In this paper, an integrated compact four-channel directly modulated analog optical transceiver is proposed and fabricated. The 3 dB bandwidth of this optical transceiver exceeds 20 GHz, and the measured spurious-free dynamic range is up to $91.2\mathrm{dB}·{\mathrm{Hz}}^{2/3}$. The optical coupling efficiency (CE) is improved by using a precise submicron alignment technique for lens coupling in a transmitter optical subassembly, and the highest CE is achieved when the oblique angle of the arrayed waveguide grating using a silica-based planar lightwave circuit (AWG-PLC) in receiver optical sub assembly is set to 42°. Based on the proposed optical transceiver, we have experimentally demonstrated a 6.624 Gbit/s $4\times 4$ multi-input multioutput (MIMO) 16-quadrature amplitude modulation orthogonal frequency division multiplexing (16QAM-OFDM) radio signal over 15.5 km standard single mode fiber, together with 1.2 m wireless transmission in both an uplink and a downlink. To cope with the channel interference and noise of the fiber-wireless transmission system, a low-complexity MIMO demodulation algorithm based on lattice reduction zero-forcing (LR-ZF) is designed. In our experiment, 1.6 dB power penalty is achieved by using the proposed LR-ZF algorithm, compared to the commonly used zero-forcing algorithm. Moreover, this LR-ZF algorithm has much less complexity than the optimal maximum-likelihood sequence estimation (MLSE) at a given transmission performance. These results not only demonstrate the feasibility of the integrated optical transceiver for MIMO fiber-wireless application but also validate that the proposed LR-ZF algorithm is effective to eliminate the interference for hybrid fiber-wireless transmission.