On Log-Normality of RSSI in Narrowband Receivers under Static Conditions

A growing set of environmental sensing applications use received signal strength measurements of a static wireless network for unobtrusive monitoring purposes. The success of these systems, which typically process low-amplitude signals, depend strongly on the distribution of the measurements when there are no changes in the channel. In this letter, a statistical model for signal strength measurements acquired when the environment is static is studied. As previously empirically verified, it is shown that the measurements have log-normal distribution even in idealistic environments, which cannot be explained using log-normal shadow fading arguments. Quantization and round-off errors induced by different measurement system components are also considered, and their impact are analyzed. As a result, it is shown that the logarithmic received signal strength measurements under static channel conditions are samples from stationary Gaussian process independent of the environment.