2 would be subjected to no more than 0.1 mw/cm with 99.99% confidence. Higher levels of confidence can be obtained by simply using a larger diameter restricted region or by tighter phase and amplitude control on the transmitter. Beam Pointing Error Statistics Using equation (6) the local power density at the receiver is proportional to Beam direction is defined as the direction of the peak of the power density function in (14). Therefore one could locate the peak or beam direction by solving the equations. In general this would be a formidable task. However, with the restrictions of small range on (x0,y0) about the no error direction and a small rms phase error on the transmitter, Taylor series approximations to the power density in (14) can be used to derive tractable forms of equations (15) (references 19, 20). One such analysis (reference 20) gives an rms pointing error of the form, Where a is the rms phase error on the transmitter, d is the center-center spacing of the subarrays, and M is the total number of subarrays. The rms beam displacement at the receiver is then
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