1304 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 61, NO. 4, APRIL 2013 OFDM AF Relaying Under I/Q Imbalance: Performance Analysis and Baseband Compensation Mohamed Mokhtar, Ahmad Gomaa, and Naofal Al-Dhahir, Fellow, IEEE Abstract—We analyze the outage performance of half-duplex amplify-and-forward relaying in an OFDM system with MRC detection in the presence of I/Q imbalance and compare it with that of the direct transmission mode. Both analytical and numer- ical results demonstrate that the direct mode can outperform the amplify-and-forward mode even under moderate levels of uncompensated I/Q imbalance. The cross-over I/Q imbalance levels are determined analytically to be inversely proportional to the cube of the signal constellation size. In addition, we present a low-complexity receiver-based digital baseband I/Q imbalance compensation scheme for the amplify-and-forward mode and analyze its EVM performance. Furthermore, we derive accurate analytical approximations for the EVM performance as a function of relay location and I/Q imbalance level with and without compensation. Index Terms—I/Q imbalance, amplify-and-forward relay, OFDM, EVM. I. I NTRODUCTION R ELAY-ASSISTED networks have received renewed sig- nificant attention in the past few years after the pio- neering work in [1]. Furthermore, relaying has been recently adopted in the long-term evolution (LTE)-advanced standard to meet the international Mobile Telecommunications (IMT)- advanced requirements [2]. Two of the most common re- laying protocols are decode-and-forward (DF) and amplify- and-forward (AF). Our focus in this paper is on AF relays because they are more cost effective since the signal is only amplified and not decoded at the relay compared to DF relays. The performance of AF-based relaying has been analyzed in several papers such as [3], assuming an ideal radio frequency (RF) front-end. In practice, and for hardware implementation reasons, the AF relays typically down-convert, amplify at baseband, and then up-convert the signal (for more details, see [4]). Moreover, and most importantly, AF relays, specifically half-duplex relays, must buffer the received signal block in the first time slot until it is transmitted (after amplification) in the second time slot which is essential for synchronization. This buffering operation cannot be efficiently done in the analog domain. Instead, it is done digitally at baseband [5]. Therefore, due to the down/up conversion operations at the AF relay and the cost constraints on its RF front end, AF relays can suffer from several major RF impairments such as carrier frequency Manuscript received August 6, 2012; revised October 19 and November 29, 2012. The associate editor coordinating the review of this paper and approving it for publication was M. Juntti. This paper is supported by a NPRP grant from QNRF. The statements made herein are solely the responsibility of the authors. The authors are with the University of Texas at Dallas, USA (e-mail: mmm096120@utdallas.edu, aarg 2010@yahoo.com, aldhahir@utdallas.edu). Digital Object Identifier 10.1109/TCOMM.2013.020813.120576 offset (CFO), phase noise (PN) and I/Q imbalance (IQI) [6]. In [5], the authors considered CFO and analyzed its effects on AF relays, while the impact of PN on the performance of AF-based relay networks was analyzed in [7] for orthogonal frequency-division multiplexing (OFDM) systems. IQI effects in AF relay networks were investigated in [8]. In contrast to this paper, the authors in [8] did not consider OFDM systems and did not consider IQI effects at the relay itself. We summarize our main contributions as follows. First, we compare the outage performances of the AF and direct (no relay) modes and show that the direct mode can outperform the relay mode even for moderate IQI levels. Second, we derive the IQI threshold level above which the direct mode outperforms the AF relay mode in the outage probability sense. Finally, we drive accurate analytical approximations for the error vector magnitude (EVM) of joint channel and IQI compensation scheme based on both zero-forcing (ZF) and conventional maximum ratio combinings (MRC) detection. To the best of our knowledge, this is the first paper to analyze IQI effects in OFDM AF relay systems and consider IQI at the relay itself. The rest of this paper is organized as follows. The system model is described in Section II and the performances of the AF and direct modes without IQI compensation are analyzed in Section III. We present channel estimation and digital baseband compensation algorithms in Section IV. In the same section, we analyze the EVM performance of the presented compensation algorithm. Simulation results and conclusions are given in Sections V and VI, respectively. Notations: Unless otherwise stated, lower and upper case bold letters denote vectors and matrices, respectively. The matrices I and F denote, respectively, the identity matrix and the Fast Fourier Transform (FFT) matrix whose middle row corresponds to the DC, and their subscripts denote theirs sizes. For matrices, A #   I N A ∗ I N , while for vectors, a #   I N a ∗ where  I N =F N F T N is the reversal (image) permutation matrix. Also, () H , () ∗ , and () T denote the matrix complex-conjugate transpose, complex-conjugate, and transpose operations, re- spectively. The operators E [] and || denote the statistical expectation and the absolute value, respectively. II. SYSTEM MODEL We consider the downlink 1 transmission scenario in relay- assisted OFDM systems with one antenna at each of the base station (BST), relay station (RS) and user equipment (UE). The RS operates in the AF mode where the transmission 1 The presented modeling approach can be easily extended to the uplink. 0090-6778/13$31.00 c  2013 IEEE