  This letter is concerned with transmit and receive filter optimization for
the K-user MIMO interference channel. Specifically, linear transmit and receive
filter sets are designed which maximize the weighted sum rate while allowing
each transmitter to utilize only the local channel state information. Our
approach is based on extending the existing method of minimizing the weighted
mean squared error (MSE) for the MIMO broadcast channel to the K-user
interference channel at hand. For the case of the individual transmitter power
constraint, however, a straightforward generalization of the existing method
does not reveal a viable solution. It is in fact shown that there exists no
closed-form solution for the transmit filter but simple one-dimensional
parameter search yields the desired solution. Compared to the direct filter
optimization using gradient-based search, our solution requires considerably
less computational complexity and a smaller amount of feedback resources while
achieving essentially the same level of weighted sum rate. A modified filter
design is also presented which provides desired robustness in the presence of
channel uncertainty
