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The capacity region of the Gaussian multiple-input multiple-output broadcast channel
- IEEE TRANS. INF. THEORY
, 2006
"... The Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC) is considered. The dirty-paper coding (DPC) rate region is shown to coincide with the capacity region. To that end, a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequa ..."
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Cited by 339 (7 self)
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The Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC) is considered. The dirty-paper coding (DPC) rate region is shown to coincide with the capacity region. To that end, a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality, to show that a superposition of Gaussian codes is optimal for the degraded vector broadcast channel and that DPC is optimal for the nondegraded case. Furthermore, the capacity region is characterized under a wide range of input constraints, accounting, as special cases, for the total power and the per-antenna power constraints.
On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming
- IEEE J. SELECT. AREAS COMMUN
, 2006
"... Although the capacity of multiple-input/multiple-output (MIMO) broadcast channels (BCs) can be achieved by dirty paper coding (DPC), it is difficult to implement in practical systems. This paper investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifica ..."
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Cited by 308 (4 self)
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Although the capacity of multiple-input/multiple-output (MIMO) broadcast channels (BCs) can be achieved by dirty paper coding (DPC), it is difficult to implement in practical systems. This paper investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifically, we show that a zero-forcing beamforming (ZFBF) strategy, while generally suboptimal, can achieve the same asymptotic sum capacity as that of DPC, as the number of users goes to infinity. In proving this asymptotic result, we provide an algorithm for determining which users should be active under ZFBF. These users are semiorthogonal to one another and can be grouped for simultaneous transmission to enhance the throughput of scheduling algorithms. Based on the user grouping, we propose and compare two fair scheduling schemes in round-robin ZFBF and proportional-fair ZFBF. We provide numerical results to confirm the optimality of ZFBF and to compare the performance of ZFBF and proposed fair scheduling schemes with that of various MIMO BC strategies.
An overview of limited feedback in wireless communication systems
- IEEE J. SEL. AREAS COMMUN
, 2008
"... It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channe ..."
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Cited by 205 (41 self)
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It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finite-rate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, single-user, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.
MIMO Broadcast Channels With Finite-Rate 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 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 signal-to-noise ratio (SNR) (in decibels) in order to achieve the full multiplexing gain. This is in sharp contrast to point-to-point multiple-input multiple-output (MIMO) systems, in which it is not necessary to increase the feedback rate as a function of the SNR.
What Is the Value of Limited Feedback for MIMO Channels?
, 2004
"... Feedbackinacommunicationssystemcan enablethetransmittertoexploitchannelcondi - tionsandavoidinterference.Inthecaseofa multiple-inputmultiple-outputchannel,feedback canbeusedtospecifyaprecodingmatrixatthe transmitter,whichactivatesthestrongestchan - nelmodes.Insituationswherethefeedbackis severelylim ..."
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Cited by 176 (31 self)
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Feedbackinacommunicationssystemcan enablethetransmittertoexploitchannelcondi - tionsandavoidinterference.Inthecaseofa multiple-inputmultiple-outputchannel,feedback canbeusedtospecifyaprecodingmatrixatthe transmitter,whichactivatesthestrongestchan - nelmodes.Insituationswherethefeedbackis severelylimited,importantissuesarehowto quantizetheinformationneededatthetransmitterandhowmuchimprovementinassociated performancecanbeobtainedasafunctionof theamountoffeedbackavailable.Wegivean overviewofsomerecentworkinthisarea.Meth - odsarepresentedforconstructingasetofpossibleprecodingmatrices, fromwhichaparticular choicecanberelayedtothetransmitter.Perfor - manceresultsshowthatevenafewbitsoffeedbackcanprovideperformanceclosetothatwith fullchannelknowledgeatthetransmitter.
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 point-to-point MIMO systems in which it is not necessary to increase the feedback rate as a function of the SNR. I.
