Table 1 Different mapping results of SM scheme with code over GF(\(\varvec{2^{4}}\))
Field elements | Binary vector | \(\varvec{N}_\textbf{t}\) = 2,8-QAM | \(\varvec{N}_\textbf{t}\) = 4,4-QAM | \(\varvec{N}_\textbf{t}\)= 8,BPSK |
|---|---|---|---|---|
Antenna index, modulated symbol | Antenna index, modulated symbol | Antenna index, modulated symbol | ||
0 | \((0\quad 0\quad 0\quad 0)\) | \((1,-3+i)\) | \((1,-1-i)\) | \((1,-1)\) |
1 | \((1\quad 0\quad 0\quad 0)\) | \((2,-3+i)\) | \((3,-1-i)\) | \((5,-1)\) |
\(\alpha\) | \((0\quad 1\quad 0\quad 0)\) | \((1,3+i)\) | \((2,-1-i)\) | \((3,-1)\) |
\(\alpha ^2\) | \((0\quad 0\quad 1\quad 0)\) | \((1,-1+i)\) | \((1,1-i)\) | \((2,-1)\) |
\(\alpha ^3\) | \((0\quad 0\quad 0\quad 1)\) | \((1,-3-i)\) | \((1,-1+i)\) | (1, 1) |
\(\alpha ^4\) | \((1\quad 1\quad 0\quad 0)\) | \((2,3+i)\) | \((4,-1-i)\) | \((7,-1)\) |
\(\alpha ^5\) | \((0\quad 1\quad 1\quad 0)\) | \((1,1+i)\) | \((2,1-i)\) | \((4,-1)\) |
\(\alpha ^6\) | \((0\quad 0\quad 1\quad 1)\) | \((1,-1-i)\) | \((1,1+i)\) | (2, 1) |
\(\alpha ^7\) | \((1\quad 1\quad 0\quad 1)\) | \((2,3-i)\) | \((4,-1+i)\) | (7, 1) |
\(\alpha ^8\) | \((1\quad 0\quad 1\quad 0)\) | \((2,-1+i)\) | \((3,1-i)\) | \((6,-1)\) |
\(\alpha ^9\) | \((0\quad 1\quad 0\quad 1)\) | \((1,3-i)\) | \((2,-1+i)\) | (3, 1) |
\(\alpha ^{10}\) | \((1\quad 1\quad 1\quad 0)\) | \((2,1+i)\) | \((4,1-i)\) | \((8,-1)\) |
\(\alpha ^{11}\) | \((0\quad 1\quad 1\quad 1)\) | \((1,1-i)\) | \((2,1+i)\) | (4, 1) |
\(\alpha ^{12}\) | \((1\quad 1\quad 1\quad 1)\) | \((2,1-i)\) | \((4,1+i)\) | (8, 1) |
\(\alpha ^{13}\) | \((1\quad 0\quad 1\quad 1)\) | \((2,-1-i)\) | \((3,1+i)\) | (6, 1) |
\(\alpha ^{14}\) | \((1\quad 0\quad 0\quad 1)\) | \((2,-3-i)\) | \((3,-1+i)\) | (5, 1) |