Embodiments of the present invention comprise systems and methods for compensating for motion of a viewer relative to a display device. A particulate filter carrying a NOx absorbent is arranged in the engine exhaust passage. Further, systems and methods for providing a discount are described which impose little or no cost on the service or product provider. Where base stations each operate with three sectors, virtual cells use three adjacent sectors of three adjacent base stations, respectively, and the coordinated orthogonal frequency hopping sequences are used for the adjacent sectors of each of the virtual cells.