3472 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 11, NOVEMBER 2010 Analytical Evaluation of Nonlinear Effects on OFDMA Signals Teresa Araújo and Rui Dinis, Member, IEEE Abstract—As with other multicarrier modulations, OFDMA signals (Orthogonal Frequency Division Multiple Access) have large envelope fluctuations making them very prone to nonlinear distortion effects. In this paper we study the impact of nonlinear devices on OFDMA signals. We present an analytical characterization of the signals at the output of a nonlinear device that can be used for obtaining the spectral characterization of the transmitted signals, as well as the computation of the nonlinear interference levels on the received signals. It is shown that the power allocated to each user has a key impact on the nonlinear distortion effects. For this reason, we should avoid having low-power and high-power users in adjacent subcarriers. It is also shown that nonlinear distortion levels are lower when just a small fraction of the subcarriers is used (i.e., when the system load is small). 1 Index Terms—OFDM signals, nonlinear effects, intermodula- tion analysis, wireless access, OFDMA. I. I NTRODUCTION O FDMA (Orthogonal Frequency Division Multiple Ac- cess) schemes [1], [2] are OFDM (Orthogonal Frequency Division Multiplexing) modulations [3], [4] where a different set of subcarriers is assigned to each user. Therefore, they combine an OFDM modulation with an FDMA (Frequency Division Multiple Access) scheme. Moreover, they are suitable for severe frequency-selective channels (also denoted time- dispersive) and allow a flexible and efficient management of the spectrum. For these reasons, they were selected for future broadband wireless systems [5]–[7]. OFDMA is used in wireless broadband access technologies IEEE 802.16a/d/e, commonly referred to as WiMAX [5], [8], and 3rd Genera- tion Partnership Project (3GPP) Long Term Evolution (LTE), named High Speed OFDM Packet Access (HSOPA) [6]. It is also the access method candidate for Wireless Regional Area Networks (WRAN) [7]. As with OFDM and other multicarrier modulations, the transmitted signals have large envelope fluctuations and high PMEPR (Peak-to-Mean Envelope Power Ratio), leading to amplification difficulties. For this reason, several techniques Manuscript received November 19, 2009; revised April 19, 2010; accepted June 17, 2010. The associate editor coordinating the review of this paper and approving it for publication was J. Olivier. T. Araújo is with the Instituto de Telecomunicações, Lisboa, Portugal, and the Departamento de Matemática, Instituto Superior de Engenharia do Porto, Porto, Portugal (e-mail: tpa@isep.ipp.pt). R. Dinis is with the Instituto de Telecomunicações, Lisboa, Portugal, and the Departamento de Engenharia Electrotécnica, Faculdade de Ciências e Tecnologia, FCT, Universidade Nova de Lisboa, Caparica, Portugal (e-mail: rdinis@fct.unl.pt). Digital Object Identifier 10.1109/TWC.2010.081810.091662 1 This work was partially published in IEEE 5 ℎ International Symposium on Wireless Communication Systems 2008 (ISWCS’08) and IEEE 67 ℎ Vehicular Technology Conference 2008 (VTC’08 Spring). have been proposed to reduce the envelope fluctuations of OFDMA signals namely through suitable pre-processing schemes [9]–[11]. As an alternative, we can employ clipping and filtering techniques, already shown to be effective for conventional OFDM signals [12]–[14], as well as MC-CDMA (Multi-Carrier Code Division Multiple Access) schemes [15]. The performance evaluation of multicarrier schemes with nonlinear transmission (either due to an imperfectly linear amplification or due to suitable signal processing schemes to reduce the envelope fluctuations of the transmitted signals), usually resorts to Monte-Carlo simulations that require a long computation time; heuristic, "semi-analytical", approaches have also been proposed so as to evaluate nonlinear distortion effects (see, e.g., [16]). When the number of subcarriers is high we can take advantage of the Gaussian nature of the transmitted signals to characterize statistically the transmitted signals [12], [15], [17]–[20]. The nonlinear devices considered in [12], [15], [17], [18] can be regarded as bandpass memory- less nonlinearities [21] ([15] considers MC-CDMA signals and [12], [17], [18] consider OFDM signals). [19], [20] consider quantization effects on OFDM signals, i.e., the nonlinear devices can be regarded as I-Q memoryless nonlinearities. This paper deals with the analytical evaluation of nonlinear distortion effects on OFDMA signals, which, as far as we know, was not addressed in detail in the literature. We consider nonlinear distortion effects that are inherent to nonlinear signal processing techniques for reducing the PMEPR of the trans- mitted signals (as the ones proposed in [12] for conventional OFDM schemes). For this purpose, we take advantage of the Gaussian-like nature of OFDMA signals with a large number of subcarriers to extend the results of [12], [17], [22] to OFDMA schemes. Our results allow an analytical spectral characterization of the transmitted signals, as well as the computation of the nonlinear interference levels on the received signals. They can also be used to compute the corresponding BER (Bit Error Rate). This allows an efficient approach for studying aspects such as the type of nonlinear device, the impact of the system load (fraction of subcarriers used), the set of subcarriers assigned to each user (continuous, randomly spaced or regularly spaced subcarriers), etc. This paper is organized as follows: Sec. II describes the OFDMA schemes considered in this paper. The analytical evaluation of nonlinear distortion effects on the transmission of OFDMA signals is made in Sec. III and a set of per- formance results is presented in Sec. IV. Finally, Sec. V is concerned with the conclusions of this paper. II. OFDMA SYSTEM In this paper we consider an OFDMA system with  users and   subcarriers assigned to the th user. The total number 1536-1276/10$25.00 c ⃝ 2010 IEEE