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A new leaky-wave antenna based on substrate integrated waveguide (SIW) with H-shaped slots is proposed and investigated. The SIW with H-shaped slots is analyzed as a rectangular waveguide with H-shaped slots. Using an aperture magnetic field integral equation (MFIE), it is found that the SIW with H-shaped slots supports a leaky waveguide mode, a surface-wave mode and a proper waveguide mode depending on frequency. The radiation property is also evaluated using the MFIE. The leaky-wave antenna based on the SIW with H-shaped slots has a narrow beam that scans from broadside to endfire with frequency. The antenna produces an elliptical polarization, including circular polarization. Measured results are consistent with the simulation from HFSS and the theoretical analysis from the MFIE.