Table 2 The multiplication times during each search for different schemes
From: Pilot allocation scheme based on coalition game for TDD massive MIMO systems
| Â | Different combining schemes | ||
|---|---|---|---|
MMSE | ZFC | MRC | |
Coalition game for different utility function | |||
 MSE-SD | \( {\displaystyle \begin{array}{l}\left(3N+2\eta \right){NM}^3+\\ {}\left[\left(N+\eta \right){\xi}^2+3{\xi}^2+2\left(N+\eta \right)\right]{NM}^2+o\left({NM}^2\right)\end{array}} \) | \( {\displaystyle \begin{array}{l}\left(3N+2\eta \right){NM}^3+\\ {}\left[\left(N+\eta \right){\xi}^2+{\xi}^2+2\left(N+\eta \right)\right]{NM}^2+o\left({NM}^2\right)\end{array}} \) | \( {\displaystyle \begin{array}{l}\left(3N+2\eta \right){NM}^3+\\ {}\left[N+\eta +1\right]{NM}^2+o\left({NM}^2\right)\end{array}} \) |
 Received SINR | \( {\displaystyle \begin{array}{l}\left(3N+2\eta \right){NM}^3+\\ {}\left[\left(N+\eta \right){\xi}^2+3{\xi}^2+2\left(N+\eta \right)\right]{NM}^2+o\left({NM}^2\right)\end{array}} \) | \( {\displaystyle \begin{array}{l}\left(3N+2\eta \right){NM}^3+\\ {}\left[\left(N+\eta \right){\xi}^2+{\xi}^2+2\left(N+\eta \right)\right]{NM}^2+o\left({NM}^2\right)\end{array}} \) | \( {\displaystyle \begin{array}{l}\left(3N+2\eta \right){NM}^3+\\ {}\left[N+\eta +1\right]{NM}^2+o\left({NM}^2\right)\end{array}} \) |
 SE | \( {\displaystyle \begin{array}{l}\left(3N+2\eta \right){NM}^3+\\ {}\left[\left(N+\eta \right){\xi}^2+3{\xi}^2+2\left(N+\eta \right)\right]{NM}^2+o\left({NM}^2\right)\end{array}} \) | \( {\displaystyle \begin{array}{l}\left(3N+2\eta \right){NM}^3+\\ {}\left[\left(N+\eta \right){\xi}^2+{\xi}^2+2\left(N+\eta \right)\right]{NM}^2+o\left({NM}^2\right)\end{array}} \) | \( {\displaystyle \begin{array}{l}\left(3N+2\eta \right){NM}^3+\\ {}\left[N+\eta +1\right]{NM}^2+o\left({NM}^2\right)\end{array}} \) |
 MSE-CE | 3NM3 + o(NM2) (without combining schemes) | ||
Random coalition | 0 (for all combining schemes) | ||
Greedy approach in [15] | |||
 MSE-CE | 3NM3 + o(NM2) (for MMSE combining scheme) | ||