Simple and Accurate Low SNR Ergodic Capacity Approximations

Abstract

Some of the existing ergodic capacity approximations for the low signal-to-noise ratio (SNR) region may lack accuracy. To overcome this, we derive two simple yet accurate Pade approximations for the low-SNR ergodic capacity. These approximations utilize the channel moments, which need not be updated for each distinct SNR value. The moments can be derived from the probability density function or from the moment generating function. For instance, we derive the general expressions for the moments of multiple input single output and multiple input multiple output channels. Numerical results demonstrate the superior accuracy of our approximations over some of the existing approximations. Moreover, we demonstrate how our approximations can be efficiently used to analyze several types of wireless links.