Energy Efficient Estimation of Gaussian Sources over Inhomogeneous Gaussian MAC Channels

In this paper, we first provide a joint source and channel coding (JSCC) approach in estimating Gaussian sources over Gaussian MAC channels, as well as its sufficient and necessary condition in restoring Gaussian sources with a prescribed distortion value. An interesting relationship between our proposed joint approach with a more straightforward separate source and channel coding (SSCC) scheme is further established. We then formulate constrained power minimization problems to minimize total transmission power consumption under a distortion constraint for arbitrary in-homogeneous networks under JSCC, SSCC and uncoded scheme (UC). They are transformed to relaxed convex geometric programming problems. Our numerical results exhibit that none of the three schemes is consistently most energy efficient. The proposed JSCC could be more energy efficient than either the uncoded scheme, or SCCC, but not both. In addition, we prove that the optimal decoding order to minimize the total transmission powers for both source and channel coding parts is solely subject to the ordering of MAC channel qualities, and has nothing to do with the ranking of measurement qualities across measuring nodes.