Analysis of Expected Route Surviving Time and Power Optimization for Cooperative Linear Multi-Hop Networks
Wireless multi-hop communications has a wide variety of applications such as in cellular and sensor networks. One of the challenging issues is to design energy efficient schemes to solve the problem of high energy consumption especially in large scale networks where massive power is needed to ensure the reliability and high transmission speed of the networks. One promising energy efficient wireless transmission technique is the opportunistic large array (OLA) where all nodes that are able to decode a message relay the message immediately after reception without the need of coordination with other relays. In this work, we would like to investigate the issue of power optimization of the OLA networks with a linear topology. We try to develop a more energy efficient transmission scheme by optimizing the power allocation within each hop, such that the overall system performance in terms of the expected route surviving time could be enhanced. In this work, we model the linear multi-hop networks as a Markov chain in discrete time. Given a certain total power budget for each hop, the system will keep the transmission of a packet through the linear network until failure at a certain hop. The sub-stochastic matrix of the Markov chain we formed helps determine the expected number of hops the transmission could reach, i.e., the expected route surviving-time. It turns out that the expected route surviving time is tightly related to the Perron-Frobenious eigenvalue of the matrix. Based on a tight lower bound of the Perron-Frobenious eigenvalue, we derived a closed-form expression of the optimum power allocation scheme for the transmission under certain total power budget for each hop. We then analyzed the scheme and compared it with the equal power allocation scheme. Our analysis and simulation results show that the optimum power allocation scheme outperforms the equal power allocation scheme by achieving significant longer transmission distance, especially in the high SNR region. It is also observed that increasing the hop size will help increase the transmission distance above certain SNRs, depending on the hop size, for both optimum and equal power allocation schemes.