# Robust Sampling Frequency Offset Estimation for OFDM over Frequency Selective Fading Channels
## 1 Introduction  
Orthogonal frequency division multiplexing (OFDM) has been widely used due to its high data rate and robustness regarding multipath fading distortions. OFDM has proven to be very effective in broadcast systems, such as digital multimedia broadcasting (DMB), digital radio mondiale (DRM), and terrestrial digital video broadcasting (DVB-T) [1; 2; 3]. Recently, a new second generation terrestrial digital video broadcasting (DVB-T2) standard has been defined to provide high definition television (HDTV) and high rate services [4]. In order to effectively offer HDTV services, the DVB-T2 standard adopts a multiple-input single-output (MISO) antenna mode. OFDM has also been adopted by numerous wireless transmission standards such as long term evolution (LTE) and wireless local area network (WLAN) [5; 6], which adopt the multiple-input multiple-output (MIMO) technique as the key technology to cope with increasing transmission reliability without any additional wireless bandwidth. There has been explosive adoption of MIMO technology in the wireless environment to improve the performance of antennas and transceivers [7; 8; 9].  
DRM has been developed to replace the current analog radio transmission in all the frequency bands, the AM broadcast bands below 30 MHz as well as above 30 MHz up to and including VHF band III [2]. Because the DRM system utilizes OFDM modulation, the frequency synchronization plays a crucial role in improving the performance of the OFDM receiver. In particular, the carrier frequency offset (CFO) and sampling frequency offset (SFO) will damage the performance of an OFDM system. If not properly estimated and compensated, the frequency error may limit the performance of an OFDM system. Therefore, time and frequency synchronization has been one of the major concerns of the OFDM-based DRM system [10; 11; 12; 13; 14; 15]. Several schemes have been proposed in literature to estimate the SFO in frequency domain in the DRM system [12; 13; 14; 15; 16]. They are based on frequency reference cell (FRC) and gain reference cell (GRC), and work for all DRM operation modes. Although they are proposed for general channel conditions, its performance is strongly influenced by frequency selective-fading distortions. Therefore, there is still room for a better estimation scheme that is robust to the fading distortion and not computationally demanding. In addition, a complete performance analysis, especially one that includes mean square error (MSE) derivation, has not been done.  
This paper considers the issue of the SFO estimation in the OFDM-based DRM system, focusing on improving the robustness of SFO estimation in the presence of the frequency selective fading and designing its receiver structure. Firstly, we present the MSE analysis of the conventional estimation schemes that can be applied in the DRM system. Then, a robust estimation scheme to the frequency selective fading is proposed. The MSE of the proposed estimator is numerically calculated. Finally, the effectiveness of the proposed estimation scheme is analyzed and verified through numerical simulations.  
This paper is organized as follows: Section 2 introduces the signal model and problem definition. In Section 3, we briefly introduce the conventional SFO estimation algorithms suitable for DRM systems. An improved unbiased SFO estimation method is proposed and its performance is numerically derived in Section 4. In Section 5, simulation results verifying the MSE analysis and the usefulness of the proposed scheme are presented. Section 6 concludes this paper.