We consider the problem of maximizing the energy efficiency (EE) for a MIMO interference channel (IC), with the power constraint on each link. To obtain totally distributed solutions, this problem is formulated as a noncooperative game. We show that this game always admits a Nash equilibra (NE). Importantly, the sufficient condition that one can check to guarantee the uniqueness of the NE is derived. To reach the NE of this game, we provide a totally distributed EE algorithm, in which each player employs the fractional programming to update his own solution. These updates can be performed in a completely distributed and asynchronous fashion. Sufficient conditions that guarantee the convergence of the algorithm have been given as well. Simulation results show that the proposed algorithm converges fast and significantly outperforms the existing algorithms in terms of the sum-EE or the sum-rate.
In contrast to the most of the above cited papers which focus on the (weighted) sum SE problem, in this work we consider the EE maximization problem. For SE optimization problems, it is known that all the transmitters use full power during transmission in order to maximize its own SE. Based on this fact, the best response strategy at the NE can be written in a closed-form water-filling solution, which can be interpreted as a projector on the convex and closed set. This interpretation enables the authors to derive the uniqueness of the game's NE @cite_49 . However, the study of EE maximization problem cannot be obtained by employing the methodologies since the transmitters in fact use a portion of the power, instead of full, to achieve energy efficient transmission.
@cite_49
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Characterizing the fundamental tradeoffs for maximizing energy efficiency (EE) versus spectrum efficiency (SE) is a key problem in wireless communication. In this paper, we address this problem for a point-to-point additive white Gaussian noise (AWGN) channel with the transmitter powered solely via energy harvesting from the environment. In addition, we assume a practical on-off transmitter model with non-ideal circuit power, i.e., when the transmitter is on, its consumed power is the sum of the transmit power and a constant circuit power. Under this setup, we study the optimal transmit power allocation to maximize the average throughput over a finite horizon, subject to the time-varying energy constraint and the non-ideal circuit power consumption. First, we consider the off-line optimization under the assumption that the energy arrival time and amount are a priori known at the transmitter. Although this problem is non-convex due to the non-ideal circuit power, we show an efficient optimal solution that in general corresponds to a two-phase transmission: the first phase with an EE-maximizing on-off power allocation, and the second phase with a SE-maximizing power allocation that is non-decreasing over time, thus revealing an interesting result that both the EE and SE optimizations are unified in an energy harvesting communication system. We then extend the optimal off-line algorithm to the case with multiple parallel AWGN channels, based on the principle of nested optimization. Finally, inspired by the off-line optimal solution, we propose a new online algorithm under the practical setup with only the past and present energy state information (ESI) known at the transmitter. We consider the minimization of the transmission completion time with a battery limited energy harvesting transmitter in an M-user AWGN broadcast channel where the transmitter is able to harvest energy from the nature, using a finite storage capacity rechargeable battery. The harvested energy is modeled to arrive (be harvested) at the transmitter during the course of transmissions at arbitrary time instants. The transmitter has fixed number of packets for each receiver. Due to the finite battery capacity, energy may overflow without being utilized for data transmission. We derive the optimal offline transmission policy that minimizes the time by which all of the data packets are delivered to their respective destinations. We analyze the structural properties of the optimal transmission policy using a dual problem. We find the optimal total transmit power sequence by a directional water-filling algorithm. We prove that there exist M-1 cut-off power levels such that user i is allocated the power between the i-1st and the ith cut-off power levels subject to the availability of the allocated total power level. Based on these properties, we propose an algorithm that gives the globally optimal offline policy. The proposed algorithm uses directional water-filling repetitively. Finally, we illustrate the optimal policy and compare its performance with several suboptimal policies under different settings. In this paper, we investigate the transmission completion time minimization problem in an additive white Gaussian noise (AWGN) broadcast channel, where the transmitter is able to harvest energy from the nature, using a rechargeable battery. The harvested energy is modeled to arrive at the transmitter during the course of transmissions. The transmitter has a fixed number of packets to be delivered to each receiver. The objective is to minimize the time by which all of the packets are delivered to their respective destinations. To this end, we optimize the transmit powers and transmission rates in a deterministic setting. We first analyze the structural properties of the optimal transmission policy in a two-user broadcast channel via the dual problem of maximizing the departure region by a fixed time T. We prove that the optimal total transmit power sequence has the same structure as the optimal single-user transmit power sequence in . In addition, the total power is split optimally based on a cut-off power level; if the total transmit power is lower than this cut-off level, all transmit power is allocated to the stronger user; otherwise, all transmit power above this level is allocated to the weaker user. We then extend our analysis to an M-user broadcast channel. We show that the optimal total power sequence has the same structure as the two-user case and optimally splitting the total power among M users involves M-1 cut-off power levels. Using this structure, we propose an algorithm that finds the globally optimal policy. Our algorithm is based on reducing the broadcast channel problem to a single-user problem as much as possible. Finally, we illustrate the optimal policy and compare its performance with several suboptimal policies under different settings. In this paper, we study resource allocation for a multicarrier-based cognitive radio (CR) network. More specifically, we investigate the problem of secondary users’ energy-efficiency (EE) maximization problem under secondary total power and primary interference constraints. First, assuming cooperation among the secondary base stations (BSs), a centralized approach is considered to solve the EE optimization problem for the CR network where the primary and secondary users are using either orthogonal frequency-division multiplexing (OFDM) or filter bank based multicarrier (FBMC) modulations. We propose an alternating-based approach to solve the joint power-subcarrier allocation problem. More importantly, in the first place, subcarriers are allocated using a heuristic method for a given feasible power allocation. Then, we conservatively approximate the nonconvex power control problem and propose a joint successive convex approximation-Dinkelbach algorithm (SCADA) to efficiently obtain a solution to the nonconvex power control problem. The proposed algorithm is shown to converge to a solution that coincides with the stationary point of the original nonconvex power control subproblem. Moreover, we propose a dual decomposition-based decentralized version of the SCADA. Second, under the assumption of no cooperation among the secondary BSs, we propose a fully distributed power control algorithm from the perspective of game theory. The proposed algorithm is shown to converge to a Nash-equilibrium (NE) point. Moreover, we propose a sufficient condition that guarantees the uniqueness of the achieved NE. Extensive simulation analyses are further provided to highlight the advantages and demonstrate the efficiency of our proposed schemes.