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Table 2 Coordinate expression with \(\theta _1, \theta _2\)

From: Secure spatial modulation based on two-dimensional generalized weighted fractional Fourier transform encryption

Constellation

\(x_1\)

\(x_2\)

\(x_3\)

\(x_4\)

\(x_1\)

\((b_1-a_1,a_1+b_1)\)

\((b_2-a_1,a_2+b_1)\)

\((b_2-a_2,a_2+b_2)\)

\((b_1-a_2,a_1+b_2)\)

\(x_2\)

\((-a_1-b_2,b_1-a_2)\)

\((-b_1-a_1,b_1-a_1)\)

\((-b_1-a_2,b_2-a_1)\)

\((-b_2-a_2,b_2-a_2)\)

\(x_3\)

\((a_2-b_2,-b_2-a_2)\)

\((a_2-b_1,-a_1-b_2)\)

\((a_1-b_1,-b_1-a_1)\)

\((a_1-b_2,-b_1-a_2)\)

\(x_4\)

\((b_1+a_2,a_1-b_2)\)

\((b_2+a_2,a_1-b_2)\)

\((a_1+b_2,-b_1+a_2)\)

\((b_1+a_1,a_1-b_1)\)