For the fully connected K user wireless interference channel where the channel coefficients are time-varying and are drawn from a continuous distribution, the sum capacity is characterized as C(SNR) = K 2 log(SNR) +o(log(SNR)). Thus, the K user time-varying interference channel almost surely has K=2 degrees of freedom. Achievability is based on the idea of interference alignment. Examples are also provided of fully connected K user interference channels with constant (not time-varying) coefficients where the capacity is exactly achieved by interference alignment at all SNR values.

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.

Establishing the capacity region of a Gaussian interference network is an open problem in information theory. Recent progress on this problem has led to the characterization of the capacity region of a general two user Gaussian interference channel within one bit. In this paper, we develop new, improved outer bounds on the capacity region. Using these bounds, we show that treating interference as noise achieves the sum capacity of the two user Gaussian interference channel in a low interference regime, where the interference parameters are below certain thresholds. We then generalize our techniques and results to Gaussian interference networks with more than two users. In particular, we demonstrate that the total interference threshold, below which treating interference as noise achieves the sum capacity, increases with the number of users.

Abstract—Consider a K-user interference channel with timevarying fading. At any particular time, each receiver will see a signal from most transmitters. The standard approach to such a scenario results in each transmitter-receiver pair achieving a rate proportional to 1 the single user rate. However, given two K well chosen time indices, the channel coefficients from interfering users can be made to exactly cancel. By adding up these two signals, the receiver can see an interference-free version of the desired transmission. We show that this technique allows each user to achieve at least half its interference-free ergodic capacity at any SNR. Prior work was only able to show that half the interference-free rate was achievable as the SNR tended to infinity. We examine a finite field channel model and a Gaussian channel model. In both cases, the achievable rate region has a simple description and, in the finite field case, we prove it is the ergodic capacity region. I.

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The degrees-of-freedom of a K-user 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 degrees-of-freedom 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 non-zero rational numbers. More specifically, for all K> 2, we find a class of K-user GIFCs that is dense in the GIFC parameter space for which K/2 degrees-offreedom are exactly achievable, and we show that the degrees-of-freedom for any GIFC with non-zero rational coefficients is strictly smaller than K/2. These results are proved using new connections with number theory and additive combinatorics. 1

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Previous work showed that the 2×2×2 interference channel, i.e., the multihop interference network formed by concatenation of two 2-user interference channels, achieves the min-cut outer bound value of 2 DoF. This work studies the 2×2×2 interference channel with one additional assumption that two relays interfere with each other. It is shown that even in the presence of the interfering links between two relays, the min-cut outer bound of 2 DoF can still be achieved for almost all values of channel coefficients, for both fixed or time-varying channel coefficients. The achievable scheme relies on the idea of aligned interference neutralization as well as exploiting memory at source and relay nodes.

An Interference Channel with Generalized Feedback (IFC-GF) is a model for a wireless network where several source-destination 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 two-part paper we study achievable strategies and outer bounds for a general IFC-GF with two source-destination 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 beam-forming of a distributed multi-antenna system–and (b) to hide the messages that can not be decoded at the non-intended destination–thus leveraging the interference “pre-cancellation” property of dirty-paper-type coding. We show that our achievable region generalizes several known achievable regions for IFC-GF and that it reduces

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