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322
On the capacity of MIMO broadcast channel with partial side information
 IEEE TRANS. INFORM. THEORY
, 2005
"... In multipleantenna broadcast channels, unlike pointtopoint multipleantenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with transmit antennas and singleantenna users, the ..."
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Cited by 349 (9 self)
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In multipleantenna broadcast channels, unlike pointtopoint multipleantenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with transmit antennas and singleantenna users, the sum rate capacity scales like log log for large if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with if it is not. In systems with large, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. In this paper, we propose a scheme that constructs random beams and that transmits information to the users with the highest signaltonoiseplusinterference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed and increasing, the throughput of our scheme scales as log log, where is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with can be obtained provided that does not not grow faster than log. We also study the fairness of our scheduling in a heterogeneous network and show that, when is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1, irrespective of its path loss. In fact, using = log transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with as well as in guaranteeing fairness.
Scaling up MIMO: Opportunities and challenges with very large arrays
, 2011
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MIMO Broadcast Channels With FiniteRate Feedback
, 2006
"... Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e., multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this correspondence, a system where each receiver has per ..."
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Cited by 189 (1 self)
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Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e., multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this correspondence, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The wellknown zeroforcing transmission technique is considered, and simple expressions for the throughput degradation due to finiterate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the signaltonoise ratio (SNR) (in decibels) in order to achieve the full multiplexing gain. This is in sharp contrast to pointtopoint multipleinput multipleoutput (MIMO) systems, in which it is not necessary to increase the feedback rate as a function of the SNR.
MIMO broadcast channels with finite rate feedback
 IEEE Trans. on Inform. Theory
, 2006
"... Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where each receiver has perfect channe ..."
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Cited by 155 (10 self)
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Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The well known zero forcing transmission technique is considered, and simple expressions for the throughput degradation due to finite rate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the SNR (in dB) in order to achieve the full multiplexing gain, which is in sharp contrast to pointtopoint MIMO systems in which it is not necessary to increase the feedback rate as a function of the SNR. I.
Linear precoding via conic optimization for fixed mimo receivers
 IEEE Trans. on Signal Processing
, 2006
"... We consider the problem of designing linear precoders for fixed multiple input multiple output (MIMO) receivers. Two different design criteria are considered. In the first, we minimize the transmitted power subject to signal to interference plus noise ratio (SINR) constraints. In the second, we maxi ..."
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Cited by 154 (3 self)
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We consider the problem of designing linear precoders for fixed multiple input multiple output (MIMO) receivers. Two different design criteria are considered. In the first, we minimize the transmitted power subject to signal to interference plus noise ratio (SINR) constraints. In the second, we maximize the worst case SINR subject to a power constraint. We show that both problems can be solved using standard conic optimization packages. In addition, we develop conditions for the optimal precoder for both of these problems, and propose two simple fixed point iterations to find the solutions which satisfy these conditions. The relation to the well known downlink uplink duality in the context of joint downlink beamforming and power control is also explored. Our precoder design is general, and as a special case it solves the beamforming problem. In contrast to most of the existing precoders, it is not limited to full rank systems. Simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders. 1
Pilot contamination and precoding in multicell TDD systems
 LU et al.: OVERVIEW OF MASSIVE MIMO: BENEFITS AND CHALLENGES 757
, 2011
"... Abstract—This paper considers a multicell multiple antenna system with precoding used at the base stations for downlink transmission. Channel state information (CSI) is essential for precoding at the base stations. An effective technique for obtaining this CSI is timedivision duplex (TDD) operati ..."
