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Resource Allocation and MIMO for 4G and Beyond pp 475–521Cite as

Null-Space Precoder for Dense 4G and Beyond Networks

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Abstract

In the last decade, cellular networks have been characterized by an ever-growing user data demand that pushed for more and more network capacity to be satisfied. This caused increasing capacity shortfall and coverage issues, aggravated by inefficient fixed spectrum management policies and obsolete network structures. The development of new technologies and spectrum management policies is seen as a necessary step to take, in order to cope with these issues. A significant research effort has been made since the beginning of the century, to investigate the advantages brought by the introduction of flexible management paradigms and new hierarchical approaches to network planning. The resulting tiered network layout may improve the capacity of current networks in several ways. In this chapter, we focus on the challenging problem arising when the two tiers share the transmit band, to capitalize on the available spectrum and avoiding possible inefficiencies. In this case, the coexistence of the two tiers is not feasible, if suitable interference management techniques are not designed to mitigate/cancel the mutual interference generated by the active transmitters in the network. We show that by intelligently designing the transmit waveform by means of an especial precoder, the two tier coexistence problem is solved for several different network configurations. Such configurations range from single to multiuser, the latter being also possible for centralized and distributed cases.

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Notes

  1. 1.

    Small-cells are sometimes referred to as femtocells. In this work small-cells refer to any kind of small access points similar to Wireless Fidelity (WIFI) access points (in terms of shape and usage), that employ advanced techniques to allow cooperation with macrocells.

  2. 2.

    The impact of ICI on the performance of a general macro-cell based network has been widely studied in the literature. The reader is directed to [29] and references therein for more details.

  3. 3.

    The extension to a multi-SUEs per SBS model could be seamlessly obtained by means of any multiuser scheduling technique [8], once the solution for single SUE case has been identified.

  4. 4.

    The frequency selective channels considered throughout the chapter, always have a number of taps \(l \le L\), to avoid Inter-Block Interference issues.

  5. 5.

    Some thoughts about the synchonization assumption (and lack thereof) are developed in Sect. 11.6.

  6. 6.

    We have explicitly dropped the “\({\text {s}}{\text {p}}\)” subscript to improve the readability.

  7. 7.

    We note that, for the semi-unitary precoder, the water-filling strategy forms an integral part of the optimal design, thus is needed to guarantee its optimality.

  8. 8.

    We recall that an orthonormalized precoder is always semi-unitary by construction.

  9. 9.

    This is an ideal assumption, never achievable in practice. However, it is usually considered in similar scenarios to focus on the ultimate bounds of proposed solutions and achieve a better understanding of their potential [29, 41].

  10. 10.

    We remark that this is only a simplification in the notation, thus we are not assuming absence of cross-tier interference from the MBS to SUEs.

  11. 11.

    Note that, the overall spectral efficiency of the second tier can be computed as \(R_{{\text {s}}}=\displaystyle \sum _{k=1}^K R_{{\text {s}}}^{(k)}\).

  12. 12.

    We note that, the cross-tier interference cancelation precoder, i.e., \(\mathbf{E}\), is the same for both the proposed strategy and the TDMA approach.

  13. 13.

    We depart from the assumption that a synchronization scheme is already employed at the first tier.

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Authors and Affiliations

  1. INRIA, CITI lab, INSA de Lyon, 6 av. des Arts, 69621, Villeurbanne, France

    Leonardo S. Cardoso

  2. Singapore University of Technology and Design, Singapore, Singapore

    Marco Maso

  3. Alcatel-Lucent Chair in Flexible Radio, Supélec, Gif-sur-Yvette, France

    Mérouane Debbah

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  1. Leonardo S. Cardoso
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Correspondence to Leonardo S. Cardoso .

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  1. Federal University of Ceara, Fortaleza-CE, Brazil

    Francisco Rodrigo Porto Cavalcanti

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S. Cardoso, L., Maso, M., Debbah, M. (2014). Null-Space Precoder for Dense 4G and Beyond Networks. In: Cavalcanti, F. (eds) Resource Allocation and MIMO for 4G and Beyond. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8057-0_11

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