telecommunications institute of Pushing IA to the (SNR) limit Pushing IA to the (SNR) Limit: M. Guillaud Experimental Results from the Vienna MIMO Testbed Objectives IA in theory... ... and in practice Maxime Guillaud Vienna MIMO Testbed IA Implementation Performance Metrics with Martin Mayer, Gerald Artner, Martin Lerch, G´ abor Hann´ ak Measurement Results Conclusion Institute of Telecommunications Vienna University of Technology Vienna, Austria guillaud@tuwien.ac.at Scandinavian Workshop on Testbed-Based Wireless Research KTH, Stockholm, November 27, 2013 1/20
Pushing IA to the Interference Alignment, Theory vs. Practice (SNR) limit M. Guillaud Objectives Previous works on IA: IA in theory... ◮ “simulated” IA [El Ayach,Peters,Heath 2009] ... and in practice Vienna MIMO Testbed IA Implementation ◮ indoor, Ettus USRPs [Gollakota, Perli, Katabi, 2009] Performance Metrics Measurement Results ◮ indoor, Lyrtech [Gonz´ alez, Ramirez, Santamaria et al, 2011] Conclusion ◮ indoor, Ettus USRPs [Zetterberg, Moghadam, 2012] Our objective: investigate the “fundamental” limits of IA ◮ over-the-air ◮ using lab-grade equipment ◮ in a standard-agnostic way 2/20
Pushing IA to the Interference Alignment, Theory vs. Practice (SNR) limit M. Guillaud Objectives Previous works on IA: IA in theory... ◮ “simulated” IA [El Ayach,Peters,Heath 2009] ... and in practice Vienna MIMO Testbed IA Implementation ◮ indoor, Ettus USRPs [Gollakota, Perli, Katabi, 2009] Performance Metrics Measurement Results ◮ indoor, Lyrtech [Gonz´ alez, Ramirez, Santamaria et al, 2011] Conclusion ◮ indoor, Ettus USRPs [Zetterberg, Moghadam, 2012] Our objective: investigate the “fundamental” limits of IA ◮ over-the-air ◮ using lab-grade equipment ◮ in a standard-agnostic way 2/20
Pushing IA to the K-user MIMO Interference Channel (SNR) limit M. Guillaud Objectives Tx 1 Rx 1 IA in theory... ... and in practice Vienna MIMO Testbed Tx 2 Rx 2 IA Implementation Performance Metrics Measurement Results Conclusion Tx 3 Rx 3 Tx K Rx K K � y k = H kk x k + H kj x j + n k ∀ k = 1 . . . K j = 1 , j � = k 3/20
Pushing IA to the K-user MIMO Interference Channel (SNR) limit M. Guillaud Objectives Tx 1 Rx 1 IA in theory... ... and in practice Vienna MIMO Testbed Tx 2 Rx 2 IA Implementation Performance Metrics Measurement Results Conclusion Tx 3 Rx 3 Tx K Rx K K � y k = H kk x k + H kj x j + n k ∀ k = 1 . . . K j = 1 , j � = k 3/20
Pushing IA to the Interference Alignment in Pictures (SNR) limit M. Guillaud n 1 N T N R Objectives H 11 s 1 IA in theory... H 21 ... and in practice Vienna MIMO Testbed n 2 IA Implementation N T N R Performance Metrics s 2 Measurement Results Conclusion n 3 N T H 23 N R s 3 H 33 ◮ Based on linear precoding: x i = V i s i with s i ∈ C d ◮ Interference (in red) from multiple Tx aligns at the Rx ◮ Interference-free subspace used for communication 4/20
Mathematical formulation of IA 1 Pushing IA to the (SNR) limit M. Guillaud Objectives IA in theory... ... and in practice ◮ interference � Vienna MIMO Testbed j � = i H ij V j s j does not occupy all receive IA Implementation Performance Metrics dimensions Measurement Results ◮ IA solution equivalent to finding matrices V i and U i Conclusion � U H i H ij V j = 0 , ∀ j � = i s . t . � � U H rank i H ii V i = d i . 1K. Gomadam, V.R. Cadambe, S.A. Jafa, “A distributed numerical approach to interference alignment and applications to wireless interference networks,” IEEE Trans. on Information Theory, June 2011. 5/20
Mathematical formulation of IA 1 Pushing IA to the (SNR) limit M. Guillaud Objectives IA in theory... ... and in practice ◮ interference � Vienna MIMO Testbed j � = i H ij V j s j does not occupy all receive IA Implementation Performance Metrics dimensions Measurement Results ◮ IA solution equivalent to finding matrices V i and U i Conclusion � U H i H ij V j = 0 , ∀ j � = i s . t . � � U H rank i H ii V i = d i . 1K. Gomadam, V.R. Cadambe, S.A. Jafa, “A distributed numerical approach to interference alignment and applications to wireless interference networks,” IEEE Trans. on Information Theory, June 2011. 5/20
