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Table 3 Computational complexity of the conventional RBD [32]

From: Low-complexity QL-QR decomposition- based beamforming design for two-way MIMO relay networks

Step

Operations

FLOPS

Case: (2,2,2)×6

1

\(\mathbf {U}^{a}_{i}\mathbf {\Sigma }^{a}_{i}\mathbf {\Lambda }^{aH}_{i}\)

\(32K(N_{T}\overline {N}^{2}_{i}+2\overline {N}^{3}_{i})\)

21,504

2

\(\left (\left (\mathbf {\Sigma }^{a}_{i}\right)^{\mathrm {T}}\mathbf {\Sigma }^{a}_{i}+\rho ^{2}\mathbf {I}\right)^{-1/2}\)

\( K\left (18N_{T}{N^{2}_{i}}-2{N^{2}_{i}}\right)\)

336

3

\(\mathbf {V}^{a}_{i}\mathbf {D}^{a}_{i}\)

\(8K{N^{3}_{T}}\)

5184

4

\(\mathbf {H}_{i}\mathbf {P}^{a}_{i}\)

\(K\left (8N_{T}{N^{2}_{i}}-2{N^{2}_{i}}\right)\)

552

5

\(\mathbf {U}^{b}_{i}\mathbf {\Sigma }^{b}_{i}\mathbf {V}^{bH}_{i}\)

\(64K\left (\frac {9}{8}{N^{3}_{i}}+N_{T}{N^{2}_{i}}+\frac {1}{2}{N^{2}_{T}}N_{i}\right)\)

13,248

Total

  

40,824