Table 1 Per-symbol computational complexity of aMGS, conventional MGS, and MMSE algorithms
Procedure | Step | Complexity |
|---|---|---|
d-MGS — Algorithm 3 | ||
Target function calculation | Lines 11–16 | \(16KN - 4N + |\mathbb {A}|\left (16N+2\right)\) |
Generation of the d-limited set | Line 19 | negligible |
Cost computation at each coordinate | Line 28 | 20N |
Θs, Eq. (13) | Line 41 | \(\frac {24}{K}\) |
Total per-symbol complexity: | \(\mathcal {C}_{T} = \mathcal {C}_{I} + {\mathcal {I}_{\text {eff}}}\left [16KN+16N+|\mathbb {A}|\left (16N+2\right) + \frac {24}{K}\right ]\) | |
aMGS — Algorithm 2 | ||
Target function calculation | Lines 8–12 | \(16KN - 4N + |\mathbb {A}|\left (16N+2\right)\) |
Averaging between samples | Line 24 | 2Le+2 |
Cost computation at each coordinate | Line 26 | 20N |
Θs, Eq. (13) | Line 41 | \(\frac {24}{K}\) |
Total per-symbol complexity: | \(\mathcal {C}_{T} = \mathcal {C}_{I} + {\mathcal {I}_{\text {eff}}}\left [16KN+16N+|\mathbb {A}|\left (16N+2\right)+(2L_{e}+2) + \frac {24}{K}\right ]\) | |
MGS — target distribution function calculation on Algorithm 1 | ||
Target distribution function calculation | Lines 4–6 | \(16KN - 4N + |\mathbb {A}|\left (16N+12\right)\) |
Evaluation of each symbol probability | Lines 8–12 | \(1238|\mathbb {A}|\) |
Cost computation of estimated vector | \(\frac {10N}{K}\) | |
Θs, Eq. (13) | \(\frac {24}{K}\) | |
Total per-symbol complexity: | \(\mathcal {C}_{T} = \mathcal {C}_{I} + {\mathcal {I}_{\text {eff}}}\left [16KN-4N+|\mathbb {A}|\left (16N+1450\right) + \frac {10N+24}{K} \right ]\) | |
MMSE algorithm | ||
Total per-symbol complexity: | \(\mathcal {C}_{T} = \left (\frac {1}{6}\right) K^{2} + \left (\frac {3}{2}\right)NK + \left (\frac {3}{2}\right)N + \left (\frac {5}{6}\right) \) | |