Optimality of Treating Interference as Noise: A Combinatorial Perspective

For single-antenna Gaussian interference channels, we reformulate the problem of determining the generalized degrees of freedom (GDoF) region achievable by treating interference as Gaussian noise (TIN) derived by Geng et al. from a combinatorial optimization perspective. We show that the TIN power control problem can be cast into an assignment problem, such that the globally optimal power allocation variables can be obtained by well-known polynomial time algorithms (e.g., centralized Hungarian method or distributed Auction algorithm). Furthermore, the expression of the TIN-achievable GDoF region (TINA region) can be substantially simplified with the aid of maximum weighted matchings. We also provide conditions under which the TINA region is a convex polytope that relax those by Geng et al. For these new conditions, together with a channel connectivity (i.e., interference topology) condition, we show TIN optimality for a new class of interference networks that is not included, nor includes, the class found by Geng et al. Building on the above insights, we consider the problem of joint link scheduling and power control in wireless networks, which has been widely studied as a basic physical layer mechanism for device-to-device communications. Inspired by the relaxed TIN channel strength condition as well as the assignment-based power allocation, we propose a low-complexity GDoF-based distributed link scheduling and power control mechanism (ITLinQ+) that improves upon the ITLinQ scheme proposed by Naderializadeh and Avestimehr and further improves over the heuristic approach known as FlashLinQ. It is demonstrated by simulation that ITLinQ+ without power control provides significant average network throughput gains over both ITLinQ and FlashLinQ, and yet still maintains the same level of implementation complexity. Furthermore, when ITLinQ+ is augmented by power control, it provides an energy efficiency substantially larger than that of ITLinQ and FlashLinQ, at the cost of additional complexity and some signaling overhead.