This letter deals with the joint information and energy processing at a receiver of a point-to-point communication channel. In particular, the trade-off between the achievable information rate and harvested energy for a multiple-antenna power splitting (PS) receiver is investigated. Here, the rate- energy region characterization is of particular interest, which is intrinsically a non-convex problem. In this letter, an efficient algorithm is proposed for obtaining an approximate solution to the problem in polynomial time. This algorithm is mainly based on the Taylor approximation in conjunction with semidefinite relaxation (SDR) which is solved by interior-point methods. Moreover, we utilize the Gaussian randomization procedure to obtain a feasible solution for the original problem. It is shown that by proper receiver design the rate-energy region can be significantly enlarged compared to the state of the art, while at the same time the receiver hardware costs is reduced by utilizing less number of energy harvesting circuitry.