  In this paper, we consider a two-cell interfering two-user multiple-input
multiple-output multiple access channel (MIMO-MAC) with limited feedback. We
first investigate the multiplexing gain of such channel when users have perfect
channel state information at transmitter (CSIT) by exploiting an interference
alignment scheme. In addition, we propose a feedback framework for the
interference alignment in the limited feedback system. On the basis of the
proposed feedback framework, we analyze the rate gap loss and it is shown that
in order to keep the same multiplexing gain with the case of perfect CSIT, the
number of feedback bits per receiver scales as $B \geq
(M\!-1\!)\!\log_{2}(\textsf{SNR})+C$, where $M$ and $C$ denote the number of
transmit antennas and a constant, respectively. Throughout the simulation
results, it is shown that the sum-rate performance coincides with the derived
results.
