Optimization of multilevel power adjustment in wireless sensor networks

Restricted to the limited battery power of nodes, energy conservation becomes a critical design issue in wireless sensor networks (WSNs). Transmission with excess power not only reduces the lifetime of sensor nodes, but also introduces immoderate interference in the shared radio channel. It is ideal to transmit packets with just enough power. In this paper, we propose a multilevel power adjustment (MLPA) mechanism for WSNs to prolong the individual node lifetime and the overall network lifetime. The energy conservation is achieved by reducing the average transmission power. The analytical model is built for the MLPA mechanism enabled with k distinct power levels (k-LPA). Under a free space loss (path loss exponent gamma=2) model, the closed-form expression of optimal power setting is derived and the average transmission power can be minimized as (k+1)/2k of original fixed power. For wireless environment other than the free space loss model (gamma not equal 2), a recursive formula expression set is established to acquire the optimal power configuration and the minimum average transmission power, which is 2P/(gamma+2) as k approaches infinity. Furthermore, to reduce the computing complexity and the effort of measuring path loss exponent, two approximated power configuration methods are proposed. The analytical results show that both the proposed approximate methods are near-optimal solutions for most of the wireless communication environments. It can be shown that lim (k -> a) P (avg) (similar to I) (k,gamma)=lim (k -> a) P (avg) (similar to II) (k,gamma)=lim (k -> a) P (avg) (min) (k,gamma)=2P/(gamma+2).