Coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems have recently become promising due to its robustness against dispersion and high spectral efficiency in long haul transmission. Because next generation optic communication requires data rate of 100 Gbps or more, the sampling rate and the operating frequency of digital signal processing (DSP) are high as well. The algorithm applicable to the practical implementation is thus indispensable. In this thesis, the real-time DSPs for high-speed CO-OFM have been investigated; wide range carrier frequency offset estimation, guard interval reduction, and symbol timing synchronization.
Wide range carrier frequency offset estimation using Chinese remainder theorem: CO-OFDM systems have an wide carrier frequency offset (CFO) range due to the instability of lasers. To widen the estimation range efficiently, the Chinese remainder theorem (CRT) is applied to obtain the integer part of CFO in the time domain. This adoption uses the circular nature of phase difference induced by CFO, which is the characteristic of modular arithmetic. For the proposed estimator, a training symbol structure consisting of two identical symbols is suggested. To further reduce overhead due to two training symbols, a training symbol consisting of single frequency is proposed. The proposed CRT-based algorithms are demonstrated in a polarization division multiplexing (PDM) 16-ary quadrature amplitude modulation (QAM) CO-OFDM system transmission over 1,600 km standard single-mode-fiber (SSMF). In addition, the hardware feasibility of the proposed systems is shown in a real-time 4 QAM CO-OFDM transmission over 200 km SSMF. The off-line and real-time experiment results showed that this estimator achieved the widest estimation range in the sampled system, high accuracy, low hardware complexity and fast acquisition at the same time.
Efficient chromatic dispersion pre-compensation using timing offset: For real-time CO-OFDM systems, hardware-efficient guard interval reduction is required to obtain higher bandwidth or longer transmission length with a small overhead while maintaining an optimum FFT size. Chromatic dispersion pre-compensation algorithms are proposed to provide hardware-efficient guard interval reduction. A transmitter which combines overlapped frequency domain equalizer (OFDE) and short-cyclic-prefix is presented to compensate for intra-subband dispersion using OFDE, and inter-subband dispersion using timing offset. The number of complex multiplications of the proposed system with two subbands is reduced to about 70% of that of a conventional system.
Also, another transmitter is introduced which efficiently implements short-cyclic-prefix CO-OFDM by using lookup table (LUT)-type IDFT with phase rotation per subcarrier. LUT-type IDFT enables to increase the number of subbands efficiently and phase rotation enables to adopt channel smoothing algorithm. In result, the proposed pre-compensation improves the transmission performance. Simulation results show that the transmission distance is increased about 4 times and the OSNR penalty is decreased about 4.1 dB at the CD of 15,000 ps/nm compared to the conventional short-cyclic-prefix CO-OFDM systems.
Efficient two-step symbol timing synchronization with simplified time metric: CO-OFDM systems operate with high speed, while field programmable gate array (FPGA) provides relatively slow clock speed. Thus, real-time implementation requires high parallelism. Because the complexity increase as parallelism of a system increases, hardware-efficient algorithm is essential. Especially accurate symbol timing synchronization algorithms requires timing metric for every sample, resulting in high complexity. To provide hardware-efficient symbol timing synchronization, simplified timing metric using only a sign bit is proposed. In addition, two-step synchronization is proposed to avoid calculation of high complexity for every sample. In the first step, timing metric with low accuracy is calculated and maximum valued samples are chosen. In the next step, timing metric with high accuracy is calculated within chosen samples and symbol start is determined by maximizing the second timing metric. Real-time experiments of 4-QAM over 200 km transmission verified that simplified timing metric could accurately estimate symbol timing offset with reduced complexity. In addition, the hardware cost is reduced about 30% by adopting the proposed two-step synchronization technique.
Keywords: Carrier frequency offset (CFO), Chromatic dispersion (CD), orthogonal frequency division multiplexing (OFDM), coherent optical OFDM (CO-OFDM), optical fiber communication, symbol timing synchronization.
Coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems have recently become promising due to its robustness against dispersion and high spectral efficiency in long haul transmission. Because next generation optic communication requires data rate of 100 Gbps or more, the sampling rate and the operating frequency of digital signal processing (DSP) are high as well. The algorithm applicable to the practical implementation is thus indispensable. In this thesis, the real-time DSPs for high-speed CO-OFM have been investigated; wide range carrier frequency offset estimation, guard interval reduction, and symbol timing synchronization.
Wide range carrier frequency offset estimation using Chinese remainder theorem: CO-OFDM systems have an wide carrier frequency offset (CFO) range due to the instability of lasers. To widen the estimation range efficiently, the Chinese remainder theorem (CRT) is applied to obtain the integer part of CFO in the time domain. This adoption uses the circular nature of phase difference induced by CFO, which is the characteristic of modular arithmetic. For the proposed estimator, a training symbol structure consisting of two identical symbols is suggested. To further reduce overhead due to two training symbols, a training symbol consisting of single frequency is proposed. The proposed CRT-based algorithms are demonstrated in a polarization division multiplexing (PDM) 16-ary quadrature amplitude modulation (QAM) CO-OFDM system transmission over 1,600 km standard single-mode-fiber (SSMF). In addition, the hardware feasibility of the proposed systems is shown in a real-time 4 QAM CO-OFDM transmission over 200 km SSMF. The off-line and real-time experiment results showed that this estimator achieved the widest estimation range in the sampled system, high accuracy, low hardware complexity and fast acquisition at the same time.
Efficient chromatic dispersion pre-compensation using timing offset: For real-time CO-OFDM systems, hardware-efficient guard interval reduction is required to obtain higher bandwidth or longer transmission length with a small overhead while maintaining an optimum FFT size. Chromatic dispersion pre-compensation algorithms are proposed to provide hardware-efficient guard interval reduction. A transmitter which combines overlapped frequency domain equalizer (OFDE) and short-cyclic-prefix is presented to compensate for intra-subband dispersion using OFDE, and inter-subband dispersion using timing offset. The number of complex multiplications of the proposed system with two subbands is reduced to about 70% of that of a conventional system.
Also, another transmitter is introduced which efficiently implements short-cyclic-prefix CO-OFDM by using lookup table (LUT)-type IDFT with phase rotation per subcarrier. LUT-type IDFT enables to increase the number of subbands efficiently and phase rotation enables to adopt channel smoothing algorithm. In result, the proposed pre-compensation improves the transmission performance. Simulation results show that the transmission distance is increased about 4 times and the OSNR penalty is decreased about 4.1 dB at the CD of 15,000 ps/nm compared to the conventional short-cyclic-prefix CO-OFDM systems.
Efficient two-step symbol timing synchronization with simplified time metric: CO-OFDM systems operate with high speed, while field programmable gate array (FPGA) provides relatively slow clock speed. Thus, real-time implementation requires high parallelism. Because the complexity increase as parallelism of a system increases, hardware-efficient algorithm is essential. Especially accurate symbol timing synchronization algorithms requires timing metric for every sample, resulting in high complexity. To provide hardware-efficient symbol timing synchronization, simplified timing metric using only a sign bit is proposed. In addition, two-step synchronization is proposed to avoid calculation of high complexity for every sample. In the first step, timing metric with low accuracy is calculated and maximum valued samples are chosen. In the next step, timing metric with high accuracy is calculated within chosen samples and symbol start is determined by maximizing the second timing metric. Real-time experiments of 4-QAM over 200 km transmission verified that simplified timing metric could accurately estimate symbol timing offset with reduced complexity. In addition, the hardware cost is reduced about 30% by adopting the proposed two-step synchronization technique.
Keywords: Carrier frequency offset (CFO), Chromatic dispersion (CD), orthogonal frequency division multiplexing (OFDM), coherent optical OFDM (CO-OFDM), optical fiber communication, symbol timing synchronization.
