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Memoryless nonlinearity model in form of decomposition in the orthogonal basis


A.V. Smirnov – Post-graduate Student, Moscow Technical University of Communications and Informatics (MTUCI) E-mail:

This paper is devoted to show the usefulness of the representation of complex transfer function of nonlinear device in form of de-composition in the properly chosen real-valued functions basis with complex weighting coefficients. Such decomposition is aimed to facilitate the nonlinear device identification process and to reduce the number of parameters that describe the model. In the opening part of an article the brief scope of the state-of-art in the adaptive digital identification of power amplifier nonlinearity is presented. A point is made that since the problem of designing the optimal behavioral model of nonlinear device is still of relevance [10] then so is the problem of nonlinear distortion analysis taking in account the random process nature of distorted input signal [3]. And it is remarked that the results in [3] suggest a useful form to describe the signal at the output of memoryless nonlinearity in form of scaled replica of input signal and the intermodulation noise components. The proposal of the paper is formulated as to establish a new model of nonlinear device which would be capable to distinguish particular components of intermodulation noise. The second section introduces the mathematical terminology to the subject. First, the basic form of a distorted modulated signal is derived from the state-variables model of nonlinear power amplifier and the assumptions that enable to adopt memoryless nonlinearity model are demonstrated. Then the reference to results of [3] is being made aiming to illuminate the structure of the signal resulting from the memoryless nonlinear distortion of Gaussian stationary random process. Then the proposition is made to determine a nonlinear transfer function decomposition with the property to discriminate each particular component of the output signal. In the third part the details of proposed memoryless nonlinear transfer function decomposition are presented. For a Gaussian stationary random process model of an input signal the expressions of the basis functions are given. It is explained that these functions may be regarded as the AM-AM functions of the elementary nonlinear devices that yield the mutually orthogonal outputs. The convergence of the decomposition is justified and the examples are provided to illustrate the approximation fidelity when using a truncated number of decomposition components. Also the extrapolation of the obtained results to non-Gaussian models of an input signal is briefly covered. The fourth section provides several examples of possible applications of the proposed model. The orthogonality of the outputs of the elementary AM-AM nonlinear devices is exploited to propose a method for the decomposition coefficients identification. The method consists in the substitution of the Expectation operator that is suggested by the orthogonality property by the averaging with exponential damping of the past which enables a low-cost implementation. For applications to adaptive identification purposes the standard least squares method to train the model coefficients is suggested. The experimental results show the fast convergence speed and the absence of ill-behavior effects during the training process. It is also noted that the model might be incorporated into a feed-forward structure for power amplifier linearization purpose and its potential performance is justified by simulation.


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