A Queueing Characterization of Information Transmission Over Block-Fading Rayleigh Channels in the Low-SNR Regime

Unlike the additive white Gaussian noise (AWGN) channel, fading channels suffer from random channel gains, in addition to the additive Gaussian noise. As a result, the instantaneous channel capacity varies randomly along time, which makes it insufficient to characterize the transmission capability of a fading channel using data rate only. In this paper, the transmission capability of a buffer-aided Rayleigh block-fading channel is examined by a constant-rate input data stream and is reflected by several parameters, such as the average queue length, stationary queue length distribution, packet delay, and overflow probability. Both infinite-buffer and finite-buffer models are considered. Taking advantage of the memoryless property of the service provided by the channel in each block in the low-SNR regime, the information transmission over the channel is formulated as a discrete-time discrete-state D/G/1 queueing problem. The obtained results show that block-fading channels are unable to support a data rate close to their ergodic capacity, no matter how long the buffer is, even when seen from the application layer. For the finite-buffer model, the overflow probability is derived with explicit expression and is shown to decrease exponentially when buffer size is increased, even when the buffer size is very small.