Research On Energy-Efficient Optimization Problem In Interference Channels

Interference channel system refers to a system in which multiple links coexists under the same frequency. Many practical communication systems can be regarded as interference chan-nel systems, such as D2D system, wireless sensor networks, femtocells and heterogeneous net-works, etc. The interference exists among the links will waste lots of energy. Hence, how to handle the interference to enhance the system energy efficiency is very important. This paper fo-cuses on the research on the energy efficiency optimization for the interference channel systems. The main contributions are listed below.Firstly, a distributed adaptive-pricing algorithm aiming at solving the weighted sum energy efficiency maximization problem for SISO interference channels is proposed. The distributed algorithm is strictly proved to converge to the Karush-Kuhn-Tucker (KKT) point of the prob-lem. To reduce the feedback overhead of the distributed algorithm, we also provide a method to implement the distributed algorithm with limited information exchange. Specifically, we assume each receiver only broadcasts the necessary information to its nearby transmitters. Sim-ulation results show that the proposed algorithm degrades gracefully when decreasing overhead of information exchange. In addition, we provide a centralized algorithm based on gradient projection combined with the Armijo rule, which is served as the performance benchmark for the proposed distributed algorithm. Simulation results show the proposed distributed algorithm converges fast and its performance is comparable with the centralized algorithm.Secondly, a distributed adaptive-pricing algorithm aiming at solving the weighted sum ener-gy efficiency maximization problem for MISO interference channels is proposed. The main idea of this algorithm is two-fold:1)Each user adaptively adjusts its own pricing factor and broad-casts it to all the other links in the network. After collecting all these prices, each user maximizes its own EE minus the interference cost; 2) Each user sequentially updates its own beam-vector. For 1), differently from the case of SISO, in the case of MISO each user not only maximizes its transmit power, but also its beam direction. This paper decomposes the beam-vector into two parts (beam direction and transmit power) and optimizes them respectively. Depending on the rank of each user’s leakage matrix, we divide each user’s beamforming optimization problem into two scenarios, for both of which we provide a near-optimal closed-form of the beam-vector. For the power allocation in the case of full rank, the closed-form optimal power allocation solu-tion is provided, while for the case of the non-full rank, the power allocation problem contains two variables. By solving the KKT equations of the problem, we also provide the globally opti- mal solution of the problem. For 2), we prove that when each user sequentially updates its own beam-vector, the algorithm is guaranteed to converge. We provide a centralized algorithm based on the gradient projection combined with the Armijo rule to solve the WS-EE maximization. It can serve as the performance benchmark for our proposed distributed algorithm.Thirdly, we study the non-cooperative EE optimization in MIMO interference channel sys-tem. The main work is as follows:1) This problem is modeled as a noncooperative game where each MIMO link competes against the others by choosing its transmit covariance matrix to maximize its own EE. We show that the NE of this game always exists and derive sufficient conditions for the uniqueness of the NE for the case of large enough transmit power constraint; 2) To reach the NE of the game, we provide a totally distributed EE algorithm named Asyn-chronous Distributed Energy-Efficient (ADEE) algorithm. The merits of this algorithms are: all users can update their transmit covariance matrices in a totally asynchronous way, that is some links may update their transmit covariance matrices more frequently than the others and they may even use the outdated information of the measurement of the interference generated by the other links. In addition, during the updating procedure of the algorithm, there is no need for the links to exchange the signaling overhead mutually. These features make our distributed algorithm more appealing for practical implementations; 3) We provide the sufficient condition-s for the global convergence of this algorithm to the unique NE of the game; 4) We study the impact of the circuit power consumption on the overall SE and EE performance of the system for one special case when the links are separated sufficiently far away. We show that the overall SE increases with the circuit power consumption, but the overall EE decreases with it; 5) The tradeoff between SE and EE is investigated for the proposed algorithm for two special cases are studied:the transmit power constraint approaches zero or infinity.Fourthly, we consider the power minimization problem for the cognitive interference chan-nels, subject to rate demands at the SUs as well as the interference constraints imposed by pri-mary users. The main work is as follows:1) Discuss the feasibility of this problem and provide a novel method to verify the feasibility of this power minimization problem. Specifically, this paper introduces an alternative optimization problem with an auxiliary variable. If the optimal variable is no less than 1, the original problem is feasible; otherwise, it is infeasible. This alter-native problem is always feasible, and the optimal auxiliary variable can be achieved through alternatively optimizing’Power control problem’and’Beam direction optimization problem’. The first power control problem means that given beam directions of all beam-vectors, we op-timize the power allocation on these beam-vectors. This problem is a SP (signomial program-ming) problem, which can be solved by a sequence of GP problems. The second beam direction optimization problem can be transformed into a convex problem, which can be solved by the dual-decomposition-based method; 2) For the feasible problem, one iterative algorithm is pro-posed to solve the power minimization problem. Similarly to phase Ⅰ, we also divide the PM problem into two subproblems:beam direction updating and power allocation optimization. We strictly prove that the iterative algorithm will finally converge to a KKT point of the PM problem.