To get channel state information (CSI) at a base station (BS), most of researches on massive multiple-input multiple-output (MIMO) systems consider time division duplexing (TDD) to get benefit from the uplink and downlink channel reciprocity. Even in TDD, however, the BS still needs to transmit downlink training signals, which are referred to as channel state information reference signals (CSI-RSs) in the 3GPP standard, to support spatial multiplexing in practice. This is because there are many cases that the number of transmit antennas is less than the number of receive antennas at a user equipment (UE) due to power consumption and circuit complexity issues. Because of this mismatch, uplink sounding reference signals (SRSs) from the UE are not enough for the BS to obtain full downlink MIMO CSI. Therefore, after receiving the downlink CSI-RSs, the UE needs to feedback quantized CSI to the BS using a pre-defined codebook to support spatial multiplexing. In this paper, possible approaches to reconstruct full downlink MIMO CSI at the BS are proposed by exploiting both the SRS and quantized downlink CSI considering practical antenna structures with reduced downlink CSI-RS overhead. Numerical results show that the spectral efficiencies by spatial multiplexing based on the proposed downlink MIMO CSI reconstruction techniques outperform the conventional methods solely based on the quantized CSI.