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Amplify-and-Forward Schemes for Wireless Communications

Amplify-and-Forward Schemes for Wireless Communications. Wireless Relay Network. Fixed channel. t. t. The network is the channel. s. s. “Tunable” channel. Problem: Design the optimal channel. Relay Networks: Advantages. Enhanced coverage. Increased throughput. Resilient communication.

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Amplify-and-Forward Schemes for Wireless Communications

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  1. Amplify-and-Forward Schemes for Wireless Communications

  2. Wireless Relay Network Fixed channel t t The network is the channel s s “Tunable” channel Problem: Design the optimal channel

  3. Relay Networks: Advantages Enhanced coverage Increased throughput Resilient communication

  4. Wireless Relay Networks Noise Source Receiver Interference Synchronization Channel Parameters Low complexity communication schemes for Wireless relay Networks Challenge:

  5. Three Candidates A: DNC “Noisy” Network Coding B: PNC Amplify-and-forward C: Quantize-map-and-forward

  6. “Noisy” Network coding n α ⁞ ⁞ Alice β Bob A single link: Overall network bit-error ~Ber(p) No more than pEmn1s (Worst-case)

  7. “Noisy” Network coding: Bounds TX(1) TX(2) pEmn 2pEmn pEmn 2pEmn TX(3) pEmn 2pEmn Q. Wang, S. Jaggi, S.-Y. R. Li. Binary error correcting network codes. In Proc. ITW 2011. For both coherent & incoherent NC

  8. Amplify-and-Forward Relaying

  9. Amplify-and-Forward in Wireless Networks “Intersymbol Interference Channel with Colored Gaussian Noise” s t

  10. Achievable Rate for AF Relay Networks 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:

  11. Part I: Approximating IAF(Ps) Computing IAF(Ps) is ``hard’’ Relay without Delay Approximation: In some scenarios, almost optimal performance Lower-bound within a constant gap from cutset upper-bound S. Agnihotri, S. Jaggi, M. Chen. Amplify-and-forward in wireless relay networks. In Proc. ITW 2011.

  12. Layered Wireless Networks “No Intersymbol Interference, White Gaussian Noise” s t

  13. AF Rate in Layered Networks Previous Work • High SNR • Max. Transmit Power • Few layers Our Work • Arbitrary SNR • Optimal Transmit Power • Any number of layers Function of βli

  14. Part II: Computing Lemma (Computing Optimal β): can be computed layer-by-layer - maximize the sum rate to the next layer - exponential reduction in the search space: NL L N Equal channel gains along all links between two adjacent layers The optimal AF rates for s t S. Agnihotri, S. Jaggi, M. Chen. Analog network coding in general SNR regime. To appear in ISIT 2012.

  15. Part III: A Greedy Scheme - The optimal AF rate for the Diamond Network - First analytical characterization s t Equal channel gains along all outgoing links from every node The optimal AF rates for s t For general layered networks: better rate approximation S. Agnihotri, S. Jaggi, M. Chen. Analog network coding in general SNR regime: performance of a greedy scheme. To appear in NetCod 2012.

  16. Part IV: Network Simplification What fraction of the optimal rate can be maintained by using k out of N relays in each layer? s t RN – Rk = log(N/k) RN/Rk = N/k Diamond Network: RN– Rk = 2L log(N/k) RN/Rk= (N/k)2L-1 ECGAL Network: s t S. Agnihotri, S. Jaggi, M. Chen. Analog network coding in general SNR regime: performance of network simplification. Submitted to ITW 2012.

  17. Project Outcome So Far New fundamental results for layered AF-networks: many firsts • New insights useful for: • characterization of the optimal rate in general AF networks • design of the optimal relay scheme for layered networks

  18. Communication over a point-to-point channel is an integer and we take its binary representation . . . = = = = = 6 0 1 0 0 0 5 42 3 19 9 . . . 5 0 0 0 1 0 . . . 4 0 1 0 0 1 . . . 3 1 0 0 0 0 . . . 2 0 1 1 1 0 . . . 1 1 0 1 1 1 = = = = = 5 42 3 19 9

