Skip to main content Accessibility help
Hostname: page-component-797576ffbb-58z7q Total loading time: 0 Render date: 2023-12-04T13:33:16.461Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "useRatesEcommerce": true } hasContentIssue false

8 - Random matrix methods for cooperation in small cell networks

Published online by Cambridge University Press:  05 May 2013

Jakob Hoydis
Supélec (École Supérieure d'Électricité)
Mérouane Debbah
Supélec (École Supérieure d'Électricité)
Tony Q. S. Quek
Singapore University of Technology and Design
Guillaume de la Roche
Mindspeed Technologies
İsmail Güvenç
Florida International University
Marios Kountouris
SUPÉLEC (Ecole Supérieure d'Electricité)
Get access



We are currently witnessing an exponentially increasing demand for wireless data services, which is mainly driven by the growing popularity of wireless modems, smartphones, and tablet personal computers (PCs). Not surprisingly, current cellular networks have already started reaching their capacity limits in densely populated areas and it is therefore necessary to assess which network architecture is most suited to carry the future data traffic. As additional spectrum resources are scarce, it seems inevitable that any future system architecture will rely to a significant extent on network densification, i.e., an increase of the number of antennas deployed per unit area. This can be achieved by either increasing the number of antennas per base station (BS) [1] or by deploying more BSs [2], or a combination of both [3]. More antennas per device lead to additional degrees of freedom, which can provide spatial multiplexing and diversity gains or can be used to cancel interference [4]. On the other hand, a denser deployment of BSs, such as femto or small cells [5], increases the spatial reuse of the radio spectrum. Although the network capacity would theoretically scale linearly with the BS density, dense networks suffer from increased inter-cell interference and user mobility becomes difficult to manage. The cooperation of multiple BSs, which jointly process user data from multiple cells [6] has shown its potential to counter inter-cell interference and to improve the cell edge coverage not only in theory [7] but also in practice [8]. Base station cooperation is therefore already considered as an essential feature of future cellular standards [9]. Apart from that, clusters of cooperating BSs forming virtual cells could also potentially reduce the amount of handover signaling between cells to enable user mobility in dense networks [10].

Small Cell Networks
Deployment, PHY Techniques, and Resource Management
, pp. 188 - 218
Publisher: Cambridge University Press
Print publication year: 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


