Research On Symbol Timing Estimation For Physical-layer Network Coding

As a new type of relay transmission scheme, Physical-layer Network Coding(PNC) recently has attracted much attention because of the advantages in its spectrum efficiency and throughput. At present, most of the research on PNC is carried out based on the assumption that symbols from two users are fully aligned at the relay without symbol synchronization error. However, this strict requirement can hardly be met in practical cases, which drastically worsens performance of the system. Therefore, the symbol timing estimation is critically indispensable for PNC.In this paper, using CAZAC training sequences, three novel estimation algorithms applicable for different sampling frequencies are proposed successively to solve the symbol timing estimation problem. The three algorithms are DFT based interpolation algorithm for an oversampling ratio(samples per symbol) Q ≥ 4, low oversampling ratio based algorithm for Q = 2, and baud-rate sampling based algorithm.Firstly, according to the PNC signal model and maximum-likelihood estimation criterion, two independent likelihood functions for nodes’ symbol timing estimation are derived with the zero autocorrelation of training sequences. Then a DFT based interpolation method is employed to estimate the timing errors. Secondly, in order to lower the sampling frequency in the above algorithm, we propose a low oversampling ratio based algorithm for Q = 2 which exploits the fact that the difference between two likelihood function values corresponds to the timing error. Based on the known transmitted pulse and least squares method, a polynomial is found to approximate the corresponding relation and then we get the timing estimate. For decreasing the sampling frequency further, a baud-rate sampling based algorithm is presented at last. This method yields the timing error estimation by estimating a timing function which contains the timing error information.All the three algorithms are evaluated by the Mean Square Error(MSE) performance in the MATLAB. Meanwhile, the effects of various parameters on the performance are also discussed. Simulation results show that, every algorithm proposed exhibits a fine estimation performance. The MSE can be as low as 1×10-4 when the length of training sequences is 32 and the signal-to-noise ratio(SNR) is 18 dB.