In this paper we jointly consider the normally distinct worlds of communication system design and circuit theory. We introduce the — up to our knowledge — first algorithm to optimize the uncoupled matching network (UC-MN) at a receiver that uses a linear MMSE equalizer in a MU-MIMO system with compact antenna array at the receiver. We design our adaptive UC-MN in order to either maximize the minimum rate of all users or to maximize the total sum rate. We compare to the conventional matching, which ignores antenna coupling, and to the cases of choosing one of the MNs that either maximizes the achievable rate or maximizes the minimum user rate for joint decoding of all data streams. In all cases, we observe a considerable performance boost. We view our results as an example of the potential of jointly considering circuit theoretical aspects and communication theory, especially for systems adopting large antenna arrays in a confined space.