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Table 2 Computational complexity

From: Location-aided uplink transmission for user-centric cell-free massive MIMO systems: a fairness priority perspective

Combining scheme Number of complex multiplications
MR 0
FZF \(\sum \limits _{n = 1}^N {\left( {\frac{{3\tau _{\mathrm{p}}^2 M}}{2} + \frac{{\tau _{\mathrm{p}} M}}{2} + \frac{{\tau _{\mathrm{p}}^3 - \tau _{\mathrm{p}} }}{3}} \right) } \times {\mathbb {I}}\left( {{\mathcal {K}}_n \ne \emptyset } \right)\)
PWPFZF \(\begin{aligned} \sum \limits _{n = 1}^N {\left[ {\left( {\frac{{3\tau _{{\mathcal {S}}_n }^2 M}}{2} + \frac{{\tau _{{\mathcal {S}}_n } M}}{2} + \frac{{\tau _{{\mathcal {S}}_n }^3 - \tau _{{\mathcal {S}}_n } }}{3}} \right) \times {\mathbb {I}}\left( {{\mathcal {S}}_n \ne \emptyset } \right) } \right. } \\ \quad \;\left. { + 2\left( {\tau _{\mathrm{p}} - \tau _{{\mathcal {S}}_n } } \right) \tau _{{\mathcal {S}}_n } M \times {\mathbb {I}}\left( {{\mathcal {W}}_n \ne \emptyset } \right) } \right] \\ \end{aligned}\)
LRZF \(\sum \limits _{n = 1}^N {\left( {\frac{{3M^2 \left| {{\mathcal {K}}_n } \right| }}{2} + \frac{{M\left| {{\mathcal {K}}_n } \right| }}{2} + \frac{{M^3 - M}}{3}} \right) } \times {\mathbb {I}}\left( {{\mathcal {K}}_n \ne \emptyset } \right)\)
LP-MMSE \(\sum \limits _{n = 1}^N {\left( {\frac{{3M^2 \left| {{\mathcal {K}}_n } \right| }}{2} + \frac{{M\left| {{\mathcal {K}}_n } \right| }}{2} + \frac{{M^3 - M}}{3}} \right) } \times {\mathbb {I}}\left( {{\mathcal {K}}_n \ne \emptyset } \right)\)
Proposed combining \(\sum \limits _{n \in {\mathcal {G}}} {\frac{{3M^2 \left| {{\mathcal {K}}_n } \right| }}{2} + \frac{{M\left| {{\mathcal {K}}_n } \right| }}{2} + \frac{{M^3 - M}}{3}}\)