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We address a lifetime maximization problem for a single-hop wireless sensor system (also known as a Gaussian sensor network) where multiple sensors encode and communicate their measurements of a Gaussian random source to a fusion center (FC). The FC is required to reconstruct the source within a prescribed distortion threshold. The lifetime optimization problem is formulated as a joint power, rate, and timeslot [for time-division multiple access (TDMA)] allocation problem under the constraints of the well-known rate distortion constraints for the Gaussian CEO problem, the capacity constraints of the wireless links, the energy constraints of the sensor nodes and the strict delay constraint within which the encoded sensor data must arrive at the FC. We study the performances of TDMA and an interference limited nonorthogonal multiple access (NOMA) (with single-user decoding)-based protocols and compare them against recently reported simple uncoded amplify and forward schemes under a nonorthogonal multiple access channel with complete phase synchronization. Since computing the exact capacity region for correlated sources in a multiaccess channel is difficult, we simply consider the Gaussian multiaccess capacity constraints pretending that the sensor data are independent (although they are clearly not). We show that the optimal lifetime achieved under these capacity constraints provides an upper bound on the optimal lifetime achieved by the TDMA and NOMA protocols. While the constrained nonlinear optimization problems for the TDMA and the Gaussian multiaccess cases are convex, the NOMA case results in a nonlinear nonconvex difference of convex functions (D.C.) programming problem. We provide a simple successive convex approximation based algorithm for the NOMA case that converges fast to a suboptimal lifetime performance that compares favorably against the upper bound provided by the Gaussian multiaccess case. Extensive numerical studies are presented for both static and- slow fading wireless environments with full channel state information at the fusion center.
Date of Publication: May 2008