Performance Evaluation of Quantization Effects on Multicarrier Modulated Signals Teresa Ara´ ujo and Rui Dinis, Member, IEEE ISR-Instituto Superior T´ ecnico, 1049-001 Lisboa, Portugal Phone: + 351 21 8418298, Fax: + 351 21 8418290, e-mail: ftaraujo, rdinisg@ist.utl.pt Abstract The numerical accuracy in the DFT/IDFT operations can have a significant impact on MC (MultiCarrier) modulated signals. This accuracy can be modeled by including appropriate quantization devices in the transmission chain. In this paper, we present an analytical approach for analyzing the impact of the quantization effects in MC signals. For this propose, we characterize statistically the signal along the transmission chain, taking advantage of the Gaussian behavior of MC signals with a high number of subcarriers and employing well- known results on Gaussian signals and memoryless nonlin- earities. This statistical characterization can then be used for performance evaluation of given quantization characteristics, in a simple and computationally efficient way, as well as to its optimization. Keywords: Multicarrier modulations, quantization, nonlin- ear effects, Gaussian processes I. Introduction In recent years, MC modulations schemes (MultiCarrier) have been selected for several digital transmission systems: the OFDM schemes (Orthogonal Frequency Division Multi- plexing) [1] were adopted for both digital broadcasting systems and wireless LANs (Local Area Network) [2] and the DMT schemes (Discrete MultiTone) were adopted by the ADSL standard (Asymmetric Digital Subscription Line) [3]. One of the main reasons for the high interest behind these MC modulations is their ability to cope with severe time-dispersive channels without requiring complex receivers, thanks to its FFT-based (Fast Fourier Transform) implementations. However, MC signals have high envelope fluctuations, mak- ing them very prone to nonlinear distortion effects. When the number of subcarriers is high, MC signals exhibit a Gaussian- like behavior, which can be used for a theoretical evaluation of nonlinear effects [4]-[8]. The clipping of a DMT signal was considered in [4]. The impact of bandpass memoryless nonlinear devices [9] on OFDM signals was considered in [5]-[7]. The analytical approach of [4] was extended to the so-called I-Q memoryless nonlinear devices (i.e., nonlinear devices operating separately in the real and imaginary parts of the complex envelope of the OFDM signal) in [8]. Another problem associated to MC signals is the numerical accuracy required in the DFT/IDFT operations, which can have a significant impact on the MC transmission performance, es- pecially when large constellations are employed. This accuracy can be modeled as appropriate quantization effects associated to the input and/or the output of each DFT/IDFT computation. The evaluation of quantization effects is a well-known problem in ADC (Analog-to-Digital Conversion). The usual approach is to assume that an uniformly-distributed noise is added to the quantized signal [10], [11]. However, this approach is not suitable if there are clipping effects (i.e., the ”saturation” of the quantizer is not a very rare event) and/or for non- uniform quantizers. Clipping effects on Gaussian noise were studied in [12] and a general theory for non-uniform quantizers can be found in [13]. An analytical approach for evaluating the impact of memoryless nonlinear devices in real-valued Gaussian signals was presented in [14] (and, more recently, in [15]) and used for evaluating quantization and clipping effects at the multicarrier receiver. The impact of the oversampling factor on the SIR levels was also considered there. In this paper, we study the quantization effects on the com- plex envelope of MC signals. These quantization effects occur at both the transmitter and the receiver and are associated to the numerical accuracy of the DFT computations. For this purpose, we include an appropriate statistical characterization of the signal along the transmission chain which takes advantage of the Gaussian behavior of the complex envelope of MC signals with a high number of subcarriers and employs well-known re- sults on Gaussian signals and memoryless nonlinearities. This statistical characterization can then be used for performance evaluation of given quantization characteristics, in a simple and computationally efficient way, as well as to its optimization. This paper is organized as follows. In sec. II we present the quantization effects, inherent to the accuracy of the DFT/IDFT operations, on MC signals. Sec. III presents an analytical, statistical characterization of the transmitted and received signals, taking into account these quantization effects. In sec. IV we present some numerical results and sec. V is concerned with the conclusions and final remarks of this paper. II. Quantization Effects on Multicarrier Modulated Signals Fig. 1.A presents the transmission chain considered for MC modulations. Each DFT/IDFT operation is modeled as an ideal DFT/IDFT operation (i.e., with infinite precision), followed and preceeded by quantization blocks, modeling numerical