Location-awareness is essential for many wireless network applications in both civil and military sectors. In this paper, we determine the localization accuracy of narrowband localization systems in which each mobile agent is equipped with an antenna array. Due to non-coherent estimators, the phases of the received signals can only be exploited for angle-of-arrival (AOA) estimation but not time-of-arrival (TOA). Based on such estimators, we derive the fundamental localization accuracy in terms of the squared position error bound (SPEB) in far-field harsh multipath environments. Moreover, we characterize the effects of the geometry of anchors and array antennas on the localization accuracy, yielding the criteria for optimal array design and network deployment. Our analysis exploits all the TOA and AOA information in the received waveform for localization using narrowband array-based systems, and the resulting SPEB serves as a fundamental limit for such systems.