The advancement of satellite communications has revealed limitations in traditional microwave communications due to restricted bandwidth resources and transmission capacity. While optical fiber communications offer alternatives, they present challenges in deployment costs and maintenance, particularly for intersatellite and deep space applications. Space coherent optical communication enables information transmission through phase modulation and coherent detection technology, utilizing light’s amplitude, frequency, and phase dimensions. This technology increases single-channel capacity to more than tenfold compared to traditional intensity modulation techniques. The system offers advantages including narrow laser emission angles, enhanced confidentiality, minimal emission aperture, and flexible deployment capabilities. However, atmospheric channels significantly constrain space optical communication development. The extended communication distance results in substantial laser signal energy loss, necessitating high receiver sensitivity in the absence of relays. Additionally, atmospheric turbulence causes fluctuations in the atmospheric refractive index, leading to laser beam intensity flickering and phase disturbances. These effects introduce random carrier phase disturbances at the receiving end, increasing the likelihood of signal phase misidentification. Digital signal processing algorithms are essential for compensating received signals to mitigate atmospheric channel impacts. Blind phase estimation, while effective for signal compensation, requires optimization due to its high complexity.

The optimization of blind phase estimation algorithms follows two primary approaches: modifying the BPS function’s error function to reduce multiplier usage, and implementing a two-step phase estimation through coarse and fine estimation. The first approach effectively reduces computational complexity but often compromises the BPS algorithm’s estimation accuracy, resulting in significant error vector amplitude performance loss. The second approach maintains estimation accuracy while moderately reducing computational complexity. However, these methods have not addressed the fundamental issue of the BPS algorithm’s high computational complexity, as numerous phase test angle calculations remain necessary. This paper addresses computational complexity reduction through optimization of the phase test angle search strategy. The methodology primarily employs piecewise parabolic interpolation for secondary estimation. The process begins with traditional BPS for coarse phase estimation, followed by piecewise parabolic interpolation iteration for refined phase estimates, with accuracy determined by predetermined termination conditions.

The piecewise parabola interpolation algorithm demonstrates comparable performance to traditional BPS in estimated angle accuracy while achieving significant computational complexity reduction. Indoor coherent optical communication experiments utilizing 5 Gbit/s QPSK verify the algorithm’s estimation effectiveness across different phase intervals [Fig. 4(a)]. Results indicate that π/16 and π/32 systems achieve 0.5 dB sensitivity improvement compared to π/8 system. Subsequent testing with π/16 phase interval compares BPS and P-BPS algorithm sensitivities at various phase test angles [Fig. 4(b)], revealing 0.5 dB sensitivity improvement at reduced computational complexity. The algorithm shows substantial computational efficiency improvements compared to previously published methods (Table 1). Error vector amplitude comparisons demonstrate enhanced accuracy of the P-BPS algorithm while maintaining reduced computational complexity (Fig. 5). Field verification experiments achieve spatial coherent optical communication over 29 km. Comparative analysis of bit error rate performance between P-BPS and BPS algorithms, with received optical power between -30 dBm and -40 dBm, demonstrates superior P-BPS performance under identical test angles (Fig. 8).

This paper presents a low-complexity P-BPS algorithm addressing the computational complexity challenges of the BPS algorithm in phase estimation. The algorithm enhances the BPS exhaustive search method through piecewise parabolic interpolation, implementing initial rough estimates with minimal test phase angles followed by interpolated phase test angle refinement. This approach eliminates comprehensive angle testing while improving receiving sensitivity and reducing computational complexity. Experimental validation through indoor coherent optical communication and field testing demonstrates P-BPS’s superior capability in correcting phase offset with reduced computational requirements compared to traditional BPS. The algorithm proves particularly effective in conditions of significant phase noise caused by atmospheric turbulence, requiring fewer phase test angles than traditional BPS for accurate estimation. P-BPS thus represents an efficient, practical solution for phase estimation in spatial coherent optical communication.