Robust adaptive beamforming (RAB) based on interference-plus-noise covariance (IPNC) matrix reconstruction can experience serious performance degradation in the presence of look direction and array geometry mismatches, particularly when the input signal-to-noise ratio (SNR) is large. In this work, we present a RAB technique to address covariance matrix reconstruction problems. The proposed method involves IPNC matrix reconstruction using a low-complexity spatial sampling process (LCSSP) and employs a virtual received array vector. In particular, we devise a power spectrum sampling strategy based on a projection matrix computed in a higher dimension. A key feature of the proposed LCSSP technique is to avoid reconstruction of the IPNC matrix by integrating over the angular sector of the interference-plus-noise region. Simulation results are shown and discussed to verify the effectiveness of the proposed LCSSP method against existing approaches.