# Analysis of Grating Lobe Effects on GEO DSC Distributed Antennas
## 1 Introduction
On the one hand, the unavoidable existence of phase drift jitter, including tropospheric and ionospheric delays, antenna pointing errors, signal transmission delays of each antenna, antenna and channel thermal ups and downs, random fluctuations in transmittance power and gain, receiver processing and other errors, will lead to the phase instability of the transmitted signals, thus lowering the signal-to-noise ratio of the signal received by the antennas and the antenna gain, which increases the difficulty of the synthesis of satellite-borne distributed antenna cooperative transmission signals [13]. On the other hand, due to the spacing between satellites being much larger than their operating wavelengths, a large number of grating lobes are easily generated during the beamforming process of satellite-mounted distributed antennas. The presence of grating lobes leads to a decrease in gain, dispersion of radiated energy, and misjudgment of target localization and direction measurement. Therefore, it is necessary to suppress grating lobes. The geometrical arrangement and antenna positions of the distributed antenna carried by the satellites are important factors that affect the occurrence of grating lobes. In this paper, we investigate the effect of grating lobes on DSC distributed antennas in GEO, assuming that the phase drift jitter error is not considered after compensating and calibrating the signal time delay and phase of the receiver side. The main contributions of this study are summarized as follows. * We established a distributed antenna cooperative transmission scenario for DSC systems, utilizing multiple DSC satellites equipped with antennas operating in the same frequency band. Moreover, we present the cooperative transmission principles of DSC distributed antennas at both the satellite and ground ends. Furthermore, mathematical expressions for the synthesis of far-field signal strength and the far-field antenna pattern of DSC distributed antennas are provided. * Considering the grating lobe effect of DSC distributed antennas during the cooperative transmission process, a simulation analysis was conducted on the far-field pattern of DSC distributed antennas by changing the relative positions and carrier phases of the distributed antennas in the scenario of two DSC satellites. The simulation resultsindicate that the relative positions of the satellites will affect the interference patterns, and changes in the carrier phase will result in the translation of interference patterns. * In order to effectively avoid the occurrence of grating lobes, we considered each individual DSC satellite as an antenna element, while the satellites themselves formed a super-sparse array with a non-periodic arrangement. The antenna patterns of two different array layouts, namely, uniform and non-periodic arrangements of 10 satellites in clusters, were simulated and analyzed. The simulation results indicate that non-periodic array can mitigate the appearance of grating lobes, but it disperses the energy of the grating lobes into the sidelobe region, resulting in an overall increase in the sidelobe level. To control the overall sidelobe level, further optimization of the layout is required. The remaining sections of this paper are organized as follows. Section 2 introduces the scene model and array configuration of the DSC distributed antenna. Section 3 analyzes the impact of grating lobes by simulating the grating lobes formed by two DSC distributed antenna arrays and proposes grating lobe suppression strategies. In Section 4, the grating lobes formed by the beamforming of 10 satellites in the distributed satellite clusters are suppressed using a non-periodic arrangement. Finally, Section 5 provides a summary of this paper.