Analysis of Inter-Modulation Products and Nonlinear Distortion in RF OFDM Transmitter Systems

Abstract —Orthogonal Frequency Division Multiplexing (OFDM) systems are significantly sensitive to the nonlinear distortion caused by RF power amplifiers. Generally, nonlinear distortion of OFDM signals, which generates a huge number of inter-modulation products (IMPs), is treated as a macro phenomenon. In this paper, low order IMPs are classified into various categories by their composition and the characteristics of IMPs in each category is presented. Relationships between single IMP and nonlinear distortion are also explored. The popular Bessel-Fourier (BF) envelope model with associated three signal representation approaches are used as analysis tools. An IEEE 802.11a signal is used and the nonlinear envelope is measured from a GaN power amplifier. Keywords- nonlinear distortion, power amplifier, OFDM, IMP I. I NTRODUCTION OFDM technology is now an established attractive digital modulation scheme for modern wireless communication systems, e.g., [1, 2]. OFDM systems, however, generally have a high peak to average power ratio (PAPR) as they may consist of large numbers of independent sub-carriers modulated with adaptive multi-level quadrature amplitude modulation (QAM) schemes. Thus OFDM systems are very sensitive to the nonlinearity of RF transmitters, and the power amplifier (PA) is the main source of nonlinear distortion. Furthermore, the operating point of PAs may have to be driven into the highly nonlinear range due to the need for better power added efficiency (PAE), since the PA consumes most power in the transmission process, [3, 4]. In practice nonlinear distortion produces a huge number of IMPs in and around the fundamental OFDM signal band and, theoretically, in all harmonic bands, [5, 6]. The IMPs within the fundamental band are the focus of this nonlinearity analysis, since harmonics and IMPs at harmonic frequencies may be removed from the output signal by filters. The IMPs within the fundamental band impair the signal modulation fidelity, e.g. as measured by Error Vector Magnitude (EVM), and also causes interference in adjacent channels, which is measured by the output spectrum mask, [7]. Due to the complexity of such distortion, comprising lots of IMPs and having a noise-like characteristic, it may be effectively treated as a macro phenomenon, e.g., [8, 9]. Complementary to and informative for this approach is an analysis which delves more into the composition of the IMPS, their distribution densities and their behaviour as a function of the level of nonlinearity. Aspects of this analysis are undertaken in this paper. Our approach is to classify IMPs into various categories by their composition. Here the characteristics of IMPs in each category, including distribution density functions and the power behaviour of each single IMP, is presented, along with their relationship to the level of nonlinear distortion. Memoryless PA nonlinear distortion only is treated here. The popular Bessel-Fourier (BF) is chosen for the PA behavioural modeling, for its accuracy, extensibility, and unique decomposability when handling multicarrier signals, [4, 10]. An appropriate signal representation technique has to be selected also. Device measurements, the AM-AM and AM-PM characteristics, are those extracted from a GaN PA operating at 2.15 GHz. The AM-AM may be seen in Fig. 1. Here the input and output are expressed as the back off from the corresponding saturation power. This saturation power is defined as where the derivative of the output gain first reaches 0.1, [12]. As it happens the AM-PM distortion is negligible over the dynamic range of interest [11]. The signal modelled is an un-coded IEEE 802.11a OFDM signal with 16-QAM applied. II. B