Pairwise error probability analysis for power delay profile fingerprinting based localization

Although most of the conventional localization algorithms rely on LOS conditions, it is possible to do positioning with Power Delay Profile-Fingerprinting (PDP-F) in multipath and even in NLOS environments. Many algorithms for position fingerprinting have been developed, but analytical investigation in this area is still not matured yet. In this paper we aim to find the pairwise error probability (PEP) for PDP-F based localization systems. The objective is to see the performance of PDP-F algorithms under different cost functions and also under different path amplitude assumptions. By PEP, what is meant is the same as in the PEP analysis in digital communication channels. Hence the approach is similar for PDP-F. However its analysis is not as straightforward as it is for the digital communication channel case. We investigate and show the results for least squares (LS) based algorithm under deterministic path amplitude modeling and Gaussian Maximum Likelihood (GML) based algorithm for the Rayleigh fading modeling of the path amplitudes.