Patent ID: 8320778

Claim:
A non-transitory computer readable medium storing computer program instructions for compensating a received signal and adaptive polarization recovery, which, when executed on a processor, cause the processor to perform operations comprising: utilizing a plurality of reference circles cascaded relative to each other to modify the received signal, wherein each reference circle has a different modulus, the reference circles defined by: Δ ( p , q ) =   z  p - C 1  q - C 2 ⁢ ⁢ C 1 = R ⁢ ⁢ 1 p + R ⁢ ⁢ 2 p 2 ⁢ ⁢ C 2 = ( R ⁢ ⁢ 1 p - R ⁢ ⁢ 2 p 2 ) q , wherein an error ε is represented by ε=ƒ 2 (ƒ 1 (| Z|,C 1 ), C 2 ) where f 1 and f 2 are two functions (of two variables) and C 1 and C 2 are two constants, such that functions, f 1 and f 2 , and constants, C 1 and C 2 , are determined to make ƒ 2 (ƒ 1 (|Z|, C 1 ), C 2 ) approach zero for an 8-QAM signal.