In this letter, we present a new metric for characterizing the geometric conditions encountered in cellular positioning based on the angular spread of the base stations (BSs). The metric is shown to be closely related to the geometric-dilutionof-precision (GDOP), yet has the benefit of being characterizable in terms of the network parameters for BS layouts modeled according to a Poisson point process (PPP). As an additional benefit, the metric is shown to immediately yield a device's probability of being inside or outside the convex hull of the BSs, which localization researchers will widely-recognize as being a strong indicator of localization performance. Index Terms-Localization, geometric dilution of precision (GDOP), hearability, stochastic geometry, point process theory. W ITH the proliferation of smart phones enabling location-based services as well as increased pressure due to federal regulations such as the FCC E911 mandate [1], cellular network localization has recently garnered increasing interest. In order to gain insight into how network parameters affect cellular localization performance, industry has typically relied on simulation-based results. This is because it is a standard practice to model BS deployments using a regular grid model, which does not lend itself well to mathematical analysis. Motivated by the current capacity-driven irregular deployments of low-power base stations (BSs), such as pico and femtocells, there have been several successful attempts at characterizing the downlink and uplink performance of cellular networks by modeling the BS locations according to a homogeneous Poisson point process (PPP) (e.g., [2], [3]). In addition to being more realistic in capturing the irregularities of current deployments, the PPP-based models lend tractability by allowing the use of tools from stochastic geometry in network analyses. The PPP-based approach is the basis of a new model proposed in [4], [5] for studying cellular positioning. The three fundamental components determining localization performance are (i) the number of participating BSs, (ii) the locations of these BSs relative to the device being localized, and (iii) the accuracy of the positioning observations. In [5] , the model was used to obtain accurate analytic expressions of BS hearability, i.e. the number of participating BSs. A well-known and fundamental metric for evaluating the geometric component is the geometric-dilution-of-precision (GDOP) [6], [7] . This metric is closely related to localization performance, but is limited to studying fixed positioning scenarios. Instead, it is desirable to understand how network parameters affect the favorability of all Manuscript
For the more realistic case of a finite number of anchors, the max-angle metric was proposed and analyzed in REF and shown to be correlated to the GDOP.
A Tractable Metric for Evaluating Base Station Geometries in Cellular Network Localization
IEEE Wireless Communications Letters
IEEE Wireless Communications Letters
Mathematics Computer Science