This paper derives an analytical driving function to synthesize an exterior sound field described by spherical harmonic expansion coefficients using a linear loudspeaker array. An exterior sound field is decomposed into both spherical and 3D cylindrical harmonic expansion coefficients. The spherical harmonic expansion coefficients are analytically converted into 3D cylindrical ones by plane wave decomposition. The angular spectrum coefficients at the synthesis reference line are then analytically obtained from the converted 3D cylindrical harmonic expansion coefficients and directly synthesized by the spectral division method with a linear loudspeaker array. The results of computer simulations indicate the effectiveness of the proposed analytical formulation.