For coherent fiber optic communications, the nonlinear XPolM impairment is the most important issue to realize over-100 Gbps high-speed transmissions. A method provides a way to cancel time-varying XPolM crosstalk by introducing multi-stage adaptive mechanism. In the method, a low-complexity adaptive filtering based on recursive least-squares (RLS) first tracks the time-varying crosstalk along with the per-survivor trellis-state decoding. The estimated channel and the decoded data are then used to calculate the empirical covariance, which is in turn exploited to obtain more accurate channel estimates by means of optimal-weighted least-squares. This is performed with a low-complexity processing over frequency domain with fast Fourier transform. The performance is significantly improved with turbo principle decoding, more specifically, iterative decoding and iterative estimation over a block.