Wireless Communications and Mobile Computing

Volume 2018, Article ID 3497694, 8 pages

https://doi.org/10.1155/2018/3497694

## Suppressing the OFDM CFO-Caused Constellation Symbol Phase Deviation by PAPR Reduction

^{1}Department of Electrical Engineering and Computing, University of Dubrovnik, Dubrovnik, Croatia^{2}Faculty of Electrical Engineering, University of Sarajevo, Sarajevo, Bosnia and Herzegovina

Correspondence should be addressed to Adriana Lipovac; rh.udinu@cavopil.anairda

Received 5 May 2018; Revised 1 July 2018; Accepted 11 July 2018; Published 1 August 2018

Academic Editor: Sujan Rajbhandari

Copyright © 2018 Adriana Lipovac et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The well-known major drawbacks of the Orthogonal Frequency-Division Multiplexing (OFDM), namely, the transmitter versus receiver Carrier Frequency Offset (CFO), and the Peak-to-Average Power Ratio (PAPR) of the transmitted OFDM signal, may degrade the error performance, by causing Intercarrier Interference (ICI), as well as in-band distortion and adjacent channel interference, respectively. Moreover, in spite of the utmost care given to CFO estimation and compensation in OFDM wireless systems, such as wireless local networks or the mobile radio systems of the fourth generation, e.g., the Long-Term Evolution (LTE), still some residual CFO remains. With this regard, though so far the CFO and the PAPR have been treated independently, in this paper, we develop an Error Vector Magnitude (EVM) based analytical model for the CFO-induced constellation symbol phase distortion, which essentially reveals that the maximal CFO-caused squared phase deviation is linear with the instantaneous (per-OFDM-symbol) PAPR. This implies that any PAPR reduction technique, such as simple clipping or coding, indirectly suppresses the CFO-induced phase deviation, too. The analytically achieved results and conclusions are tested and successfully verified by conducted Monte Carlo simulations.

#### 1. Introduction

Orthogonal Frequency-Division Multiplexing (OFDM) has become widely accepted due to its excellent transmission performance and high data rate under multipath fading conditions [1]. However, though OFDM performance has been subject to extensive investigations in the last two decades, specifically with regard to practical local area wireless networks (WiFi) and the fourth-generation (4G) mobile communication systems, the Long-Term Evolution (LTE) in particular [2–4], still it remains affected mainly by two OFDM drawbacks. These are the shift between the carrier frequency at the transmitter and the one used at the receiver, which is commonly referred to as Carrier Frequency Offset (CFO), and the excessive Peak-to-Average Power Ratio (PAPR) that is inherent to the transmitted OFDM signal, being effectively a sum of many sinusoids, which can mutually combine either constructively, or destructively [5, 6].

Specifically, the CFO compromises the orthogonality between subcarriers, causing mutual interference of subchannels, i.e., the Intercarrier Interference (ICI), and so severely degrades the performance. Therefore, utmost care is given to CFO estimation and compensation in OFDM wireless systems [6–9]. However, following the CFO compensation, still some residual CFO remains, which can degrade the OFDM transmission performance [1].

On the other hand, high OFDM PAPR implies large peaks of the signal that is therefore not appropriate to pass through the nonlinear High-Power Amplifier (HPA) at the transmitter, operating close to the saturation region and so introducing in-band distortion and adjacent channel interference [5].

Several methods for PAPR reduction in OFDM systems have been explored and can generally be classified as follows: clipping, coding, and distortionless, where the latter can be with or without side information sent to the receiver [10, 11].

Nevertheless, as so far the CFO and the PAPR have been treated independently, in the following, we develop an analytical model for the constellation symbol peak CFO-induced phase deviation, which essentially reveals that reducing the OFDM PAPR indirectly suppresses the impact of the (residual) CFO, too.

In Section 2, we develop the Error Vector Magnitude (EVM) based model for the OFDM CFO-induced modulation symbol phase deviation, which, in Section 3, we find to be simply expressible in terms of PAPR. In Section 4, we verify the model by means of the Monte Carlo (MC) simulations, while conclusions are summarized in Section 5.

#### 2. CFO-Induced EVM and Constellation Symbol Phase-Deviation Model

Consider OFDM subchannels with complex baseband -long symbols , aggregated into the observed -th transmitted OFDM symbol , where is the sampling time. Assuming distortionless transmission, ideally, a particular* k*-th original symbol can be extracted from the incoming overall OFDM symbol at the receiver, by exploiting the orthogonality within the overall OFDM symbol time , as follows [1]:

Unfortunately, a number of impairments prevent such an ideal scenario from being realistic. So, although we can justifiably consider that the cyclic prefix guard time protection against Intersymbol Interference (ISI) is sufficient to prevent long error bursts due to multipath fading [2] and also that, in many practical situations of interest, the Signal-to-Noise Ratio (*SNR*) is very high, implying just sporadic bit error occurrences, still the ideal detection (1) is far from reality.

With this regard, among various impairments that can degrade the physical layer transmission performance, let us consider one out of two major inherent weaknesses of OFDM systems—the CFO [1–6]. Although, strictly speaking, CFO is a random variable with certain distribution, it is always considered constant and equal for all subcarriers.

If the* k*-th subcarrier at the receiver exhibits the offset with respect to the nominal transmitted frequency , then the detection model results in distorted actual symbol :Let us develop the integral in (2):

Now, justifiably assuming that the (residual) CFO is much smaller than the frequency increment between the neighboring subcarriersthen (3) becomes and it simplifies toSubstituting (6) into (3), the received symbol is expressed asand finally aswhere, in addition to the distortionless transmitted* k*-th symbol , the second term represents the CFO-caused ISI—actually the Error Vector* EV*_{k} with magnitude* EVM*_{k} (from now on, without “*n*” and “” in the indices) [2]:

Apparently, out of very large number of subcarriers in (9) (which is justifiable assumption, e.g., with LTE), only a few neighboring symbols within the , long sliding window around the actual (*k*-th) symbol, really influence and so , while the vast majority of symbols associated with the subchannels out of the window (i.e., the terms in the sum with large denominators) practically have no impact at all.

Furthermore, as is large enough, the Central Limit Theorem applies here implying that is a Rayleigh-distributed random variable, while the phase is uniformly distributed between and [12].

As is illustrated in Figure 1, the CFO-induced* ISI*_{k}, i.e., , actually modulates the amplitude and the phase of the received nominal (ideal) symbol, where the maximal error of the latter occurs with perpendicular to the nominal symbol vector :