  Measurement-Device-Independent (MDI) QKD eliminates detector side channels in
QKD and allows an untrusted relay between two users. A desirable yet highly
challenging application is to implement MDI-QKD through free-space channels.
One of the major factors that affect the secure key rate in free-space MDI-QKD
is atmospheric turbulence. In this work we show two important results: First,
the independent fluctuations of transmittances in the two channels can
significantly reduce MDI-QKD performance due to turbulence-induced channel
asymmetry. Second, we consider the Prefixed Real-Time Selection (P-RTS) method
we formerly introduced to BB84 and extend it to MDI-QKD. Users can monitor
classical transmittances in their channels and improve performance by
post-selecting signals in real-time based on pre-calculated thresholds. We show
that we can establish a 2-dimensional threshold between Alice and Bob to
post-select signals with both high signal-to-noise ratio and low channel
asymmetry in real time, and greatly extend the maximum range of MDI-QKD in the
presence of turbulence, which can be an important step towards future
free-space MDI-QKD experiments.