  19. Communication over a point-to-point channel is an integer and we take its binary representation . . . . . . 6 0 1 0 0 0 6 0 1 0 0 0 . . . . . . 5 0 0 0 1 0 5 0 0 0 1 1 . . . . . . 4 0 1 0 0 1 4 1 1 0 0 1 . . . . . . 3 1 0 0 0 0 3 1 1 0 0 0 . . . . . . 2 0 1 1 1 0 2 0 0 0 0 1 . . . . . . 1 1 0 1 1 1 1 0 0 0 1 1 = = = = = Bit flips 5 42 3 19 9

  20. Communication over a point-to-point channel is an integer and we take its binary representation . . . . . . 6 0 1 0 0 0 6 0 1 0 0 0 . . . . . . 5 0 0 0 1 0 5 0 0 0 1 1 . . . . . . 4 0 1 0 0 1 4 1 1 0 0 1 . . . . . . 3 1 0 0 0 0 3 1 1 0 0 0 . . . . . . 2 0 1 1 1 0 2 0 0 0 0 1 . . . . . . 1 1 0 1 1 1 1 0 0 0 1 1 = = = = = Bit flips 5 42 3 19 9

  21. Communication over a point-to-point channel is an integer and we take its binary representation Dependent bit flips . . . . . . 6 0 1 0 0 0 6 0 1 0 1 0 . . . . . . 5 0 0 0 1 0 5 0 0 0 1 1 . . . . . . 4 0 1 0 0 1 4 1 1 0 0 1 . . . . . . 3 1 0 0 0 0 3 1 1 0 0 0 . . . . . . 2 0 1 1 1 0 2 0 0 0 0 1 . . . . . . 1 1 0 1 1 1 1 0 0 0 1 1 = = = = = Bit flips 5 42 3 19 9

  22. Communication over a point-to-point channel is an integer and we take its binary representation Dependent bit flips . . . . . . 6 0 1 0 0 0 6 0 1 0 1 0 . . . . . . 5 0 0 0 1 0 5 0 0 0 1 1 . . . . . . 4 0 1 0 0 1 4 1 1 0 0 1 . . . . . . 3 1 0 0 0 0 3 1 1 0 0 0 Less noisy bit levels Very noisy bit levels . . . . . . 2 0 1 1 1 0 2 0 0 0 0 1 . . . . . . 1 1 0 1 1 1 1 0 0 0 1 1 = = = = = Bit flips 5 42 3 19 9

  23. Communication over a point-to-point channel T. Dikaliotis, H. Yao, A. S. Avestimehr, S. Jaggi, T. Ho. Low-Complexity Near-Optimal Codes for Gaussian Relay Networks. In SPCOM 2012. is an integer and we take its binary representation . . . Code to correct adversarial errors . . . 6 0 1 0 0 0 6 0 1 0 1 0 . . . . . . 5 0 0 0 1 0 5 0 0 0 1 1 . . . . . . 4 0 1 0 0 1 4 1 1 0 0 1 . . . . . . 3 1 0 0 0 0 3 1 1 0 0 0 Less noisy bit levels Very noisy bit levels . . . . . . 2 0 1 1 1 0 2 0 0 0 0 1 . . . . . . 1 1 0 1 1 1 1 0 0 0 1 1 = = = = = Bit flips 5 42 3 19 9

  24. Publications S. Agnihotri, S. Jaggi, M. Chen. Amplify-and-forward in wireless relay networks. In Proc. ITW 2011. Q. Wang, S. Jaggi, S.-Y. R. Li. Binary error correcting network codes. In Proc. ITW 2011. S. Agnihotri, S. Jaggi, M. Chen. Analog network coding in general SNR regime. To appear in ISIT 2012. S. Agnihotri, S. Jaggi, M. Chen. Analog network coding in general SNR regime: performance of a greedy scheme. To appear in NetCod 2012. S. Agnihotri, S. Jaggi, M. Chen. Analog network coding in general SNR regime: performance of network simplification. To appear in ITW 2012. T. Dikaliotis, H. Yao, A. S. Avestimehr, S. Jaggi, T. Ho. Low-Complexity Near-Optimal Codes for Gaussian Relay Networks. To appear in SPCOM 2012. S. Agnihotri, S. Jaggi, M. Chen. Analog network coding in general SNR regime. In preparation for submission to Trans. Info. Theory.

  25. Current and Future Work Optimal and efficient relay schemes for layered networks Distributed relay schemes “Back to general AF networks” - the optimal rate, distributed schemes General wireless relay networks - resource-performance tradeoff - optimal relay scheme, capacity Incorporating “simple” error-correction “The capacity of relay channel”

  26. Thank You

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