New bounds on the mutual information for discrete constellations and application to wireless channel estimation

The lack of closed-form expressions of the mutual information for discrete constellations has limited its uses for analyzing reliable communication over wireless fading channels. In order to address this issue, this paper proposes analytically-tractable lower bounds on the mutual information based on Arithmetic-Mean-Geometric-Mean (AM-GM) inequality. The new bounds can apply to a wide range of discrete constellations and reveal some insights into the rate behavior at moderate to high Signal-to-Noise Ratio(SNR) values. The usability of the bounds is further demonstrated to approximate the optimum pilot overhead in stationary fading channels.