IEEE 802.11 Wi-Fi access point density estimation with capture-recapture models

The estimation of IEEE 802.11 Wi-Fi access point (AP) densities is an important cornerstone in deriving accurate models for the deployment structure of opportunistic wireless networks. Such densities are usually derived through large-scale wardriving-like measurement campaigns with COTS devices. Due to shielding, limited receiver sensitivity, and sampling density constraints, in general only a subset of Wi-Fi APs can be observed. Furthermore, repeated measurement campaigns show that even if an AP has been observed in one visit to a study area, it may not be observed in subsequent visits, due to small-scale deviations in the measurement locations and unavoidable changes in the radio environment such as moving vehicles and pedestrians. This motivates our study of the application of capture-recapture models to establish more accurate estimates of the actual number of APs in a study area. We approach this problem by first developing a general system model and mathematical framework for AP observability. As we assume temporally constant population sizes but potential inhomogeneities in observation probabilities, we then assess the performance of two applicable population density estimators, namely the Lincoln-Petersen and jackknife estimators, through a simulation study. We demonstrate the practical significance of the proposed capture-recapture methodology by applying it to a data set from an extensive urban Wi-Fi measurement campaign that we have carried out in Cologne, Germany, quantifying the achievable gains and the estimators´ sensitivity to the measurement campaign design. We show that applying the capture-recapture techniques provides the practical advantage of yielding a similar accuracy in the estimation of Wi-Fi density even with significantly fewer measurement locations than surveyed in the full campaign. However, our results indicate that a high receiver sensitivity remains essential for such wardriving-like measurements, i.e. less sophisticated measuremen- setups such as smartphones will introduce high errors in the AP density estimation.