Harnessing interference for analog function computation in wireless sensor networks

IEEE Transactions on Signal Processing

Volumn 61, Issue 20, 2013, Pages 4893-4906

  Goldenbaum, Mario ^a,b   Boche, Holger ^b   Stanczak, Slawomir ^a,c  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^c FRAUNHOFER HEINRICH HERTZ INSTITUTE   (Germany)

Author keywords

13th Hilbert problem; Computation over multiple access channels; Pre and post processing; Wireless sensor networks

Indexed keywords

ARBITRARY TOPOLOGY; COMPUTATION OVER MULTIPLE-ACCESS CHANNELS; EFFICIENT COMPUTATION; HILBERT PROBLEM; NONLINEAR FUNCTIONS; POST PROCESSING; SIGNALING OVERHEADS; SUPERIMPOSED SIGNAL;

ANALOG COMPUTERS; COMPLEX NETWORKS; WIRELESS SENSOR NETWORKS;

SENSOR NODES;

EID: 84883822678     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2013.2272921     Document Type: Article

References (53)

1. F. Zhao andL.Guibas,Wireless Sensor Networks: An Information Processing Approach. San Francisco, CA, USA: Elsevier/Morgan Kaufmann, 2004
2. R. F.Wyrembelski andH. Boche, "Physical layer integration of private, common, and confidential messages in bidirectional relay networks," IEEE Trans. Wireless Commun., vol. 11, no. 9, pp. 3170-3179, Sep. 2012
3. A. Giridhar and P. R. Kumar, "Toward a theory of in-network computation in wireless sensor networks," IEEE Commun. Mag., vol. 44, no. 4, pp. 98-107, Apr. 2006 (Pubitemid 43792675)
4. M. Gastpar and M. Vetterli, "Source-channel communication in sensor networks," in Proc. 2nd Int. Workshop Inf. Process. Sensor Netw. (IPSN), Palo Alto, CA, USA, Apr. 2003, pp. 162-177
5. M. Goldenbaum, S. Sta?czak, andM. Kaliszan, "On function computation via wireless sensor multiple-access channels," in Proc. IEEEWireless Commun. Netw. Conf. (WCNC), Budapest, Hungary, Apr. 2009
6. M. Goldenbaum and S. Sta?czak, "Computing the geometric mean over multiple-access channels: Error analysis and comparisons," in Proc. 44th Asilomar Conf. Signals, Syst., Comput., Pacific Grove, CA, USA, Nov. 2010, pp. 2172-2178
7. G.Mergen and L. Tong, "Type based estimation overmultiaccess channels," IEEE Trans. Signal Process., vol. 54, no. 2, pp. 613-626, Feb. 2006 (Pubitemid 43141907)
8. W. U. Bajwa, J. D. Haupt, A. M. Sayeed, and R. D. Nowak, "Joint source-channel communication for distributed estimation in sensor networks," IEEE Trans. Inf. Theory, vol. 53, no. 10, pp. 3629-3653, Oct. 2007 (Pubitemid 47534518)
9. J.-J. Xiao, S. Cui, Z.-Q. Luo, and A. J. Goldsmith, "Linear coherent decentralized estimation," IEEE Trans. Signal Process., vol. 56, no. 2, pp. 757-770, Feb. 2008 (Pubitemid 351285070)
10. M. K. Banavar, C. Tepedelenlio?lu, and A. Spanias, "Estimation over fading channelswith limited feedback using distributed sensing," IEEE Trans. Signal Process., vol. 58, no. 1, pp. 414-425, Jan. 2010
11. S. Sta?czak, M.Wiczanowski, and H. Boche, "Distributed power control for optimizing a weighted sum of link-layer QoS levels," in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), St. Louis,MO, USA, Nov. 2005, pp. 3539-3543 (Pubitemid 46178186)
12. T. M. Duman and M. Salehi, "Decentralized detection over multipleaccess channels," IEEE Trans. Aerosp. Electron. Syst., vol. 34, no. 2, pp. 469-476, Apr. 1998
