Linear and Non-Linear Strategies for Power Mapping in Gaussian Sensor Networks Franco Davoli, Mario Marchese, Maurizio Mongelli DIST - Department of Communications, Computer and Systems Science CNIT - National Inter-University Consortium for Telecommunications University of Genoa, Via Opera Pia 13, 16145, Genova, Italy { franco.davoli, mario.marchese, maurizio.mongelli }@unige.it Abstract—This paper deals with non-linear coding-decoding strategies for Gaussian sensor networks that obey a global power constraint and are decentralized (each sensor’s decision is based solely on the variable it observes). The sensors and the sink act as the members of a team, i.e., they possess different information and they share a common goal, which consists in minimizing the expected distortion on the variables of interest. As the inherent power allocation, derived in “static” conditions (stationarity of the stochastic environment, fixed topology), reveals to be optimal [1], the main interest is to analyze its robustness to variable system conditions. To this aim, this paper goes deep inside the generalization capabilities of the proposed approach, by showing some interesting insights into the structure of the problem. The overall surprising outcome is that a quasi-static application of the approach reveals to be sufficient to maintain suboptimal performance even under a dynamic environment. Keywords—Gaussian sensor networks, neural control, power allocation, sensitivity analysis I. INTRODUCTION HE DEPLOYMENT of sensor networks is often such that measurements acquired by the sensor nodes are conveyed toward a sink, where they need to be processed and analyzed. Recently, there has been a growing interest in understanding the peculiarities of wireless sensor networks from both an information theoretic and decision theoretic point of view, particularly when the measured quantities can be represented as Gaussian random variables (see, e.g., [1]- [3]). In particular, when the measured variables are analog quantities, they can either be transmitted as such, or they can be quantized and transmitted according to a digital scheme. Given a distortion measure for the reconstruction of the variables at the sink, and the statistical characteristics of the communication channel and of the sources, it is not straightforward to determine whether joint source-channel coding (with analog transmission) can outperform the separation that is typical of digital communications [2]. In [1], we introduced decentralized decision models in the setting of team theory [4], based on the approximation of the optimal decision strategies by means of fixed-structure parametrized nonlinear functions, by applying the Extended Ritz Method (ERIM) [5]. The reason for seeking numerical approximations to the optimal coding/decoding strategies stems from the fact that a team optimization approach to these problems presents formidable analytical difficulties (originally pointed out in [6], even in a scalar source-channel model). More specifically, in [1] we used neural approximating functions to derive a non-uniform power distribution among the encoders at each sensor node. We show that, in the presence of correlated measurements from the same source representing a physical phenomenon, a large reduction in the overall transmission power can be obtained, at the expense of very little increase in distortion, with respect to linear encoding strategies. This is achieved by selecting a few “representative” sensors from the total available pool. The inherent optimization algorithm achieves optimal solutions under static conditions (stationarity of the stochastic environment, fixed topology). As such, there is the need of investigating:  how is the solution sensitive to changes in the topology and in the statistical environment?  how much computational and bandwidth effort is required? A simulation-based sensitivity analysis of the approach is outlined here with respect to several system parameters. The rest of the paper is organized as follows. We define the problem formally in the next section. Section III outlines our functional approximation approach. The sensitivity analysis is presented in Section IV and conclusions in Section V. II. PROBLEM STATEMENT We consider a number N of sensors deployed over a geographical area, each one observing a realization of some physical phenomenon described by a random variable (r.v.) S (the source). We adopt the model of [3], which we describe in the following. We suppose the observations to take place at discrete time instants, but, since we are interested in real- time, single-letter coding, we do not introduce the time index in the following for simplicity of notation. Successive source outputs are uncorrelated; however, there is spatial correlation between the source and the event observed by sensor i, represented by the r.v. i S . As a consequence, the r.v.’s i S T 2010 Australasian Telecommunication Networks and Applications Conference 978-1-4244-8172-9/10/$26.00 ©2010 IEEE 7