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The radiation pattern of a traveling-wave waveguide array with narrow-wall slots is analyzed accurately using higher order basis functions (HOBs) in the context of method of moments (MoM). The use of HOBs can significantly reduce the number of unknowns in MoM compared to the use of piece-wise Rao-Wilton-Glisson basis functions (RWGs). To prevent the formation of a secondary beam due to reflected waves originating from the terminations of the waveguides, the concept of the perfectly matched layer (PML) in differential-equation methods is introduced to design the matched loads terminating the waveguides. In the analysis, the MoM with HOBs is applied to the electric field integral equation (EFIE) with the free-space Green's function. The simulated data is compared to the RWG-function and experimental results to validate the HOB-function analysis.