Hybrid Beamforming Based Millimeter Wave Massive MIMO Channel Estimation

Jingze Huang; Xuwen Liang; Zhuochen Xie

doi:10.3788/LOP202259.0506002

Journals >Laser & Optoelectronics Progress >Volume 59 >Issue 5 >Page 0506002 > Article

Laser & Optoelectronics Progress
Vol. 59, Issue 5, 0506002 (2022)

Hybrid Beamforming Based Millimeter Wave Massive MIMO Channel Estimation

Jingze Huang^1、2, Xuwen Liang¹, and Zhuochen Xie^1、*

Author Affiliations

¹Innovation Academy for Microsatelite, Chinese Academy of Sciences, Shanghai , 201203, China

²University of Chinese Academy of Sciences, Beijing 100049, China

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DOI: 10.3788/LOP202259.0506002 Cite this Article Set citation alerts

Jingze Huang, Xuwen Liang, Zhuochen Xie. Hybrid Beamforming Based Millimeter Wave Massive MIMO Channel Estimation[J]. Laser & Optoelectronics Progress, 2022, 59(5): 0506002 Copy Citation Text

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Fig. 1. Hybrid beamforming architecture

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Fig. 2. Comparison of mean square error under different conditions. (a) T=300; (b) T=600; (c) T=900; (d) T=1200

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Fig. 3. Comparison of achievable spectral efficiency under different conditions. (a) T=300; (b) T=600; (c) T=900; (d) T=1200

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Fig. 4. Comparison of mean square error under different path numbers

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Fig. 5. Comparison of calculation time of each algorithm

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Fig. 6. Convergence of ALADIN_based plan

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$a, a a n d A$	Scaler， vector and matrix
$A^{T}, A^{H} a n d A^{*}$	Matrix transpose， conjugate transpose and conjugate
${‖(\cdot)‖}_{F}, {‖(\cdot)‖}_{*}, {‖(\cdot)‖}_{0} a n d {‖(\cdot)‖}_{1}$	Frobenius norm， nuclear norm， $l_{0}$ -norm and $l_{1}$ -norm
$\circ a n d \otimes$	Matrix Hadamard and Kronecker products
$v e c (\cdot)$	Vectorization of matrix
$u n v e c (\cdot)$	Inverse operation of $v e c (\cdot)$
$d i a g (\cdot)$	Diagonal of （·）
$E \{\cdot\}$	Expected value of （·）
$t r (\cdot)$	Trace of matrix
$R e (\cdot)$	Real part of the complex variable
$I m (\cdot)$	Imaginary part of the complex variable

Table 1. Notation definition

Input： $H$ ， $Ω$ ， $D_{R}$ ， $D_{T}^{}$ ， $ρ$ ， $τ_{H}$ ， $τ_{Z}$ ，I_max
Output： $H$ ^（^I^max）
Initialization： $H^{(0)} = Z^{(0)} = C^{(0)} = 0, Y = H_{Ω}$ and $τ_{H}$ ， $τ_{Z}$ ， $ρ$
for $i = 0, 1, . . ., I_{m a x} - 1$ do
1： Update $H^{(i + 1)}$ using （9）.
2： Solve （11）， then $Y^{(i + 1)} = u n v e c (y^{(i + 1)})$ .
3： Update $Z^{(i + 1)}$ by solving （13）
4： Update $C^{(i + 1)}$ using （16）.
5： Update $λ_{1}$ ， $λ_{2}$ using （17） and （18）
end for

Table 2. ALADIN_based millimeter wave massive MIMO channel estimation

Jingze Huang, Xuwen Liang, Zhuochen Xie. Hybrid Beamforming Based Millimeter Wave Massive MIMO Channel Estimation[J]. Laser & Optoelectronics Progress, 2022, 59(5): 0506002

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