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arXiv 0903.1496cs.ITmath.IT
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在一个相关随机场上无线自组网能获取多少信息?

How Much Information can One Get from a Wireless Ad Hoc Sensor Network over a Correlated Random Field?

Youngchul Sung, H. Vincent Poor, Heejung Yu

摘要:

得到了一般$d$维($d$ -D)平稳高斯场的渐近信息率的新的大偏差结果.通过将一般结果应用于二维(2-D)格上的传感器节点,研究了部署在相关随机场上的ad hoc传感器网络的统计推断的渐近行为。在具有对称一阶条件自回归的2-D隐高斯-马尔可夫随机场模型下,在不进行网内数据融合的假设下,得到了总可获得信息量[nats]和能量效率[nats/J]随覆盖区域、节点密度和能量变化的行为。当传感器节点密度固定时,随着网络节点数量$N_t$的增加,能量效率以速率$Θ({area}^{-1/2})$减小到零,并且固定每节点能量下的每节点信息也以速率$O(N_t^{-1/3})$减小到零。随着传感器间距$d_n$的增加,对于给定的扩散速率$α$,每个节点的信息以速率$D-\sqrt{d_n}e^{-αd_n}$收敛到其极限$D$。当覆盖区域固定且节点密度增加时,每节点信息与节点密度成反比。随着网络中消耗的总能量$E_t$增加,对于固定节点密度和固定覆盖情况,可从网络获得的总信息由$O(\log E_t)$给出,对于固定每节点感测能量和固定密度以及增加覆盖情况,可从网络获得的总信息由$Θ(E_t^{2/3})$给出。

英文摘要:

New large deviations results that characterize the asymptotic information rates for general $d$-dimensional ($d$-D) stationary Gaussian fields are obtained. By applying the general results to sensor nodes on a two-dimensional (2-D) lattice, the asymptotic behavior of ad hoc sensor networks deployed over correlated random fields for statistical inference is investigated. Under a 2-D hidden Gauss-Markov random field model with symmetric first order conditional autoregression and the assumption of no in-network data fusion, the behavior of the total obtainable information [nats] and energy efficiency [nats/J] defined as the ratio of total gathered information to the required energy is obtained as the coverage area, node density and energy vary. When the sensor node density is fixed, the energy efficiency decreases to zero with rate $Θ({area}^{-1/2})$ and the per-node information under fixed per-node energy also diminishes to zero with rate $O(N_t^{-1/3})$ as the number $N_t$ of network nodes increases by increasing the coverage area. As the sensor spacing $d_n$ increases, the per-node information converges to its limit $D$ with rate $D-\sqrt{d_n}e^{-αd_n}$ for a given diffusion rate $α$. When the coverage area is fixed and the node density increases, the per-node information is inversely proportional to the node density. As the total energy $E_t$ consumed in the network increases, the total information obtainable from the network is given by $O(\log E_t)$ for the fixed node density and fixed coverage case and by $Θ(E_t^{2/3})$ for the fixed per-node sensing energy and fixed density and increasing coverage case.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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