Robust Beamforming Optimization for Multi-Antenna Wireless Networks Under Channel Uncertainty

Abstract

Movable Antennas (MAs) introduce an extra degree of freedom to space because they enable the mobility of the radiating antenna within a finite space. This feature may increase the gain of the instantaneous channel and thus enhance the reliability and spectrum efficiency of wireless communication channels. Nonetheless, this advantage relies On Channel State Information (CSI), which in turn is not independent of the position and is imprecise in practice. Current robust MAs have been studied by modeling the uncertainty in CSI through either fixed error or stochastic channel parameters. These kinds of models are helpful in analyzing the problem; nonetheless, they do not explicitly show the uncertainty in channel reconstruction.A simple robust beamforming scheme that incorporates a CSI uncertainty radius dependent on displacement from a reference point is proposed in this work.The model is physically motivated by channel reconstruction error, measurement uncertainty, and local spatial interpolation. For a two-antenna multiple-input single-output system, a closed-form worst-case received signal expression is derived using the norm-bounded uncertainty model. This leads to a simple robust design rule: antenna movement is beneficial only when the nominal channel-gain improvement exceeds the increase in uncertainty caused by displacement. The resulting position-selection problem reduces to a one-dimensional maximization of an effective robust channel margin. Numerical evaluation shows that the proposed criterion can select a position close to the calibration point rather than the position having the largest nominal channel gain. Monte Carlo simulations further show that this conservative movement strategy can eliminate outage in the considered example while requiring substantially less transmit power than a fixed reference-position design. The proposed model provides a low-complexity analytical tool for incorporating practical CSI-reconstruction limitations into MA position optimization.