1Performance Limits and Geometric Properties of Narrowband Array Localization

Abstract—Location-aware networks have been of great impor-tance and interest in many applications for both civil and military use since recent years. This paper studies the wireless network consisting of several anchor nodes and one agent equipped with an antenna array whose position is to be estimated in a far-field multipath environment. To exploit all the information in the received signal, the localization accuracy is determined based on the waveform directly rather than the metrics extracted from the signal under the narrowband system assumption treating baseband signal and carrier frequency differently. Then the Cramér-Rao bound on localization accuracy shows that the localization information can be decomposed into distance and direction parts, both of which have clear physical interpretations. Moreover, we show that the Doppler shift of a moving agent contributes to direction information, with information intensity larger than that obtained via angle-of-arrival (AOA) methods. Furthermore, the anchor-agent and antenna-array geometries are also studied in this paper, which concludes that uniformly circular oriented array (UCOA) and anchors with diversified direction are optimal in localization, respectively. Keywords—Cramér-Rao bound, Doppler shift, Geometric prop-erty, TOA/AOA, Wireless localization precisio