The far field noise due to a random near field noise is an stochastic process, and it will be shown that for a white gaussian space stationary near field noise, the far field noise is a gaussian non-stationary in elevation and coloured in azimuth process, with a variance dependent on the measurement probe. The full characterization of the far field noise allows to compute a far field pattern upper and Jower bound for a given probability, giving a deeper understanding of the effect of a random error in the radiation pattern. This is ofutmost interest in low side Jobe antenna measurements, where random errors become a limiting factor in the final accuracy . The validity of this formulation has been checked with actual measurements.

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