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The random phase error caused by a statistical free-running frequency distribution in a coupled oscillator array is studied. Analysis shows that the array phase error is closely related to the departure of free-running frequencies of individual oscillators. Phase error is also related to the array size. A closed-form solution to the beam-pointing error in a one-dimensional (1-D) array is derived. Result shows that, for 1-D arrays, the beam-pointing error increases with array size. An analytical solution is also obtained for the side-lobe level of radiation patterns from 1-D arrays.