The system also includes components that combine contributions from different signals so as to generate composite signals that each carries the LIDAR data. Each composite signal is associated with a polarization state and is also a signal component selected from a quadrature component and an in-phase component. Each of the composite signals is associated with a different combination of polarization state and signal component. The system also includes electronics that combine the composite signals so as to generate an in-phase component of a complex LIDAR data signal and a quadrature component of the LIDAR data signal. The electronics extract the LIDAR data from the complex LIDAR data signal.