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Gaussian interference channel capacity to within one bit
 5534–5562, 2008. EURASIP Journal on Advances in Signal Processing
"... Abstract—The capacity of the twouser Gaussian interference channel has been open for 30 years. The understanding on this problem has been limited. The best known achievable region is due to Han and Kobayashi but its characterization is very complicated. It is also not known how tight the existing o ..."
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Cited by 445 (27 self)
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Abstract—The capacity of the twouser Gaussian interference channel has been open for 30 years. The understanding on this problem has been limited. The best known achievable region is due to Han and Kobayashi but its characterization is very complicated. It is also not known how tight the existing outer bounds are. In this work, we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges, and by deriving new outer bounds, we show that a very simple and explicit Han–Kobayashi type scheme can achieve to within a single bit per second per hertz (bit/s/Hz) of the capacity for all values of the channel parameters. We also show that the scheme is asymptotically optimal at certain high signaltonoise ratio (SNR) regimes. Using our results, we provide a natural generalization of the pointtopoint classical notion of degrees of freedom to interferencelimited scenarios. Index Terms—Capacity region, Gaussian interference channel, generalized degrees of freedom.
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 264 (46 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.
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 245 (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.
Degrees of freedom for MIMO interference channel
 IEEE Transactions on Information Theory
, 2007
"... Abstract — We show that the exact number of spatial degrees of freedom for a two user nondegenerate (full rank channel matrices) MIMO Gaussian interference channel with M1,M2 (respectively) antennas at transmitters 1, 2 and N1, N2 antennas at the corresponding receivers, and perfect channel knowled ..."
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Cited by 163 (32 self)
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Abstract — We show that the exact number of spatial degrees of freedom for a two user nondegenerate (full rank channel matrices) MIMO Gaussian interference channel with M1,M2 (respectively) antennas at transmitters 1, 2 and N1, N2 antennas at the corresponding receivers, and perfect channel knowledge at all transmitters and receivers, is min{M1 +M2, N1 + N2,max(M1, N2),max(M2, N1)}. A constructive achievability proof shows that zero forcing is sufficient to achieve all the available degrees of freedom on the two user MIMO interference channel. This is in contrast to the MIMO X channel where the combination of zero forcing, dirty paper coding, and successive decoding schemes is shown to achieve more degrees of freedom than are possible with spatial zero forcing [1] alone. We also study a shareandtransmit scheme and show how the gains of transmitter cooperation are entirely offset by the cost of enabling that cooperation so that the available DoF are not increased. I.
Capacity bounds for the Gaussian interference channel
 IEEE TRANS. INFORM. THEORY
"... The capacity region of the twouser Gaussian Interference Channel (IC) is studied. Three classes of channels are considered: weak, onesided, and mixed Gaussian ICs. For the weak Gaussian IC, a new outer bound on the capacity region is obtained that outperforms previously known outer bounds. The cha ..."
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Cited by 154 (6 self)
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The capacity region of the twouser Gaussian Interference Channel (IC) is studied. Three classes of channels are considered: weak, onesided, and mixed Gaussian ICs. For the weak Gaussian IC, a new outer bound on the capacity region is obtained that outperforms previously known outer bounds. The channel sum capacity for some certain range of the channel parameters is derived. It is shown that when Gaussian codebooks are used, the full HanKobayashi achievable rate region can be obtained by using the naive HanKobayashi achievable scheme over three frequency bands (equivalently, three subspaces). For the onesided Gaussian IC, a new proof for Sato’s outer bound is presented. We derive the full HanKobayashi achievable rate region when Gaussian code books are utilized. For the mixed Gaussian IC, a new outer bound is obtained that again outperforms previously known outer bounds. For this case, the channel sum capacity for all ranges of parameters is derived. It is proved that the full HanKobayashi achievable rate region using Gaussian codebooks is equivalent to that of the onesided Gaussian IC for a particular range of the channel gains.
Capacity of interference channels with partial transmitter cooperation
 IEEE Transactions on Information Theory
"... Abstract—Capacity regions are established for several twosender, tworeceiver channels with partial transmitter cooperation. First, the capacity regions are determined for compound multipleaccess channels (MACs) with common information and compound MACs with conferencing. Next, two interference chan ..."
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Cited by 98 (10 self)
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Abstract—Capacity regions are established for several twosender, tworeceiver channels with partial transmitter cooperation. First, the capacity regions are determined for compound multipleaccess channels (MACs) with common information and compound MACs with conferencing. Next, two interference channel models are considered: an interference channel with common information (ICCI) and an interference channel with unidirectional cooperation (ICUC) in which the message sent by one of the encoders is known to the other encoder. The capacity regions of both of these channels are determined when there is strong interference, i.e., the interference is such that both receivers can decode all messages with no rate penalty. The resulting capacity regions coincide with the capacity region of the compound MAC with common information. Index Terms—Capacity region, cooperation, strong interference. I.
