We propose a novel recursive-algorithm based maximum a posteriori probability (MAP) detector in spectrally-efficient coherent wavelength division multiplexing (CoWDM) systems, and investigate its performance in a 1-bit/s/Hz on-off keyed (OOK) system limited by optical-signal-to-noise ratio. The proposed method decodes each sub-channel using the signal levels not only of the particular sub-channel but also of its adjacent sub-channels, and therefore can effectively compensate deterministic inter-sub-channel crosstalk as well as inter-symbol interference arising from narrow-band filtering and chromatic dispersion (CD). Numerical simulation of a five-channel OOK-based CoWDM system with 10Gbit/s per channel using either direct or coherent detection shows that the MAP decoder can eliminate the need for phase control of each optical carrier (which is necessarily required in a conventional CoWDM system), and greatly relaxes the spectral design of the demultiplexing filter at the receiver. It also significantly improves back-to-back sensitivity and CD tolerance of the system.