In this letter, we investigate the randomized gossip (RG) algorithm by taking the power consumption over wireless sensor networks (WSNs) into account for distributed averaging. The convergence of the classic RG problem can be improved by optimizing the second largest eigenvalue of the average update matrix, leading to the fastest distributed linear averaging (FDLA). As the total transmission power determines the lifetime of WSNs, we propose to jointly optimize the power consumption and the second largest eigenvalue, such that a trade-off between the power consumption and the convergence rate is obtained. Further, since each sensor node usually has a limited energy budget, we incorporate an additional constraint on the local power consumption for the FDLA formulation, such that the survival of nodes can be guaranteed. Numerical simulations using a WSN validate the effectiveness of the proposed methods.

中文翻译：

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无线传感器网络的功率优化和功率受限随机八卦方法

在这封信中，我们通过考虑无线传感器网络（WSNs）上的功耗进行分布式平均，研究了随机八卦（RG）算法。通过优化平均更新矩阵的第二大特征值，可以提高经典RG问题的收敛性，从而实现最快的分布式线性平均（FDLA）。由于总发射功率决定了无线传感器网络的寿命，因此我们建议共同优化功耗和第二大特征值，从而在功耗和收敛速度之间进行权衡。此外，由于每个传感器节点通常都具有有限的能量预算，因此对于FDLA公式，我们在本地功耗上加入了额外的约束，从而可以确保节点的生存。