High spectral efficiency in wavelengthdivision multiplexing (WDM) coherent optical communications can be achieved by lowering the channel spacing to a value close to the baud rate. As a result, such communication systems are subject to a high level of two-dimensional (2D) interference, originating from both chromatic dispersion (CD) within WDM channels and cross talk between WDM channels. We propose to digitally restore the transmitted information at the receiver side by jointly processing the WDM channels, using 2D interference cancellation methods interacting with a forward error correction decoder. Such schemes have been investigated extensively for known channel parameters; however, little is known about the error performance in the absence of channel state information. This issue is important, since in practice uncertainties about the physical parameters of the optical fiber and noise levels are unavoidable. In this paper, we propose optical channel parameter estimation schemes with limited impact on the overall complexity. First, a decision-aided carrier phase recovery, taking the presence of 2D interference into account, is designed to compensate the laser beat linewidth. Then we provide a technique to estimate the linear channel impairments for each WDM channel, based on a limited number of training symbols. The validity of the proposed method is evaluated by numerical simulations taking into account linear and nonlinear fiber impairments. In particular, we show that for high-order modulations, joint processing of spectrally overlapping WDM channels becomes mandatory to obtain satisfactory performances