NDLI: Interference Alignment With Asymmetric Complex Signaling—Settling the Høst-Madsen

Content Provider	IEEE Xplore Digital Library
Author	Cadambe, V.R. Jafar, S.A. Chenwei Wang
Copyright Year	1963
Abstract	It has been conjectured by Hø-Madsen and Nosratinia that complex Gaussian interference channels with constant channel coefficients have only one degree-of-freedom regardless of the number of users. While several examples are known of constant channels that achieve more than 1 degree-of-freedom, these special cases only span a subset of measure zero. In other words, for almost all channel coefficient values, it is not known if more than 1 degree-of-freedom is achievable. In this paper, we settle the Høst-Madsen-Nosratinia conjecture in the negative. We show that at least 1.2 degrees-of-freedom are achievable for all values of complex channel coefficients except for a subset of measure zero. For the class of linear beamforming and interference alignment schemes considered in this paper, it is also shown that 1.2 is the maximum number of degrees-of-freedom achievable on the complex Gaussian 3 user interference channel with constant channel coefficients, for almost all values of channel coefficients. To establish the achievability of 1.2 degrees-of-freedom we use the novel idea of asymmetric complex signaling - i.e., the inputs are chosen to be complex but not circularly symmetric. It is shown that unlike Gaussian point-to-point, multiple-access and broadcast channels where circularly symmetric complex Gaussian inputs are optimal, for interference channels optimal inputs are in general asymmetric. With asymmetric complex signaling, we also show that the 2 user complex Gaussian X channel with constant channel coefficients achieves the outer bound of 4/3 degrees-of-freedom, i.e., the assumption of time-variations/frequency-selectivity used in prior work to establish the same result, is not needed.
Sponsorship	IEEE Information Theory Society
Starting Page	4552
Ending Page	4565
Page Count	14
File Size	275216
File Format	PDF
ISSN	00189448
Volume Number	56
Issue Number	9
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-09-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Interference channels Wireless networks Signal processing Signal to noise ratio Array signal processing Broadcasting Frequency Information theory Communication system control $X$ networks Asymmetric complex signaling capacity of wireless networks degrees-of-freedom interference alignment interference management interference networks
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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