While interference alignment schemes have been employed to realize the full multiplexing gain of K-user interference channels, the analyses performed so far have predominantly focused on the case when global channel knowledge is available at each node of the network. This paper considers the problem where each receiver knows its channels from all the transmitters and feeds back this information using a limited number of bits to all other terminals. In particular, channel quantization over the composite Grassmann manifold is proposed and analyzed. It is shown, for K-user multiple-input, multiple-output (MIMO) interference channels, that when the transmitters use an interference alignment strategy as if the quantized channel estimates obtained via this limited feedback are perfect, the full sum degrees of freedom of the interference channel can be achieved as long as the feedback bit rate scales sufficiently fast with the signal-to-noise ratio. Moreover, this is only one extreme point of a continuous tradeoff between achievable degrees of freedom region and user feedback rate scalings which are allowed to be non-identical. It is seen that a slower scaling of feedback rate for any one user leads to commensurately fewer degrees of freedom for that user alone. Index TermsComposite Grassmann manifold, finite-rate feedback, interference alignment, interference channel, MIMO, quantization.

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Volume estimates of balls in Riemannian manifolds find many applications in information theory such as in the determination of the rate-distortion tradeoff for the quantization of a source randomly distributed over such surfaces. This paper computes the precise power series expansion of volume of small geodesic balls in a real Stiefel manifold of arbitrary dimension. An application of the result obtained is also demonstrated.

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