Joint Optimization of Transmit Power-Time and Bit Energy Efficiency in CDMA Wireless Sensor Networks

In this paper, we address the problem of minimizing energy consumption in a CDMA-based wireless sensor network (WSN). A comprehensive energy consumption model is proposed, which accounts for both the transmit and circuit energies. Energy consumption is minimized by jointly optimizing the transmit power and transmission time for each active node in the network. The problem is formulated as a non-convex optimization. Numerical as well as closed-form approximate solutions are provided. For the numerical solution, we show that the formulation can be transformed into a convex geometric programming (GP), for which fast algorithms, such as interior point method, can be applied. For the closed-form solution, we prove that the joint power/time optimization can be decoupled into two sequential sub-problems: optimization of transmit power with transmission time serving as a parameter, and then optimization of the transmission time. We show that the first sub-problem is a linear program while the second one can be well approximated as a convex programming problem. Taking advantage of these analytical results, we further derive the per-bit energy efficiency. Our results are verified through numerical examples and simulations