Table 2 Computational complexity of the non-regenerative MIMO relay system [33]
From: Low-complexity QL-QR decomposition- based beamforming design for two-way MIMO relay networks
Step | Operations | FLOPS | Case: (2,2,2)×6 |
|---|---|---|---|
1 | \(\mathbf {U}^{a}_{i}\mathbf {\Sigma }^{a}_{i}\mathbf {\Lambda }^{aH}_{i}\) | \(8K\left (4{N^{2}_{T}}N_{i}+8N_{T}{N^{2}_{i}}+9{N^{3}_{i}}\right)\) | 13,248 |
2 | \(\mathbf {U}^{a}_{j}\mathbf {\Sigma }^{a}_{j}\mathbf {\Lambda }^{aH}_{i}\) | \( 8K\left (4{N^{2}_{T}}N_{i}+8N_{T}{N^{2}_{i}}+9{N^{3}_{i}}\right)\) | 13,248 |
3 | \(\mathbf {H}^{\mathrm {H}}_{i}\mathbf {H}_{i}\) | 4KN i N T (N i +1) | 432 |
4 | \(\mathbf {H}^{\mathrm {H}}_{j}\mathbf {H}_{j}\) | 4KN i N T (N i +1) | 432 |
5 | \(\mathbf {H}^{\mathrm {H}}_{i}\left [\sigma ^{2}_{1}{\sigma ^{2}_{2}}(\mathbf {H}_{j}\mathbf {F})^{\mathrm {H}} \mathbf {H}_{j}\mathbf {F}+\mathbf {I}\right ]^{-1}\mathbf {H}_{i}\) | \(2K\left ({N^{3}_{i}}+8N_{i}{N^{2}_{T}}+4{N^{2}_{i}}N_{T} +2N_{i}N_{T}-{N^{2}_{i}}+N_{i}\right)\) | 4212 |
6 | \(\mathbf {V}_{A}\mathbf {\Lambda }_{A}\mathbf {V}^{\mathrm {H}}_{A}\) | \(8K\left (4{N^{2}_{T}}N_{i}+8N_{T}{N^{2}_{i}} +9{N^{3}_{i}}+\frac {1}{2}N_{i}\right)\) | 13,272 |
7 | \(\text {diag}(\widetilde {\mathbf {G}})\) | \(K\left [4N_{i}N_{T}(N_{i}+1) +2{N^{3}_{i}}-2{N^{2}_{i}}+N_{i}\right ]\) | 462 |
Total | Â | Â | 45,306 |