Precoding for 2 x 2 Doubly-Dispersive WSSUS Channels

Optimal link adaption to the scattering function of wide sense stationary uncorrelated scattering (WSSUS) mobile communication channels is still an unsolved problem despite its importance for next-generation system design. In multicarrier transmission such link adaption is performed by pulse shaping which in turn is equivalent to precoding with respect to the second order channel statistics. In the present framework a translation of the precoder optimization problem into an optimization problem over trace class operators is used. This problem which is also wellknown in the context of quantum information theory is unsolved in general due to its non-convex nature. However in very low dimensions the problem formulation reveals an additional analytic structure which admits the solution to the optimal precoder and multiplexing scheme. Hence, in this contribution the analytic solution of the problem for the 2 x 2 doubly-dispersive WSSUS channel is presented.