Multi-antenna downlink channels with limited feedback and user selection
- IEEE J. Select. Areas Commun
, 2007
"... Abstract — We analyze the sum-rate performance of a multiantenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to ..."
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Cited by 119 (2 self)
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Abstract — We analyze the sum-rate performance of a multiantenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to directional information, information regarding the quality of each channel. Such information should reflect both the channel magnitude and the quantization error. Expressions for the SINR distribution and the sum-rate are derived, and tradeoffs between the number of feedback bits, the number of users, and the SNR are observed. In particular, for a target performance, having more users reduces feedback load. Index Terms — MIMO, quantized feedback, limited feedback, zero-forcing beamforming, multiuser diversity, broadcast channel,
Degrees of freedom region of the MIMO X Channel
, 2007
"... hop, is especially interesting, as the intermediate hop takes place over an interference channel with single antenna nodes. While the two user interference channel with single antenna nodes has only one degree of freedom by itself, it is able to deliver degrees of freedom when used as an intermediat ..."
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Cited by 92 (28 self)
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hop, is especially interesting, as the intermediate hop takes place over an interference channel with single antenna nodes. While the two user interference channel with single antenna nodes has only one degree of freedom by itself, it is able to deliver degrees of freedom when used as an intermediate stage between a antenna source and a antenna destination [5]. The key is an amplify and forward scheme where the relay nodes, instead of trying to decode the messages, simply scale and forward their received signals. [1]–[3] consider end to end channel orthogonalization with distributed sources, relays and destination nodes and determine the capacity scaling behavior with the number of relay nodes. It is shown that distributed orthogonalization can be obtained even with synchronization errors if a minimum amount of coherence at the relays can be sustained. Degrees of freedom for linear interference networks with local side-information are explored in [22] and cognitive message sharing is found to improve the degrees of freedom for certain structured channel matrices. The MIMO MAC and BC channels show that there is no loss in degrees of freedom even if antennas are distributed among users at one end (either transmitters or receivers) making joint signal processing infeasible, as long as joint signal processing is possible at the other end of the communication link. The multiple hop example of [5], described above, shows that there is no loss of degrees of freedom even with distributed antennas at both ends of a communication hop (an interference channel) as long as the distributed antenna stages are only intermediate
Degrees of freedom region of the MIMO . . .
, 2008
"... We provide achievability as well as converse results for the degrees of freedom region of a multiple-input multipleoutput (MIMO) X channel, i.e., a system with two transmitters, two receivers, each equipped with multiple antennas, where independent messages need to be conveyed over fixed channels fr ..."
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Cited by 91 (19 self)
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We provide achievability as well as converse results for the degrees of freedom region of a multiple-input multipleoutput (MIMO) X channel, i.e., a system with two transmitters, two receivers, each equipped with multiple antennas, where independent messages need to be conveyed over fixed channels from each transmitter to each receiver. The inner and outer bounds on the degrees of freedom region are tight whenever integer degrees of freedom are optimal for each message. With M =1antennas at each node, we find that the total (sum rate) degrees of freedom are bounded above and below as 1? 4 X.IfM>1 and channel
Pilot contamination and precoding in multi-cell TDD systems
- LU et al.: OVERVIEW OF MASSIVE MIMO: BENEFITS AND CHALLENGES 757
, 2011
"... Abstract—This paper considers a multi-cell 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 ob-taining this CSI is time-division duplex (TDD) operati ..."
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Cited by 76 (6 self)
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Abstract—This paper considers a multi-cell 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 ob-taining this CSI is time-division 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 multi-cell multiple antenna systems. When non-orthogonal 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 multi-cell systems. Furthermore, it develops a new multi-cell MMSE-based precoding method that mitigates this problem. In addition to being linear, this precoding method has a simple closed-form expression that results from an intuitive optimization. Numerical results show significant performance gains compared to certain popular single-cell precoding methods. Index Terms—Time-division duplex systems, uplink training, pilot contamination, MMSE precoding. I.