This paper proposes a novel channel estimation scheme for the multiuser massive multiple-input multiple-output (MIMO) systems. A discrete Fourier transform (DFT) aided spatial basis expansion model (SBEM) is first introduced to represent the uplink (UL)/downlink (DL) channels with much few parameter dimensions by exploiting the physical characteristics of the uniform linear array (ULA). With SBEM, pilot contamination in the UL training can be relieved by user scheduling exploiting their spatial information. Moreover, the UL spatial information can help to simplify the DL training based on the angle reciprocity. Compared to existing low-rank models, the newly proposed SBEM does not need any information of channel statistics and is suitable for both time division duplex (TDD) and frequency division duplex (FDD) systems. Moreover, the proposed method can be efficiently deployed by the fast Fourier transform (FFT) followed by linear estimator. Various numerical results are provided to corroborate the proposed studies.