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

2026-04-02

AI Summary

This work investigates the two-user additive-multiplicative multiple-access channel (AM-MAC) in symbiotic radio systems, where an active transmitter coexists with a passive backscatter device, and characterizes its capacity region under both average power and peak amplitude constraints. Through information-theoretic analysis, nonlinear optimization, and input distribution design, the study establishes that the sum-capacity equals the point-to-point capacity of the primary transmitter. It further proposes a jointly optimal strategy wherein the primary transmitter employs constant-envelope signaling and the backscatter device adopts a concentric circular discrete input distribution. The analysis demonstrates that at arbitrary boundary points of the capacity region, the optimal input distributions for both users are either discrete or mixed. These theoretical results fully characterize the AM-MAC capacity region, and numerical experiments confirm the associated performance gains.

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.

Problem

• capacity region
• additive-multiplicative MAC
• heterogeneous input constraints
• symbiotic radio
• backscatter communication

Innovation

• additive-multiplicative MAC
• heterogeneous input constraints
• backscatter communication
• capacity region
• optimal signaling