Beamforming Optimization for Multiuser Two-Tier Networks

  • Jeong, Young-Min (Department of Electronics and Radio Engineering, Kyung Hee University) ;
  • Quek, Tony Q.S. (Institute for Infocomm Research, A*STAR) ;
  • Shin, Hyun-Dong (Department of Electronics and Radio Engineering, Kyung Hee University)
  • Received : 2010.12.11
  • Published : 2011.08.31

Abstract

With the incitation to reduce power consumption and the aggressive reuse of spectral resources, there is an inevitable trend towards the deployment of small-cell networks by decomposing a traditional single-tier network into a multi-tier network with very high throughput per network area. However, this cell size reduction increases the complexity of network operation and the severity of cross-tier interference. In this paper, we consider a downlink two-tier network comprising of a multiple-antenna macrocell base station and a single femtocell access point, each serving multiples users with a single antenna. In this scenario, we treat the following beamforming optimization problems: i) Total transmit power minimization problem; ii) mean-square error balancing problem; and iii) interference power minimization problem. In the presence of perfect channel state information (CSI), we formulate the optimization algorithms in a centralized manner and determine the optimal beamformers using standard convex optimization techniques. In addition, we propose semi-decentralized algorithms to overcome the drawback of centralized design by introducing the signal-to-leakage plus noise ratio criteria. Taking into account imperfect CSI for both centralized and semi-decentralized approaches, we also propose robust algorithms tailored by the worst-case design to mitigate the effect of channel uncertainty. Finally, numerical results are presented to validate our proposed algorithms.

