# Total active reflection coefficient

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In computation of radiation performance of multi-port antennas especially in multiple-input multiple-output (MIMO) antenna systems total active reflection coefficient, TARC, relates the total incident power to the radiated power. The total active reflection coefficient (TARC) is the square root of the sum of all incident powers at the ports minus radiated power, divided by the sum of all incident powers at the ports of an N-port antenna. The TARC is a function of frequency. With this definition we can characterize the multi-port antenna’s frequency bandwidth and radiation performance. TARC can be computed directly from the scattering matrix for different excitations.

${\displaystyle \Gamma _{a}^{t}={\frac {\sqrt {\sum _{i=1}^{N}|b_{i}|^{2}}}{\sqrt {\sum _{i=1}^{N}|a_{i}|^{2}}}}.}$

where: ${\displaystyle [b]=[S][a].}$ ${\displaystyle [S]}$ is the antenna's scattering matrix, ${\displaystyle [a]}$ is the excitation vector, and ${\displaystyle [b]}$ 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.