Conference Paper

# On the degrees-of-freedom of the MIMO interference channel

Lincoln Lab., MIT, Lexington, MA

DOI: 10.1109/CISS.2008.4558496 Conference: Information Sciences and Systems, 2008. CISS 2008. 42nd Annual Conference on Source: IEEE Xplore

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**ABSTRACT:**The N+1 user, 1 × N single input multiple output (SIMO) Gaussian interference channel where each transmitter has a single antenna and each receiver has N antennas is studied. The symmetric capacity within O(1) is characterized for the symmetric case where all direct links have the same signal-to-noise ratio (SNR) and all undesired links have the same interference-to-noise ratio (INR). The gap to the exact capacity IS a constant which iS independent of SNR and INR. On the achievability side, an interesting conclusion is that the generalized degrees of freedom (GDOF) regime where treating interference as noise is found to be optimal in the 2 user interference channel, does not appear in the N + 1 user, 1 × N SIMO case. On the converse side, new multi-user outer bounds emerge out of this work that do not follow directly from the 2 user case. We also provide an outer bound on the capacity region of the 3 user SIMO Gaussian interference channel with 2 antennas at each receiver. This outer bound directly leads to the capacity region of this channel if the channel vectors satisfy certain conditions.IEEE Transactions on Information Theory 04/2011; 57(4):1932-1958. · 2.62 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The paper establishes the optimal generalized degrees of freedom (GDOF) of 3-user $M \times N$ multiple-input multiple-output (MIMO) Gaussian interference channel (GIC) in which each transmitter has $M$ antennas and each receiver has $N$ antennas. A constraint of $2M \leq N$ is imposed so that random coding with message-splitting achieves the optimal GDOF. Unlike symmetric case, two cross channels to unintended receivers from each transmitter can have different strengths, and hence, well known Han-Kobayashi common-private message splitting would not achieve the optimal GDOF. Instead, splitting each user's message into three parts is shown to achieve the optimal GDOF. The capacity of the corresponding deterministic model is first established which provides systematic way of determining side information for converse. Although this deterministic model is philosophically similar to the one considered by Gou and Jafar, additional constraints are imposed so that capacity description of the deterministic model only contains the essential terms for establishing the GDOF of Gaussian case. Based on this, the optimal GDOF of Gaussian case is established with $\mathcal{O}(1)$ capacity approximation. The behavior of the GDOF is interestingly different from that of the corresponding symmetric case. Regarding the converse, several multiuser outer bounds which are suitable for asymmetric case are derived by non-trivial generalization of the symmetric case.07/2012; - [Show abstract] [Hide abstract]

**ABSTRACT:**It has been shown recently by Geng et al. that in a $K$ user Gaussian interference network, if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all signal strengths measured in dB scale), then power control and treating interference as noise (TIN) is sufficient to achieve the entire generalized degrees of freedom (GDoF) region. Motivated by the intuition that the deterministic model of Avestimehr et al. (ADT deterministic model) is particularly suited for exploring the optimality of TIN, the results of Geng et al. are first re-visited under the ADT deterministic model, and are shown to directly translate between the Gaussian and deterministic settings. Next, we focus on the extension of these results to parallel interference networks, from a sum-capacity/sum-GDoF perspective. To this end, we interpret the explicit characterization of the sum-capacity/sum-GDoF of a TIN optimal network (without parallel channels) as a minimum weighted matching problem in combinatorial optimization, and obtain a simple characterization in terms of a partition of the interference network into vertex-disjoint cycles. Aided by insights from the cyclic partition, the sum-capacity optimality of TIN for $K$ user parallel interference networks is characterized for the ADT deterministic model, leading ultimately to corresponding GDoF results for the Gaussian setting. In both cases, subject to a mild invertibility condition the optimality of TIN is shown to extend to parallel networks in a separable fashion.01/2014;

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