Battery-Aware Power Allocation for Lifetime Maximization of Wireless Sensor Networks Muhammad Hafeez Chaudhary, Student Member, IEEE and Luc Vandendorpe, Fellow, IEEE Communications and Remote Sensing Lab., Universit´ e Catholique de Louvain, LLN-1348, Belgium {Muhammad.Chaudhary, Luc.Vandendorpe}@uclouvain.be Abstract— We consider a wireless sensor network deployed to observe a physical phenomenon. The sensors amplify and forward their observations to a remote fusion center via single hop. The objective is to maximize the operational lifetime of the network such that the estimate of the underlying source at FC satisfies a certain fidelity criterion given by the maximum tolerable estimation distortion. Each sensor is powered by a battery which limits its lifetime and consequently of the network also. Recent studies show that the battery discharge behavior is dependent on the load current: higher current leads to higher losses inside the battery due to the non-linearities of the electrochemical reaction in the battery. This work presents a power allocation design where goal is to maximize the network lifetime incorporating the non-linear discharging behavior of the batteries. The design is based on the knowledge of the instantaneous channel gains as well as when we only know the channel statistics. The numerical examples illustrate that the impact of battery-aware power scheduling on the network life is substantial. I. I NTRODUCTION A wireless sensor network (WSN) consists of spatially distributed sensors that cooperatively monitor physical or environmental conditions - temperature, vibration, pressure, motion or pollutants. Here we assume that the sensors transmit their noisy observations via single-hop to a remote fusion center (FC) which forms the global estimate of the under- lying source. Each sensor node is powered by a battery with limited energy which is assumed to be non-rechargeable and irreplaceable because the nodes may be deployed in a hostile or inaccessible terrain. The objective is to keep the network operational to the maximum possible time such that the estimation distortion is less than a maximum tolerable threshold. As each sensor is powered by a non-rechargeable battery, the objective of network lifetime maximization can be achieved by minimizing the consumed energy in each observation instance. To this end, minimal-energy estimation techniques have been considered in [1]- [3]. There are other schemes which deal with the minimal-energy data collection at a central access point from the sensors [4]. Very recently Li et al. in [5] presented a joint source coding and routing design for lifetime maximization in a multihop network. All these schemes, assume ideal battery with fixed usable capacity. However, recent studies show that the discharge behavior of the battery is not ideal. Due to non-linearities, in addition to the energy delivered to the load, some energy is locked inside the The authors would like to thank the Walloon region ministry DGTRE framework program COSMOS/TSARINE and EU project FP7 NEWCOM++ for the financial support and the scientific inspiration. battery which is unavailable [6], [7]. Consequently the total apparent consumed energy is always greater than the actual energy delivered to the load. Moreover, some of the locked energy is recovered by introducing rest periods. The battery is dead when the apparent consumed energy reaches a certain threshold value. In this work, we first develop a theoretical model for the energy consumption of the battery which takes into account the nonlinear discharge behavior and the recovery effect. Subsequently from this model, we introduce a cost function which takes into consideration the load history for a particular sensor. Then based on the cost function we propose a battery- aware power allocation for the network-lifetime maximization in a single-hop network such that the estimation distortion does not exceed a maximum tolerable limit. The proposed scheme assumes perfect knowledge of the fading channel gains from the sensors to the FC in each observation instance. However, in practical systems due to resource constraints we may only know the statistics of the channels. To this end, we develop an expression for the average estimation distortion assuming the channel gains are independently Rayleigh distributed and subsequently we propose the power-allocation scheme. II. PRELIMINARIES A. System Model We consider the sensor network comprising N sensors deployed to observe a source s. Each sensor node amplifies and forwards the noisy observation to the fusion center (FC) via some orthogonal multiple-access scheme, e.g. FDMA. The received signal is z i (n)= h i (n)α i (n)(s(n)+ n i (n)) + w i (n), ∀i, where n i (n) is the observation noise, w i (n) is the receiver noise, the |h i (n)| is the channel gain and α i (n) is the amplifying factor for sensor i at discrete time n. We assume that the observation and the receiver noises are respectively zero-mean and independently distributed across sensors and time with variances σ 2 ni and σ 2 wi , ∀i. The channel gains from the sensors to the FC are independently flat fading. The task of the FC is to estimate the source s(n) based on the received observations from the sensors. We assume that the parameter s(n) is deterministic and we have the second order statistics of the observation and the communication noises. The estimate ˆ s(n) is based on BLUE estimation rule [8]: ˆ s(n)=  N  k=1 |h k (n)| 2 α 2 k (n) |h k (n)| 2 α 2 k (n)σ 2 n k + σ 2 w k  −1