Amplify-and-Forward in Wireless Relay Networks Samar Agnihotri, Sidharth Jaggi, Minghua Chen Institute of Network Coding The Chinese University of Hong Kong

In the Beginning … … there was ITW 2011 Analog network coding in the high-SNR regime - Marić, Goldsmith, Médard. WiNC Layered networks - High SNR 2

ITW 2011 Relay Channel s t Capacity is known only for some special cases Capacity of the general relay channel is not known st 3

Achievability Schemes Decode-and-Forward (Cover/El Gamal 1979) Compress-and-Forward (Cover/El Gamal 1979) Amplify-and-Forward (Laneman/Tse 2002) Compute-and-Forward (Nazer/Gastpar 2006) Quantize-map-and-Forward (ADT 2010) ITW 20114

Achievability Schemes Decode-and-Forward (Cover/El Gamal 1979) Compress-and-Forward (Cover/El Gamal 1979) Amplify-and-Forward (Laneman/Tse 2002) Compute-and-Forward (Nazer/Gastpar 2006) Quantize-map-and-Forward (ADT 2010) ITW 20115

Amplify-and-Forward Relaying ITW 20116

Amplify-and-Forward Relaying Cooperative communication Capacity estimation ANC ITW 20117

General Wireless Networks Any Size Topology Received SNR s t ITW 20118

Network Model ITW Bidirectional links -Single antenna -Full-duplex 9 -Fixed channel gains, known throughout

Amplify-and-Forward in Wireless Networks st “Intersymbol Interference Channel with Colored Gaussian Noise” ITW

Achievable Rate for AF Relay Network ITW 2011 Lemma (Achievable rate for AF relay network): For an AF-relay network with M nodes, the rate achievable with a given amplification vector β is Maximum Achievable rate: W. Hirt, J. L. Massey, Capacity of the discrete-time Gaussian channel with intersymbol interference, Trans. IT, vol IT-34, Proof technique: circular convolution, DFT

“Shout Only If You Make Sense” ITW 2011 s t R2 R Ps = P1 = P2 = 10 Scale-and-Forward Amplify-and-Forward 12

Approximating I AF (P s ) ITW 2011 Computing I AF (P s ) is ``hard’’ Relay without Delay Approximation 13 S. Katti, I. Marić, A. Goldsmith, D. Katabi, M. Médard, Joint relaying and network coding in wireless networks, Proc. IEEE ISIT 2007, Nice, France, June *

Lower Bound Computation-I ITW 2011 β i = β, 1≤ i ≤ M No Attenuation Constant Total Relay Power Type-A Network 14

Lower Bound Computation-II ITW 2011 β i = β, 1≤ i ≤ M No Attenuation Constant Total Relay Power Type-B Network 15

Cut-set Upper Bounds ITW 2011 C ≤ min(C BC, C MAC ) 16 M Relays BC Cut MAC Cut s t

Asymptotic Capacity ITW 2011 No Attenuation, Constant Total Relay Power (Type-A Network) (Type-B Network) 17

Conclusions A unified framework for AF relay networks ITW 2011 Tighter lower bounds for AF relay networks AF relaying can be capacity achieving for a broader class of networks ANC in a class of general networks 18

Current and Future Work Half-duplex networks, multiple-antennas/node, … ITW 2011 Distributed schemes Resource-Performance trade-off – rates beyond AF 19

ITW 2011 Thank You! 20 Samar Agnihotri Web: