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28
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 344 (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.
Breaking Spectrum Gridlock with Cognitive Radios: An Information Theoretic Perspective
, 2008
"... Cognitive radios hold tremendous promise for increasing spectral efficiency in wireless systems. This paper surveys the fundamental capacity limits and associated transmission techniques for different wireless network design paradigms based on this promising technology. These paradigms are unified b ..."
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Cited by 247 (3 self)
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Cognitive radios hold tremendous promise for increasing spectral efficiency in wireless systems. This paper surveys the fundamental capacity limits and associated transmission techniques for different wireless network design paradigms based on this promising technology. These paradigms are unified by the definition of a cognitive radio as an intelligent wireless communication device that exploits side information about its environment to improve spectrum utilization. This side information typically comprises knowledge about the activity, channels, codebooks and/or messages of other nodes with which the cognitive node shares the spectrum. Based on the nature of the available side information as well as a priori rules about spectrum usage, cognitive radio systems seek to underlay, overlay or interweave the cognitive radios ’ signals with the transmissions of noncognitive nodes. We provide a comprehensive summary of the known capacity characterizations in terms of upper and lower bounds for each of these three approaches. The increase in system degrees of freedom obtained through cognitive radios is also illuminated. This information theoretic survey provides guidelines for the spectral efficiency gains possible through cognitive radios, as well as practical design ideas to mitigate the coexistence challenges in today’s crowded spectrum.
A comparison of timesharing, DPC, and beamforming for MIMO broadcast channels with many users
 IEEE Trans. Commun
, 2007
"... In this paper, we derive the scaling laws of the sum rate for fading MIMO Gaussian broadcast channels using timesharing to the strongest user, dirty paper coding (DPC), and beamforming when the number of users (receivers) n is large. Throughout the paper, we assume a fix average transmit power and ..."
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Cited by 59 (2 self)
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In this paper, we derive the scaling laws of the sum rate for fading MIMO Gaussian broadcast channels using timesharing to the strongest user, dirty paper coding (DPC), and beamforming when the number of users (receivers) n is large. Throughout the paper, we assume a fix average transmit power and consider a block fading Rayleigh channel. First, we show that for a system with M transmit antennas and users equipped with N antennas, the sum rate scales like M log log nN for DPC and beamforming when M is fixed and for any N (either growing to infinity or not). On the other hand, when both M and N are fixed, the sum rate of timesharing to the strongest user scales like min(M, N) log log n. Therefore, the asymptotic gain of DPC over timesharing for the sum rate is M min(M,N) when M and N are fixed. It is also shown that if M grows as log n, the sum rate of DPC and beamforming will grow linearly in M, but with different constant multiplicative factors. In this region, the sum rate capacity of timesharing scales like N log log n.
On the capacity of interference channels with one cooperating transmitter
 EUROP. TRANS. TELECOMMUN. (SPECIAL ISSUE: NEW DIRECTIONS IN INFORMATION THEORY
, 2007
"... Inner and outer bounds are established on the capacity region of twosender, tworeceiver interference channels where one transmitter knows both messages. The transmitter with extra knowledge is referred to as being cognitive. The inner bound is based on strategies that generalize prior work, and i ..."
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Cited by 51 (3 self)
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Inner and outer bounds are established on the capacity region of twosender, tworeceiver interference channels where one transmitter knows both messages. The transmitter with extra knowledge is referred to as being cognitive. The inner bound is based on strategies that generalize prior work, and include ratesplitting, Gel’fandPinsker coding and cooperative transmission. A general outer bound is based on the NairEl Gamal outer bound for broadcast channels. A simpler bound is presented for the case in which one of the decoders can decode both messages. The bounds are evaluated and compared for Gaussian channels.
How much does transmit correlation affect the sumrate scaling of MIMO Gaussian broadcast channels
 IEEE Trans. Commun
, 2009
"... This paper considers the effect of spatial correlation between transmit antennas on the sumrate capacity of the MIMO broadcast channel (i.e., downlink of a cellular system). Specifically, for a system with a large number of users, we analyze the scaling laws of the sumrate for the dirty paper codi ..."
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Cited by 24 (2 self)
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This paper considers the effect of spatial correlation between transmit antennas on the sumrate capacity of the MIMO broadcast channel (i.e., downlink of a cellular system). Specifically, for a system with a large number of users, we analyze the scaling laws of the sumrate for the dirty paper coding and for different types of beamforming transmission schemes. When the channel is i.i.d., it has been shown that for large the sum rate is equal to where is the number of transmit antennas, is the average signal to noise ratio, and refers to terms that go to zero!# " as. When the channel exhibits some spatial correlation with a covariance $ matrix (nonsingular %' & ($)+*, with), we prove that the sum rate of dirty paper coding. / 0 21 3546($) 7 is. We further show that the sumrate of various beamforming schemes +27 / 7 +8 0 9: achieves 8<; = where depends on the type of beamforming. We can in fact 8 compute for random beamforming proposed in [24] and more generally, for random beamforming with precoding in which beams are premultiplied by a fixed matrix. Simulation results are presented at the end of the paper.
Fundamental Limits in MIMO Broadcast Channels
 IEEE J. Sel. Areas Commun
, 2007
"... Abstract — This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sumrate capacity of the system as a function of system paramaters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit ..."
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Cited by 14 (0 self)
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Abstract — This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sumrate capacity of the system as a function of system paramaters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling. Index Terms — MIMO broadcast channels, sumrate capacity, asymptotics, channel state information. I.
Robust multiuser opportunistic beamforming for sparse networks
 In Proceedings of the IEEE Workshop on Signal Processing Advances in Wireless Communications
, 2005
"... A scheme exploiting reduced feedback for the purpose of opportunistic multiuser beamforming is proposed. The scheme builds on recent promising advances realized in the area of multiuser downlink precoding and scheduling based on partial transmitter channel state information (CSIT) using random bea ..."