13. W. Li and H. Dai, "Distributed detection in wireless sensor networks using a multiple access channel," IEEE Trans. Signal Process., vol. 55, no. 3, pp. 822-833, Mar. 2007 (Pubitemid 46444225)
14. G. Mergen, V. Naware, and L. Tong, "Asymptotic detection performance of type-based multiple access over multiaccess fading channels," IEEE Trans. Signal Process., vol. 55, no. 3, pp. 1081-1092, Mar. 2007 (Pubitemid 46444245)
15. K. Liu and A. M. Sayeed, "Type-based decentralized detection in wireless sensor networks," IEEE Trans. Signal Process., vol. 55, no. 5, pp. 1899-1910, May 2007 (Pubitemid 46691637)
16. M. K. Banavar, A. D. Smith, C. Tepedelenlio?lu, and A. Spanias, "On the effectiveness of multiple antennas in distributed detection over fading MACs," IEEE Trans. Wireless Commun., vol. 11, no. 5, pp. 1744-1752, May 2012
17. F. Li, J. S. Evans, and S. Dey, "Design of distributed detection schemes formultiaccess channels," IEEE Trans. Aerosp. Electron. Syst., vol. 48, no. 2, pp. 1552-1569, Apr. 2012
18. P. Jakimovski, F. Becker, S. Sigg,H. R. Schmidtke, and M. Beigl, "Collective communication for dense sensing environments," in Proc. 7th Int. Conf. Intell. Environments (IE), Nottingham, U.K., July 2011, pp. 157-164
19. S. Sigg, P. Jakimovski, and M. Beigl, "Calculation of functions on the RF-channel for IoT," in Proc. 3rd Int. Conf. Internet of Things (IOT), Wuxi, China, Oct. 2012, pp. 107-113
20. S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah, "Randomized gossip algorithms," IEEE Trans. Inf. Theory, vol. 52, no. 6, pp. 2508-2530, June 2006 (Pubitemid 43898906)
21. R. Olfati-Saber, J. A. Fax, and R. M. Murray, "Consensus and cooperation in networked multi-agent systems," Proc. IEEE, vol. 95, no. 1, pp. 215-233, Jan. 2007
22. D. Mosk-Aoyama and D. Shah, "Fast distributed algorithms for computing separable functions," IEEE Trans. Inf. Theory, vol. 54, no. 7, pp. 2997-3007, July 2008
23. A. G. Dimakis, S. Kar, J.M. F.Moura, M. G. Rabbat, and A. Scaglione, "Gossip algorithms for distributed signal processing," Proc. IEEE, vol. 98, no. 11, pp. 1847-1864, Nov. 2010
24. B. Nazer, A. G. Dimakis, and M. Gastpar, "Local interference can accelerate gossip algorithms," IEEE J. Sel. Topics Signal Process., vol. 5, no. 4, pp. 876-887, Aug. 2011
25. A. Orlitsky and J. R. Roche, "Coding for computing," IEEE Trans. Inf. Theory, vol. 47, no. 3, pp. 903-917, Mar. 2001 (Pubitemid 32425425)
26. V. Doshi, D. Shah, M. Médard, and M. Effros, "Functional compression through graph coloring," IEEE Trans. Inf. Theory, vol. 56, no. 8, pp. 3901-3917, Aug. 2010
27. B. Nazer and M. Gastpar, "Computation over multiple-access channels," IEEE Trans. Inf. Theory, vol. 53, no. 10, pp. 3498-3516, Oct. 2007 (Pubitemid 47534510)
28. M. Goldenbaum, H. Boche, and S. Sta?czak, "Reliable computation of nomographic functions over Gaussian multiple-access channels," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Vancouver, Canada, May 2013, pp. 4814-4818
29. L. Keller, N. Karamchandani, and C. Fragouli, "Function computation over linear channels," in Proc. IEEE Int. Symp. Netw. Coding (NetCod), Toronto, ON, Canada, June 2010, pp. 1-6
30. A. N. Kolmogorov, "On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition," Dokl. Akad. Nauk SSSR, no. 114, pp. 953-956, 1957, engl. translation
