## FANDOM

186 Pages

We investigate the effective throughput performance of overhead signaling systems from the viewpoint of Shannon Theory 2.0. Assume that $R$ is the achievable throughput of the perfect information system and $\Delta R$ is the difference of the achievable throughput performance between the perfect information system and the limited information system. We denote the overhead signaling time as $T_\mathrm{OS}$ and the total available time as $T$. Then, the effective throughput performance of the limited information system is defined as[1]

$\mathcal{R}_\mathrm{eff} = (1 - \tau_\mathrm{OS}) R_\mathrm{OS}(\tau_\mathrm{OS})$

where $\tau_\mathrm{OS} = T_\mathrm{OS}/T$ and $R_\mathrm{OS}(\tau_\mathrm{OS}) = R - \Delta R_\mathrm{OS}(\tau_\mathrm{OS})$. The equation above shows that if the time resource for overhead signaling $\tau_\mathrm{OS}$ goes to sufficiently large, the real transmission time of $T_\mathrm{DL} = 1 - \tau_\mathrm{OS}$ becomes smaller and the performance difference of $\Delta R_\mathrm{OS}(\tau_\mathrm{OS})$ becomes smaller. Therefore, it is obvious that there is an optimal point for $\tau_\mathrm{OS}$ to achieve the maximum of $\mathcal{R}_\mathrm{eff}$.

For non-perfect pilot signaling system, the throughput performance is given by the function of the noise density, $R_\mathrm{OS}( \mathrm{SNR}_\mathrm{eff}(\tau_\mathrm{OS}))$ where
$\mathrm{SNR}_\mathrm{eff} = \frac{ \mathrm{SNR}( 1 - \mathrm{MMSE})}{1 + \mathrm{SNR} \cdot \mathrm{MMSE}}$
where $\mathrm{MMSE} = E[ | \tilde{H}|^2]$ and $\tilde{H}$ is the measured channel information at the receiver[1].