Higher order Ambisonics (HOA) is one of the most promising technology in the reproduction of spatial audio in terms of spatial resolution. However binaural reproduction of spatial audio is ubiquitously used in several popular applications like AR. A novel method for binaural reproduction of HOA signals using sparse plane wave expansion is proposed in this paper. Unlike the parametric methods, the proposed method does not require prior information about the number of the discrete sources. The plane wave expansion of the encoded signals is obtained in the spherical harmonics domain using the multiple measurement vector projections, while upscaling of the input encoded signal is done to preserve the spatial resolution. Head-related transfer function (HRTF) cues are subsequently used to develop the binaural decoder. Unlike the virtual loudspeakers based approach it provides more accuracy in terms of spatial resolution as it removes the diffuse component. The efficacy of this method is illustrated using objective and subjective evaluations.