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Balancing for Interference-Limited Multi-User Satellite Communications

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Communications in Interference Limited Networks

Part of the book series: Signals and Communication Technology ((SCT))

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Abstract

The challenges in satellite communication for serving many (mobile) terminals simultaneously in higher carrier frequencies with reuse one are due to the interference and the various fading sources. Thus, the imposed downlink beamforming for the interference management has to account also for the link reliability. This chapter details the forward-link model of a modern multi-spotbeam satellite with generalized transmit power limitations, that also includes the basic rain-fading and scattering that is visible for the transmission to mobile terminals. In particular, the channel model consists of an additive and a multiplicative random channel error. Two kinds of rate balancing beamformer design strategies are studied when the satellite has statistical information about the fading channels, namely, the epsilon-outage rate balancing optimization and the average rate balancing optimization. Each of these robust approaches is detailed for fading that leads to a rank-one channel covariance or (at worst) a full-rank channel covariance due to scattering. While the epsilon-outage rate for the rank-one channel covariance can straightforwardly be rewritten into a standard rate balancing problem, but with increased noise, this is impossible for full-rank channel covariances. Then, the idea is to split the outage probability and the optimization into two parts for the multiplicative and the additive channel errors. An inner problem takes conservatively the additive channel errors into account, assuming prior information of the multiplicative errors, and the outer optimization adjusts this kind of information for the inner problem. For the average rate balancing optimization, already rank-one channel fading leads to unattractive rate expressions for a direct optimization. However, rate bounds with a standard logarithmic structure and an adapted effective noise power (and small offsets) are almost tight. This changes for a (worst-case) scattering that leads to full-rank channel covariance matrices. Then, a mean square error lower bound for the rate is sequentially optimized instead.

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Notes

  1. 1.

    Interference becomes especially severe if the frequency band reuse factor is one, i.e., the same bandwidth is used in all cells, or the increased number of spotbeams is obtained by decreasing the beamwidth below the usually assigned \(3\,{\text {dB}}\) area.

  2. 2.

    Instead of a single antenna, a spotbeam may also be created by an active or semi-active phased-array architecture, so that the spotbeams become (partly) adaptive.

  3. 3.

    Fixed terminal data services work with the DVB-S2 standard [45], for example.

  4. 4.

    Mobile data services are according to the DVB-SH standard [40], for example.

  5. 5.

    A probabilistic model for the environment and fading changes, e.g., via a two- or three-state Markov chain (cf. [42] and ITU-Recommendation R.681 [53]), are beyond the scope of this work.

  6. 6.

    Here, already the complementary event is defined.

  7. 7.

    Necessary requirements for rank-one solutions consider a sum transmit power constraint (e.g., see [16, 60]). For other power constraints, rank-one solutions are likely if the \(\varepsilon _k\) are small (cf. [20]).

  8. 8.

    The power minimization reformulations in [66] or the iterative SINR constrained power minimizations via uplink-downlink duality in [22, 55, 68] may be employed for the feasibility test.

  9. 9.

    The work by Bogale and Vandendorpe [9, 10] is for imperfect transmitter and terminal CSI.

  10. 10.

    The outer equal prior restriction and the inner Bernstein’s type inequality approach are used, which is less conservative than directly restricting the additive channel errors to lie in a sphere [65].

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Acknowledgments

The work of Andreas Gründinger was supported by the German Research Foundation (DFG) under Grants Jo 724/1-1 and Jo 724/1-2.

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  1. Fachgebiet Methoden der Signalverarbeitung, Technische Universität München, 80290, München, Germany

    Andreas Gründinger, Michael Joham & Wolfgang Utschick

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  1. Andreas Gründinger
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Correspondence to Andreas Gründinger .

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  1. Technische Universität München, Muenchen, Germany

    Wolfgang Utschick

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Gründinger, A., Joham, M., Utschick, W. (2016). Balancing for Interference-Limited Multi-User Satellite Communications. In: Utschick, W. (eds) Communications in Interference Limited Networks. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-22440-4_7

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  • DOI: https://doi.org/10.1007/978-3-319-22440-4_7

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