On the DegreesofFreedom of the KUser Gaussian Interference Channel
 IEEE Transactions on Information Theory
, 2008
"... The degreesoffreedom of a Kuser Gaussian interference channel (GIFC) has been defined to be the multiple of (1/2)log 2 P at which the maximum sum of achievable rates grows with increasing P. In this paper, we establish that the degreesoffreedom of three or more user, real, scalar GIFCs, viewed ..."
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Cited by 78 (0 self)
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The degreesoffreedom of a Kuser Gaussian interference channel (GIFC) has been defined to be the multiple of (1/2)log 2 P at which the maximum sum of achievable rates grows with increasing P. In this paper, we establish that the degreesoffreedom of three or more user, real, scalar GIFCs, viewed as a function of the channel coefficients, is discontinuous at points where all of the coefficients are nonzero rational numbers. More specifically, for all K> 2, we find a class of Kuser GIFCs that is dense in the GIFC parameter space for which K/2 degreesoffreedom are exactly achievable, and we show that the degreesoffreedom for any GIFC with nonzero rational coefficients is strictly smaller than K/2. These results are proved using new connections with number theory and additive combinatorics. 1
Capacity of a Class of Cognitive Radio Channels: Interference Channels with Degraded Message Sets
"... This paper is motivated by two different scenarios. The first is a cognitive radio system where a cognitive radio knows a “dumb ” radio’s message and the second is a sensor network in a correlated field where sensors possessing a nested message structure assist one another’s in information transmis ..."
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Cited by 68 (3 self)
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This paper is motivated by two different scenarios. The first is a cognitive radio system where a cognitive radio knows a “dumb ” radio’s message and the second is a sensor network in a correlated field where sensors possessing a nested message structure assist one another’s in information transmission. Both scenarios are modeled using the framework of discrete memoryless interference channels with degraded message sets (IFCDMS), a setting where one of the two transmitters in an interference channel knows both the messages to be conveyed to the receivers. Both inner and outer bounds are provided in this paper for a class of IFCDMS channels. The case of the Gaussian interference channels with degraded message sets is also investigated. In this case, achievability and converse arguments are presented for a class of “weak” interference channels, resulting in a characterization of this class’ capacity region.
On interference channels with generalized feedback
 In Proceedings of IEEE Int. Symp. on Inform. Theory, ISIT2007
, 2007
"... An Interference Channel with Generalized Feedback (IFCGF) is a model for a wireless network where several sourcedestination pairs compete for the same channel resources, and where the sources have the ability to sense the current channel activity. The signal overheard from the channel provides inf ..."
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Cited by 47 (8 self)
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An Interference Channel with Generalized Feedback (IFCGF) is a model for a wireless network where several sourcedestination pairs compete for the same channel resources, and where the sources have the ability to sense the current channel activity. The signal overheard from the channel provides information about the activity of the other users, and thus furnishes the basis for cooperation. In this twopart paper we study achievable strategies and outer bounds for a general IFCGF with two sourcedestination pairs. We then evaluate the proposed regions for the Gaussian channel. Part I: Achievable Region. We propose that the generalized feedback is used to gain knowledge about the message sent by the other user and then exploited in two ways: (a) to relay the messages that can be decoded at both destinations–thus realizing the gains of beamforming of a distributed multiantenna system–and (b) to hide the messages that can not be decoded at the nonintended destination–thus leveraging the interference “precancellation” property of dirtypapertype coding. We show that our achievable region generalizes several known achievable regions for IFCGF and that it reduces
On the Capacity of Vector Gaussian Interference Channels
 IEEE ITW,2004
"... Abstract — The capacity of a vector Gaussian interference channel is investigated. Outer bounds, and where possible, capacity regions of a class of interference channels is characterized. The analysis of single transmit multiple receive antenna (SIMO) Gaussian interference channels with strong int ..."
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Cited by 45 (6 self)
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Abstract — The capacity of a vector Gaussian interference channel is investigated. Outer bounds, and where possible, capacity regions of a class of interference channels is characterized. The analysis of single transmit multiple receive antenna (SIMO) Gaussian interference channels with strong interference can be easily seen to be exactly analogous to that of a single transmit single receive antenna system. This paper demonstrates that, in contrast, multiple transmit single receive antenna (MISO) Gaussian interference channels are much harder to characterize. In this paper, the capacity region for a class of MISO interference channels with very strong interference is characterized. Also, the rank of the optimal transmit policy in a MISO Gaussian interference channel is shown to be bounded by the number of users in the system. Finally, outer bounds on the capacity region of the general multiple transmit and receive antenna (MIMO) Gaussian Interference Channels are derived. A new outer bound is obtained, which combines and improves previously known strategies for bounding the capacity of interference channels. I.