31. D. Hilbert, "Mathematical problems," Bull. Amer. Math. Soc., vol. 8, no. 10, pp. 437-479, 1902
32. S. Verdu, Multiuser Detection. Cambridge, U.K.: Cambridge Univ. Press, 1998
33. D. Tse and P. Viswanath, Fundamentals of Wireless Communications. Cambridge, U.K.: Cambridge Univ. Press, 2005
34. M. Goldenbaum and S. Sta?czak, "Computing functions via SIMO multiple-access channels: How much channel knowledge is needed?," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Dallas, TX, USA, Mar. 2010, pp. 3394-3397
35. R. C. Buck, "Approximate complexity and functional representation," J. Math. Anal. Appl., vol. 70, pp. 280-298, 1979
36. L. I. Epstein, Nomography. New York, NY, USA: Interscience Publishers, 1958
37. D. A. Sprecher, "A representation theorem for continuous functions of several variables," Amer.Math. Soc., vol. 16, no. 2, pp. 200-203, 1965
38. J. V. Neumann, "Ein System algebraisch unabhangiger Zahlen," Math. Ann., vol. 99, pp. 134-141, 1928
39. R. C. Buck, "Nomographic functions are nowhere dense," in Proc. Amer. Math. Soc., June 1982, vol. 85, no. 2, pp. 195-199
40. V. I. Arnol'd, "On the representation of functions of two variables in the form ," Uspekhi Math. Nauk, vol. 12, no. 2, pp. 119-121, 1957, engl. translation
41. A. G. Vitushkin, "On Hilbert's thirteenth problem and related questions," Russian Math. Surveys, vol. 59, no. 1, pp. 11-25, 2004 (Pubitemid 38882310)
42. J. Braun and M. Griebel, "On a constructive proof of Kolmogorov's superposition theorem," Constr. Approx., vol. 30, no. 3, pp. 653-675, Dec. 2009
43. W. Hurewicz and H. Wallman, Dimension Theory. Princeton,NJ, USA: Princeton Univ. Press, 1948
44. Y. Sternfeld, "Dimension, superposition of functions and separation of points, in compact metric spaces," Israel J. Math., vol. 50, pp. 13-52, 1985
45. A. G. Vitushkin and G. M. Khenkin, "Linear superpositions of functions," Russian Math. Surveys, vol. 22, no. 1, pp. 77-125, 1967
46. M. Goldenbaum and S. Sta?czak, "Robust analog function computation via wireless multiple-access channels," IEEE Trans. Commun. 2012 [Online]. Available: http://arxiv.org/abs/1210.2967, [Online]. Available:
47. H. Boche and U. J. Mönich, "Sampling of deterministic signals and systems," IEEE Trans. Signal Process., vol. 59, no. 5, pp. 2101-2111, May 2011
48. H. Boche and U. J. Mönich, "Behavior of the quantization operator for bandlimited, nonoversampled signals," IEEE Trans. Inf. Theory, vol. 56, no. 5, pp. 2433-2440, May 2010
49. H. Boche andU. J. Mönich, "Unboundedness of thresholding and quantization for bandlimited signals," Signal Process., vol. 92, no. 12, pp. 2821-2829, Dec. 2012
50. R. Hecht-Nielsen, "Kolmogorov's mapping neural network existence theorem," in Proc. IEEE 1st Int. Conf. Neural Netw., San Diego, CA, USA, June 1987, vol. III, pp. 11-14
51. V. Kurková, "Kolmogorov's theorem and multilayer neural networks," Neural Netw., vol. 5, no. 3, pp. 501-506, 1992
52. P. A. Ostrand, "Dimension of metric spaces and Hilbert's problem 13," Bull. Amer. Math. Soc., vol. 71, no. 4, pp. 619-622, July 1965
53. L. Bieberbach, "Operationsbereiche von Funktionen," in Proc. Int. Congr. Mathematicians (ICM), Zurich, Switzerland, Sept. 1932, vol. I, pp. 162-172.