无线传感器网络中统计相关测量量联合概率密度函数的指数紧近似因式分解
An Exponentially-Tight Approximate Factorization of the Joint PDF of Statistical Dependent Measurements in Wireless Sensor Networks
AI总结：
针对无线传感器网络中衰落信道导致能量测量量统计相关、联合PDF难以计算的问题，提出基于特征函数的指数紧近似方法，构建近似似然比检验，性能优于现有检测器。
摘要：
我们研究利用可测量接收信号能量的无线传感器网络，对时间相关的随机无线电源信号进行分布式检测的问题。众所周知，Neyman-Pearson（奈曼-皮尔逊）框架下的最优检验基于似然比检验（LRT），在该设置中，LRT 会计算源信号存在与不存在两种情况下测量量的概率密度函数（PDF）的比值。当源信号存在时，计算各节点能量测量量的联合 PDF 是一个具有挑战性的问题，这是因为无线电源经衰落信道传播后，会给接收信号引入统计相关性。我们利用该（难以直接处理的）联合 PDF 的特征函数来解决这一问题，并提出了一种对该特征函数的近似方法。我们推导了慢衰落和快衰落这两种无线传播场景下近似误差的界，并且证明当时间-带宽积足够高时，所提近似的精度随节点数量呈指数级提升。我们将该近似用作精确联合 PDF 的替代，构建了一种近似 LRT；Monte Carlo（蒙特卡洛）仿真验证表明，该检测器的性能优于其他知名检测器。
英文摘要：
We consider the distributed detection problem of a temporally correlated random radio source signal using a wireless sensor network capable of measuring the energy of the received signals. It is well-known that optimal tests in the Neyman-Pearson setting are based on likelihood ratio tests (LRT), which, in this set-up, evaluate the quotient between the probability density functions (PDF) of the measurements when the source signal is present and absent. When the source is present, the computation of the joint PDF of the energy measurements at the nodes is a challenging problem. This is due to the statistical dependence introduced to the received signals by the radio source propagated through fading channels. We deal with this problem using the characteristic function of the (intractable) joint PDF, and proposing an approximation to it. We derive bounds for the approximation error in two wireless propagation scenarios, slow and fast fading, and show that the proposed approximation is exponentially tight with the number of nodes when the time-bandwidth product is sufficiently high. The approximation is used as a substitute of the exact joint PDF for building an approximate LRT, which performs better than other well-known detectors, as verified by Monte Carlo simulations.
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