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A proposal for the realization of highly sensitive optical direct-detection (incoherent) multilevel transmission with arbitrary signal constellation without optical chromatic dispersion (CD) compensation is reviewed in this paper. We introduce transmitter-side signal processing, ??CD pre-equalization,?? and ??phase preintegration?? techniques to realize direct-detection CD-compensation free transmission of arbitrary optical quadrature-amplitude modulation (QAM) signals. We also adopt receiver-side signal processing, ??multi-symbol phase estimation (MSPE),?? and ??non-Euclidean metric-based symbol detection?? to improve the optical SNR (OSNR) sensitivity. We have performed up to 160-km standard single-mode fiber transmission of a 40-Gbit/s 16QAM signal and achieved the OSNR sensitivities only 0.5-2.4 dB away from those of coherent detection.