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Cited by 76 (6 self)
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Abstract—This paper considers a multicell multiple antenna system with precoding used at the base stations for downlink transmission. Channel state information (CSI) is essential for precoding at the base stations. An effective technique for obtaining this CSI is timedivision duplex (TDD) operation where uplink training in conjunction with reciprocity simultaneously provides the base stations with downlink as well as uplink channel estimates. This paper mathematically characterizes the impact that uplink training has on the performance of such multicell multiple antenna systems. When nonorthogonal training sequences are used for uplink training, the paper shows that the precoding matrix used by the base station in one cell becomes corrupted by the channel between that base station and the users in other cells in an undesirable manner. This paper analyzes this fundamental problem of pilot contamination in multicell systems. Furthermore, it develops a new multicell MMSEbased precoding method that mitigates this problem. In addition to being linear, this precoding method has a simple closedform expression that results from an intuitive optimization. Numerical results show significant performance gains compared to certain popular singlecell precoding methods. Index Terms—Timedivision duplex systems, uplink training, pilot contamination, MMSE precoding. I.
Fast transfer of channel state information in wireless systems
 IEEE Transactions on Signal Processing
, 2006
"... Knowledge of accurate and timely channel state information (CSI) at the transmitter is becoming increasingly important in wireless communication systems. While it is often assumed that the receiver (whether basestation or mobile) needs to know the channel for accurate power control, scheduling and d ..."
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Cited by 62 (3 self)
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Knowledge of accurate and timely channel state information (CSI) at the transmitter is becoming increasingly important in wireless communication systems. While it is often assumed that the receiver (whether basestation or mobile) needs to know the channel for accurate power control, scheduling and datademodulation, it is now known that the transmitter (especially the basestation) can also benefit greatly from this information. For example, recent results in multiantenna multiuser systems show that large throughput gains are possible when the basestation uses multiple antennas and a known channel to transmit distinct messages simultaneously and selectively to many singleantenna users. In timedivision duplex systems, where the basestation and mobiles share the same frequency band for transmission, the basestation can exploit reciprocity to obtain the forward channel from pilots received over the reverse channel. Frequencydivision duplex systems are more difficult because the basestation transmits and receives on different frequencies and therefore cannot use the received pilot to infer anything about the multiantenna transmit channel. Nevertheless, we show that the time occupied in frequencyduplex CSI transfer is generally less than one might expect, and falls as the number of antennas increases. Thus, although the total amount of channel information increases with the number of antennas at the basestation,
On the capacity of fading MIMO broadcast channels with imperfect transmitter sideinformation
 in Annual Allerton Conference on Communication, Control, and Computing
, 2005
"... A fading broadcast channel is considered where the transmitter employs two antennas and each of the two receivers employs a single receive antenna. It is demonstrated that even if the realization of the fading is precisely known to the receivers, the high signaltonoise (SNR) throughput is greatly ..."
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Cited by 57 (3 self)
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A fading broadcast channel is considered where the transmitter employs two antennas and each of the two receivers employs a single receive antenna. It is demonstrated that even if the realization of the fading is precisely known to the receivers, the high signaltonoise (SNR) throughput is greatly reduced if, rather than knowing the fading realization precisely, the trasmitter only knows the fading realization approximately. The results are general and are not limited to memoryless Gaussian fading. 1
Latticereductionaided broadcast precoding
 IEEE Trans. Commun
, 2004
"... Abstract—A precoding scheme for multiuser broadcast communications is described, which fills the gap between the lowcomplexity Tomlinson–Harashima precoding and the sphere decoderbased system of Peel et al. Simulation results show that, replacing the closestpoint search with the Babai approximatio ..."
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Cited by 55 (4 self)
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Abstract—A precoding scheme for multiuser broadcast communications is described, which fills the gap between the lowcomplexity Tomlinson–Harashima precoding and the sphere decoderbased system of Peel et al. Simulation results show that, replacing the closestpoint search with the Babai approximation, the full diversity order supported by the channel is available to each user, as in the system of Peel et al., and unlike Tomlinson–Harashima precoding, which suffers some diversity penalty. The complexity of the scheme is similar to that of Tomlinson–Harashima precoding. Index Terms—Lattice reduction, multipleinput multipleoutput (MIMO) broadcast channels, MIMO precoding.
Large system analysis of linear precoding in correlated MISO broadcast channels under limited feedback
 IEEE TRANS. INF. THEORY
, 2012
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