We report the use of implicit training-aided channel estimation (ITA-CE) for polarization-division-multiplexed (PDM) single-carrier coherent optical systems. With the concept of ITA-CE, where the training sequence (TS) is arithmetically added onto the information symbols rather than appearing in separate time slots, overhead-free transmission can be achieved with minor optical signal to noise ratio (OSNR) penalty. ITA-CE system enables simple digital pilot-tone based frequency-offset compensation, and inherits the benefits from typical training-aided channel acquisition and data recovery. Furthermore, we address the issue of self-interference to channel estimation (CE) of ITA-CE system in this paper. The data-induced interference can be eliminated by removing the cyclic mean of the transmitted signal, which can accelerate the convergence of the CE and allows smaller power to be allocated to the TS, leading to enhanced system performance. Numerical simulations and experiments for both PDM-QPSK and PDM-16-QAM systems have been conducted to verify the proposed scheme. Comparable performance to the conventional blind equalization system can be achieved when employing the transmitter side pre-distortion approach to the ITA-CE system.