A technique to estimate the DOAs of coherent sources using a passive frequency beam scanning leaky-wave antenna (FBS-LWA) with a subspace based method is presented. To do so, a combination of enhanced principal-singular-vector utilization for modal analysis (EPUMA) algorithm and linear interpolation technique is proposed. The simulation results show the effectiveness of the proposed method for DOA estimation of multiple coherent signals with hyper-resolution capabilities. With respect to classical antenna arrays, such FBS-LWAs reduce system complexity since only one radio-frequency receiver is required to perform DOA estimation in one angular plane.