[1] T. L., Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas,” IEEE Trans. Wireless Commun., vol. 9, no. 11, pp. 3590600, Nov. 2010.Google Scholar
[2] J., Hoydis, M., Kobayashi, and M., Debbah, “Green small-cell networks,” IEEE Veh. Technol. Mag., vol. 6, no. 1, pp. 37–43, Mar. 2011.Google Scholar
[3] S. A., Ramprashad, H. C., Papadopoulos, A., Benjebbour, Y., Kishiyama, N., Jindal, and G., Caire, “Cooperative cellular networks using multi-user MIMO: trade-offs, overheads, and interference control across architectures,” IEEE Commun. Mag., vol. 49, no. 5, pp. 70–7, May 2011.Google Scholar
[4] J., Andrews, “Interference cancellation for cellular systems: a contemporary overview,” IEEE Wireless Commun., vol. 12, no. 2, pp. 19–29, Apr. 2005.Google Scholar
[5] H., Claussen, “The future of small-cell networks,” IEEE COMMSOC MMTC E-Lett., pp. 32–6, Sep. 2010.Google Scholar
[6] D., Gesbert, S. V., Hanly, H., Huang, S., Shamai, O., Simeone, and W., Yu, “Multi-cell MIMO cooperative networks: a new look at interference,” IEEE J. Sel. Areas Commun. (JSAC), vol. 28, no. 9, pp. 1380–408, Dec. 2010.Google Scholar
[7] S., Venkatesan, A., Lozano, and R., Valenzuela, “Network MIMO: overcoming intercell interference in indoor wireless systems,” in Proc. Asilomar Conf. on Signals, Systems, and Computers (ASILOMAR), Pacific Grove, CA, US, Nov. 2007, pp. 83–7.Google Scholar
[8] P., Marsch and G. P., Fettweis, Coordinated Multi-point in Mobile Communications: From Theory to Practice. Cambridge: Cambridge University Press, 2011.Google Scholar
[9] S., Sesia, M., Baker, and I., Toufik, LTE: The UMTS Long Term Evolution: From Theory to Practice. Wiley-Blackwell, July 2011.Google Scholar
[10] P., Charriere, J., Brouet, and V., Kumar, “Optimum channel selection strategies for mobility management in high traffic TDMA-based networks with distributed coverage,” in Proc. IEEE Int. Conf. Personal Wireless Commun. (ICPWC), Mumbay, India, Dec. 1997.Google Scholar
[11] J. G., Andrews, F., Baccelli, and R. K., Ganti, “A tractable approach to coverage and rate in cellular networks,” IEEE Trans. Commun., vol. 59, no. 11, pp. 3122–34, Nov. 2011.Google Scholar
[12] J., Hoydis, S., ten Brink, and M., Debbah, “Massive MIMO: how many antennas do we need?” in Proc. Allerton Conference on Communication, Control, and Computing, Urbana-Champaign, Illinois, US, Sep. 2011, pp. 545–50.Google Scholar
[13] J., Dumont, W., Hachem, S., Lasaulce, P., Loubaton, and J., Najim, “On the capacity achieving covariance matrix for Rician MIMO channels: an asymptotic approach,” IEEE Trans. Inf. Theory, vol. 56, no. 3, pp. 1048–69, Mar. 2010.Google Scholar
[14] J., Hoydis, M., Kobayashi, and M., Debbah, “Optimal channel training in uplink network MIMO systems,” IEEE Trans. Signal Process., vol. 59, no. 6, pp. 2824–33, June 2011.Google Scholar
[15] H., Huh, G., Caire, H. C., Papadopoulos, and S. A., Ramprashad, “Achieving massive MIMO spectral efficiency with a not-so-large number of antennas,” IEEE Trans. Wireless Commun., 2012.Google Scholar
[16] R., Couillet and M., Debbah, Random Matrix Methods for Wireless Communications. Cambridge: Cambridge University Press, 2011.Google Scholar
[17] S. M., Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall, Inc.Upper Saddle River, NJ, USA, 1993.Google Scholar
[18] Z. D., Bai and J. W., Silverstein, “No eigenvalues outside the support of the limiting spectral distribution of large dimensional sample covariance matrices,” Ann. Probab., vol. 26, no. 1, pp. 316–45, Jan. 1998.Google Scholar
[19] S., Wagner, R., Couillet, M., Debbah, and D. T. M., Slock, “Large system analysis of linear precoding in correlated MISO broadcast channels under limited feedback,” IEEE Trans. Inf. Theory, vol. 58, no. 7, pp. 4509–37, July 2012.Google Scholar
[20] J. W., Silverstein and Z. D., Bai, “On the empirical distribution of eigenvalues of a class of large dimensional random matrices,” Journal of Multivariate Analysis, vol. 54, no. 2, pp. 175–92, 1995.Google Scholar
[21] M. J. M., Peacock, I. B., Collings, and M. L., Honig, “Eigenvalue distributions of sums and products of large random matrices via incremental matrix expansions,” IEEE Trans. Inf. Theory, vol. 54, no. 5, pp. 2123–38, May 2008.Google Scholar
[22] S., Wagner, “MU-MIMO transmission and reception techniques for the next generation of cellular wireless standards (LTE-A),” Ph.D. dissertation, EURECOM, 2011.Google Scholar
[23] T., Cover and J. A., Thomas, Elements of Information Theory, 2nd edn. John Wiley & Sons, Inc., 2006.Google Scholar
[24] M., Medard, “The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel,” IEEE Trans. Inf. Theory, vol. 46, no. 3, pp. 933–46, May 2000.Google Scholar
[25] T., Yoo and A., Goldsmith, “Capacity and power allocation for fading MIMO channels with channel estimation error,” IEEE Trans. Inf. Theory, vol. 52, no. 5, pp. 2203–14, May 2006.Google Scholar
[26] B., Hassibi and B. M., Hochwald, “How much training is needed in multiple-antenna wireless links?IEEE Trans. Inf. Theory, vol. 49, no. 4, pp. 951–63, Apr. 2003.Google Scholar
[27] G., Caire, N., Jindal, M., Kobayashi, and N., Ravindran, “Multiuser MIMO achievable rates with downlink training and channel state feedback,” IEEE Trans. Inf. Theory, vol. 56, no. 6, pp. 2845–66, June 2010.Google Scholar
[28] D., Hoesli, Y.-H., Kim, and A., Lapidoth, “Monotonicity results for coherent MIMO Rician channels,” IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4334–9, Dec. 2005.Google Scholar
[29] M., Kang and M., Alouini, “Capacity of MIMO Rician channels,” IEEE Trans. Wireless Commun., vol. 5, no. 1, pp. 112–22, Jan. 2006.Google Scholar
[30] W., Hachem, P., Loubaton, and J., Najim, “Deterministic equivalents for certain functionals of large random matrices,” Ann. Appl. Probab., vol. 17, pp. 875–930, 2007.Google Scholar
[31] J., Dumont, P., Loubaton, S., Lasaulce, and M., Debbah, “On the asymptotic performance of MIMO correlated Rician channels,” in Proc. IEEE Int. Conf. on Acoustics, Speech, and Sig. Proc. (ICASSP), vol. 5, Mar. 2005, pp. 813–16.Google Scholar
[32] A., Kammoun, M., Kharouf, R., Couillet, J., Najim, and M., Debbah, “On the fluctuations of the SINR at the output of the Wiener filter for non centered channels: the non Gaussian case,” in Proc. IEEE Int. Conf. on Acoustics, Speech, and Sig. Proc. (ICASSP), Kyoto, Japan, Mar. 2012.Google Scholar
[33] W., Hachem, P., Loubaton, J., Najim, and P., Vallet, “On bilinear forms based on the resolvent of large random matrices,” Annales de l'IHP: Probability and Statistics, 2011 [Online]. Available: Scholar
[34] J., Hoydis, A., Müller, R., Couillet, and M., Debbah, “Analysis of multicell cooperation with random user locations via deterministic equivalents,” in Proc. Workshop on Spatial Stochastic Models for Wireless Networks (SPASWIN'12), Paderborn, Germany, May 2012.Google Scholar
[35] K., Huang and J. G., Andrews, “A stochastic-geometry approach to coverage in cellular networks with multi-cell cooperation,” in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), Houston, Texas, US, Dec. 2011.Google Scholar
[36] R., Couillet, M., Debbah, and J. W., Silverstein, “A deterministic equivalent for the analysis of correlated MIMO multiple access channels,” IEEE Trans. Inf. Theory, vol. 57, no. 6, pp. 3493–514, June 2011.Google Scholar
[37] P., Billingsley, Probability and Measure, 3rd edn. Wiley, 1995.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the or variations. ‘’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats