Table 4 Computational complexity of the CD-BD algorithm [2]

1

\(\mathbf {U}^{\mathrm {H}}_{i,1}\mathbf {\Sigma }_{i,1}\mathbf {\Lambda }_{i,1}\)

\(8K(4{N^{2}_{T}}N_{i}+8N_{T}{N^{2}_{i}}+9{N^{3}_{i}})\)

13,248

2

\(\mathbf {\Lambda }^{\mathrm {H}}_{i,2}\mathbf {\Sigma }_{i,2}\mathbf {U}_{i,2}\)

\(8K\left (4{N^{2}_{T}}N_{i}+8N_{T}{N^{2}_{i}}+9{N^{3}_{i}}\right)\)

13,248

3

H _i,2 W H _i,1

\(K\left [8N_{i}{N^{2}_{T}}-2N_{i}N_{T}+4N_{i}N_{T}\times (N_{i}+1)\right ]\)

2088

4

\(\mathbf {L}^{\mathrm {H}}_{i}\mathbf {L}_{i}\)

\(2K\left (N_{i}+2N_{T}N_{i}\times (N_{i}+1) +4{N^{3}_{i}}/3\right)\)

508

5

\(\mathbf {H}^{\dag }_{\text {mse}}\)

\(4{N^{3}_{R}}/3+12{N^{2}_{R}}N_{T}-2{N^{2}_{R}}-2N_{T}N_{R}\)

2736

6

\(\mathbf {H}_{i,i}\mathbf {V}^{a}_{i}\mathbf {V}^{b}_{i}\)

\(8K\left [4N_{T}{N^{2}_{i}}-4{N^{3}_{i}}/3 +{N^{2}_{i}}(N_{i}+1)\right ]\)

2336

7

\(\left (\mathbf {Q}_{i}\mathbf {Q}^{\mathrm {H}}_{i}+{\sigma ^{2}_{i}}\Psi _{i}\right)^{-1}\)

\(K\left [4N_{R}N_{i}\times (N_{i}+1) +3N_{i}+2{N^{3}_{i}}-2{N^{2}_{i}}\right ]\)

474

Total

34,638