Two-Timescale Design for Rotatable-Antenna Systems With Imperfect CSI: Rate Analysis and Orientation Optimization

This paper studies uplink multiuser MIMO with a rotatable antenna (RA) array under imperfect channel state information (CSI), where each base-station antenna can adjust its boresight direction within an angular region. To balance performance and control overhead, we propose a two-timescale design: RA orientations are optimized from statistical CSI on a large timescale, while linear receive combiners are updated per coherence block from linear minimum-mean-squared-error (LMMSE) channel estimates. Under this framework, we derive a closed-form use-and-then-forget (UatF)-based rate expression for maximum-ratio combining (MRC) and a closed-form statistical rate surrogate for weighted zero-forcing (wZF) under imperfect CSI, revealing how RA rotation influences useful signal strength, estimation-error-induced self-interference, and multiuser interference. The analysis shows that the orientation minimizing channel-estimation error differs from the rate-maximizing one, and that MRC and wZF prefer different rotation configurations due to their distinct mechanisms of signal aggregation and error-aware user separation. For the resulting non-convex rotation design problems, we develop a projected-gradient algorithm over a product of spherical caps with explicit derivatives of the required channel statistics and rate metrics. Numerical results verify the accuracy of the large-timescale surrogates and show substantial performance gains from RA optimization.