## 1 Introduction  
For LEO EO satellites, the orbit characteristics lead to limited time for satellite-to-ground data transmission [1]. Technological advancements in satellite engineering have made it feasible to develop EO satellite systems with high spatial, spectral, temporal and radiometric resolutions [2, 3, 4, 5]. With the development of multifunction and high-resolution payloads, there is an obvious boost of the on-board storage and downlink transmission data volume. Therefore, it is necessary to increase the satellite-to-ground data transmission rate and meet the increasing demand for the realization of high-resolution earth observation missions [6]. For the mostly used X-band [7] CCM data transmission scheme, as applied with LEO satellites WorldView-3 [8] and GaoFenDuoMo-1 [9], the link condition variance during a single transmission arc segment can reach 10 dB with the elevation angles ranging between 5\({}^{\circ}\) and 90\({}^{\circ}\)[10]. Additionally, the VCM data transmission scheme is proposed for better use of this margin caused by dynamic link conditions. The GaoFen-7 satellite of China, launched in 2019, adopts the X-band VCM for the first time [11, 12]. However, the 375 MHz bandwidth of X-band has been saturated for higher data rate requirements. Therefore, the Ka-band with 1.5 GHz bandwidth [5] has become the development trend of data transmission [13; 14]. The Ka-band data-transmission suffers a much greater impact of atmospheric environment, whose rain attenuation could exceed 10 dB [15]. This unpredictable variance of the link condition leads to even larger waste of link resources compared with traditional CCM or VCM scheme. Additionally, more link margins need to be designed and reserved to overcome the larger atmospheric attenuation at Ka-band. Based on the above consideration, a close-loop ACM system for Ka-band data transmission could be realized by adding a feedback channel with real-time signal-to-noise ratio (SNR) estimation. According to the real-time feedback of the dynamic downlink condition caused by distance and atmospheric attenuation, the appropriate modulation and coding mode can be adaptively selected at the transmitter, so as to improve the data throughput of the downlink [16]. ACM has been proposed in some communication protocols by European Telecommunications Standards Institute (ETSI) and Consultative Committee for Space Data Systems (CCSDS) [17; 18; 19]. Some literature has developed research on Ka-band CCM, VCM and ACM systems of LEO satellites. Ref. [16] compares the data throughput of CCM, VCM and ACM at Sanya G/S under sunny and rainstorm conditions with one transmission arc segment, and only partially indicates the effect of various attenuations. Refs. [20; 21] analyze the characteristics and link condition of the VCM system, while Ref. [22] focuses on comparing and analyzing different estimation algorithms of the received SNR of the ACM system. Based on the modulation and coding schemes (MCS) recommended by CCSDS using 26.65 GHz signals of Sentinel-1, Ref. [23] analyzes the link availability of CCM, S-VCM, D-VCM and ACM at Matera G/S and Svalbard G/S in Europe. The whole transmission arc segment is divided into six sectors of equal duration, and transmission efficiency analysis is carried out based on the minimum link availability of 99.5% regarding to the specific selected G/S, which might not be applicable to all scenarios. However, the correlation between transmission efficiency and link availability has not been noticed in the above papers. For LEO EO satellites, if only pursuing high link availability, sufficient margin needs to be reserved to compensate the atmospheric attenuation, especially for small elevation angles, which will result in lower useful data rate and could not meet the requirement of high-rate data transmission.