Recursive Waterfilling for Wireless Links With Energy Harvesting Transmitters

Energy harvesting is often used for green communications. The problem of power allocation is then to maximize the throughput, taking into account the fact that channel conditions and energy sources are time varying. In particular, for the constraints of the target problem, besides the allocated power values being nonnegative, the successively harvested energy sum leads to the triangle coefficient matrix of the power sum constraints. In this paper, we propose a geometric waterfilling (GWF) algorithm in place of the conventional waterfilling (CWF) algorithm for power allocation with a sum power constraint. We then recursively apply the GWF as a functional block to sequentially solve the power allocation problem for energy harvesting transmission in a fading channel. This algorithm is referred to as RGWF. The proposed RGWF is further extended to solving the minimization of the transmission completion time (referred to as RGWFn) by inserting a condition to check if the preset information transmission data bits are achieved. Since RGWF is defined by recursion and along natural progress of time, we can compute a family of solutions for subprocesses from epoch 1 to epoch k, for k = 1, ..., K, where K is the index of the final epoch for the entire process. Thus, RGWF can be utilized for efficiently carrying out the computation of RGWFn. RGWF and RGWFn belong to dynamical recursive algorithms. Compared with the existing results in the open literature, the proposed algorithms have distinguished features: 1) They provide the exact optimal solutions via efficient finite computation under the recursive category, and 2) the optimality of the proposed algorithms is strictly proven. Numerical examples are provided to illustrate the procedures to obtain the optimal power allocation by using the proposed algorithms.