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Of the many challenges in building a wireless network at terahertz frequencies, link discovery remains one of the most critical and least explored. In a network of mobile receivers using narrow directional beams, how do the nodes rapidly locate each other? This direction information is crucial for beam forming and steering, which are fundamental operations for maintaining link quality. As the carrier frequency increases into the terahertz range, the conventional methods used by existing networks become prohibitively time-consuming, so an alternative strategy is required. Using a leaky-wave antenna with a broadband transmitter, we demonstrate a single-shot approach for link discovery which can be accomplished much more rapidly. Our method relies on measurements of the width of a broad spectrum, and does not require any information about the phase of the received signal. This protocol, which relies on a detailed understanding of the radiation from leaky-wave devices, offers a realistic approach for enabling mobility in directional networks.