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A comprehensive analysis is presented for the rectangular waveguide edge slot array with finite wall thickness. To analyze the waveguide structure accurately and efficiently, the magnetic currents are introduced on both the inner and outer surfaces of the slot apertures, and the electric currents are employed on the boundary surfaces of both slot apertures and waveguide exterior area. Moreover, the new coupled integral equations are established according to the boundary conditions, and the method of moments (MoM) with the higher-order basis functions is employed to solve for the equivalent electric and magnetic currents. The proposed method results in less number of unknowns without loss of accuracy compared to the direct methods with the rigorous modeling of waveguide edge slots. Numerical results including the radiation patterns as well as the reflection and transmission coefficients are presented.