Keywords

Acknowledgement

Supported by : NRF

References

  1. G. Staple and K. Werbach, "The end of spectrum scarcity," IEEE Spectrum, vol. 41, no. 3, pp. 49-52, Mar. 2004. https://doi.org/10.1109/MSPEC.2004.1318185
  2. D. Lopez-Perez, ˙I. Güvenc, G. de la Roche, M. Kountouris, T. Q. S. Quek, and J. Zhang, "Enhanced intercell interference coordination challenges in heterogeneous networks," IEEE Commun. Mag., vol. 18, no. 3, pp. 22-30, June 2011.
  3. V. Chandrasekhar, J. G. Andrews, and A. Gatherer, "Femtocell networks: A survey," IEEE Commun. Mag., vol. 46, no. 9, pp. 59-67, Sept. 2008. https://doi.org/10.1109/MCOM.2008.4623708
  4. W. C. Chung, T. Q. S. Quek, and M. Kountouris, "Throughput optimization in two-tier femtocell networks," IEEE J. Sel. Areas Commun., revised, July 2011.
  5. Y. Jeong, H. Shin, and M. Z. Win, "Optimum combining in femtocell networks," IEEE J. Sel. Areas Commun., revised, July 2011.
  6. V. Chandrasekhar, J. G. Andrews, T. Muharemovic, Z. Shen, and A. Gatherer, "Power control in two-tier femtocell networks," IEEE Trans. Wireless Commun., vol. 8, no. 8, pp. 4316-4328, Aug. 2009. https://doi.org/10.1109/TWC.2009.081386
  7. O. Simeone, E. Erkip, and S. Shamai (Shitz), "Robust transmission and interference management for femtocells with unreliable network access," IEEE J. Sel. Areas Commun., vol. 28, no. 9, pp. 1469-1478, Dec. 2010. https://doi.org/10.1109/JSAC.2010.101208
  8. V. Chandrasekhar and J. G. Andrews, "Uplink capacity and interference avoidance for two-tier femtocell networks," IEEE Trans. Wireless Commun., vol. 8, no. 7, pp. 3498-3509, July 2009. https://doi.org/10.1109/TWC.2009.070475
  9. V. Chandrasekhar and J. G. Andrews, "Coverage in multi-antenna two-tier networks," IEEE Trans. Wireless Commun., vol. 8, no. 10, pp. 5314-5327, Oct. 2009. https://doi.org/10.1109/TWC.2009.090241
  10. M. Husso, J. Hamalainen, R. Jantti, J. Li, E. Mutafungwa, R. Wichman, Z. Zhend, and A. M. Wyglinski, "Interference mitigation by practical transmit beamforming methods in closed femtocells," EURASIP J. Wireless Commun. and Networking, vol. 2010, pp. 1-12, 2010, article ID 186815.
  11. D. Lopez-Perez, A. Valcarce, G. de la Roche, and J. Zhang, "OFDMA femtocells: A roadmap on interference avoidance," IEEE Commun. Mag., vol. 9, pp. 41-48, Sept. 2009.
  12. M. Yavuz, F. Meshkati, S. Nanda, A. Pokhariyal, N. Johnson, B. Raghothaman, and A. Richardson, "OFDMA femtocells: A roadmap on interference avoidance," IEEE Commun. Mag., vol. 9, pp. 102-109, Sept. 2009.
  13. H. Shin and J. H. Lee, "Capacity of multiple-antenna fading channels: Spatial fading correlation, double scattering, and keyhole," IEEE Trans. Inf. Theory, vol. 49, no. 10, pp. 2636-2647, Oct. 2003. https://doi.org/10.1109/TIT.2003.817439
  14. H. Shin and J. H. Lee, "Performance analysis of space-time block codes over keyhole Nakagami-m fading channels," IEEE Trans. Veh. Technol., vol. 53, no. 2, pp. 351-362, Mar. 2004. https://doi.org/10.1109/TVT.2004.823540
  15. H. Shin, M. Z. Win, J. H. Lee, and M. Chiani, "On the capacity of doubly correlated MIMO channels," IEEE Trans. Wireless Commun., vol. 5, no. 8, pp. 2253-2265, Aug. 2006. https://doi.org/10.1109/TWC.2006.1687741
  16. H. Shin and M. Z. Win, "MIMO diversity in the presence of double scattering," IEEE Trans. Inf. Theory, vol. 54, no. 7, pp. 2976-2996, July 2008. https://doi.org/10.1109/TIT.2008.924672
  17. H. Shin and M. Z. Win, "Gallager's exponent for MIMO channels: A reliability-rate tradeoff," IEEE Trans. Commun., vol. 57, no. 4, pp. 972-985, Apr. 2009. https://doi.org/10.1109/TCOMM.2008.04.050673
  18. F. Rashid-Farrokhi, K. J. R. Liu, and L. Tassiulas, "Transmit beamforming and power control for cellular wireless systems," IEEE J. Sel. Areas Commun., vol. 16, no. 8, pp. 1437-1450, Oct. 1998. https://doi.org/10.1109/49.730452
  19. A.Wiesel, Y. C. Eldar, and S. Shamai (Shitz), "Linear precoding via conic optimization for fixed MIMO receivers," IEEE Trans. Signal Process., vol. 54, no. 1, pp. 161-176, Jan. 2006. https://doi.org/10.1109/TSP.2005.861073
  20. S. Shi, M. Schubert, and H. Boche, "Dowinlink MMSE transceiver optimization for multiuser MIMO systems: MMSE balancing," IEEE Trans. Signal Process., vol. 56, no. 8, pp. 3702-3712, Aug. 2008. https://doi.org/10.1109/TSP.2008.920487
  21. J. Yu, Y.-D. Yao, A. F. Molisch, and J. Zhang, "Performance evaluation of CDMA reverse links with imperfect beamforming in a multicell environment using a simplified beamforming model," IEEE Trans. Veh. Technol., vol. 55, no. 3, pp. 1019-1031, May 2006. https://doi.org/10.1109/TVT.2006.874556
  22. M. Sadek, A. Tarighat, and A. H. Sayed, "A leakage-based precoding scheme for downlink multi-user MIMO channels," IEEE Trans. Wireless Commun., vol. 6, no. 5, pp. 1711-1721, May 2007. https://doi.org/10.1109/TWC.2007.360373
  23. W. W. L. Ho, T. Q. S. Quek, S. Sun, and R. W. Heath Jr., "Decentralized precoding for multicell MIMO downlink," IEEE Trans. Wireless Commun., vol. 10, no. 6, pp. 1798-1809, June 2011. https://doi.org/10.1109/TWC.2011.040511.100519
  24. H. Zhang, N. B. Mehta, A. F. Molisch, J. Zhang, and H. Dai, "Asynchronous interference mitigation in cooperative base station systems," IEEE Trans. Wireless Commun., vol. 7, no. 1, pp. 155-165, Jan. 2008. https://doi.org/10.1109/TWC.2008.060193
  25. Y. Ma, D. I. Kim, and Z. Wu, "Optimization of OFDMA-based cellular cognitive radio networks," IEEE Trans. Commun., vol. 58, no. 8, pp. 2265-2276, Aug. 2010. https://doi.org/10.1109/TCOMM.2010.08.080444
  26. Y. Ma and D. I. Kim, "Centralized and distributed optimization of ad-hoc cognitive radio network," in Proc. IEEE GLOBECOM, Honolulu, Hawaii, USA, Nov. 2009, pp. 1-7.
  27. S. A. Vorobyov, A. B. Gershman, and Z.-Q. Luo, "Robust adaptive beamforming using worst-case performance optimization: A solution to the signal mismatch problem," IEEE Trans. Signal Process., vol. 51, no. 2, pp. 313-324, Feb. 2003. https://doi.org/10.1109/TSP.2002.806865
  28. T. Q. S. Quek, H. Shin, and M. Z. Win, "Robust wireless relay networks: Slow power allocation with guaranteed QoS," IEEE J. Select. Topics Signal Process., vol. 1, no. 4, pp. 700-713, Dec. 2007. https://doi.org/10.1109/JSTSP.2007.910271
  29. A. Ben-Tal and A. Nemirovski, "Robust convex optimization," Math. Oper. Res., vol. 21, no. 4, pp. 769-805, Nov. 1998.
  30. L. E. Ghaoui, F. Oustry, and H. Lebret, "Robust solutions to uncertain semidefinite programs," SIAM J. Optim., vol. 9, no. 1, pp. 33-52, 1998. https://doi.org/10.1137/S1052623496305717
  31. D. Guo, S. Shamai (Shitz), and S. Verdú, "Mutual information and minimum mean-square error in Gaussian channels," IEEE Trans. Inf. Theory, vol. 51, no. 4, pp. 1261-1282, Apr. 2005. https://doi.org/10.1109/TIT.2005.844072
  32. M. Gruber, O. Blume, D. Ferling, D. Zeller, M. A. Imran, and E. C. Strinati, "EARTH-energy aware radio and network technologies," in Proc. IEEE PIMRC, Tokyo, JAPAN, Sept. 2009, pp. 1-5.
  33. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, UK: Cambridge University Press, 2004.
  34. T. Q. S. Quek, M. Z. Win, and M. Chiani, "Robust power allocation algorithms for wireless relay networks," IEEE Trans. Commun., vol. 58, no. 7, pp. 1931-1938, July 2010. https://doi.org/10.1109/TCOMM.2010.07.080277
  35. J. Zander, "Performance of optimum transmitter power control in cellular radio systems," IEEE Trans. Veh. Technol., vol. 41, no. 1, pp. 57-62, Feb. 1992. https://doi.org/10.1109/25.120145
  36. M. Bengtsson and B. Ottersten, Optimal and Suboptimal Transmit Beamforming. CRC Press, 2001.