  In this paper, we theoretically investigate a new technique for simultaneous
information and power transfer (SWIPT) in multiple-input multiple-output (MIMO)
point-to-point with radio frequency energy harvesting capabilities. The
proposed technique exploits the spatial decomposition of the MIMO channel and
uses the eigenchannels either to convey information or to transfer energy. In
order to generalize our study, we consider channel estimation error in the
decomposition process and the interference between the eigenchannels. An
optimization problem that minimizes the total transmitted power subject to
maximum power per eigenchannel, information and energy constraints is
formulated as a mixed-integer nonlinear program and solved to optimality using
mixed-integer second-order cone programming. A near-optimal mixed-integer
linear programming solution is also developed with robust computational
performance. A polynomial complexity algorithm is further proposed for the
optimal solution of the problem when no maximum power per eigenchannel
constraints are imposed. In addition, a low polynomial complexity algorithm is
developed for the power allocation problem with a given eigenchannel
assignment, as well as a low-complexity heuristic for solving the eigenchannel
assignment problem.
