A Generic $\alpha-\eta- \kappa-\mu$ Fading Environment based Indoor Localization

Aditya Singh, Gaurav Prasad, Sudhir Kumar

Abstract: In this work, we consider a generic $\alpha-\eta-\kappa-\mu$ fading environment representing all small-scale signal variations in Received Signal Strength (RSS) for localization, which was not considered earlier. The major challenge is accurately modeling fluctuating RSS signals due to shadowing and multi-path effects. The existing ranging methods are inefficient and consider only the shadowing effect modeled as a standard log-normal distribution; however, the effects of multipath fading must also be considered along with it. The localization methods based on established fading distributions such as Rayleigh, $\kappa-u$. and ct-KMS, to list some, are context-specific and do not capture all the effects of fading. By utilizing the generic $\alpha-\eta-\kappa-\mu$; fading model, our proposed location estimation strategy can be extended to many more diverse fading scenarios to estimate unknown locations accurately when provided with correct values of the channel parameters, $\alpha, \eta, \kappa, \mu$. However, the derived likelihood function of received power is non-convex and unstable in nature. We introduce a distance-normalized Gradient Ascent algorithm to compute maximum likelihood estimates of devices' locations, which also addresses the non-convexity and instability of the estimator. The evaluation on a simulated testbed demonstrates superior performance in comparison to current state-of-the-art ranae-based localization techniques.