performed on a percell basis; outofcell interference is treated as background noise. This paper considers the benefit of coordinating basestations across multiple cells in a multiantenna beamforming system, where multiple ..."
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Cited by 107 (6 self)
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Abstract—In a conventional wireless cellular system, signal processing is performed on a percell basis; outofcell interference is treated as background noise. This paper considers the benefit of coordinating basestations across multiple cells in a multiantenna beamforming system, where multiple basestations may jointly optimize their respective beamformers to improve the overall system performance. This paper focuses on a downlink scenario where each remote user is equipped with a single antenna, but where multiple remote users may be active simultaneously in each cell. The design criterion is the minimization of the total weighted transmitted power across the basestations subject to signaltointerferenceandnoiseratio (SINR) constraints at the remote users. The main contribution is a practical algorithm that is capable of finding the joint optimal beamformers for all basestations globally and efficiently. The proposed algorithm is based on a generalization of uplinkdownlink duality to the multicell setting using the Lagrangian duality theory. The algorithm also naturally leads to a distributed implementation. Simulation results show that a coordinated beamforming system can significantly outperform a conventional system with percell signal processing. I.
Network Planning in Wireless Ad hoc Networks: A CrossLayer Approach
, 2005
"... allocating information carrier supplies such that certain endtoend communication demands, as a collection of multicast sessions, are fulfilled. This formulation necessitates a crosslayer coupling. We aim at a computational characterization of the performance theoretically achievable with joint ..."
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Cited by 90 (7 self)
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allocating information carrier supplies such that certain endtoend communication demands, as a collection of multicast sessions, are fulfilled. This formulation necessitates a crosslayer coupling. We aim at a computational characterization of the performance theoretically achievable with joint optimizations spanning the network stack.
Transceiver optimization for multiuser MIMO systems
 IEEE Tran. on Signal Processing, 52(1):214 – 226
, 2004
"... Abstract—We consider the uplink of a multiuser system where the transmitters as well as the receiver are equipped with multiple antennas. Each user multiplexes its symbols by a linear precoder through its transmit antennas. We work with the systemwide mean squared error as the performance measure a ..."
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Cited by 72 (10 self)
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Abstract—We consider the uplink of a multiuser system where the transmitters as well as the receiver are equipped with multiple antennas. Each user multiplexes its symbols by a linear precoder through its transmit antennas. We work with the systemwide mean squared error as the performance measure and propose algorithms to find the jointly optimum linear precoders at each transmitter and linear decoders at the receiver. We first work with the case where the number of symbols to be transmitted by each user is given. We then investigate how the symbol rate should be chosen for each user with optimum transmitters and receivers. The convergence analysis of the algorithms is given, and numerical evidence that supports the analysis is presented. Index Terms—MMSE receivers, multiuser MIMO system, receiver beamforming, transmitter beamforming.
Transmit beamforming in multipleantenna systems with finite rate feedback: A VQbased approach
 IEEE Trans. Inform. Theory
, 2006
"... Abstract—This paper investigates quantization methods for feeding back the channel information through a lowrate feedback channel in the context of multipleinput singleoutput (MISO) systems. We propose a new quantizer design criterion for capacity maximization and develop the corresponding iterat ..."
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Cited by 57 (4 self)
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Abstract—This paper investigates quantization methods for feeding back the channel information through a lowrate feedback channel in the context of multipleinput singleoutput (MISO) systems. We propose a new quantizer design criterion for capacity maximization and develop the corresponding iterative vector quantization (VQ) design algorithm. The criterion is based on maximizing the meansquared weighted inner product (MSwIP) between the optimum and the quantized beamforming vector. The performance of systems with quantized beamforming is analyzed for the independent fading case. This requires finding the density of the squared inner product between the optimum and the quantized beamforming vector, which is obtained by considering a simple approximation of the quantization cell. The approximate density function is used to lowerbound the capacity loss due to quantization, the outage probability, and the bit error probability. The resulting expressions provide insight into the dependence of the performance of transmit beamforming MISO systems on the number of transmit antennas and feedback rate. Computer simulations support the analytical results and indicate that the lower bounds are quite tight. Index Terms—Bit error probability, channel capacity, channel state information, multiple antennas, transmit beamforming, outage probability, vector quantization (VQ). I.
Optimum linear joint transmitreceive processing for MIMO channels with QoS constraints
 IEEE Transactions on Signal Processing
, 2004
"... Abstract—This paper considers vector communications through multipleinput multipleoutput (MIMO) channels with a set of quality of service (QoS) requirements for the simultaneously established substreams. Linear transmitreceive processing (also termed linear precoder at the transmitter and linear ..."
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Cited by 51 (8 self)
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Abstract—This paper considers vector communications through multipleinput multipleoutput (MIMO) channels with a set of quality of service (QoS) requirements for the simultaneously established substreams. Linear transmitreceive processing (also termed linear precoder at the transmitter and linear equalizer at the receiver) is designed to satisfy the QoS constraints with minimum transmitted power (the exact conditions under which the problem becomes unfeasible are given). Although the original problem is a complicated nonconvex problem with matrixvalued variables, with the aid of majorization theory, we reformulate it as a simple convex optimization problem with scalar variables. We then propose a practical and efficient multilevel waterfilling algorithm to optimally solve the problem for the general case of different QoS requirements. The optimal transmitreceive processing is shown to diagonalize the channel matrix only after a very specific prerotation of the data symbols. For situations in which the resulting transmit power is too large, we give the precise way to relax the QoS constraints in order to reduce the required power based on a perturbation analysis. We also propose a robust design under channel estimation errors that has an important interest for practical systems. Numerical results from simulations are given to support the mathematical development of the problem. Index Terms—Array signal processing, beamforming, joint transmitreceive equalization, linear precoding, MIMO channels, spacetime filtering, waterfilling. I.
Joint Transmitter Receiver Diversity for Efficient Space Division Multiaccess
 IEEE Trans. Wireless Commun
, 2002
"... Abstract—Beamforming problem is studied in wireless networks where both transmitters and receivers have linear adaptive antenna arrays. Algorithms are proposed that find antenna array weight vectors at both transmitters and receivers as well as the transmitter powers with one of the following two ob ..."
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Cited by 49 (0 self)
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Abstract—Beamforming problem is studied in wireless networks where both transmitters and receivers have linear adaptive antenna arrays. Algorithms are proposed that find antenna array weight vectors at both transmitters and receivers as well as the transmitter powers with one of the following two objectives: 1) to maximize the minimum signaltointerferenceandnoise ratio (SINR) over all receivers and 2) to minimize the sum of the total transmitted power satisfying the SINR requirements at all links. Numerical study is performed to compare the network capacity and the power consumption among systems having different number of antenna array elements in a code division multiple access network. Index Terms—Adaptive antenna arrays, adaptive beamforming, joint transmit and receive beamforming, power control. I.