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• W2144183710 abstract "We consider vector space interference alignment strategies over the <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$K$ </tex-math></inline-formula> -user interference channel and derive an upper bound on the achievable degrees of freedom as a function of the channel diversity <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$L$ </tex-math></inline-formula> , where the channel diversity is modeled by <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$L$ </tex-math></inline-formula> real-valued parallel channels with coefficients drawn from a nondegenerate joint distribution. The seminal work of Cadambe and Jafar shows that when <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$L$ </tex-math></inline-formula> is unbounded, vector space interference alignment can achieve 1/2 degrees of freedom per user independent of the number of users <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$K$ </tex-math></inline-formula> . However, wireless channels have limited diversity, in practice, dictated by their coherence time and bandwidth, and an important question is the number of degrees of freedom achievable at finite <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$L$ </tex-math></inline-formula> . When <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$K=3$ </tex-math></inline-formula> and if <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$L$ </tex-math></inline-formula> is finite, Bresler <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>et al.</i> show that the number of degrees of freedom achievable with vector space interference alignment is bounded away from 1/2, and the gap decreases inversely proportional to <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$L$ </tex-math></inline-formula> . In this paper, we show that when <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$Kgeq 4$ </tex-math></inline-formula> , the gap is significantly larger. In particular, the gap to the optimal 1/2 degrees of freedom per user can decrease at most like <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$1/sqrt {L}$ </tex-math></inline-formula> , and when <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$L$ </tex-math></inline-formula> is smaller than the order of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$2^{(K-2)(K-3)}$ </tex-math></inline-formula> , it decays at most like <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$1/sqrt [{4}]{L}$ </tex-math></inline-formula> ." @default.
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• W2144183710 date "2016-04-01" @default.
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• W2144183710 title "Channel Diversity Needed for Vector Space Interference Alignment" @default.
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• W2144183710 doi "https://doi.org/10.1109/tit.2016.2529844" @default.
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