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Cited by 13 (3 self)
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A scheme exploiting reduced feedback for the purpose of opportunistic multiuser beamforming is proposed. The scheme builds on recent promising advances realized in the area of multiuser downlink precoding and scheduling based on partial transmitter channel state information (CSIT) using random beamformingbased SDMA. Although random precoding followed by SDMA scheduling is optimal within the set of unitary precoders, it is only so in the asymptotic number of users K. Forpractically relevant sparse networks (i.e. with low to moderate number of users) random beamforming SDMA yields severely degraded performance. In this work we present a scheme allowing to restore robustness with respect to cell sparsity. The core idea here is to preserve the low complexity low feedback advantage of random opportunistic beamforming in selecting a target group of users, while much more efficient beamforming schemes can be used to serve the group of users once it has been identified. We propose different designs, optimal and suboptimal, based upon variable levels of feedback requirement. We show substantial gain over opportunistic beamforming for a range of K. 1.
Delay considerations for opportunistic scheduling in broadcast fading channels
 IEEE Trans. Wireless Commun
, 2007
"... We consider a singleantenna broadcast block fading channel with users where the transmission is packetbased. We define the (packet) delay as the minimum number of channel uses that guarantees all users successfully receive packets. This is a more stringent notion of delay than average delay and is ..."
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Cited by 13 (1 self)
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We consider a singleantenna broadcast block fading channel with users where the transmission is packetbased. We define the (packet) delay as the minimum number of channel uses that guarantees all users successfully receive packets. This is a more stringent notion of delay than average delay and is the worst case (access) delay among the users. A delay optimal scheduling scheme, such as roundrobin, achieves the delay of. For the opportunistic scheduling (which is throughput optimal) where the transmitter sends the packet to the user with the best channel conditions at each channel use, we derive the mean and variance of the delay for any and. For large and in a homogeneous network, it is proved that the expected delay in receiving one packet by all the receivers scales as, as opposed to for the roundrobin scheduling. We also show that when grows faster than, for some, then the delay scales as. This roughly determines the timescale required for the system to behave fairly in a homogeneous network. We then propose a scheme to significantly reduce the delay at the expense of a small throughput hit. We further look into the advantage of multiple transmit antennas on the delay. For a system with antennas in the transmitter where at each channel use packets are sent to different users, we obtain the expected delay in receiving one packet by all the users. Index terms: broadcast channel, fading, opportunistic scheduling, packet delay, longest queue. 1
Scaling laws of sum rate using timesharing, DPC, and beamforming for MIMO broadcast channels
 in Proc. Inter. Symp. on Information Theory
, 2004
"... Abstract — We derive the scaling laws of the sum rate throughput for MIMO Gaussian broadcast channels using timesharing to the strongest user, dirty paper coding (DPC), and beamforming when the number of users (receivers) n is large. Assuming a fixed total average transmit power, we show that for a ..."
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Cited by 11 (5 self)
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Abstract — We derive the scaling laws of the sum rate throughput for MIMO Gaussian broadcast channels using timesharing to the strongest user, dirty paper coding (DPC), and beamforming when the number of users (receivers) n is large. Assuming a fixed total average transmit power, we show that for a system with M transmit antennas and users equipped with N antennas, the sum rate scales like M log log nN for DPC and beamforming when M is fixed and for any N (either growing to infinity or not). On the other hand, when both M and N are fixed, the sum rate of timesharing to the strongest user scales like min(M,N)loglogn. It is also shown that if M grows as log n, the sum rate of DPC and beamforming will grow linearly in M, but with different constant multiplicative factors. In this region, the sum rate capacity of timesharing scales like N log log n. I.
A delay analysis for opportunistic transmission in fading broadcast channel,” ro be submitted io IEEE Tmns. Info. { d o w n h d muiiable at wivw.its.calteci~ e d d  m o d
, 2004
"... Abstract We consider a singleantenna broadcast block fading channel (downlink scheduling) with TL users where the transmission is packetbased and all users are backlogged. We define the delay as the minimum number of channel uses that guarantees ull n users successfully receive m packets. This i ..."
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Cited by 7 (2 self)
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Abstract We consider a singleantenna broadcast block fading channel (downlink scheduling) with TL users where the transmission is packetbased and all users are backlogged. We define the delay as the minimum number of channel uses that guarantees ull n users successfully receive m packets. This is a more stringent notion o f delay than average delay and is the worst case delay among the users. A delay optimal scheduling scheme, such as roundrobin, achieves the delay of mn. In a heterogeneous network and for the optimal throughput strategy where the transmitter sends the packet to the wet with the best channel conditions, we derive the moment generating function of the delay for any m and n. For large n and in a homogeneous network, the expected delay in receiving one packet by all the receivers scales as n log n, as opposed to n for the roundtobin scheduling. We also show that when m grows faster than (logn)‘, for some P> 1, then the expected value of delay scales like mn, This roughly determines the timescale required for the system to behave fairly in a homogeneous network. We then propose a scheme to signikantly reduce the delay at the expense of a small throughput hit. We further look into two generalizations of our work: i) the effect of temporal channel correlation and i i) the advantage of multiple transmit antennas on the delay. For a channel with memory of two, we prove that the delay scales again like n log n no matter how severe the correlation is. For a system with A4 transmit antennas, we prove that the expected deky in receiving one packet by all the users scales like nf+”dF$,,, for large n and when M is not growing faster than logn. Thus, when the temporal channel correlation is zero, multiple transmit antenna systems do not reduce the delay significantly. However, when channel correlation is present, they can lead to significant gains by “decorrehting ” the effective channel through means such as random beamforming.