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Sparse Blind Demixing

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Abstract

This chapter extends the models presented in Chaps. 2 and 3 to the scenario involving device activity detection. The new setting induces a sparse blind demixing model for developing methods for joint device activity detection, data decoding, and channel estimation in IoT networks. The signal model is first presented, in the scenario with either a single-antenna or multi-antenna BS. A convex relaxation approach is first introduced as a basic method to solve the nonconvex estimation problem. We further present a difference-of-convex-functions (DC) approach which turns out to be a powerful tool to solve the resulting sparse and low-rank optimization problem with matrix lifting. Furthermore, a smooth Riemannian optimization algorithm operating on the product manifold is introduced for solving the sparse blind demixing problem directly.

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References

  1. Absil, P.A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton (2009)

    MATH  Google Scholar 

  2. Aghasi, A., Bahmani, S., Romberg, J.: A tightest convex envelope heuristic to row sparse and rank one matrices. In: Proceedings of the IEEE Global Conference on Signal and Information Processing (GlobalSIP), p. 627. IEEE, Piscataway (2013)

    Google Scholar 

  3. Dong, J., Shi, Y.: Nonconvex demixing from bilinear measurements. IEEE Trans. Signal Process. 66(19), 5152–5166 (2018)

    Article  MathSciNet  Google Scholar 

  4. Dong, J., Shi, Y., Ding, Z.: Sparse blind demixing for low-latency signal recovery in massive IoT connectivity. In: Proceedings of the IEEE International Conference on Acoustics Speech Signal Processing (ICASSP), pp. 4764–4768. IEEE, Piscataway (2019)

    Google Scholar 

  5. Dong, J., Yang, K., Shi, Y.: Blind demixing for low-latency communication. IEEE Trans. Wireless Commun. 18(2), 897–911 (2019)

    Article  Google Scholar 

  6. Fu, M., Dong, J., Shi, Y.: Sparse blind demixing for low-latency wireless random access with massive connectivity. In: Proceedings of the IEEE Vehicular Technology Conference (VTC), pp. 4764–4768. IEEE, Piscataway (2019)

    Google Scholar 

  7. Gotoh, J.Y., Takeda, A., Tono, K.: DC formulations and algorithms for sparse optimization problems. Math. Program. 169(1), 141–176 (2018)

    Article  MathSciNet  Google Scholar 

  8. Lee, K., Wu, Y., Bresler, Y.: Near-optimal compressed sensing of a class of sparse low-rank matrices via sparse power factorization. IEEE Trans. Inf. Theory 64(3), 1666–1698 (2018)

    Article  MathSciNet  Google Scholar 

  9. Ling, S., Strohmer, T.: Blind deconvolution meets blind demixing: algorithms and performance bounds. IEEE Trans. Inf. Theory 63(7), 4497–4520 (2017)

    Article  MathSciNet  Google Scholar 

  10. Lu, C., Tang, J., Yan, S., Lin, Z.: Nonconvex nonsmooth low rank minimization via iteratively reweighted nuclear norm. IEEE Trans. Image Process. 25(2), 829–839 (2016)

    Article  MathSciNet  Google Scholar 

  11. Shi, Y., Mishra, B., Chen, W.: Topological interference management with user admission control via Riemannian optimization. IEEE Trans. Wireless Commun. 16(11), 7362–7375 (2017)

    Article  Google Scholar 

  12. Tao, P.D., An, L.T.H.: Convex analysis approach to DC programming: theory, algorithms and applications. Acta Math. Vietnam. 22(1), 289–355 (1997)

    MathSciNet  MATH  Google Scholar 

  13. Zhang, Y., Kuo, H.W., Wright, J.: Structured local optima in sparse blind deconvolution (2018). Preprint. arXiv: 1806.00338

    Google Scholar 

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Shi, Y., Dong, J., Zhang, J. (2020). Sparse Blind Demixing. In: Low-overhead Communications in IoT Networks. Springer, Singapore. https://doi.org/10.1007/978-981-15-3870-4_4

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  • DOI: https://doi.org/10.1007/978-981-15-3870-4_4

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-3869-8

  • Online ISBN: 978-981-15-3870-4

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