Sensor Selection and Precoding Strategies for Wireless Sensor Networks

Sensor selection has recently received a growing interest in the literature, motivated by the worldwide deployment of wireless sensor networks and by the increase in the number of available applications. In our framework, sensors take remote measurements of a quantity of interest and communicate their observations through a noisy, multiantenna wireless communication link. In this context, we propose a scheme for optimally selecting κ out of K sensor nodes on the basis of the amount of information they convey to a common receiver/actuator. Moreover, a suitable linear precoder is employed and optimized at each transmitter with the aim of maximizing the mutual information between the observed variable and the signal received by the actuator. The sensor selection problem is known to be combinatorial, and several computable relaxations are available in the literature. In this paper, the optimality conditions are formally expressed in an information-theoretic context, and both semi-definite-programming relaxations and greedy schemes, leading to computable techniques for large values of κ and K, are presented. Moreover, specific results for the cases of high and low signal-to-noise ratio on the wireless channel are derived. Numerical simulations show that knowledge of the channel state at the transmitter may lead to an increase of the achievable mutual information and determine a different choice of sensors, thus pointing out that our approach significantly improves upon selection schemes that neglect the characteristics of the communication layer.