Renewable Energy Scheduling for Fading Channels with Maximum Power Constraint Zhe Wang Electrical Engineering Department Columbia University New York, NY 10027 Email: zhewang@ee.columbia.edu Vaneet Aggarwal AT&T Labs-Research Florham Park, NJ 07932 Email: vaneet@alumni.princeton.edu Xiaodong Wang Electrical Engineering Department Columbia University New York, NY 10027 Email: wangx@ee.columbia.edu Abstract—In this paper, we develop efficient algorithm to obtain the optimal energy schedule for fading channel with energy harvesting. We assume that the side information of both the channel states and energy harvesting states for K time slots is known a priori, and the battery capacity and the maximum transmission power in each time slot are limited. To obtain the achievable transmission rate, we formulate a convex optimization problem with O(K) constraints. Since the compu- tational complexity of a generic convex solver is exponential in the number of constraints, it is hard to solve using a general convex solver and this paper gives an efficient energy scheduling algorithm, called the dynamic water-filling algorithm, obtaining the optimal energy schedule within a computational complexity of O(K 2 ). Indifferent to the traditional water-filling algorithm, the water level in dynamic water-filling is not constant but changes when the battery overflows or depletes. Moreover, the numerical results show that the proposed algorithm achieves the optimal performance, providing a significant improvement from the traditional native scheduling policies. I. I NTRODUCTION The employment of the renewable energy source has grown from long-established concepts into devices for powering ubiquitously deployed sensor networks and mobile electron- ics, prolonging the lifetime of a transmitter [1], [2]. How- ever, many challenging research issues arise from the new paradigm of communication powered by harvested energy. In particular, the maximum achievable rate under the dynamic energy constraints is one fundamental problem, especially for the case of fading channel [3]. This paper addresses this by developing an optimal energy scheduling algorithm for a fading channel with Gaussian input distribution. To best use of the energy, a few works discussed the energy scheduling problem for the transmitter. In [4], the traditional water-filling algorithm was discussed to provide the optimal power control for fading channels with an average power constraint. Employing the renewable source, [5] proposed a shortest-path-based algorithm to schedule the harvested energy in a static channel with finite battery capacity. The authors of [6] analyzed the optimality properties based on the energy causality and provide an algorithm to obtain the energy schedule. In [7], the optimal utilization of the har- vested energy was considered to optimize packet transmission time. For dynamic fading channels with side information, the optimal energy allocation with energy harvesting constraints was treated in [8], and a staircase water-filling algorithm is proposed for the case of infinite battery capacity. The energy- flow behavior with an energy harvesting device was discussed in [9] for the case of finite battery capacity and the method of the directional water-filling was also proposed. However, so far no study considers the maximum trans- mission power (the maximum energy consumption in a time slot) in a fading channel with a finite battery capacity for the energy harvesting transmitter. In this paper we develop an optimal energy scheduling algorithm, called the dynamic water-filling algorithm, for fading channels with both battery capacity and maximum power constraints. In particular, we consider the energy scheduling for a fading channel with energy harvesting, constrained by the availability of the energy, the capacity of the battery, and the maximum power of the transmitter. We assume that both the channel state and the energy harvesting state are non-causally known and we use the sum-rate of the channel over K time slots as the performance metric of the energy scheduler. In this paper, we propose a dynamic water-filling algorithm that consists of three phases. In the first phase, we calculate the optimal energy wastage schedule. Using this energy wastage schedule, in the second phase, we calculate the optimal battery depletion points (BDPs) and battery fully- charged points (BFPs) that represent the time slots where the water levels change. In the third phase, we apply the traditional water-filling method to each segment between adjacent optimal BDPs and/or BFPs. The optimality of this dynamic water-filling algorithm is shown. Moreover, when the battery capacity and the transmission power are unconstrained, the proposed dynamic water-filling algorithm reduces to the staircase water-filling method given in [8], with non-decreasing water levels over time slots. The remainder of the paper is organized as follows. In Section II, we describe the system model and formulate the energy scheduling problem as a convex optimization problem. In Section III, we use the greedy energy consuming policy to obtain the optimal energy wastage schedule. In