Equivalent Baseband Models and Corresponding Digital Predistortion for Compensating Dynamic Passband Nonlinearities in Phase-Amplitude Modulation-Demodulation Schemes

Abstract

We consider baseband equivalent representation of transmission circuits, in the form of a nonlinear dynamical system S in discrete time (DT) defined by a series interconnection of a phase-amplitude modulator, a nonlinear dynamical system F in continuous time (CT), and an ideal demodulator. We show that when F is a CT Volterra series model, the resulting S is a series interconnection of a DT Volterra series model of same degree and memory depth, and an LTI system with special properties. The result suggests a new, non-obvious, analytically motivated structure of digital pre-compensation of analog nonlinear distortions such as those caused by power amplifiers in digital communication systems. The baseband model and the corresponding digital compensation structure readily extend to OFDM modulation. MATLAB simulation is used to verify proposed baseband equivalent model and demonstrate effectiveness of the new compensation scheme, as compared to the standard Volterra series approach.1 Notation and Terminology j is a fixed square root of −1. C, R, Z N are the standard sets of complex, real, integer, and positive integer numbers. X d , for a set X, is the set of all d-typles (x 1 , . . . , x d ) with x i ∈ X. For a set S, |S| denotes the number of elements in S (|S| = ∞ when S is not finite). In this paper, (scalar) CT signals are uniformly bounded square integrable functions R → R. The set of all CT signals is denoted by L. n-dimensional DT signals are the elements of n (or simply for n = 1), the set of all square summable functions Z → C n . For w ∈ , w[n] denotes the value of w at n ∈ Z. In contrast, x(t) refers to the value of x ∈ L at t ∈ R. The Fourier transform F applies to both CT and DT signals. For x ∈ L, its Fourier transform X = Fx is a square integrable function X : R → C. For x ∈ n , the Fourier transform X = Fx is a 2π-periodic function X : R → C, square integrable on its period. Systems are viewed as functions L → L, L → , → L, or k → m . Gf denotes the response of system G to signal f (even when G is not linear), and the series composition K = QG of systems Q and G is the system mapping f to Q(Gf ). A system G : L → L (or G : → ) is said to be linear and time invariant (LTI) with frequency response H : R → C when FGx = H · Fx for all x ∈ L (respectively x ∈ ). has increased over time, it has been recognized that short and long memory effects play significant role in PA's behavior [5], and should be incorporated into the model. Since then several memory baseband models and corresponding predistorters have been proposed to compensate memory effects: memory polynomials [6,7], Hammerstein and Wiener models [8], pruned Volterra series [9], generalized memory polynomials [10], dynamic deviation reduction-based Volterra models [11,12], as well as the most recent neural networks based behavioral models [13], and generalized rational functions based models [14]. These papers emphasize capturing the whole range of the output signal's spectrum, which is proportional to the order of nonlinearity of the RF PA, and i...

A Real-Valued 4D Memory Polynomial Algorithm for Mixer Modeling

“…Based on the analysis in [10], we can consider the base-band equivalent signals of the input and output signals without any loss of generality, which means that we can observe all kinds of non-linear behaviours in the performance of a mixer.…”