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.

翻译：本文刻画了异构输入约束下两用户加性-乘性多址接入信道（AM-MAC）的容量域。该模型捕捉了共生无线电的基本极限：主动发射机（PT）在平均功率约束下通过主动传输传递信息，而无源反向散射设备（BD）在峰值幅度约束下通过反向散射调制信号。我们的主要结果有三方面：首先，我们证明和速率容量等于PT的点对点容量，当PT采用高斯信号且BD作为纯反射器辅助PT传输时可达此容量。其次，为实现BD的最大可达速率，PT必须采用恒包络信号策略，而最优BD分布呈现具有均匀相位的同心圆结构。第三，对于其余边界点，我们证明最优PT信号由连续均匀相位和离散幅度构成，而最优BD分布完全离散。最后，通过求解特定非线性优化问题，数值结果刻画了整个容量域。为展示实际意义，我们还刻画了基准速率对并评估了AM-MAC的整体性能。