Transmission Time Analysis for Adaptive Modulation System over Block Fading Channels

In this paper, we investigate the statistics of packet transmission time of wireless transmission systems employing adaptive modulation. Unlike traditional transmission systems, where the transmission time of a fixed-size packet is typically regarded as a constant, the transmission time of adaptive modulation systems depends on the channel realization as the transmission rate varies with the fading channel conditions. In this paper, we derive the exact statistical distribution of packet transmission time for adaptive modulation systems over block fading channels. The exact expressions of the probability mass function (PMF) and cumulative distribution function (CDF) of packet transmission time are obtained for both slow and fast fading scenarios. We further present an approximate PMF for fast fading scenario to reduce the computation complexity. Selected numerical results are presented to illustrate the mathematical formulation.