Digital signal processing system for phase noise correction in a coherent optical channel multi-carrier optical system for signal transmission, wherein the multi-carrier system comprises a transmitter with a laser to emit two or more subcarriers (SC) and a receiver with a laser to receive said subcarriers (SC); wherein the optical channel has chromatic dispersion (CD), the laser of the emitter has phase noise (Pt), and the laser of the receiver has phase noise (Pr); wherein the digital signal processing system comprises an electronic data processor configured to obtain a receiver phase noise estimate (Pr') through the linear combination of the transmitter phase noise and the receiver phase noise, when said linear combination is received at the receiver, by the steps of: selecting a first subcarrier (Pm) and a second subcarrier (Pn), wherein m and n designate, respectively, the index of the first subcarrier (Pm) and the index of the second subcarrier (Pn); from said selected subcarriers, obtaining a phase estimate of the first subcarrier (Pm') and a phase estimate of the second subcarrier (Pn'); characterized in that the calculation of the linear combination of the transmitter phase noise and the receiver phase noise to obtain the receiver phase noise estimate (Pr') comprise the step of estimating the receiver phase noise (Pr') by first order integration of the multiplication of Ts/((n-m)Tcd) by the difference between the phase estimate of the first subcarrier (Pm') and the phase estimate of the second subcarrier (Pn'); wherein Ts is the symbol period and Tcd the time delay between two adjacent subcarriers, imposed by the chromatic dispersion during the signal propagation through the optical channel. wherein the optical channel has chromatic dispersion (CD), the laser of the emitter has phase noise (Pt), and the laser of the receiver has phase noise (Pr); wherein the digital signal processing system comprises an electronic data processor configured to obtain a receiver phase noise estimate (Pr') through the linear combination of the transmitter phase noise and the receiver phase noise, when said linear combination is received at the receiver, by the steps of: selecting a first subcarrier (Pm) and a second subcarrier (Pn), wherein m and n designate, respectively, the index of the first subcarrier (Pm) and the index of the second subcarrier (Pn); from said selected subcarriers, obtaining a phase estimate of the first subcarrier (Pm') and a phase estimate of the second subcarrier (Pn'); selecting a first subcarrier (Pm) and a second subcarrier (Pn), wherein m and n designate, respectively, the index of the first subcarrier (Pm) and the index of the second subcarrier (Pn); from said selected subcarriers, obtaining a phase estimate of the first subcarrier (Pm') and a phase estimate of the second subcarrier (Pn'); characterized in that the calculation of the linear combination of the transmitter phase noise and the receiver phase noise to obtain the receiver phase noise estimate (Pr') comprise the step of estimating the receiver phase noise (Pr') by first order integration of the multiplication of Ts/((n-m)Tcd) by the difference between the phase estimate of the first subcarrier (Pm') and the phase estimate of the second subcarrier (Pn'); wherein Ts is the symbol period and Tcd the time delay between two adjacent subcarriers, imposed by the chromatic dispersion during the signal propagation through the optical channel. <EOS>