Achievable Rate Region for Active RIS-Aided MISO Interference Channels

Interference poses a significant challenge in wireless communications due to the broadcast and superposition nature of wireless media. Reconfigurable intelligent surfaces (RIS), a promising 6G technology, can manage interference by customizing radio propagation with controllable reflecting elements (REs). Active RIS, which amplifies signal amplitudes and adjusts phases with enhanced REs, shows potential in addressing strong interference. This paper investigates the active RIS-aided multiple-input single-output (MISO) interference channel, characterizing the achievable rate region under transmit-power constraints, maximum amplitude constraint on each RE, and a power budget constraint at the active RIS. Utilizing multiple antennas at transmitters and multiple enhanced REs at the active RIS, we explore the Pareto Boundary of the achievable rate region with the rate profile method. A general alternating optimization framework iteratively optimizes the transmit beamforming vector and the reflection coefficient matrix through convex optimization techniques. We also consider a stringent case where active RIS ensures interference-free transmissions, deriving a reflection coefficient matrix structure via subspace decomposition. Additionally, a suboptimal algorithm combining this structure with maximum-ratio-transmission (MRT) and zero-forcing (ZF) beamforming characterizes the achievable rate region. Simulation results demonstrate that active RIS significantly improves the rate region and ensures interference-free transmissions compared to passive RIS and relay under the same power budget.