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Exploiting Multiple Polarizations in Extra Large Holographic MIMO

Adrian Agustin, Xavier Mestre

Abstract

The proliferation of large multi-antenna configurations operating in high frequency bands has recently challenged the conventional far-field, rich-scattering paradigm of wireless channels. Extra large antenna arrays must usually work in the near field and in the absence of multipath, which are far from traditional assumptions in conventional wireless communication systems. The present study proposes to analyze the spatial multiplexing capabilities of large multi-antenna configurations under line-of-sight, near field conditions by considering the use of multiple orthogonal diversities at both transmitter and receiver. The analysis is carried out using a holographic approximation to the problem, whereby the number of radiating elements is assumed to become large while their separation becomes asymptotically negligible. This emulates the operation of a continuous aperture of infinitesimal radiating elements, also recently known as holographic surfaces. The present study characterizes the asymptotic MIMO channel as seen by extra large uniform linear and planar arrays, as well as their associated achievable rates assuming access to perfect channel state information (CSI). It is shown, in particular, that for a given distance between the receiver and the center of the array and a given signal quality, there exists an optimum dimension of the multi-antenna surface that maximizes the spectral efficiency.

Exploiting Multiple Polarizations in Extra Large Holographic MIMO

Abstract

The proliferation of large multi-antenna configurations operating in high frequency bands has recently challenged the conventional far-field, rich-scattering paradigm of wireless channels. Extra large antenna arrays must usually work in the near field and in the absence of multipath, which are far from traditional assumptions in conventional wireless communication systems. The present study proposes to analyze the spatial multiplexing capabilities of large multi-antenna configurations under line-of-sight, near field conditions by considering the use of multiple orthogonal diversities at both transmitter and receiver. The analysis is carried out using a holographic approximation to the problem, whereby the number of radiating elements is assumed to become large while their separation becomes asymptotically negligible. This emulates the operation of a continuous aperture of infinitesimal radiating elements, also recently known as holographic surfaces. The present study characterizes the asymptotic MIMO channel as seen by extra large uniform linear and planar arrays, as well as their associated achievable rates assuming access to perfect channel state information (CSI). It is shown, in particular, that for a given distance between the receiver and the center of the array and a given signal quality, there exists an optimum dimension of the multi-antenna surface that maximizes the spectral efficiency.

Paper Structure

This paper contains 18 sections, 5 theorems, 61 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Degrees of freedom for spatial multiplexing (spatial modes)
  3. Use of polarization
  4. Contributions
  5. System and Signal Model
  6. Effective number of DoF
  7. Asymptotic behavior (holographic regime)
  8. Transmitter with ULA and receiver with a single element
  9. Transmitter with UPA and receiver with a single element
  10. Numerical Analysis
  11. Eigenvalue distribution
  12. Optimal antenna dimensions
  13. Increasing the number of receiving antennas
  14. Receive antenna separation
  15. Conclusion
  16. ...and 3 more sections

Key Result

Lemma 2.1

Define the error matrix The spectral norm of this matrix accepts the upper bound where $d_{\inf} = \inf_{k,m}r_{k,m}$ is the distance between the UPA and the receiver. When $t_{\mathrm{pol}}=3$ the upper bound simplfies to

Figures (9)

  • Figure 1: Scenario configuration. The transmitter is based on a UPA consisting of $2K+1$ ULAs with $2M+1$ antenna elements each. In this paper, these elements consist of 2 dipoles (red and green in the figure) or 3 dipoles (fully polarized).
  • Figure 2: Geometry of the UPA scenario with the definition of the main angles at the transmitter(bottom) and distances and angles from receiver (top).
  • Figure 3: Comparison of the expressions in the holographic regime with the simulated data. Magnitude of the eigenvalues of the Gramian in (\ref{['eq:defW']}) normalized by the total number of radiating elements $(2M+1)(2K+1)$ when a terminal is placed at $D=4$ m with elevation $\theta$.
  • Figure 4: Top: Spectral Efficiency obtained for the different polarization configurations as function of the elevation $\theta$. Bottom: Optimal Aperture Length ($\Lambda$) as a function of the elevation. Receiver at $D=4$ m.
  • Figure 5: Normalized aperture length of UPA with respect the distance to the RX (D). receiver with elevation $\theta=0, \theta=40º$. Results compared with the aperture length derived when a ULA is considered.
  • ...and 4 more figures

Theorems & Definitions (6)

  • Lemma 2.1
  • Remark 2.2
  • Proposition 4.1
  • Proposition 4.2
  • Proposition 4.3
  • Proposition 4.4