Optimal Sensor Selection Strategies in the Presence of Wireless Communication Links

The problem of selecting in an optimal way k sensors from a given set of K sensors providing noisy measurements of some physical variable has received a growing interest in the literature. The problem has been shown to be combinatorial, and several computable relaxations have been presented. In this paper, we consider a particularly interestingvariant of the sensor selection problem. Motivated by the increase in the application of wireless sensor networks, i.e. networks of sensors which take remote measurements of the quantity of interest and then communicate their values through a (noisy) wireless communication link, we propose a schemefor optimally selecting the wireless sensors taking into account also the available channel state information. The optimality conditions are formally derived in an information-theoretic context, and specific semi-definite programming relaxations leading to computable techniques for large values of k and K are presented. Also, we derive specific results for the cases of high and low signal-to-noise ratios. Numerical simulations show how knowledge of the channel state information may lead to an increase of the achievable mutual information, and determine a different choice of sensors.