Network Lifetime Optimization by KKT Optimality Conditions in Wireless Sensor Networks

摘要

Energy saving is a critical issue for typical wireless sensor networks (WSNs) and the energy consumption is a big challenge to the design of WSNs. In this paper, we investigate this problem by a cross-layer design approach to minimize energy consumption and maximize network lifetime (NL) for a multiple-source and single-sink (MSSS) WSN with energy constraints. The optimization problem for the MSSS WSNs can be formulated as a mixed integer convex optimization problem with adoption of time division multiple access (TDMA) at medium access control (MAC) layer and it becomes a convex problem by relaxing an integer constraint on time slots. First of all, we have employed the Karush-Kuhn-Tucker(KKT) optimality conditions to derive analytical expressions of the globally optimal NL for a linear SSSS topology. Then a decomposition and combination (D&C) approach has been proposed to obtain suboptimal solutions. As a result, an analytical expression of the suboptimal NL has been derived for WSNs with a linear MSSS topology. To validate the analysis, numerical results show that the upper-bounds of the NL obtained by our proposed optimization models are tight. Important insights into the NL and benefits of cross-layer design for WSN NLM are also summarized.