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Compressed Sensing in Information Processing pp 337–367Cite as

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Active Channel Sparsification: Realizing Frequency-Division Duplexing Massive MIMO with Minimal Overhead

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Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

Multiuser multiple-input multiple-output (MIMO) consists of exploiting multiple antennas at the base station (BS) side, in order to multiplex over the spatial-domain several data streams to a number of users sharing the same time–frequency transmission resource (channel bandwidth and time slots).

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Notes

  1. 1.

    This is the number of signal dimensions over which the fading channel coefficients can be considered constant over time and frequency [56].

  2. 2.

    With this term, we indicate the number of spatial-domain data streams supported by the system, such that each stream has spectral efficiency that behaves as an interference-free Gaussian channel, i.e., \(\log \text{SNR} + O(1)\). In practice, although the system may be interference-limited (e.g., due to inter-cell interference in multicell cellular systems), a well-designed system would exhibit a regime of practically relevant SNR for which its sum rate behaves as an affine function of \(\log \text{SNR}\) [36].

  3. 3.

    As commonly defined in the CS literature, we say that a reconstruction method is stable if the resulting MSE vanishes as 1∕SNR, where SNR denotes the signal-to-noise ratio of the measurements.

  4. 4.

    From the BS perspective, AoD for the DL and AoA for the UL indicate the same domain. Hence, we shall simply refer to this as the “angle domain,” while the meaning of departure (DL) or arrival (UL) is clear from the context.

  5. 5.

    An extension of the idea to general arrays will follow later in this chapter.

  6. 6.

    By N 0 ↓ 0, we mean that N 0 is approaching 0 from above.

  7. 7.

    Note that this coincides with (11.13) with B = I M, i.e., without the sparsifying precoder.

  8. 8.

    A minor of a matrix G is the determinant of some square submatrix of G.

  9. 9.

    This approach is appropriate in the medium to high-SNR regime. For low SNR, it is often convenient to increase P th in order to serve less users with a larger beamforming energy transfer per user.

  10. 10.

    Notice that by introducing noisy feedback, the relative gain with respect to J-OMP is even larger, since CS schemes are known to be more noise-sensitive than plain MMSE estimation using estimated DL covariance matrices.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Technische Universität Berlin, Berlin, Germany

    Mahdi Barzegar Khalilsarai & Giuseppe Caire

  2. SynSense AG, Zurich, Switzerland

    Saeid Haghighatshoar

  3. Department of Electrical Engineering and Electronics, University of Liverpool, Liverpool, UK

    Xinping Yi

  4. Freie Universität Berlin, Berlin, Germany

    Gerhard Wunder

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  4. Giuseppe Caire
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Correspondence to Mahdi Barzegar Khalilsarai .

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Editors and Affiliations

  1. Mathematisches Institut, Ludwig Maximilian University of Munich, München, Bayern, Germany

    Gitta Kutyniok

  2. Lehrstuhl für Mathematik, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Holger Rauhut

  3. Lehrstuhl für Mathematik, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Robert J. Kunsch

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Khalilsarai, M.B., Haghighatshoar, S., Yi, X., Caire, G., Wunder, G. (2022). Active Channel Sparsification: Realizing Frequency-Division Duplexing Massive MIMO with Minimal Overhead. In: Kutyniok, G., Rauhut, H., Kunsch, R.J. (eds) Compressed Sensing in Information Processing. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-09745-4_11

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