Carrier frequency offset estimation for OFDM systems with time-varying DC Offset

Orthogonal frequency division multiplexing (OFDM) systems with direct-conversion architecture suffer from both carrier frequency offset (CFO) and dc offset (DCO). In this paper, we study CFO estimation problem for OFDM systems with time-varying DCO (TV-DCO) caused by gain mode switch of low noise amplifier (LNA). Based on linear approximation of TV-DCO, a blind algorithm is proposed for CFO estimation by means of DCO compensation and power leakage minimization. Performance of the proposed algorithm is demonstrated by simulations. Introduction Orthogonal frequency division multiplexing (OFDM) [1] is a promising technology for wireless communications to achieve efficient spectrum utilization, robustness to multi-path fading and easy implementation based on fast Fourier transform (FFT) and inverse FFT (IFFT), and has been widely adopted by emerging wireless applications such as digital audio broadcasting (DAB) [2], digital video broadcasting (DVB) [3], wireless local area network (WLAN) [4] and 3GPP long term evolution (LTE) [5] etc. Despite of the attractive advantages, OFDM is vulnerable to various disturbances in practice. Carrier frequency offset (CFO) is one of most well-known disturbances for OFDM. It generates inter-carrier interference (ICI) and degrades OFDM performance [1]. In order to mitigate the negative influence, CFO is usually estimated and compensated accordingly during OFDM reception. CFO estimation for OFDM systems had been excessively studied and various algorithms had been proposed in literatures such as [6-8]. In [6], maximum likelihood (ML) CFO estimation for OFDM systems in additive white Gaussian noise (AWGN) channel was presented, while its performance degrades in multi-path dispersive channel. Liu et al. proposed in [7] a MUSIC-like blind CFO estimator which was proved in [9] to be equivalent to ML estimator in fading channel. *Correspondence: [email protected] 1School of Automation & Electrical Engineering, University of Science and Technology Beijing, Beijing, 100083, China Full list of author information is available at the end of the article In addition to CFO, OFDM may also suffer from other disturbances such as direct current offset (DCO). For the sake of cost and power efficiency, mobile receiver architecture is under evolution from superheterodyne to direct conversion [10-13] in recent years. DCO is one of the most common disturbances of direct conversion receiver (DCR). It comes from self-mixing of local oscillator (LO) signal or radio frequency (RF) signal due to the finite isolation between input ports of mixer [10-13], as shown in Figure 1. In OFDM systems,DCOnot only degrades demodulation performance but also violates CFO estimation [14-19]. CFO estimation for OFDM systems with static DCO had been well addressed in literatures [14-19]. Impacts of static DCO on CFO estimation can either be eliminated by analog high pass filter (HPF) [20] or be compensated in digital domain with data-aided [14-16] or blind approaches [17-19]. Besides static DCO, DCR may also introduce time-varying DCO (TV-DCO). In order to cover the high dynamic range of faded OFDM signals, low noise amplifier (LNA) with multiple gain modes [20-27] is usually employed by DCR in OFDM systems. During the gain mode switch stage shown in Figure 2, a sudden change of DCO level may occur [20,28-36] and high frequency components of the sudden change may pass through the HPF succeeding LNA, which results in TV-DCO [28-36]. Only a fewworks were reported to address CFO estimation for OFDM systems with TV-DCO. Inamori et al. proposed in [29] to suppress the influence of TV-DCO on CFO estimation with differential filter (DFE). Yunus et al. presented a least square estimation (LSE) algorithm in [34,35], which © 2012 Liu and Li; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Liu and Li EURASIP Journal on Advances in Signal Processing 2012, 2012:156 Page 2 of 6 http://asp.eurasipjournals.com/content/2012/1/156 Figure 1 Generation of DCO in DCR. achieves better performance than DFE at costs of higher computation efforts. The DFE and LSE algorithms were respectively extended in [28,30] and [36] to address CFO estimation for OFDM systems with both TV-DCO and in-phase/quadrature (I/Q) imbalance. The established CFO estimation algorithms for OFDM systems with TV-DCO, e.g. DFE and LSE, are all dataaided algorithms. They depend on transmission of training sequences and/or pilots, which reduces effective data transmission rate. Different from the established works, we in this paper propose a blind CFO estimation algorithm for OFDM systems with TV-DCO. Based on linear approximation of TV-DCO, the proposed algorithm estimates CFO by means of DCO compensation and power leakage minimization. As it is a generalization of our recent work, the eigen-decomposition based estimator (EDE) [37], the proposed algorithm is named LVDEDE, i.e. EDE in the presence of linear varying DCO. Performance of LVD-EDE is demonstrated by simulations in comparison with established algorithms including the maximum likelihood CFO estimation algorithm for OFDM systems with no DCO [7], with static DCO Time A m pl itu de HPF Input Time A m pl itu de HPF Output Figure 2 Generation of TV-DCO during LNA gain mode switch stage. [17-19] and blind version of the DFE [29] and LSE algorithms [34,35]. The reminder of this paper is organized as follows. Model of OFDM system with TV-DCO is established in the second section. The proposed LVD-EDE algorithm is developed in detail in the third section. In the fourth section, simulation results and corresponding analysis are provided to demonstrate the performance of LVD-EDE. Finally, conclusions are drawn in the last section. Model of OFDM systemwith CFO and TV-DCO Consider an OFDM system with totally N sub-carriers, among which the K sub-carriers occupied by data transmission are referred to as real sub-carriers, and the other N − K unoccupied ones are referred to as virtual subcarriers. Let Ts T N denote the sample spacing in digital signal processing (DSP) stage, where T is the duration of OFDM block without cyclic prefix (CP). After CP removal, the received samples that belong to the m-th OFDM block can be expressed as