Efficient energy allocation in wireless sensor networks based on non-cooperative game over Gaussian fading channel

In this paper, we solve the energy optimization of Lloyd quantizer (LQ) based Robust iterative water-filling (LQ-RIWF) for a multiple-input multiple-output (MIMO) channel by minimizing the gradient of the local cost function (LCF) of each node by canceling the cross-interference through assigning a nulling set. This technique is known as LCF-LQ-RIWF. Our goal of this work is to design a non-cooperative game for an arbitrary Gaussian channel while guaranteeing convergence into an Nash Equilibrium (NE) state at minimum energy constraint. We first present the LQ-RIWF power allocation in NE state, and then extend the result for LCF-LQ-RIWF with global power constraint. We compare the sum-rate performance of LCF-LQ-RIWF with conventional power allocation techniques. A sufficient condition for the convergence of the proposed algorithm in NE state is derived and verified under the assumption that each node approaches a common water level based on instantaneous channel gain. Based on the theoretical investigation, we have carried out Matlab simulations and the results show that our proposed power allocation provides better performance compare to general sub-optimal techniques.