In this paper we present results of investigation of the main optical properties of East Asian clouds with a ground-based polarization lidar placed in Daejeon, Republic of Korea. Asian dust is located in elevated layers of the atmosphere in spring, travels long distances, and causes significant damage to ecology. We present backscattering matrices of clouds obtained from polarimetric remote measurements which comprise information on the scattering and absorption properties of cloud particles, their morphology, and spatial orientation. Theory of our applied lidar polarization experiment is presented in terms of the instrumental vectors of a transmitter and a receiver. Methods of solving linear and nonlinear systems of equations comprising echo signals are considered. Some numerical and measurement results are presented to illustrate the efficiency and versatility of the method of estimating the cloud parameters.