###### Abstract  
A ranging communication system is a key technology for achieving precise ranging and scientific data exchange in space gravitational wave detection, with the aim of realizing the symmetry of interferometer arms. This system is integrated into the phase measurement payload, the 'phasemeter'. Achieving high-ranging accuracy and low-bit error rate communication while mitigating the impact of phase noise has become a focus of current research. This paper starts with the coding methods for ranging communication and analyzes phase modulation noise based on Binary Phase Shift Keying (BPSK). The study found that the main lobe phase noise caused by BPSK modulation is approximately \(158\upmu\)rad\(/\sqrt{\mathrm{Hz}}\), which is two orders of magnitude higher than the phase-tracking criteria for gravitational wave detection. To address this, this paper proposes a Bit-Balanced Code (BBC) sequence design and optimization method aimed at eliminating main lobe noise. The experimental results show that the optimized BBC sequence improves the metrics of even autocorrelation, odd autocorrelation, maximum spectral amplitude, and even cross-correlation by 7.17, 2.83, 1.22, and 7.16, respectively, compared to the original sequence. Furthermore, experiments have demonstrated that the BBC sequence is insensitive to random data and can achieve dynamic bit balancing to eliminate the DC component. The proposed BBC sequence design method can serve as a reference for technologies related to space gravitational wave detection. space gravitational wave detection; ranging communication; bit-balanced code (BBC); phase noise; binary phase shift keying (BPSK) +
Footnote †: journal: Applied Optics and Photonics  
**Copyright**  
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different satellites caused by gravitational waves are converted into phase changes in the interferometric signal, thereby enabling high-precision distance measurements. However, in an actual space environment, the satellites experience relative orbital motion, resulting in a lack of symmetry in the interferometric arm lengths. This causes laser frequency noise, as the frequency jitter of the laser is proportional to the arm length difference. Such frequency noise is one of the main noise sources in space-based gravitational wave detection. To suppress this noise, a three-level technique is typically employed, including frequency stabilization (Pound-Drever-Hall), arm-locking, and Time Delay Interferometry (TDI). These methods reduce the laser frequency instability noise to the order of \(10^{-6}\) Hz\({}^{1/2}\), meeting the detection requirements. This is essentially achieved through inter-satellite ranging and time synchronization, creating an equivalent equal-arm interferometer [3; 4; 5; 6; 7]. Therefore, ranging and communication technologies are employed in space gravitational wave detection to achieve inter-satellite distance measurement while simultaneously enabling scientific data exchange, thereby generating an equivalent equal-arm interferometer. The principle is based on spread spectrum communication, where the Pseudo-Random Noise (PRN) ranging code sequence is combined with communication data through an XOR operation to generate the ranging communication code. This ranging communication code is then modulated onto the laser phase using BPSK and transmitted to a remote satellite. Unlike conventional inter-satellite communication and satellite navigation communication, the modulation depth of the ranging communication code in the laser phase is limited to only 0.1 rad to minimize its impact on gravitational wave detection signals. Additionally, space gravitational wave detection integrates the ranging communication system into the critical phase measurement payload, the \"phasemeter\", necessitating the consideration of the effects of phase modulation on phase measurement [8; 9; 10].