  In satellite-based free-space continuous-variable QKD (CV-QKD), the parameter
estimation for the atmospheric channel fluctuations due to the turbulence
effects and attenuation is crucial for analyzing and improving the protocol
performance. In this paper, compressive sensing (CS) theory is applied to
free-space CV-QKD to achieve the channel parameter estimation with low
computational complexity and small amount of data. According to CS theory, the
possibility of the sparse representation for free-space channel is analyzed and
the two types of sparse reconstruction models for the channel parameters are
constructed combining with the stability of the sub-channels. The most part of
variable for parameter estimation is saved by using the model relying on the
variables in the quantum signals, while all the variables can be used to
generate the secret key by using the model relying on the second-order
statistics of the variables. The methods are well adapted for the cases with
the limited communication time since a little or no variable is sacrificed for
parameter estimation. Finally, simulation results are given to verify the
effectiveness of the proposed methods.
