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

Abstract

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). It is assumed that the transmitted signals have circularly symmetric complex Gaussian distributions and are independent over time. 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, which serves as a performance benchmark for existing heuristic algorithms.

Revenue Sharing Based Resource Allocation for Dynamic Spectrum Access Networks

“…At each AP , the PU's minimum throughput is ,min 0 = 2Mbps, and its maximum throughput is ,max 0 = 15Mbps. We use a distance-based model, which is similar to [33], to determine the channel gain from the PU (or each SU) to different APs. Specifically, the channel gain from the PU to AP is quantified by 0 = ||¯0 || 2 ( 0 ) 3 , where 0 denotes the distance between the PU and AP , and the random parameter¯0 follows the identical and independent Gaussian distribution with zero mean and unit variance.…”

“…The iteration process continues until we find the best vertex that falls within (or close enough to) the feasible region of the optimization problem, and this best vertex can be considered as the optimal solution. Although it is still an open question to quantify the computational complexity of PA algorithm, the PA algorithm is shown to be able to solve the monotonic optimization problems efficiently [33], [34]. The monotonic structure of Problem (PNO-P-Rate') in Lemma 5 enables us to adopt the PA algorithm to solve Problem (PNO-P-Rate') efficiently, under the given set Ω 1 and set Ω 2 .…”

Optimal Resource Allocation in Coordinated Multi-Cell Systems

“…17 This line-search approach was suggested in [218,274,275] and utilized for multi-cell resource allocation with single-antenna interference channels in [206], coordinated MISO beamforming in [153,276], and general multi-cell MISO systems in [26]. Other types of curves r(τ ) can also be used to capture certain properties of f (·) -one should always try to utilize any structure that exists in the problem.…”

“…Output: Final interval [f min ,f max ] on optimal value; Output: Feasible point g * ε = g feasible with f min = f (g * ε ); coordinated beamforming in [153,276]. The convergence of the PA algorithm to the global optimum is established by the following theorem.…”

Coordinated Linear Precoding in Downlink Multicell MU-MISO OFDMA Networks

“…Though the beamforming design methods presented in [3], [4] achieve optimum capacity, these methods may be practically inapplicable since the complexity evolves exponentially with the optimization problem size. Therefore, computationally inexpensive suboptimal beamforming design is very appealing.…”