Energy efficiency of channels under additive Gaussian-mixture noise in the low-power regime

This paper investigates the energy efficiency of communication channels subject to additive Gaussian mixture interference in the low-power regime. This channel is widely used to capture the asynchronism in heterogeneous cellular networks. In particular, we characterize the low-signal-to-noise-ratio (low-SNR) metrics of minimum energy per bit or capacity per unit cost and the wideband slope of the spectral-efficiency curve. Instead of directly maximizing the mutual information or determining the optimal input, we make use of the characterization that the first derivative of the capacity with respect to SNR at SNR= 0 can be determined from the Kullback-Leibler divergence without identifying the optimal input. We also identify the wideband slope of spectral efficiency in closed-form by relying on the discreteness in amplitude of the capacity-achieving input. The characterization of these fundamental energy efficiency metrics allows us to find the signaling strategies that are optimally efficient in the low-SNR regime and obtain an analytical confirmation of the earlier information-theoretic findings.