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The distortion from massive MIMO (multiple-input--multiple-output) basestations with nonlinear amplifiers is studied and its radiation pattern isderived. The distortion is analyzed both in-band and out-of-band. By using anorthogonal Hermite representation of the amplified signal, the spatialcross-correlation matrix of the nonlinear distortion is obtained. It showsthat, if the input signal to the amplifiers has a dominant beam, the distortionis beamformed in the same way as that beam. When there are multiple beamswithout any one being dominant, it is shown that the distortion is practicallyisotropic. The derived theory is useful to predict how the nonlinear distortionwill behave, to analyze the out-of-band radiation, to do reciprocitycalibration, and to schedule users in the frequency plane to minimize theeffect of in-band distortion.

Spatial Characteristics of Distortion Radiated from Antenna Arrays with Transceiver Nonlinearities