A simple harmonic-based multiple-input multiple-output (MIMO) transceiver based on the time-modulated array (TMA) is proposed and verified, including detailed performance analysis, comparisons with state-of-the-art works and experiment verification. The essential concept is utilizing the time modulation technique to linearly map the actual multipath channels between multiple users and the antenna elements of the TMA to the equivalent virtual channels between users and harmonics with different frequencies. Models of the received and transmitted signals in both uplink and downlink transmissions based on the multi-user single-input multiple-output (SIMO) and multiple-input single-output (MISO) scenario are analyzed and derived, followed by the proposed harmonic channel estimation, detection and beamforming methods. Simulations on the performance of the proposed harmonic-based MIMO transceiver are provided and compared to the also TMA-based space division multiple access (SDMA) scheme, showing that the latter is more like a special case of the proposed scheme. An experimental 2-user wireless communication prototype based on a 4-element TMA is fabricated and tested to verify the feasibility and effectiveness of uplink signal transmission.