This paper considers a multi-input multi-output(MIMO) interference network in which each transmitter intendsto communicate with its dedicated receiver at a certain fixed rate. It is known that when perfect CSI is available at each terminal, the interference alignment technique can be applied to align theinterference signals at each receivers in a subspace independent of the desired signal subspace. The impact of interference canhence be eliminated. In practice, however, terminals in general can acquire only noisy CSI. Interference alignment cannot be perfectly performed to avoid interference leakage in the signal subspace. Thus, the quality of each communication link dependson the transmission power of the unintended transmitters. Tosolve this problem, we propose an iterative algorithm to performstochastic power control and transceiver design based on onlynoisy local CSI. The transceiver design is conducted based on the interference alignment concept, and the power control seeks solutions of efficiently assigning transmit powers to provide successful communications for all transmitter-receiver pairs.