Abstract
In this paper, we investigate the transmission time of a large amount of data over fading wireless channel with adaptive modulation and coding (AMC). Unlike traditional transmission systems, where the transmission time of a fixed amount of data is typically regarded as a constant, the transmission time with AMC becomes a random variable, as the transmission rate varies with the fading channel condition. To facilitate the design and optimization of wireless transmission schemes for big data applications, we present an analytical framework to determine statistical characterizations for the transmission time of big data with AMC. In particular, we derive the exact statistics of transmission time over block fading channels. The probability mass function and the cumulative distribution function of transmission time are obtained for both slow and fast fading scenarios. We further extend our analysis to the Markov channel, where transmission time becomes the sum of a sequence of exponentially distributed time slots. Analytical expression for the probability density function of transmission time is derived for both fast fading and slow fading scenarios. These analytical results are essential to the optimal design and the performance analysis of future wireless transmission systems for big data applications.