## 1 Introduction  
Quantum key distribution (QKD) can generate keys to encrypt information. Theoretically, based on quantum mechanics, the security is absolutely guaranteed [1, 2]. In 1984, BB84 protocol, the first QKD protocol, was proposed by [PERSON] [3]. After BB84 protocol was proposed, decades have passed. QKD has much progress [4]. However, due to the imperfect technology, there are some unavoidable security leaks [5, 6, 7]. Methods for different leaks are raised [8, 9, 10]. In 2012, MDI-QKD protocol was put forward by [PERSON] [11], which can solve the problem of unsafe measurement, and it has been improved [12, 13]. It adds an untrust measurement Charlie for bell-state measurement. Besides, [PERSON] and Bob generate keys according to the postelection. In practice we use a weak coherent pulse (WCP) [14] source to emit single photon, whose number of photons obeys Poisson Distribution. So it must have multiphoton part. For this part, there is an attack called photon-number splitting (PNS). In order to solve this problem, decoy-state protocol was proposed and combined with MDI-QKD [15, 16, 17]. In this protocol, [PERSON] and [PERSON] can generate different intensities' pulses to hide the real signal states so that no one knows whether it is signal state except senders. Now MDI-QKD protocol with decoy-state is promising. It can communicate in optical-fiber-based links, and the max communication distance is up to 404 km [12], which can be widely used.  
However, the optical-fiber-based links' loss limits the max communication distance and it leads to difficulties of building the long-distance quantum communication network. Quantum repeater, relying on quantum memory, is a way to solve this problem. We can connect many short-distance links to achieve long-distance communication. In 2021, [PERSON] and [PERSON] et al. [18] reported an elementary link of a quantum repeater based on absorptive quantum memories, which is a promising way of conducting quantum repeater's scheme. Another way is using satellite-based links to realize quantum key distribution in long distance. Classical light in atmosphere has been well improved [19, 20, 21].  
Quantum light in atmosphere has also made some progress [22; 23; 24; 25]. From 2016 to 2020, [PERSON] et al. [26; 27] showed model of probability distribution of transmittance (PDT) in atmosphere under different weather conditions; [PERSON] et al. [28] applied PDT to satellite-based links and studied BB84 protocol in satellite-based links; [PERSON] et al. [29] used MDI-QKD protocol instead of BB84 protocol in [29]. In 2021, [PERSON]'s team [30] reported an integrated space-to-ground quantum communication network by BB84. They used Micius satellite to connect quantum communication network on the ground over 4600 km. However, [PERSON] et al.'s work [28] using BB84 is not safe enough and satellite's position and weather conditions are single in [PERSON] et al.'s work [29], which lead to lack of practicality. Considering that the operation of the satellite and different weather conditions, this paper further researches on the performance of satellite-based links for MDI-QKD protocol when the satellite's height is from 500 km to 2000 km and the angle from zenith is from \(0^{\circ}\) to \(80^{\circ}\).