Interference Alignment Under Limited Feedback for MIMO Interference Channels

This paper analyzes multiple-input, multiple-output interference channels where each receiver knows its channels from all the transmitters and feeds back this information using a limited number of bits to all the other terminals. It is shown that as long as the feedback bit rate scales sufficiently fast with the signal-to-noise ratio, the transmitters can use an interference alignment strategy by treating the quantized channel estimates as being perfect to achieve the sum degrees of freedom of the interference channel attainable with perfect and global channel state information. A tradeoff between the feedback rate and the achievable degrees of freedom is established by showing that a slower scaling of feedback rate for any one user leads to commensurately fewer degrees of freedom for that user alone. It is then shown that under the same fixed transmission strategy but with random quantization, the above mentioned sufficient condition on the feedback scaling rate to attain a given sum degrees of freedom (up to the maximum attainable) is also necessary in this setting.