The paper presents an adaptive algorithm named adaptive threshold nonlinear algorithm for use in adaptive filters in the complex-number domain (c-ATNA) in applications to digital QAM systems. Although the c-ATNA is very simple to implement, it makes adaptive filters highly robust against impulse noise and at the same time it ensures filter convergence as fast as that of the well-known LMS algorithm. Analysis is developed to derive a set of difference equations for calculating transient behavior as well as steady-state performance. Experiment with simulations and theoretical calculations for some examples of filter convergence in the presence of Contaminated Gaussian Noise demonstrates that the c-ATNA is effective in combating impulse noise. Good agreement between simulated and theoretical convergence proves the validity of the analysis.

In this paper, we propose a transmitter structure in digital QAM systems where pre-compensator compensates for nonlinearity with "memory effects" at the output amplifier. The nonlinearity is modeled as a linear time-invariant filter cascaded by memoryless nonlinearity (Wiener model), whereas the pre-compensator comprises an FIR-type adaptive filter that follows a memoryless predistorter based on a series expansion with orthogonal polynomials for digital QAM data. The predistorter and the adaptive filter of the pre-compensator are stochastically and directly adapted using the error signal. The theoretically optimum parameters of the predistorter are approximately solved whence the steady-state mean square compensation error is calculated. Simulations show that the proposed pre-compensator can be adapted to achieve a sufficiently small compensation error, restoring the original QAM constellation through linearization and equalization of the nonlinearity with memory effects.

This paper derives a set of orthogonal polynomials for a complex random variable that is uniformly distributed in two dimensions (2D). The polynomials are used in a series expansion to approximate memoryless nonlinearities in digital QAM systems. We also study stochastic identification of nonlinearities using the orthogonal polynomials through analysis and simulations.