Orthogonal frequency division multiplexing (OFDM) signals have high peak-to-average power ratio (PAPR) and cause large nonlinear distortions in power amplifiers (PAs). Memory effects in PAs also become no longer ignorable for the wide bandwidth of OFDM signals. Digital baseband predistorter is a highly efficient technique to compensate the nonlinear distortions. But it usually has many parameters and takes long time to converge. This paper presents a novel predistorter design using a set of orthogonal polynomials to increase the convergence speed and the compensation quality. Because OFDM signals are approximately complex Gaussian distributed, the complex Hermite polynomials which have a closed-form expression can be used as a set of orthogonal polynomials for OFDM signals. A differential envelope model is adopted in the predistorter design to compensate nonlinear PAs with memory effects. This model is superior to other predistorter models in parameter number to calculate. We inspect the proposed predistorter performance by using an OFDM signal referred to the IEEE 802.11a WLAN standard. Simulation results show that the proposed predistorter is efficient in compensating memory PAs. It is also demonstrated that the proposal acquires a faster convergence speed and a better compensation effect than conventional predistorters.

An explicit expression for the impulse response coefficients of the predictive FIR digital filters is derived. The formula specifies a four-parameter family of smoothing FIR digital filters containing the Savitsky-Goaly filters, the Heinonen-Neuvo polynomial predictors, and the smoothing differentiators of arbitrary integer orders. The Hahn polynomials, which are orthogonal with respect to a discrete variable, are the main tool employed in the derivation of the formula. A recursive formula for the computation of the transfer function of the filters, which is the z-transform of a terminated sequence of polynomial ordinates, is also introduced. The formula can be used to design structures with low computational complexity for filters of any order.

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.

This paper deals with an orthogonal functional expansion of a non-linear stochastic functional of a stationary binary sequence taking 1 with unequal probability. Several mathematical formulas, such as multivariate orthogonal polynomials, recurrence formula and generating function, are given in explicit form. A formula of an orthogonal functional expansion for a stochastic functional is presented; the completeness of expansion is discussed in Appendix.