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A novel direction of arrival (DoA) estimation system based on a leaky-wave antenna (LWA) is presented. Compared to traditional array-based DoA techniques, which require multiple radiating elements, a large feeding network, and expensive phase shifters consuming power, the proposed scheme requires only a simple, compact, and low-cost radiating element consuming no power. The system estimates the DoA by measuring the received power at both ports of the LWA using detectors as the beam is scanned. It is implemented here using a composite right/left-handed (CRLH) leaky-wave antenna (LWA), selected for its efficient electronic full-space scanning capability. A detailed theoretical explanation is presented. Three methods of operation are described: forward scanning, backward scanning, and full-space scanning. Furthermore, full-wave simulation and experimental results both validate the theoretical analysis. To the best of the authors' knowledge, this is the first time a LWA is employed in a DoA system.