NDLI: Diophantine Approach to Blind Interference Alignment of Homogeneous K-User 2x1 MISO Broadcast Channels

Content Provider	IEEE Xplore Digital Library
Author	Zhou, Q.F. Zhang, Q.T. Lau, F.C.M.
Copyright Year	1983
Abstract	The sufficient condition for a blindly interference-aligned 2-user 2 × 1 broadcast channel (BC) in homogeneous block fading to achieve its maximal 4/3 degree-of-freedom (DoF) is well understood. However, the condition for the general case, i.e., a homogeneous K-user 2 × 1 BC, to achieve the corresponding optimal 2K/2+K-1 DoF remains unsolved and is, thus, the focus of this paper. Here, a K-user 2×1 BC is said to be BIA-feasible if it achieves the optimal DoF via blind interference alignment (BIA). In this paper, we cast this general BIA-feasibility problem in the framework of finding solutions for a system of linear Diophantine equations. Then by studying the solvability of the Diophantine system, we derive the necessary and sufficient conditions on the K users' fading block offsets to ensure the BIA feasibility of the K-user BC. Using the results above, we also examine a 2 × 1 broadcast network with M homogeneous users, in which their offsets are independent of one another and are uniformly distributed over a coherence block. We show by simulations that when the network contains M = 11 homogeneous users, there is more than 95% chance of finding 3 users to form a BIA-feasible 3-user 2 × 1 BC. Furthermore, increasing M to infinity ensures a virtual multiple-input multiple-output (MIMO) channel to be formed from the DoF perspective.
Starting Page	2141
Ending Page	2153
Page Count	13
File Size	1034035
File Format	PDF
ISSN	07338716
Volume Number	31
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-10-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fading Interference Coherence Transmitters Mathematical model Equations Vectors virtual MIMO Blind IA DoF homogeneous block fading MISO BC
Content Type	Text
Resource Type	Article
Subject	Computer Networks and Communications Electrical and Electronic Engineering

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