The first term in the brackets of (7) is just the usual power density for an ideal antenna but decremented by an exponential factor related to the variance of the transmitter phase error. The second term also has the form of an antenna pattern but being more extensive in coverage since it is determined by the subarray size. The equivalent power into this second pattern can be interpreted as scattered power being a function of not only the phase error but the mean square amplitude error as well. In Figure 5 the result of adding two such patterns is shown for the particular case of 10 degrees rms phase error, 10% rms amplitude error, and for 18 x 18 meter subarrays. This also assumes a 1 km transmitter having a particular distribution of power (reference 9) with an edge power densitylo db less than the peak power density. The effect of the scattered power pattern is to fill in the nulls of the coherent pattern and raise the sidelobe level slightly. For example, in the case cited, the main lobe power density would be degraded by 3% and the expected far sidelobe level could be raised as much as 2-3 db. One should keep in mind that this represents only what one should expect on the average. A particular radiation pattern could have significant variation about this mean pattern (references 16, 18).
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