Capacity bounds for bandlimited Gaussian channels with peak-to-average-power-ratio constraint

TL;DR

This paper derives tighter capacity bounds for bandlimited Gaussian channels under peak-to-average-power-ratio constraints, improving understanding of channel limits and extending to optical intensity channels.

Contribution

It introduces a new capacity lower bound for PAPR constrained channels, optimizes it with parametric pulses, and refines existing bounds for optical intensity channels.

Findings

Capacity bounds are within a finite gap that vanishes as PAPR increases.

Optimized pulse shapes improve the lower bounds.

Enhanced bounds for high SNR optical intensity channels.

Abstract

We revisit Shannon's problem of bounding the capacity of bandlimited Gaussian channel (BLGC) with peak power constraint, and extend the problem to the peak-to-average-power-ratio (PAPR) constrained case. By lower bounding the achievable information rate of pulse amplitude modulation with independent and identically distributed input under a PAPR constraint, we obtain a general capacity lower bound with respect to the shaping pulse. We then evaluate and optimize the lower bound by employing some parametric pulses, thereby improving the best existing result. Following Shannon's approach, capacity upper bound for PAPR constrained BLGC is also obtained. By combining our upper and lower bounds, the capacity of PAPR constrained BLGC is bounded to within a finite gap which tends to zero as the PAPR constraint tends to infinity. Using the same approach, we also improve existing capacity lower bounds for bandlimited optical intensity channel at high SNR.