Hybrid Beamforming Based Millimeter Wave Massive MIMO Channel Estimation

$a, a a n d A$	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 2. ALADIN_based millimeter wave massive MIMO channel estimation

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Table 2. ALADIN_based millimeter wave massive MIMO channel estimation

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

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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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Paper Information

Category: Fiber Optics and Optical Communications

Received: Mar. 15, 2021

Accepted: May. 24, 2021

Published Online: Feb. 22, 2022

The Author Email: Zhuochen Xie (huangjz@mail.ustc.edu.cn)

DOI:10.3788/LOP202259.0506002

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology