Successive Convex Approximation Algorithm Research Articles

Feasible Point Pursuit and Successive Approximation of Non-Convex QCQPs

Quadratically constrained quadratic programs (QCQPs) have a wide range of applications in signal processing and wireless communications. Non-convex QCQPs are NP-hard in general. Existing approaches relax the non-convexity using semi-definite relaxation (SDR) or linearize the non-convex part and solve the resulting convex problem. However, these techniques are seldom successful in even obtaining a feasible solution when the QCQP matrices are indefinite. In this paper, a new feasible point pursuit successive convex approximation (FPP-SCA) algorithm is proposed for non-convex QCQPs. FPP-SCA linearizes the non-convex parts of the problem as conventional SCA does, but adds slack variables to sustain feasibility, and a penalty to ensure slacks are sparingly used. When FPP-SCA is successful in identifying a feasible point of the non-convex QCQP, convergence to a Karush-Kuhn-Tucker (KKT) point is thereafter ensured. Simulations show the effectiveness of our proposed algorithm in obtaining feasible and near-optimal solutions, significantly outperforming existing approaches.

Outage-Constrained Coordinated Beamforming With Opportunistic Interference Cancellation

In this paper, interference management is considered for the K-user multiple-input single-output (MISO) block-faded interference channel. It is assumed that perfect channel state information (CSI) can be obtained at the receivers, whereas only channel distribution information (CDI) is available to the transmitters. Furthermore, the receivers are assumed to be capable of implementing opportunistic interference cancellation (OIC). Based on these assumptions, the beamforming design problem for the MISO interference channel under consideration is formulated as a rate utility maximization problem under outage constraints and individual power constraints. By implementing OIC at the receivers, the outage probability is expected to be reduced, leading to a potential improvement on the utility value. However, this flexibility complicates the outage constraint, resulting in an optimization problem that is non-convex and difficult to handle. We propose a successive convex approximation (SCA) method that employs first-order approximation techniques and semi-definite relaxation (SDR) to efficiently obtain an approximate beamforming solution to this problem. Our proposed SCA algorithm has been shown to yield solutions that are stationary points of the original beamforming design problem. Furthermore, a decentralized version of the SCA algorithm is proposed, in which only local CDI and a limited amount of information exchange between transmitters are required. Our simulation results demonstrate that both of our proposed algorithms achieve near-optimal performance for the two-user case, and that enabling the receivers to implement OIC indeed improves the system performance by as large as 260% at high signal-to-noise ratios when user fairness is considered.

Joint Cooperative Beamforming and Artificial Noise Design for Secrecy Sum Rate Maximization in Two-Way AF Relay Networks

In this letter, a joint design of cooperative beamforming (CB) and artificial noise (AN) is proposed for two-way amplify-and-forward (AF) relay networks to improve the security of the date exchange. Based on secrecy sum rate maximization (SSRM) criterion, such joint design problem under individual relay power constraints is mathematically hard due to the non-convex objective function. By utilizing the semidefinite relaxation (SDR) technique and successive convex approximation (SCA) algorithm, we efficiently develop a stationary point for the original SSRM design problem. Proof is also given to show that SDR is always tight and yields a rank-one solution. Simulations are presented to validate the efficiency and merits of our proposed joint CB and AN design in enhancing the secrecy sum rate.

Joint Beamforming and User Selection in Multicast Downlink Channel under Secrecy-Outage Constraint

In this letter, we study the beamforming and user selection problem in multicast MISO wiretap-channel, where a base station (BS) with Nt antennas broadcasts a common confidential message to M legitimate users (Bobs) and N unauthorized users (Eves) attempt to eavesdrop the message. We target at maximizing the minimum secrecy-outage rate of Bobs and propose an iterative successive convex approximation (SCA) algorithm to tackle the original nonconvex problem. We further develop joint semidefinite programming (SDP) and SCA algorithm to find a feasible subset where legitimate users are guaranteed to their requirements. Simulation results are provided to evaluate the proposed approaches.

Coordinated Beamforming for Multiuser MISO Interference Channel Under Rate Outage Constraints

This paper studies the coordinated beamforming design problem for the multiple-input single-output (MISO) interference channel, assuming only channel distribution information (CDI) at the transmitters. Under a given requirement on the rate outage probability for receivers, we aim to maximize the system utility (e.g., the weighted sum rate, weighted geometric mean rate, and the weighed harmonic mean rate) subject to the rate outage constraints and individual power constraints. The outage constraints, however, lead to a complicated, nonconvex structure for the considered beamforming design problem and make the optimization problem difficult to handle. {Although} this nonconvex optimization problem can be solved in an exhaustive search manner, this brute-force approach is only feasible when the number of transmitter-receiver pairs is small. For a system with a large number of transmitter-receiver pairs, computationally efficient alternatives are necessary. The focus of this paper is hence on the design of such efficient approximation methods. In particular, by employing semidefinite relaxation (SDR) and first-order approximation techniques, we propose an efficient successive convex approximation (SCA) algorithm that provides high-quality approximate beamforming solutions via solving a sequence of convex approximation problems. The solution thus obtained is further shown to be a stationary point for the SDR of the original outage constrained beamforming design problem. {Furthermore}, we propose a distributed SCA algorithm where each transmitter optimizes its own beamformer using local CDI and information obtained from limited message exchange with the other transmitters. Our simulation results demonstrate that the proposed SCA algorithm and its distributed counterpart indeed converge, and near-optimal performance can be achieved for all the considered system utilities.