A simple limited feedback scheme is proposed for interference alignment on the K-user Multiple-Input-Multiple-Output Interference Channel (MIMO-IC). The scaling of the number of feedback bits with the transmit power required to preserve the multiplexing gain that can be achieved using perfect channel state information (CSI) is derived. This result is obtained through a reformulation of the interference alignment problem in order to exploit the benefits of quantization on the Grassmann manifold, which is well investigated in the single-user MIMO channel. Furthermore, through simulations we show that the proposed scheme outperforms the naive feedback scheme consisting in independently quantizing the channel matrices, in the sense that it yields a better sum rate performance for the same number of feedback bits.
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