Fluid Antenna Port Selection in Underlay Cognitive Radio Networks

We study fluid antenna (FA) port selection in underlay cognitive radio (CR) networks, where a single FA-enabled secondary transmitter serves a single-antenna secondary receiver under the underlay CR mechanism that caps the interference at the primary user via instantaneous power control. For each FA port, we formalize the resulting signal-to-noise ratio (SNR) and propose a CR-aware selection rule that prioritizes ports offering a favorable balance between the secondary-link gain and the power-control link to the primary user. This contrasts with the conventional main-channel maximization (MCM) rule, which ignores the power-control link imposed by underlay CR—a choice often adopted in non-CR scenarios. Through rigorous mathematical derivations, we establish the exact diversity orders of both FA policies and show that each attains a diversity order equal to the rank of the FA port correlation matrix. For comparison, we further consider a traditional multi-antenna transmitter employing maximum-ratio transmission under the same underlay constraint and prove that its diversity order equals the number of transmit antennas. Monte Carlo simulations over Rayleigh fading channels validate the analysis, demonstrating sizable outage gains of the proposed CR-aware selection over MCM, and performance comparable to that of traditional multi-antenna transmission.