On the High-SNR Capacity of the Gaussian Interference Channel and New Capacity Bounds

The best outer bound on the capacity region of the two-user Gaussian Interference Channel (GIC) is known to be the intersection of regions of various bounds including genie-aided outer bounds, in which a genie provides noisy input signals to the intended receiver. The Han and Kobayashi (HK) scheme provides the best known inner bound. The rate difference between the best known lower and upper bounds on the sum capacity remains as large as 1 bit per channel use especially around $g^2=P^{-1/3}$, where $P$ is the symmetric power constraint and $g$ is the symmetric real cross-channel coefficient. In this paper, we pay attention to the \emph{moderate interference regime} where $g^2\in (\max(0.086, P^{-1/3}),1)$. We propose a new upper-bounding technique that utilizes noisy observation of interfering signals as genie signals and applies time sharing to the genie signals at the receivers. A conditional version of the worst additive noise lemma is also introduced to derive new capacity bounds. The resulting upper (outer) bounds on the sum capacity (capacity region) are shown to be tighter than the existing bounds in a certain range of the moderate interference regime. Using the new upper bounds and the HK lower bound, we show that $R_\text{sym}^*=\frac{1}{2}\log \big(|g|P+|g|^{-1}(P+1)\big)$ characterizes the capacity of the symmetric real GIC to within $0.104$ bit per channel use in the moderate interference regime at any signal-to-noise ratio (SNR). We further establish a high-SNR characterization of the symmetric real GIC, where the proposed upper bound is at most $0.1$ bit far from a certain HK achievable scheme with Gaussian signaling and time sharing for $g^2\in (0,1]$. In particular, $R_\text{sym}^*$ is achievable at high SNR by the proposed HK scheme and turns out to be the high-SNR capacity at least at $g^2=0.25, 0.5$.Comment: Submitted to IEEE Transactions on Information Theory on June 2015, revised on November 2016, and accepted for publication on Feb. 28, 201

Achieving Global Optimality for Weighted Sum-Rate Maximization in the K-User Gaussian Interference Channel with Multiple Antennas

Characterizing the global maximum of weighted sum-rate (WSR) for the K-user Gaussian interference channel (GIC), with the interference treated as Gaussian noise, is a key problem in wireless communication. However, due to the users' mutual interference, this problem is in general non-convex and thus cannot be solved directly by conventional convex optimization techniques. In this paper, by jointly utilizing the monotonic optimization and rate profile techniques, we develop a new framework to obtain the globally optimal power control and/or beamforming solutions to the WSR maximization problems for the GICs with single-antenna transmitters and single-antenna receivers (SISO), single-antenna transmitters and multi-antenna receivers (SIMO), or multi-antenna transmitters and single-antenna receivers (MISO). Different from prior work, this paper proposes to maximize the WSR in the achievable rate region of the GIC directly by exploiting the facts that the achievable rate region is a "normal" set and the users' WSR is a "strictly increasing" function over the rate region. Consequently, the WSR maximization is shown to be in the form of monotonic optimization over a normal set and thus can be solved globally optimally by the existing outer polyblock approximation algorithm. However, an essential step in the algorithm hinges on how to efficiently characterize the intersection point on the Pareto boundary of the achievable rate region with any prescribed "rate profile" vector. This paper shows that such a problem can be transformed into a sequence of signal-to-interference-plus-noise ratio (SINR) feasibility problems, which can be solved efficiently by existing techniques. Numerical results validate that the proposed algorithms can achieve the global WSR maximum for the SISO, SIMO or MISO GIC.Comment: This is the longer version of a paper to appear in IEEE Transactions on Wireless Communication