In this paper, a practical solution to implement the distributed interference alignment (IA) algorithm of  in a cellular communication system is proposed. In the training period of the proposed strategy, the User Equipment (UE) and the Base Station (BS), without knowing a priori the interference covariance matrix, update directly the precoding and interference suppression matrices based on the received signals by a minor subspace tracking algorithm. At the end of the training phase, the precoding and interference suppression matrices are then used at the UE and BS, respectively, for the transmission period. A special spatial reuse method is also proposed for the training period to lower the system overhead. Numerical system performance results are provided, showing that the algorithm, referred to as Interference Subspace Tracking IA (IST-IA), yields a good trade-off between throughput gains, on one side, and training overhead and computational complexity, on the other. It is also argued that IST-IA is a promising solution not only for training but also for the tracking phase, if applicable.