The performance of a coherent Doppler lidar is determined by the stati
stics of the coherent Doppler signal. The derivation and calculation o
f the covariance of the Doppler lidar signal for random atmospheric wi
nd fields and wind shear are presented. The signal parameters are defi
ned for a general coherent Doppler lidar system in terms of the atmosp
heric parameters. There are two distinct physical regimes: one in whic
h the transmitted pulse determines the signal statistics and the other
in which the wind field and the atmospheric parameters dominate the s
ignal statistics. When the wind fields dominate the signal statistics,
Doppler lidar data are nonstationary and the signal correlation time
is proportional to the operating wavelength of the lidar. The signal c
ovariance is derived for signal-shot and multiple-shot conditions. For
a single shot, the parameters of the signal covariance depend on the
random, instantaneous atmospheric parameters. For multiple shots, vari
ous levels of ensemble averaging over the temporal scales of the atmos
pheric processes are required. The wind turbulence is described by a K
olmogorov spectrum with an outer scale of turbulence. The effects of t
he wind turbulence are demonstrated with calculations for a horizontal
propagation path in the atmospheric surface layer.