Interference alignment for the MIMO interference channel

Abstract

We study vector space interference alignment for the MIMO interference channel with no time or frequency diversity, and no symbol extensions. We prove both necessary and sufficient conditions for alignment. In particular, we characterize the feasibility of alignment for the symmetric three-user channel where all users transmit along d dimensions, all transmitters have M antennas and all receivers have N antennas, as well as feasibility of alignment for the fully symmetric (M=N) channel with an arbitrary number of users. An implication of our results is that the total degrees of freedom available in a K-user interference channel, using only spatial diversity from the multiple antennas, is at most 2. This is in sharp contrast to the K/2 degrees of freedom shown to be possible by Cadambe and Jafar with arbitrarily large time or frequency diversity. Moving beyond the question of feasibility, we additionally discuss computation of the number of solutions using Schubert calculus in cases where there are a finite number of solutions.

16 pages, 7 figures, final submitted version

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Cited by in corpus (18)

• Data Shuffling in Wireless Distributed Computing via Low-Rank Optimization
• Degrees of freedom in vector interference channels
• Genie Chains: Exploring Outer Bounds on the Degrees of Freedom of MIMO Interference Networks
• On the Feasibility of Interference Alignment in Compounded MIMO Broadcast Channels with Antenna Correlation and Mixed User Classes
• Linear Degrees of Freedom of the X-Channel with Delayed CSIT
• Channel Diversity needed for Vector Space Interference Alignment
• Fundamental Storage-Latency Tradeoff in Cache-Aided MIMO Interference Networks
• The Feasibility of Interference Alignment for Reverse TDD Systems in MIMO Cellular Networks
• Cellular Interference Alignment
• Low-Rank Matrix Completion for Topological Interference Management by Riemannian Pursuit
• The Interference Channel Revisited: Aligning Interference by Adjusting Receive Antenna Separation
• Topological Interference Management with User Admission Control via Riemannian Optimization
• The DoF of the Asymmetric MIMO Interference Channel with Square Direct Link Channel Matrices
• Linear Degrees of Freedom of the MIMO X-Channel with Delayed CSIT
• Achievable Degrees of Freedom for Closed-form Solution to Interference Alignment and Cancellation in Gaussian Interference Multiple Access Channel
• Replication-based Outer bounds and the Optimality of "Half the Cake" for Rank-Deficient MIMO Interference Networks
• A Closed-form Transceiver Design for Interference Alignment and Cancellation (IAC) in MIMO Interference Channel
• Numerical Schubert Calculus in Macaulay2