  Energy efficiency is a key requirement in the design of wireless sensor
networks. While most theoretical studies only account for the energy
requirements of communication, the sensing process, which includes measurements
and compression, can also consume comparable energy. In this paper, the problem
of sensing and communicating parallel sources is studied by accounting for the
cost of both communication and sensing. In the first formulation of the
problem, the sensor has a separate energy budget for sensing and a rate budget
for communication, while, in the second, it has a single energy budget for both
tasks. Assuming that sources with larger variances have lower sensing costs,
the optimal allocation of sensing energy and rate that minimizes the overall
distortion is derived for the first problem. Moreover, structural results on
the solution of the second problem are derived under the assumption that the
sources with larger variances are transmitted on channels with lower noise.
Closed-form solutions are also obtained for the case where the energy budget is
sufficiently large. For an arbitrary order on the variances and costs, the
optimal solution to the first problem is also obtained numerically and compared
with several suboptimal strategies.
