This paper considers the implementation and application possibilities of a compact full duplex multiple-input multiple-output (MIMO) architecture where direct communication exists between users, e.g., device-to-device (D2D) and cellular link coexisting on the same spectrum. For the architecture of the compact full duplex radio, we combine an analog self-interference canceler based dual-polarization with high cross-polarization discrimination (XPD) and Long Term Evolution (LTE)-based per-subcarrier digital self-interference canceler. While we consider the compactness and power efficiency of an analog solution, we focus on the digital canceler design with robustness to a frequency-selective channel and high compatibility with a conventional LTE system. For an over-the-air wireless experiment of full duplex testbed with a two-user-pair, we implement a full duplex MIMO physical layer (PHY), supporting 20 MHz bandwidth, on an FPGA-based software-defined radio platform. Further, we propose a novel timing synchronization method to construct a more viable full duplex MIMO link. By having the full duplex link prototype fully operating in real-time, we present the first characterization of the proposed compact full duplex MIMO performance depending on the transmit power of the full duplex node. We also show the link quality between nodes. One of the crucial insights of this work is that the full duplex operation of a user is capable of acquiring the throughput gain if the user has self-interference capability with guaranteed performance.