The dynamic nature of indoor environments poses unique challenges for next-generation millimeter-wave (mmwave) connectivity. These challenges arise from blockages due to mobile obstacles, mm-wave signal scattering caused by indoor surfaces, and imperfections in phased antenna arrays. Consequently, traditional compressed sensing (CS) techniques for beam alignment become ineffective in practice under such settings. This paper proposes a novel beam alignment technique suited for mm-wave systems operating in indoor environments. The proposed technique exploits the energy compaction property of the discrete cosine transform to compressively sense and identify the strongest cluster locations in the transform domain for robust beamforming. Experimental results at 60 GHz demonstrate successful beam alignment with limited measurements even in the presence of partial blockages during the beam training phase.