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• W3217635768 abstract "We consider 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 Multiple Input Multiple Output (MIMO) Gaussian interference channel with <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$M$ </tex-math></inline-formula> antennas at each transmitter and <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$N$ </tex-math></inline-formula> antennas at each receiver. It is assumed that channel coefficients are constant real numbers and are available at all transmitters and at all receivers. The main objective of this paper is to characterize the number of Degrees of Freedom (DoF) of this channel. Using the real interference alignment technique introduced in Motahari <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>et al.</i> , 2014, we show that <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$frac {MN}{M+N} K$ </tex-math></inline-formula> degrees of freedom can be achieved for almost all channel realizations. Also, a new upper-bound on the DoF of this channel is provided. This upper-bound coincides with our achievable DoF for <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$Kgeq K_{u} triangleq frac {M+N}{gcd (M,N)}$ </tex-math></inline-formula> , where <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$gcd (M,N)$ </tex-math></inline-formula> denotes the greatest common divisor of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$M$ </tex-math></inline-formula> and <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$N$ </tex-math></inline-formula> . This gives an exact characterization of DoF for <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$Mtimes N$ </tex-math></inline-formula> MIMO Gaussian interference channel in the case of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$Kgeq K_{u}$ </tex-math></inline-formula> . Since there is no cooperation between transmit (or receive) antennas of each user in our transmission scheme, this result shows that the DoF benefit of joint processing in collocated antennas vanishes when the number of users is greater than a certain threshold." @default.
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• W3217635768 date "2022-03-01" @default.
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• W3217635768 title "Interference Alignment for the <i>K</i>-User MIMO Interference Channel" @default.
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