SCIENCE CHINA Information Sciences, Volume 61, Issue 2: 022305(2018) https://doi.org/10.1007/s11432-017-9084-8

Capacity improvement analysis of 3D-beamforming in small cell systems

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  • ReceivedJan 27, 2017
  • AcceptedFeb 27, 2017
  • PublishedAug 25, 2017


We analyze three dimensional (3D) beamforming characteristics and applications in wireless small cell communication based on physical structure of array antenna, addressing on the 3D beampattern property of planar rectangular array antenna beamforming. Firstly, array manifold vector is formulated based on rectangular array antenna, and formulas are derived pertaining to antenna beampattern parameters in detail. Secondly, the effect of array antenna configuration on 3D beamforming is analyzed. Thirdly, 3D beamforming is extended and applied to massive MIMO small cell wireless communication scenario by analyzing capacity gain of single small cell over that of two dimensional (2D) beamforming. Numerical results are presented to show properties of the 3D beamforming.


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  • Figure 1

    (Color online) 3D beamforming massive MIMO small cell system.

  • Figure 2

    (Color online) 3D beamforming system model (d_1, d_2, d_k): Distance between user and small cell.

  • Figure 3

    (Color online) Coordinates of 3D beamforming rectangular array antenna.

  • Table 1   Mainlobe and second nulls of beampattern
    (þeta_rm null) (phi_rm null) $M$ $N$
    14.48$^{\circ}$ 30$^{\circ}$ 8 8
    7.18$^{\circ}$ 14.48$^{\circ}$ 16 16
  • Table 2   Beampattern nulls in broadside
    (þeta_rm HPBW) (phi_rm HPBW) $M$ $N$
    12.71$^\circ$ 12.71$^\circ$ 8 8
    6.35$^\circ$ 6.35$^\circ$ 16 16
  • Table 3   Beampattern nulls along diagonal direction
    (þeta_rm HPBW) (phi_rm HPBW) $M$ $N$
    13.05$^\circ$ 13.05$^\circ$ 8 8
    6.51$^\circ$ 6.51$^\circ$ 16 16
  • Table 4   Beampattern nulls with $h=R$
    (βx) (βy) (þeta) (phi) $M$ $N$ (l)
    0 0 12.71$^\circ$ 12.71$^\circ$ 8 8 3.54
    0 0 6.35$^\circ$ 6.35$^\circ$ 16 16 7.08
    45$^\circ$ 45$^\circ$ 12.71$^\circ$ 12.71$^\circ$ 8 8 3.45
    45$^\circ$ 45$^\circ$ 6.35$^\circ$ 6.35$^\circ$ 16 16 6.91
  • Table 5   Beampattern nulls with $h~\neq~R$
    (βx) (βy) $M$ $N$ (h) (R) (l)
    0 0 8 8 30 90 5.63
    0 0 16 16 30 90 11.26
    45$^\circ$ 45$^\circ$ 8 8 30 90 5.48
    45$^\circ$ 45$^\circ$ 16 16 30 90 10.99
    0 0 8 8 30 900 6.93
    0 0 16 16 30 900 13.86
    45$^\circ$ 45$^\circ$ 8 8 30 900 6.75
    45$^\circ$ 45$^\circ$ 16 16 30 900 13.53

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