论文标题
无线传感器网络中统计依赖测量值的关节PDF的指数近似近似分解
An Exponentially-Tight Approximate Factorization of the Joint PDF of Statistical Dependent Measurements in Wireless Sensor Networks
论文作者
论文摘要
我们考虑使用能够测量接收信号能量的无线传感器网络的时间相关的随机无线电信号的分布式检测问题。众所周知，Neyman-Pearson设置中的最佳测试基于似然比测试（LRT），在此设置中，当存在源信号时，该设置评估了测量概率密度函数（PDF）之间的商，当时源信号存在和缺失。当存在源时，节点上能量测量的关节PDF计算是一个具有挑战性的问题。这是由于通过褪色通道传播的无线电源引入了接收信号的统计依赖性。我们使用（顽固性）关节PDF的特征功能来处理这个问题，并提出了与之近似的近似值。在两个无线传播方案中，我们得出了近似误差的边界，缓慢而快速褪色，并表明当时间带宽产物足够高时，提出的近似值与节点的数量成倍紧密。该近似值用作构建近似LRT的精确关节PDF的替代品，该LRT的性能优于其他众所周知的检测器，这是通过Monte Carlo Simulates验证的。
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.
