Abstract—This article addresses the signal distortion caused by receiver phase noise (PN) on OFDM waveforms in direct- conversion radio receivers. A closed-form solution for the observed signal-to-interference-plus-noise ratio (SINR) is derived, describing the level of intercarrier interference (ICI) stemming from PN. Compared to existing literature, the analysis is valid for arbitrary oscillator spectral shape, the only assumption being that reasonably small phase noise values are observed. The analysis results can be used to derive practical circuit-level oscillator design criteria in terms of the allowable PN spectral density. The applicability and validity of the derived analysis are verified with extensive computer simulations. Index Terms—Inter-carrier interference, OFDM, performance analysis, phase noise I. INTRODUCTION OMMUNICATIONS systems using orthogonal frequency division multiplexing (OFDM) are highly vulnerable to non-idealities of radio device components [1]. Performance- wise one of the most remarkable of these non-idealities is oscillator phase noise [2], [3]. Phase noise spreads the spectral content of the used subcarriers destroying the orthogonality between them. This causes inter-carrier interference (ICI) in addition to well known effect of symbol constellation rotation called common phase error (CPE) [2]. Due to the relatively complex nature of the phase noise induced waveform distortion, and its dependency on the used oscillator characteristics, a closed-form tool describing the level of ICI as a function of the used oscillator spectral density is developed in this article. Such tool can be used already in the design process of the oscillator, e.g., to find out the properties of oscillators that are the most significant from the applied waveform point of view. The effects of phase noise on the performance of OFDM communications systems are widely studied in the literature, This work was supported by TUT Graduate School, Finnish Foundation for Technology Promotion, HPY Research Foundation, the Finnish Funding Agency for Technology and Innovation (Tekes, under the project “Advanced Techniques for RF Impairment Mitigation in Future Wireless Radio Systems”), the Technology Industries of Finland Centennial Foundation and EUREKA CELTIC E!3187 B21C-Broadcasting for 21st Century. Authors are with Department of Communications Engineering, Tampere University of Technology, P.O. Box 553, 33101 Tampere, Finland. (email: {ville.syrjala, mikko.e.valkama, yaning.zou, nikolay.n.tchamov, jukka.rinne}@tut.fi). e.g., in [4], [5] and [6]. However, the oscillator models in the reported studies are typically fixed or restricted to highly- simplified models, such as the free-running oscillator (FRO) [3]. In this paper, the effective signal-to-interference-plus- noise ratio (SINR) is analyzed for OFDM systems under the influence of phase noise caused ICI. The phase noise process in this study is based on arbitrary phase noise spectral mask, thus making the model generally applicable for practical oscillators. Only an assumption of an oscillator with reasonably small phase noise values is made without restricting the spectral shape of the phase noise to any predefined criteria. To authors’ knowledge, analysis without any restrictions to the spectral shape of the oscillator cannot be found in existing literature. The rest of this article is organized as follows: Section II gives a compact subcarrier-wise OFDM link model including the radio channel and receiver phase noise. This forms the basis for the SINR analysis. Then, Section III formulates and carries out the actual SINR analysis in detail, while Section IV verifies the derived expressions with the help of link computer simulations. Finally, the work is concluded in Section V. II. OFDM LINK MODEL In OFDM systems, the phase noise effects can be divided in two distinct parts [2]. The first effect is called CPE that is the common complex multiplicative effect the phase noise has on all subcarrier symbols within one OFDM symbol. The second effect is called ICI, which is the loss of orthogonality due to frequency spread of the subcarriers on top of each other. The CPE is easily cancelled out in the receiver with help of pilot subcarriers [3]. ICI, however, has more complicated effect on the OFDM systems, thus making its mitigation much more burdensome [3], [7]. This is why the ICI is much more interesting also from the performance analysis point-of-view. Therefore, in this work, we assume that the CPE is known, namely part of the useful signal, while the actual interference is coming from the neighbouring subcarriers. Furthermore, to simplify the analysis, we assume that the interference from adjacent RF bands is negligible, meaning that we focus on the in-band effects only. Next, to form the basis for SINR analysis, a link model is shortly established taking into account a noisy multipath channel and receiver phase noise. In effect, the observation at subcarrier k can be written as On OFDM Link Performance under Receiver Phase Noise with Arbitrary Spectral Shape Ville Syrjälä, Mikko Valkama, Yaning Zou, Nikolay N. Tchamov, and Jukka Rinne C