US Patent 10461972 Using multi-level pulse amplitude modulation with probabilistic shaping

An optical receiver apparatus includes a photo detector that detects amplitude modified optical signals transmitted through an optical transmission channel and mapped to constellation points and converts the optical signal into electrical signals, a sampling circuit that samples the electrical signals and generates digital signals, and a signal processing circuit that has a two-step equalization algorithm converging actual constellation points into desired constellation points. The two-step equalization algorithm includes a first equalization algorithm that uses multiple modulus in performing an error signal calculation, and a second equalization algorithm that includes a filtering procedure that compares actual constellation points with desired constellation points and an adjustment procedure that iteratively adjusts parameters of the filtering procedure in accordance with the comparison result.