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In a wireless communications network served by a high altitude platform (HAP) the cochannel interference is a function of the antenna beamwidth, angular separation and sidelobe level. At the millimeter wave frequencies proposed for HAPs, an array of aperture type antennas on the platform is a practicable solution for serving the cells. We present a method for predicting cochannel interference based on curve-fit approximations for radiation patterns of elliptic beams which illuminate cell edges with optimum power, and a means of estimating optimum beamwidths for each cell of a regular hexagonal layout. The method is then applied to a 121 cell architecture. Where sidelobes are modeled as a flat floor at 40-dB below peak directivity, a cell cluster size of four yields carrier-to-interference ratios (CIRs), which vary from 15 dB at cell edges to 27 dB at cell centers. On adopting a cluster size of seven, these figures increase, respectively, to 19 and 30 dB. On reducing the sidelobe level, the improvement in CIR can be quantified. The method also readily allows for regions of overlapping channel coverage to be shown.