Abstract
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.
Highlights
A STATIC nonlinear single-input single-output (SISO) system with a Gaussian input signal can be modeled as a linear system with a noise term, where the noise is uncorrelated to the input signal according to the Bussgang theorem [1]
The model in (15) cannot be decomposed into SISO subsystems that are static nonlinearities, such that the SISO Bussgang theorem can be used. In such decompositions the input signal of each SISO system is a linear combination of the input signals to the multiple-input multiple-output (MIMO) system
We have rederived matrix formulae for linear models of static nonlinear MIMO systems, in which the distortion noise is uncorrelated to the input signals, and related them to the cumulant expansion of multivariate Gaussian processes distorted by static nonlinear functions
Summary
A STATIC nonlinear single-input single-output (SISO) system with a Gaussian input signal can be modeled as a linear system with a noise term, where the noise is uncorrelated to the input signal according to the Bussgang theorem [1]. The matrix formalism has been used to analyze 1-bit quantization effects in transmitters [17]–[19] and receivers [20], [21] in MIMO systems, or amplifier nonlinearities [22] in MIMO systems, and quantization effects on positioning in satellite navigation systems [23] In these applications the different signals go through different nonlinear devices and the matrix corresponding to the Bussgang attenuation in SISO systems becomes diagonal. The output signals at different center frequencies are downconverted separately in the receivers and such transmitters are analyzed as MIMO systems. The matrix formalism is used for systems with signals at different center frequency and the effects of observation bandwidth of the output signals and its relation to the nonlinear order are discussed. An index (·)Q of a matrix means that the system has been rewritten to be full rank. σi represents the variance of signal i; ρ is used for the polynomial coefficients of third order nonlinearities
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