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} $.

Pilot Overhead Edit

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].

References Edit

  1. 1.0 1.1 N. Jindal and A. Lozano, Optimum Pilot Overhead in Wireless Communication: A Unified Treatment of Continuous and Block-Fading Channels, Submitted to IEEE Trans. Wireless Communications, March 2009