## 1 Introduction  
In 2016, the Laser Interferometer Gravitational-Wave Observatory (LIGO) [1] successfully detected gravitational wave phenomena that proved the existence of gravitational waves. Space-based gravitational wave detection missions have been proposed and performed in recent years because of the surface vibrations of the Earth, the noise of the gravitational gradient, and limitations of the ground test baseline length [2]. These missions include the Laser Interferometer Space Antenna (LISA) mission [3, 4] and the Taiji [5, 6, 7] and Tianqin programs [8]. Space-based gravitational-wave detection usually uses the laser interferometry principle [9] and employs a three-spacecraft constellation placed in an equilateral triangle [3, 4, 5, 6, 8]; many functions are achieved by laser beams exchanged between the spacecrafts (S/Cs), such as scientific interferometry, absolute inter-spacecraft distance measurements, digital data communication, and clock-noise transfer [10; 11; 12]. In a three-spacecraft constellation, the laser on one S/C interferes with the laser received from another S/C. The beat-note signal of two laser is digitized by an analog-to-digital converter (ADC) and analyzed by a high-precision phasemeter (PM). Both the ADC and the PM are triggered by an ultrastable oscillator (USO) that provides a time reference. The frequency instability of the trigger signal introduces additional ranging noise, affecting the arm length measurements. Additionally, the inherent jitter of the ADC distorts the sampling process. A pilot tone (i.e., a stable sinusoidal reference signal derived from the USO) has been inserted to correct the clock and ADC noise [6; 13; 14]. Considering the differential jitter and relative drift of three onboard USOs on different S/Cs, a clock-tone transfer chain has been proposed via an electro-optic modulator (EOM) to modulate the USO signal to sidebands on the outgoing beam to remove clock noise and correct the relative clock drift by using postprocessing [10; 11; 12]. To realize the functions listed above, the frequencies of the USO, sideband, pilot tone, ADC sampling, and beat note must be comprehensively considered and optimized. Moreover, total laser power is a limited resource used to ensure the effectiveness of scientific signal interference, and the readout displacement noise of the signal is affected by the power ratio of the sideband and carrier. The power ratio needs to be reasonably designed to minimize readout displacement noise. Different frequency-setting schemes have been established for the LISA mission to address different concerns. For example, [PERSON] [15] conducted a detailed, in-depth device experiment for the setting of the ADC sampling and pilot-tone frequencies involved in the LISA mission. They concluded that when the pilot-tone frequency was 72 MHz and the ADC sampling frequency was 50 MHz, sampling the beat-note frequency from 2 to 20 MHz could meet the noise requirements of this component of LISA. [PERSON] [13] designed an inter-satellite frequency distribution scheme for the LISA program for beat-note frequencies in the range of [7 MHz, 23 MHz]; the ADC sampling and pilot-tone frequencies were 80 and 75 MHz, respectively. [PERSON] [16] analyzed the Taiji mission orbit and a possible phase-locking scheme and developed an offset frequency-setting scheme for beat-note frequencies in the range of [5 MHz, 25 MHz]. Although all these schemes have considered the problem of frequency setting in space-based gravitational-wave detection missions from different perspectives, they have not provided complete constraints or optimal setting schemes that include the beat-note frequency range as well as the frequencies of USO, ADC sampling, pilot tone, and sideband, and none of them consider the coupling relationship between frequency parameters. The unified consideration of these factors avoids the one-sidedness of individual parameter settings and reduces unnecessary redundancy between parameters, further improving the detection capability.