The performance of millimeter wave (mmWave) communications strongly relies on accurate beamforming both at base station and user terminal sides, referred to as beam alignment (BA). Existing BA algorithms provide initial yet coarse angle estimates as they typically use a codebook of a finite number of discreteized beams (angles). Towards emerging applications requiring timely and precise tracking of dynamically changing state of users, we consider a system where a base station with a co-located radar receiver estimates relevant state parameters of users and simultaneously sends OFDM-modulated data symbols. In particular, based on a hybrid digital analog data transmitter/radar receiver architecture, we propose a simple beam refinement and initial state acquisition scheme that can be used for beam and user location tracking in a dynamic environment. Numerical results inspired by IEEE802.11ad parameters demonstrate that the proposed method is able to improve significantly the communication rate and further achieve accurate state estimation.