Total active reflection coefficient

$\Gamma^t_a = \frac{\sqrt{\sum_{i=1}^N |b_i|^2}}{\sqrt{\sum_{i=1}^N |a_i|^2}}.$
where: $[b]=[S][a].$ $[S]$ is the antenna's scattering matrix, $[a]$ is the excitation vector, and $[b]$ represents the scattered vector. The TARC is a real number between zero and one. When the value of the TARC is equal to zero, all the delivered power is radiated and when it is equal to one, all the delivered power is either reflected back to sources or goes to the other ports.