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Table 3 Outer precoders

From: Two-level frame precoding with non-cooperative gateways

\({\mathcal {G}}_{m} = \frac {1}{ N_{U}} \sum _{i=1}^{N_{U}} {\mathbf {H}_{m,m}^{{[i]} \, H }} {\mathbf {H}_{m,m}^{[i]}}\), \(\widetilde {\mathcal {G}}_{m} ={ \frac {1}{ N_{U}} \sum _{i=1}^{N_{U}} \widetilde {\mathbf {H}}_{m}^{[i] \, H} {\widetilde {\mathbf {H}}_{m}^{[i]}} }\)

GEVD: \({\mathcal {G}}_{m} \mathbf {Z} = (\widetilde {\mathcal {G}}_{m} +\mu _{m} \cdot \mathbf {I}_{n}) \mathbf {Z} \boldsymbol {\Gamma }\)

Z1 comprises the first k columns of Z

Bm=U1 with the SVD: \(\mathbf {Z}_{1} = \mathbf {U}_{1}\mathbf {S}_{1} \mathbf {V}_{1}^{H}\)

Fully adaptive

NU=NG and the design is made for each group of users

Sector-based

NU= and an infinite number of users within the sector is assumed

Robust

NU= and an infinite number of users within the beam is assumed