Precoding for 2x2 Doubly-Dispersive WSSUS Channels

TL;DR

This paper derives an analytical solution for optimal precoding in 2x2 doubly-dispersive WSSUS channels, addressing a complex, previously unsolved problem in multicarrier communication link adaptation.

Contribution

It provides the first explicit analytical solution for optimal precoding in 2x2 doubly-dispersive WSSUS channels, leveraging trace class operator optimization.

Findings

Analytic solution for 2x2 channel precoding derived

Optimal multiplexing scheme identified for the specific channel model

Addresses a previously unsolved non-convex optimization problem

Abstract

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 well-known in the context of quantum information theory is unsolved in general due to its non-convex nature. However in very low dimension the problem formulation reveals an additional analytic structure which again admits the solution to the optimal precoder and multiplexing scheme. Hence, in this contribution the analytic solution of the problem for the 2x2 doubly--dispersive WSSUS channel is presented.