Low complexity channel estimation algorithm using paired spatial signatures for UAV 3D MIMO systems

Xie, Peizhong; Wan, Yingqing; Li, Ting; Ju, Renjie

doi:10.1186/s13638-020-01885-0

EURASIP Journal on Wireless Communications and Networking

Table 1 Computational complexity

From: Low complexity channel estimation algorithm using paired spatial signatures for UAV 3D MIMO systems

Method	Phase	Calculation	Computational complexity	Total computational complexity
Proposed method	UL preamble	LS method to \({\mathbf{Y}}_{x}\) and \({\mathbf{Y}}_{y}\) DFT and spatial rotation method	\(8{{ML}}^{2} + 8{{NL}}^{2}\) \(8{{M}}^{2} + 8{{N}}^{2} + {{N}}_{{{\text{ro}}}} \times \left( {6{{M}} + 6{{N}}} \right)\)	Total: \({{K}} \times \left( {8{{ML}}^{2} + 8{{NL}}^{2} + 8{{M}}^{2} + 8{{N}}^{2} + {{N}}_{{{\text{ro}}}} \times \left( {6{{M}} + 6{{N}}} \right)} \right) + {{N}}_{{{\text{co}}}} \times {{G}} \times \left( {8{{ML}}^{2} + 8{{NL}}^{2} } \right) + {{N}}_{{{\text{co}}}} \times {{G}} \times {{N}}_{g} \times \left( {8{{M}}^{2} + 8{{N}}^{2} + \left( {6{{M}} + 6{{N}}} \right) + 8{{N}}_{b} \left( {{{M}}^{2} + {{M}} + {{N}}^{2} + {{N}}} \right) + 8{{M}}^{2} + 8{{N}}^{2} + {{N}}_{{{\text{ro}}}} \times \left( {6{{M}} + 6{{N}}} \right) + 6{{MN}}} \right)\)
Proposed method	one coherence time in \({\mathcal{U}}_{1}\)	LS method to \({\mathbf{Y}}_{{{\mathcal{U}}_{1} ,x}} \left( n \right)\) and \({\mathbf{Y}}_{{{\mathcal{U}}_{1} ,y}} \left( n \right)\) Get \({\hat{\mathbf{h}}}_{k,x}^{{{\text{SBEM}}}} \left( n \right)\) and \({\hat{\mathbf{h}}}_{k,y}^{{{\text{SBEM}}}} \left( n \right)\) with SBEM Angle Update with DFT and spatial rotation Reconstructing channel	\(8{{ML}}^{2} + 8{{NL}}^{2}\) \(8{{M}}^{2} + 8{{N}}^{2} + \left( {6{{M}} + 6{{N}}} \right) + 8{{N}}_{b} \left( {{{M}}^{2} + {{M}} + {{N}}^{2} + {{N}}} \right)\) \(8{{M}}^{2} + 8{{N}}^{2} + {{N}}_{{{\text{ro}}}} \times \left( {6{{M}} + 6{{N}}} \right)\) 6MN
SBEM in [21]	UL preamble	LS method to \({\mathbf{Y}}\) DFT and spatial rotation method	\(8{{ML}}^{2}\) \(8{{M}}^{2} + {{N}}_{{{\text{ro}}}} \times 6{{M}}\)	Total: \({{K}} \times \left( {8{{ML}}^{2} + 8{{M}}^{2} + {{N}}_{{{\text{ro}}}} \times 6{{M}}} \right) + {{N}}_{{{\text{co}}}} \times {{G}} \times 8{{ML}}^{2} + {{N}}_{{{\text{co}}}} \times {{G}} \times {{N}}_{g} \times \left( {8{{M}}^{2} + 6{{M}} + 8{{N}}_{b} \left( {{{M}}^{2} + {{M}}} \right) + 8{{M}}^{2} + 6{{M}} \times {{N}}_{{{\text{ro}}}} } \right)\)
SBEM in [21]	one coherence time in \({\mathcal{U}}_{1}\)	LS method to \({\mathbf{Y}}_{{{\mathcal{U}}_{1} }} \left( n \right)\) Get \({\hat{\mathbf{h}}}_{k,x}^{{{\text{SBEM}}}} \left( n \right)\) with SBEM Angle update with DFT and spatial rotation	\(8{{ML}}^{2}\) \(8{{M}}^{2} + 6{{M}} + 8{{N}}_{b} \left( {{{M}}^{2} + {{M}}} \right)\) \(8{{M}}^{2} + 6{{M}} \times {{N}}_{{{\text{ro}}}}\)
2D-DFT and spatial rotation in [26]	UL preamble	LS method to \({\mathbf{Y}}\) 2D-DFT and spatial rotation method	\(8{{MNL}}^{2}\) \(8{{M}}^{2} {{N}} + 8{{MN}}^{2} + 12{{MN}} \times {{N}}_{{{{ro}}}}^{2}\)	Totall: \({{K}} \times \left( {8{{MNL}}^{2} + 8{{M}}^{2} {{N}} + 8{{MN}}^{2} + 12{{MN}} \times {{N}}_{{{\text{ro}}}}^{2} } \right) + {{ N}}_{{{\text{co}}}} \times {{G}} \times 8{{MNL}}^{2} + {{N}}_{{{\text{co}}}} \times {{G}} \times {{N}}_{g} \left( {8{{M}}^{2} {{N}} + 8{{MN}}^{2} + 12{{MN}} + 8\left( {{{MN}}_{b} } \right)^{2} + 8\left( {{{NN}}_{b} } \right)^{2} + 6{{M}}^{2} {{N}}_{b} + 6{{N}}^{2} {{N}}_{b} + 8{{M}}^{2} {{N}} + 8{{MN}}^{2} + 12{{MN}} \times {{N}}_{{{{ro}}}}^{2} } \right)\)
2D-DFT and spatial rotation in [26]	one coherence time in \({\mathcal{U}}_{1}\)	LS method to \({\mathbf{Y}}\) Get \({\hat{\mathbf{h}}}_{k} \left( n \right)\) with 2D-DFT and spatial rotation Angle Update	\(8{{MNL}}^{2}\) \(8{{M}}^{2} {{N}} + 8{{MN}}^{2} + 12{{MN}} + 8\left( {{{MN}}_{b} } \right)^{2} + 8\left( {{{NN}}_{b} } \right)^{2} + 6{{M}}^{2} {{N}}_{b} + 6{{N}}^{2} {{N}}_{b}\) \(8{{M}}^{2} {{N}} + 8{{MN}}^{2} + 12{{MN}} \times {{N}}_{{{\text{ro}}}}^{2}\)

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