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119
On the capacity of MIMO broadcast channel with partial side information
 IEEE Trans. Inform. Theory
, 2005
"... Abstract—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 use ..."
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Cited by 173 (6 self)
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Abstract—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. Index Terms—Broadcast channel, channel state information (CSI), multiuser diversity, wireless communications. I.
The capacity region of the Gaussian multipleinput multipleoutput broadcast channel
 IEEE Trans. Inf. Theory
, 2006
"... (MIMO) broadcast channel (BC) is considered. The dirtypaper 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 Gaussia ..."
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Cited by 156 (3 self)
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(MIMO) broadcast channel (BC) is considered. The dirtypaper 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 perantenna power constraints. Index Terms—Broadcast channel, capacity region, dirtypaper coding (DPC), enhanced channel, entropy power inequality, Minkowski’s inequality, multipleantenna. I.
A VectorPerturbation technique for NearCapacity . . .
 IEEE TRANS. COMMUN
, 2005
"... Recent theoretical results describing the sum capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity. We introduce a simple encoding algorithm that achi ..."
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Cited by 131 (3 self)
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Recent theoretical results describing the sum capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity. We introduce a simple encoding algorithm that achieves nearcapacity at sum rates of tens of bits/channel use. The algorithm is a variation on channel inversion that regularizes the inverse and uses a “sphere encoder ” to perturb the data to reduce the power of the transmitted signal. This paper is comprised of two parts. In this first part, we show that while the sum capacity grows linearly with the minimum of the number of antennas and users, the sum rate of channel inversion does not. This poor performance is due to the large spread in the singular values of the channel matrix. We introduce regularization to improve the condition of the inverse and maximize the signaltointerferenceplusnoise ratio at the receivers. Regularization enables linear growth and works especially well at low signaltonoise ratios (SNRs), but as we show in the second part, an additional step is needed to achieve nearcapacity performance at all SNRs.
Achievable Rates in Cognitive Radio Channels
 IEEE Trans. Inf. Theory
, 2006
"... Cognitive radio promises a low cost, highly flexible alternative to the classic single frequency band, single protocol wireless device. By sensing and adapting to its environment, such a device is able to fill voids in the wireless spectrum and dramatically increase spectral efficiency. In this pape ..."
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Cited by 129 (18 self)
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Cognitive radio promises a low cost, highly flexible alternative to the classic single frequency band, single protocol wireless device. By sensing and adapting to its environment, such a device is able to fill voids in the wireless spectrum and dramatically increase spectral efficiency. In this paper, the cognitive radio channel is defined as an ntransmitter, mreceiver interference channel in which sender i obtains the messages senders 1 through i − 1 plan to transmit. The two sender, two receiver case is considered. In this scenario, one user, a cognitive radio, obtains (genie assisted, or causally) knowledge of the data to be transmitted by the other user. The cognitive radio may then simultaneously transmit over the same channel, as opposed to waiting for an idle channel as in a traditional cognitive radio channel protocol. Dirtypaper coding and ideas from achievable region constructions for the interference channel are used, and an achievable region for the cognitive radio channel is computed. It is shown that in the Gaussian case, the described achievable region approaches the upper bounds provided by the 2×2 Gaussian MIMO broadcast channel, and an interferencefree channel. Results are extended to the case in which the message is causally obtained.
On the optimality of multiantenna broadcast scheduling using zeroforcing beamforming
 IEEE J. SELECT. AREAS COMMUN
, 2006
"... Although the capacity of multipleinput/multipleoutput (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 116 (5 self)
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Although the capacity of multipleinput/multipleoutput (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 zeroforcing 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 roundrobin ZFBF and proportionalfair 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.
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 94 (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.
Cognitive Radio: An InformationTheoretic Perspective”, http://arxiv.org/abs/cs/0604107 32 A. Lapidoth, “Nearestneighbor decoding for additive nonGaussian noise channels
 IEEE Transactions on Information Theory
, 1996
"... We consider a communication scenario in which the primary and the cognitive radios wish to communicate to different receivers, subject to mutual interference. In the model that we use, the cognitive radio has noncausal knowledge of the primary radio’s codeword. We characterize the largest rate at w ..."
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Cited by 88 (0 self)
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We consider a communication scenario in which the primary and the cognitive radios wish to communicate to different receivers, subject to mutual interference. In the model that we use, the cognitive radio has noncausal knowledge of the primary radio’s codeword. We characterize the largest rate at which the cognitive radio can reliably communicate under the constraint that (i) no rate degradation is created for the primary user, and (ii) the primary receiver uses a singleuser decoder just as it would in the absence of the cognitive radio. The result holds in a “low interference ” regime in which the cognitive radio is closer to its receiver than to the primary receiver. In this regime, our results are subsumed by the results derived in a concurrent and independent work [24]. We also demonstrate that, in a “high interference ” regime, multiuser decoding at the primary receiver is optimal from the standpoint of maximal jointly achievable rates for the primary and cognitive users. Index Terms — Cognitive radio, Costa precoding, dirtypaper coding, interference channel, spectral reuse, wireless networks.
Sum power iterative waterfilling for multiantenna Gaussian broadcast channels
 IEEE Trans. Inform. Theory
, 2005
"... In this paper we consider the problem of maximizing sum rate of a multipleantenna Gaussian broadcast channel. It was recently found that dirty paper coding is capacity achieving for this channel. In order to achieve capacity, the optimal transmission policy (i.e. the optimal transmit covariance str ..."
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Cited by 82 (16 self)
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In this paper we consider the problem of maximizing sum rate of a multipleantenna Gaussian broadcast channel. It was recently found that dirty paper coding is capacity achieving for this channel. In order to achieve capacity, the optimal transmission policy (i.e. the optimal transmit covariance structure) given the channel conditions and power constraint must be found. However, obtaining the optimal transmission policy when employing dirty paper coding is a computationally complex nonconvex problem. We use duality to transform this problem into a wellstructured convex multipleaccess channel problem. We exploit the structure of this problem and derive simple and fast iterative algorithms that provide the optimum transmission policies for the multipleaccess channel, which can easily be mapped to the optimal broadcast channel policies.
Dirtypaper coding versus TDMA for MIMO broadcast channels
 IEEE Trans. Inf. Theory
, 2005
"... Abstract—We compare the capacity of dirtypaper coding (DPC)to that of timedivision multiple access (TDMA)for a multipleantenna (multipleinput multipleoutput (MIMO)) Gaussian broadcast channel (BC). We find that the sumrate capacity (achievable using DPC)of the multipleantenna BC is at most ��� ..."
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Cited by 42 (3 self)
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Abstract—We compare the capacity of dirtypaper coding (DPC)to that of timedivision multiple access (TDMA)for a multipleantenna (multipleinput multipleoutput (MIMO)) Gaussian broadcast channel (BC). We find that the sumrate capacity (achievable using DPC)of the multipleantenna BC is at most ��� @ A times the largest singleuser capacity (i.e., the TDMA sumrate)in the system, where is the number of transmit antennas and is the number of receivers. This result is independent of the number of receive antennas and the channel gain matrix, and is valid at all signaltonoise ratios (SNRs). We investigate the tightness of this bound in a timevarying channel (assuming perfect channel knowledge at receivers and transmitters)where the channel experiences uncorrelated Rayleigh fading and in some situations we find that the dirty paper gain is upperbounded by the ratio of transmittoreceive antennas. We also show that ��� @ A upperbounds the sumrate gain of successive decoding over TDMA for the uplink channel, where is the number of receive antennas at the base station and is the number of transmitters. Index Terms—Broadcast channel (BC), channel capacity, dirtypaper coding (DPC), multipleinput multipleoutput (MIMO) systems, timedivision multiple access (TDMA). I.