Raul Hernan Etkin

Gaussian Interference Channel Capacity to Within One Bit

The capacity of the two-user 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 signal-to-noise ratio (SNR) regimes. Using our results, we provide a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios.

Spectrum sharing for unlicensed bands

We study a spectrum sharing problem in an unlicensed band where multiple systems coexist and interfere with each other. Due to asymmetries and selfish system behavior, unfair and inefficient situations may arise. We investigate whether efficiency and fairness can be obtained with self-enforcing spectrum sharing rules. These rules have the advantage of not requiring a central authority that verifies compliance to the protocol. Any self-enforcing protocol must correspond to an equilibrium of a game. We first analyze the possible outcomes of a one shot game, and observe that in many cases an inefficient solution results. However, systems often coexist for long periods and a repeated game is more appropriate to model their interaction. In this repeated game the possibility of building reputations and applying punishments allows for a larger set of self-enforcing outcomes. When this set includes the optimal operating point, efficient, fair, and incentive compatible spectrum sharing becomes possible. We present examples that illustrate that in many cases the performance loss due to selfish behavior is small. We also prove that our results are tight and quantify the best achievable performance in a non-cooperative scenario

Degrees of freedom in some underspread MIMO fading channels

Consider a multiple-input multiple-output (MIMO) fading channel in which the fading process varies slowly over time. Assuming that neither the transmitter nor the receiver have knowledge of the fading process, do multiple transmit and receive antennas provide significant capacity improvements at high signal-to-noise ratio (SNR)? For regular fading processes, recent results show that capacity ultimately grows doubly logarithmically with the SNR independently of the number of transmit and receive antennas used. We show that for the Gauss-Markov fading process in all regimes of practical interest the use of multiple antennas provides large capacity improvements. Nonregular fading processes show completely different high-SNR behaviors due to the perfect predictability of the process from noiseless observations. We analyze the capacity of MIMO channels with nonregular fading by presenting a lower bound, which we specialize to the case of band-limited slowly varying fading processes to show that the use of multiple antennas is still highly beneficial. In both cases, regular and nonregular fading, this capacity improvement can be seen as the benefit of having multiple spatial degrees of freedom. For the Gauss-Markov fading model and all regimes of practical interest, we present a communication scheme that achieves the full number of degrees of freedom of the channel with tractable complexity. Our results for underspread Gauss-Markov and band-limited nonregular fading channels suggest that multiple antennas are useful at high SNR.

The Degrees-of-Freedom of the

The degrees-of-freedom of a K-user Gaussian interference channel (GIC) has been defined to be the multiple of (1/2)log 2 P at which the maximum sum of achievable rates grows with increasing power P. In this paper, we establish that the degrees-of-freedom of three or more user, real, scalar GICs, 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 K-user GICs that is dense in the GIC parameter space for which K/2 degrees-of-freedom are exactly achievable, and we show that the degrees-of-freedom for any GIC with nonzero rational coefficients is strictly smaller than K/2. These results are proved using new connections with number theory and additive combinatorics.

K

The degrees-of-freedom of a K-user Gaussian interference channel (GIFC) has been defined to be the multiple of (1/2) log2 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-of-freedom 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.

-User Gaussian Interference Channel Is Discontinuous at Rational Channel Coefficients

The capacity of the two-user Gaussian interference channel has been open for thirty years. The understanding on this problem has been limited. The best known achievable region is due to Han-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 simplified Han-Kobayashi type scheme can achieve to within a single bit the capacity for all values of the channel parameters. We also show that the scheme is asymptotically optimal at certain high SNR regimes. Using our results, we provide a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios

On the Degrees-of-Freedom of the K-user Gaussian interference channel

We present an experimental performance evaluation study of WiFi links in an open-space outdoor environment. We consider a large scale wireless sensor network scenario of seismic data collection from sensors that are buried in ground and a set of access points (APs) form the hierarchical aggregation layer and the backbone of the network. We conduct two different link characterization studies. First, we evaluate the links between the sensor nodes and a wireless AP using IEEE 802.11a/b/g. We construct the path loss model and investigate the reachability distance of this link for different protocols and different sensor node antenna heights. We then characterize the long distance wireless backhaul links between the APs. We use 802.11n and high gain directional antenna for high throughput and long distance. We evaluate how different PHY and MAC layer enhancements of 802.11n impacts its performance in an open outdoor environment. We observed up to 148 Mb/s throughput at 800 meter line-of-sight links without sophisticated tuning of antenna orientation. We believe our findings can be a benchmark for WiFi based outdoor network deployment, especially for high throughput long distance links.

Gaussian Interference Channel Capacity to Within One Bit: the Symmetric Case

The characterization of the capacity region of the two-user Gaussian interference channel has been an open problem for thirty years. The understanding on this problem has been limited. The best known achievable region is due to Han-Kobayashi but its characterization is very complicated. It is also not known how tight the existing outer bounds are. In this work, we extend our results of [1] to general (i.e. possibly asymmetric) channels for the complete capacity region. 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 simplified Han-Kobayashi type scheme can achieve to within a single bit the capacity for all values of the channel parameters. Using our results, we provide a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios.

Characterizing WiFi link performance in open outdoor networks

The capacity or approximations to capacity of various single-source single-destination relay network models has been characterized in terms of the cut-set upper bound. In principle, a direct computation of this bound requires evaluating the cut capacity over exponentially many cuts. We show that the minimum cut capacity of a relay network under some special assumptions can be cast as a minimization of a submodular function, and as a result, can be computed efficiently. We use this result to show that the capacity, or an approximation to the capacity within a constant gap for the Gaussian, wireless erasure, and Avestimehr-Diggavi-Tse deterministic relay network models can be computed in polynomial time. We present some empirical results showing that computing constant-gap approximations to the capacity of Gaussian relay networks with around 300 nodes can be done in order of minutes. For Gaussian networks, cut-set capacities are also functions of the powers assigned to the nodes. We consider a family of power optimization problems and show that they can be solved in a polynomial time. In particular, we show that the minimization of the sum of powers assigned to the nodes subject to a minimum rate constraint (measured in terms of cut-set bounds) can be computed in the polynomial time. We propose a heuristic algorithm to solve this problem and measure its performance through simulations on random Gaussian networks. We observe that in the optimal allocations, most of the power is assigned to a small subset of relays, which suggests that network simplification may be possible without excessive performance degradation.

Gaussian Interference Channel Capacity to Within One Bit: the General Case

We explore the design of a high capacity multi-radio wireless network using commercial 802.11n hardware. We first use extensive real-life experiments to evaluate the performance of closely located 802.11n radios. We discover that even when tuned to orthogonal channels, co-located 802.11n radios interfere with each other and achieve significantly less throughput than expected. Our analysis reveals that the throughput degradation is caused by three link-layer effects: (i) triggering of carrier sensing, (ii) out of band collisions and (iii) unintended frequency adaptation. Using physical layer statistics, we observe that these effects are caused by fundamental limitations of co-located radios in achieving signal isolation. We then consider the use of beamforming antennas, shielding and antenna separation distance to achieve better signal isolation and to mitigate these problems. Our work profiles the gains of different physical isolation approaches and provides insights to network designers to realize high-performance wireless networks without requiring synchronization or protocol modifications.