Pushing IA to the Why the hype ? (SNR) limit M. Guillaud Objectives Some attractive properties IA in theory... ... and in practice ◮ Low-complexity processing, just linear filters Vienna MIMO Testbed IA Implementation ◮ Achieves the full channel degrees of freedom at high SNR Performance Metrics Measurement Results Conclusion C i ( SNR ) DoF = lim log SNR = d SNR → + ∞ BUT... ◮ Extensive CSI requirements: H ij ∀ j � = i ◮ What good is the DoF result at finite SNR ? 6/20
Pushing IA to the Why the hype ? (SNR) limit M. Guillaud Objectives Some attractive properties IA in theory... ... and in practice ◮ Low-complexity processing, just linear filters Vienna MIMO Testbed IA Implementation ◮ Achieves the full channel degrees of freedom at high SNR Performance Metrics Measurement Results Conclusion C i ( SNR ) DoF = lim log SNR = d SNR → + ∞ BUT... ◮ Extensive CSI requirements: H ij ∀ j � = i ◮ What good is the DoF result at finite SNR ? 6/20
Pushing IA to the Why the hype ? (SNR) limit M. Guillaud Objectives Some attractive properties IA in theory... ... and in practice ◮ Low-complexity processing, just linear filters Vienna MIMO Testbed IA Implementation ◮ Achieves the full channel degrees of freedom at high SNR Performance Metrics Measurement Results Conclusion C i ( SNR ) DoF = lim log SNR = d SNR → + ∞ BUT... ◮ Extensive CSI requirements: H ij ∀ j � = i ◮ What good is the DoF result at finite SNR ? 6/20
Pushing IA to the Why the hype ? (SNR) limit M. Guillaud Objectives Some attractive properties IA in theory... ... and in practice ◮ Low-complexity processing, just linear filters Vienna MIMO Testbed IA Implementation ◮ Achieves the full channel degrees of freedom at high SNR Performance Metrics Measurement Results Conclusion C i ( SNR ) DoF = lim log SNR = d SNR → + ∞ BUT... ◮ Extensive CSI requirements: H ij ∀ j � = i ◮ What good is the DoF result at finite SNR ? 6/20
Pushing IA to the Why the hype ? (SNR) limit M. Guillaud Objectives Some attractive properties IA in theory... ... and in practice ◮ Low-complexity processing, just linear filters Vienna MIMO Testbed IA Implementation ◮ Achieves the full channel degrees of freedom at high SNR Performance Metrics Measurement Results Conclusion C i ( SNR ) DoF = lim log SNR = d SNR → + ∞ BUT... ◮ Extensive CSI requirements: H ij ∀ j � = i ◮ What good is the DoF result at finite SNR ? 6/20
Pushing IA to the The Vienna MIMO Testbed Set-Up (SNR) limit M. Guillaud ◮ Replicate an urban outdoor-to-indoor and indoor-to-indoor Objectives scenario, with 3 Tx / 1 Rx IA in theory... ... and in practice Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results Conclusion 7/20
Pushing IA to the The Vienna MIMO Testbed Set-Up: Tx side (SNR) limit M. Guillaud ◮ 2 rooftop TX, Kathrein Scala Division XX-pol BTS antennas Objectives IA in theory... ... and in practice Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results Conclusion ◮ Indoor Tx, 2 × Kathrein Scala Division X-pol directional ant. 8/20
Pushing IA to the The Vienna MIMO Testbed Set-Up: Rx side (SNR) limit M. Guillaud Objectives IA in theory... ◮ Rx using 4 custom-built λ ... and in practice 2 dipoles in a laptop shell Vienna MIMO Testbed IA Implementation ◮ On a positioning table Performance Metrics Measurement Results Conclusion 9/20
Pushing IA to the Testbed Characteristics (SNR) limit M. Guillaud Objectives IA in theory... ◮ 4 nodes (3 Tx + 1 Rx), 4 antennas per node ... and in practice Vienna MIMO Testbed ◮ Rubidium-synchronized clocks IA Implementation Performance Metrics Measurement Results ◮ No duplexing, but high-speed feedback over dedicated fiber Conclusion LAN ◮ Center frequency 2.503 GHz ◮ 200 MHz sampling rate ◮ OFDM with 15.02 kHz subcarrier spacing ◮ One instance of MATLAB at each node 10/20
Pushing IA to the IA-Specific Implementation Details (SNR) limit M. Guillaud Objectives ◮ Two additional “ghost” receivers to simulate the 3-user IC IA in theory... ... and in practice Vienna MIMO Testbed IA Implementation Performance Metrics Measurement Results Conclusion ◮ System dimensions allow IA with d = 2 streams per user ◮ IA precoder computed in closed-form based on eigendecomposition ◮ Consider a single subcarrier to keep complexity low 11/20
Pushing IA to the Measurement Methodology (SNR) limit M. Guillaud Objectives IA in theory... ... and in practice Vienna MIMO Testbed IA Implementation ◮ Closed-loop system with periodic training sequences Performance Metrics Measurement Results Conclusion ( T p ≈ 70ms) 12/20
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