Estimation of Probability Density Function Using Multi-bandwidth Kernel Density Estimation for Throughput

In manufacturing and logistics, various applications exploiting IoT devices are started to be used. Although there is a demand for wireless connection between the IoT devices to networks, obstacles such as radio frequency interference, multipath-rich propagation, and movement of objects make communication unstable. The instability can cause a system failure of IoT applications. Estimation of probability density function (PDF) of throughput is an important technique for the communication failure prediction and control of data rate of wireless communication applications. Because wireless environment in factories change complicatedly, the PDF of throughput is a mixture of narrow and wide distributions. For such PDF, the conventional kernel density estimation which uses uni-bandwidth kernel can not accurately estimate the distribution. To overcome this problem, we propose a novel kernel density estimation method which uses multiple bandwidths kernels. In addition, we extend a likelihood cross validation method to the multi-bandwidth kernel density estimation to determined the suboptimum bandwidths of kernels and combining weights. To confirm the effectiveness of the proposed method, we conduct numerical simulation assuming image transmission for car body inspection at an automobile factory.