On the Capacity Region of Additive-Multiplicative MAC with Heterogeneous Input Constraints

TL;DR

This paper characterizes the capacity region of a two-user additive-multiplicative MAC with heterogeneous input constraints, revealing optimal signaling strategies for primary and backscatter devices and providing numerical capacity region characterizations.

Contribution

It provides the first comprehensive analysis of the capacity region for AM-MAC with heterogeneous constraints, including optimal signaling strategies and numerical characterizations.

Findings

Sum-rate capacity equals the primary transmitter's point-to-point capacity with Gaussian signaling.

The backscatter device achieves maximum rate with a concentric-circle distribution and uniform phase.

Optimal signaling involves constant-envelope for the primary and discrete amplitude with uniform phase for the backscatter.

Abstract

This paper characterizes the capacity region of a two-user additive-multiplicative multiple access channel (AM-MAC) under heterogeneous input constraints. This model captures the fundamental limits of symbiotic radio, where an active primary transmitter (PT) conveys information via active transmission subject to an average power constraint, while a passive backscatter device (BD) modulates signals through backscattering under a peak amplitude constraint. Our main results are threefold. Firstly, we prove that the sum-rate capacity equals the PT's point-to-point capacity, achieved when the PT employs Gaussian signaling and the BD acts as a pure reflector to assist the PT's transmission. Secondly, to achieve the BD's maximum achievable rate, the PT must adopt a constant-envelope signaling strategy, while the optimal BD distribution exhibits a concentric-circle structure with a uniform phase. Thirdly, for the remaining boundary points, we establish that the optimal PT signal consists of a continuous uniform phase and a discrete amplitude, whereas the optimal BD distribution is fully discrete. Finally, numerical results are provided to characterized the capacity region by solving a specialized nonlinear optimization problem. To demonstrate the practical implications, we also characterize an baseline rate pair and evaluate the overall performance of the AM-MAC.