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A simple polarization-multiplexed (PM) discrete multitone (DMT) system with intensity modulation and direct detection (IM-DD) is proposed for short-reach optical communications. Only four photodetectors (PDs) are required at the receiver, and no extra 90° hybrid and balanced detection is necessary. Novel digital signal processing (DSP) algorithms are proposed for state-of-polarization (SOP) estimation and subsequent mixed polarization beat interference (MPBI) elimination. These enable polarization demultiplexing and channel estimation to be implemented by a simple 2 × 2 multiple-input and multiple-output (MIMO) frequency-domain equalizer. The feasibility of the proposed PM-DMT-DD system and the effectiveness of the novel DSP algorithms are investigated via theoretical and simulation studies.