Degrees of freedom in vector interference channels
David Stotz and Helmut Bölcskei
Allerton Conference on Communication, Control, and Computing, Monticello, IL, pp. 1755 - 1760, Oct. 2012
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This paper continues the Wu-Shamai-Verdú program  on characterizing the degrees of freedom (DoF) of interference channels (ICs) through Rényi information dimension. Concretely, we find a general formula for the DoF of vector ICs, encompassing multiple-input multiple-output (MIMO) ICs, time- and/or frequency-selective ICs, and combinations thereof, as well as constant single-antenna ICs considered in . As in the case of constant single-antenna ICs, achieving full DoF requires the use of singular input distributions. Strikingly, in the vector case it suffices to enforce singularity on the joint distribution of individual transmit vectors. This can be realized through signaling in subspaces of the ambient signal space, which is in accordance with the idea of interference alignment, and, most importantly, allows the scalar components of the transmit
vectors to have non-singular distributions. We recover the result by Cadambe and Jafar on the non-separability of parallel ICs  and we show that almost all parallel ICs are separable. Finally, our results extend the main finding in  to the complex case.
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