## 1 Introduction  
LDPC codes can approach Shannon's capacity with moderate decoding complexity at low SNRs [1, 2]. However, maximizing the full potential of the LDPC codes requires accurate timing recoveries in the baseband process of the receivers. Traditionally, timing recovery is performed independently from channel decoding. However, the metrics generated from channel decoding can generate more reliable information in iterative timing recovery [3]. The generated information can be applied to assist timing recovery in order to obtain accurate synchronization at very low SNRs. Traditional methods are usually ineffective at low SNRs. Iterative timing recovery uses the metrics from the codewords output of the channel decoding process [3]. A method with LDPC decoding hard decision metrics (i.e., code constraint feedback) to obtain good timing recovery has been proposed in [4]. However, it suffered from insufficient hard metrics, or unreliable satisfaction percentages of decoded codewords for the parity check equation for just few iterations [4, 5]. Studies also suggested the use of timing recovery based on soft LDPC metrics with complex optimization calculations [6]. Other expectation maximization (EM)-based timing recovery methods for turbo or LDPC coding have also been suggested [7, 8]. The EM-based timing recovery method is implemented between the detection and estimation processes, where the expectation of symbols is calculated by a maximum a posteriori (MAP) decoder. Afterwards, the cost function is maximized to acquire excellent symbol timings. For instance, the EM algorithm has been applied in solving the time and frequency synchronisation in a multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) system [9]. However, the function has highly complex EM steps. Several turbo decoding-aided timing recovery, with timing recoveries incorporated into iterative decoding, have been proposed for blind turbo detection of synchronization parameters [10]. Here, a turbo component decoder is applied in the synchronization parameters to perform blind joint synchronization detection and decoding with decoded metrics. In [11], synchronisation is incorporated into Turbo decoding as the blind detection of synchronisation parameters. It uses a turbo component decoder to perform blind synchronisation detection and Turbo decoding by the decoding metrics. In [12], a new objective function is maximised to exploit the output turbo decoder's soft decision to improve synchronisation iteratively. Thus, it is suited for short bursts of data transmissions at low SNRs. In [13], a Turbo soft metric based cost function is maximized to exploit the turbo soft decision and iteratively improve the synchronization. Thus, turbo-decoding metrics are calculated for obtaining good timing recoveries at low SNRs. However, turbo code-based methods are highly difficult due to complex turbo decoding. Because large sampling frequency offset can cause huge synchronization searching calculation and delay, a sampling frequency synchronization method to eliminate initial sampling frequency offset can also help reduce the overall synchronization time for the coarse symbol timing recovery [14]. So the communication receives require the iterative timing recovery to acquire rather large timing frequency and phase offsets for good timing synchronizations. In addition, the iterative timing recovery can be performed by the means of MAP criterion as the iterative carrier synchronization but with much high complexity [15]. Therefore, an iterative timing recovery with high precision and low complexity is needed for using in space communications which usually work at low SNRs. In this study, we mainly propose a new iterative timing recovery scheme by using the LDPC decoding metrics to correct timing errors for better timing precision and lower complexity. The timing recovery mechanism are modelled as an optimization problem of maximizing the sum of the squares of selected LDPC decoding metrics for precise estimation of timing offsets.