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Cyclic Interference Alignment Via Polynomial Rings for Multi-user Communication Channels

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Communications in Interference Limited Networks

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

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Abstract

This chapter deals with the basic concept of interference alignment (IA) as introduced by Cadambe et al., particularly focusing on IA by propagation delay (IAP). This specific type of IA addresses the problem of interference in multi-user communication systems with long propagation delays as observed in satellite or underwater communication systems for instance. So far, IAP was conceptually described by the linear deterministic channel model (LDCM) by Avestimehr et al. The impact of channel gains is described by linear shifted and superimposed signal vectors between transmitters and receivers. However, a closed-form information-theoretic capacity analysis of such channels is challenging for asymmetric channel gains with more than two transmitter-receiver pairs communicating simultaneously. Our main contribution in this chapter is a novel channel model extending the LDCM to cyclic shifts—the cyclic polynomial channel model (CPCM). It is inspired by the algebraically convenient description of cyclic codes. We investigate the 3-user interference channel, the 2-user X-channel and the \(2 \times 2 \times 2\) relay-interference channel in terms of the CPCM with arbitrary cyclic shifts. We derive upper bounds and formulate optimal interference alignment and interference neutralization schemes to show their achievability.

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Notes

  1. 1.

    There is also a related example in [4] for a 2-user X- channel.

  2. 2.

    The DoF are also known as multiplexing gain as in [10, 12].

  3. 3.

    This property should not be confused with the related concept of the reciprocity of alignment in [7], where IA on the reciprocal channel with swapped transmitter-receiver pairs is considered instead.

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Acknowledgments

The work of H. Maier, J. Schmitz and R. Mathar was supported by the German Research Foundation (DFG) under Grants PACIA Ma 1184/15.

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Authors and Affiliations

  1. Chair of Theoretical Information Technology, KopernikusstraĂźe 16, 52074, Aachen, Germany

    Henning Maier, Johannes Schmitz & Rudolf Mathar

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  1. Henning Maier
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  2. Johannes Schmitz
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Correspondence to Henning Maier .

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  1. Technische Universität München, Muenchen, Germany

    Wolfgang Utschick

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Maier, H., Schmitz, J., Mathar, R. (2016). Cyclic Interference Alignment Via Polynomial Rings for Multi-user Communication Channels. 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_9

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  • DOI: https://doi.org/10.1007/978-3-319-22440-4_9

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  • Print ISBN: 978-3-319-22439-8

  • Online ISBN: 978-3-319-22440-4

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