  Reconfigurable multiple-input multiple-output can provide performance gains
over traditional MIMO by reshaping the channels, i.e., introducing more channel
realizations. In this paper, we focus on the achievable rate maximization
pattern design for reconfigurable MIMO systems. Firstly, we introduce the
matrix representation of pattern reconfigurable MIMO (PR-MIMO), based on which
a pattern design problem is formulated. To further reveal the effect of the
radiation pattern on the wireless channel, we consider pattern design for both
the single-pattern case where the optimized radiation pattern is the same for
all the antenna elements, and the multi-pattern case where different antenna
elements can adopt different radiation patterns. For the single-pattern case,
we show that the pattern design is equivalent to a redistribution of gains
among all scattering paths, and an eigenvalue optimization based solution is
obtained. For the multi-pattern case, we propose a sequential optimization
framework with manifold optimization and eigenvalue decomposition to obtain
near-optimal solutions. Numerical results validate the superiority of PR-MIMO
systems over traditional MIMO in terms of achievable rate, and also show the
effectiveness of the proposed solutions.
