Nonlinear Distortion Noise and Linear Attenuation in MIMO Systems—Theory and Application to Multiband Transmitters

Nonlinear static multiple-input multiple-output (MIMO) systems are analyzed. The matrix formulation of Bussgang's theorem for complex Gaussian signals is rederived and put in the context of the multivariate cumulant series expansion. The attenuation matrix is a function of the input signals’ covariance and the covariance of the input and output signals. The covariance of the distortion noise is in addition a function of the output signal's covariance. The effect of the observation bandwidth is discussed. Models of concurrent multiband transmitters are analyzed. For a transmitter with dual non-contiguous bands expressions for the normalized mean square error (NMSE) vs input signal power are derived for uncorrelated, partially correlated, and correlated input signals. A transmitter with arbitrary number of non-contiguous bands is analysed for correlated and uncorrelated signals. In an example, the NMSE is higher when the input signals are correlated than when they are uncorrelated for the same input signal power and it increases with the number of frequency bands. A concurrent dual band amplifier with contiguous bands is analyzed; in this case the NMSE depends on the bandwidth of the aggregated signal.