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

**ABSTRACT** The high signal-to-noise ratio capacity of the symmetric MIMO interference channel is characterized as a function of the interference-to-noise ratio. This work is a multiple antenna extension of the degrees of freedom expressions derived by Etkin et al. for the single antenna case. This characterization considers the case where the number of receive antennas is greater than or equal to the number of transmit antennas and shows the number of degrees of freedom available for communication as a function of log(INR)/log(SNR).

- [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. - [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; DOI:10.1109/ISIT.2013.6620397 -
##### Conference Paper: Aligned interference neutralization and the degrees of freedom of the 2 × 2 × 2 interference channel

[Show abstract] [Hide abstract]

**ABSTRACT:**We show that the 2 × 2 × 2 interference network, 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, for almost all values of channel coefficients, for both time-varying or fixed channel coefficients. The key to this result is a new idea, called aligned interference neutralization, that provides a way to align interference terms over each hop in a manner that allows them to be cancelled over the air at the last hop.Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on; 09/2011