Underwater acoustic channels are characterized by severe bandwidth limitations, long inter-symbol interference (ISI) spans, and large Doppler spreads, which lead to significant challengers for reliable communications. Owning to the advantages of high spectral efficiency and robustness against channel fading, orthogonal frequency division multiplexing (OFDM) has been applied in modern communication system extensively such as WLAN, WiMAX, LTE, and DVB-T. OFDM is also a good alternative transmission scheme for underwater communication that both remedies the problem of ISI and provides low complexity solutions. However, OFDM is sensitive to inter-carrier interference (ICI) caused by channel variations. Underwater channels vary fast due to the large ratio of the platform motion relative to the sound propagation speed. Even with stationary transmitters and receivers, significant ICI could still exist due to wave action and water motion. One of the solutions for eliminating ICI is to estimate and correct the frequency shift adaptively in the synchronization procedure. Therefore, the synchronization scheme for OFDM system used in underwater communications is a critical issue [1].

The sampling clock synchronization in an OFDM system is to mitigate the sampling clock errors due to the mismatch of the crystal oscillators between the transmitter and the receiver. The sampling clock error can essentially be divided into two parts: sampling clock frequency offset (SFO) and sampling timing error (STE). SFO means the offset of sampling frequency between transmitter and receiver. STE implies that the sampling does not align at the central of the samples, which was also named sampling clock phase offset in some literatures [2, 3]. The sampling clock error will cause ICI, and a drift in the symbol timing and further worsen ISI [3, 4]. The effects of SFO on the system performance are analyzing in terms of BER degradation and ISI in [4, 5], respectively.

In the aspect of sampling clock synchronization, there are two different kinds of methods: synchronous sampling and asynchronous sampling [6]. Synchronous sampling methods [7, 8] have large timing fluctuation due to high-level phase noise when compared with asynchronous sampling methods [5, 9, 10], but the asynchronous sampling methods traditionally needs the interpolation in time domain, which is computationally complex and needs more processing time. Therefore, it cannot be applied to the area where there is a strict requirement on estimation delay time. Moreover, asynchronous sampling method is more sensitive to carrier frequency offset (CFO). A combined SFO and CFO estimation algorithm is presented in [11, 12]. However, it has such prerequisite that the timing offset and the initial CFO should been corrected ideally.

In many wireless communication systems, such as WiMAX, there are the constraints of low cost and miniaturization for mobile communication device, and the specification requires that the same crystal must be used to drive the sampling and the channel frequency, which is adopted for many personal handheld terminals (e.g., Smart phone) especially. However, the same reference clock property introduces a new challenge for the design of joint carrier and sampling clock synchronization, where the frequency offsets have relationship with the sampling frequency offset besides the Doppler shift. It is seen that most research on joint sampling and frequency synchronization [11–15] have only considered the sampling clock frequency synchronization but ignored the STE. In addition, they view the synchronization of sampling clock frequency all at once whereas neglecting the permanent drift of sampling clock frequency.

In this article, an asynchronous scheme for sampling clock synchronization in an OFDM receiver system with the same driving clock source is proposed and analyzed: First, the preliminary SFO is jointly acquired with carrier frequency offset by taking the benefit of the same crystal for both sampling and channel frequencies. Second, by introducing a phase looped lock (PLL) with dynamic adjustable parameters, the timing drift resulted from the residual SFO and STE is tracked and periodically corrected. The proposed scheme has not used the interpolation and consequently lowered the computation complexity and processing time consumption. The requirements of ideal timing offset and the initial CFO are not needed previously because the estimation and correction of SFO was jointly deal with CFO and timing error simultaneously.

This article is organized as follows. First, we, respectively, analyzed the effect of SFO and STE on the performance of OFDM system in Section 2. After that, we have derived the theoretical solution for the estimation of SFO and timing error in Section 3. Based on the derivation result, a practical estimation and correction of sampling clock error scheme is proposed in Section 4. The simulation results and discussion are given in Section 5. Section 6 concludes the article briefly.