###### Abstract  
In this paper, a low-complexity joint compensation scheme of carrier recovery (JCSCR) for coherent free-space optical (CFSO) communication is proposed. We applied the carrier recovery joint compensation approach to a CFSO communication system in the quadrature phase shift keying (QPSK) modulation format. A signal-preprocessing stage, which effectively avoided the repetitive operations found in traditional carrier recovery schemes, was proposed. Unlike in existing carrier recovery algorithms, the modulated phase of the received signal could be accurately removed using only the sum and subtraction of real absolute values in the signal-preprocessing stage, greatly reducing the complexity of the operation. Since this algorithm avoids the traditional fourth operation, the system's complexity is reduced while additional noise generated by fourth cross-terms would be prevented and system noise immunity would be greatly enhanced. In addition, this algorithm uses joint compensation of phase errors in the final compensation stage, further reducing the complexity of the computation of the whole algorithmic scheme. A 10 Gbps QPSK CFSO communication transmission experiment was conducted in an atmospheric turbulence channel to verify the proposed technique and improvement in receiver sensitivity. coherent free-space optical communication; digital signal processing; carrier phase recovery; phase modulation; atmospheric turbulence +
Footnote †: journal: _Photonics_
DSP involves two stages in the carrier-phase- recovery module. The carrier frequency offset estimation (CFOE) algorithm is used in the first stage to compensate for the frequency offset (FO) in the carrier waveform, limiting the FO to within the tolerance of the carrier phase estimation. Subsequently, carrier-phase error caused by atmospheric turbulence, laser linewidth, and ASE noise is further corrected with the help of the second-stage carrier phase offset estimation (POE) algorithm, allowing achievement of the correct judgment and demodulation of the received signal. Traditional time-domain carrier recovery modules (abbreviated 4 th-PD-VV algorithm) usually use a combination of the fourth phase difference (4 th-PD) method [11] and the Viterbi-Viterbi phase-estimation (VVPE) algorithm [12; 13] to estimate and compensate for signal carrier frequency and phase offset. The 4 th-PD-VV scheme requires separate fourth-power operations in the CFOE module and the POE module to remove the modulated phase information of a signal. This repetitive operation increases the operational complexity of the whole scheme. In addition, when the modulated phase is removed using the fourth-power operation, a large amount of additional noise appears in the cross-terms generated in the operation, which greatly reduces the noise immunity and receiver sensitivity of the system. Designing an efficient and low-complexity carrier recovery algorithm for CSFO communication systems is a challenging task. In this paper, for the problem of high computational complexity and low noise immunity of the 4 th-PD-VV algorithm, we propose a low-complexity joint compensation scheme of carrier recovery (JCSCR) for high-speed CFSO systems. This scheme's design includes a signal-preprocessing stage that removes the modulated phase information of the signal using real-absolute-value addition and subtraction. This approach reduces the complexity of the system while avoiding the system performance impact of the additional noise generated by the fourth-power operation in the 4 th-PD-VV algorithm. Finally, we propose that joint compensation of the FOE value and the POE value is used in the signal-compensation-estimation error stage, further reducing the complexity of the overall scheme. Due to the benefit of the optimization of the signal-preprocessing stage, the number of multipliers required in the operation of the proposed scheme is less than \(\frac{1}{3}\) of the those for the 4 th-PD-VV scheme.