on-axis, as shown in Fig. 12. The 45° off-axis subarray pattern nulls are much deeper and wider; hence, antenna tilts produce much lower grating lobe peaks for lobes off the main X and Y axes. Subarray Pattern and Grating Lobe Shifts with Antenna Tilt A small antenna tilt of magnitude 0T in a polar direction </>r changes the subarray aperture attitude with the result that all portions of the subarray pattern are shifted across the ground about the new subarray boresight. The boresight location is shifted from the rectenna origin by an amount rT, to a new ground location at (XT, YT, Zo). The entire subarray pattern shifts correspondingly along the shift vector, rT (see Fig. 13, inset). where |fT|, 0T is the magnitude and direction of subarray pattern shift due to antenna tilt and XT, YT is the distance of subarray pattern shift in the X and Y directions: For a tilt of 3 arc-min in the 0T = 0° direction, the subarray pattern is shifted 31.4 km along the X axis. For the grating lobes, the effects of antenna tilt are somewhat complicated by the pilot beam phasing system. The pilot signal corrects for path length differences from the center of each subarray (or power module) to the pilot beam transmitter at the rectenna boresight. Before tilt, the grating lobes occur at angles, 0gl, where Sxsin0gl = n\ as given in Eq. 3. After tilt the path length correction
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