  We consider the problem of linear transceiver design to achieve max-min
fairness in a downlink MIMO multicell network. This problem can be formulated
as maximizing the minimum rate among all the users in an interfering broadcast
channel (IBC). In this paper we show that when the number of antennas is at
least two at each of the transmitters and the receivers, the min rate
maximization problem is NP-hard in the number of users. Moreover, we develop a
low-complexity algorithm for this problem by iteratively solving a sequence of
convex subproblems, and establish its global convergence to a stationary point
of the original minimum rate maximization problem. Numerical simulations show
that this algorithm is efficient in achieving fairness among all the users.
