Consider a downlink MIMO heterogeneous wireless network with multiple cells, each containing many mobile users and a number of base stations with varying capabilities. A central task in the management of such a network is to assign each user to a base station and design a linear transmit strategy to ensure a satisfactory level of network performance. In this work, we propose a formulation for the joint base station assignment and linear transceiver design problem based on the maximization of a system wide utility. We first establish the NP-hardness of the resulting optimization problem for a large family of α-fairness utility functions. Then, we propose an efficient algorithm to approximately solve this problem for a variety of different utility functions. Our numerical experiments show that the proposed algorithm can achieve significantly higher levels of system throughput and user fairness than what is possible by optimizing the precoders alone.