We present in this letter a blind frame synchronization method based on a Maximum A Posteriori probability (MAP) approach. Applied to coded communication systems, this method is based on the calculation of the Log-likelihood Ratios (LLR) of the syndrome obtained according to the parity check matrix of the code. After presenting the proposed method, we compare it to an existing blind synchronization method previously introduced. Simulation results show that the proposed method outperforms the existing one and presents good performance when applied to codes having a sparse parity check matrix such as Low Density Parity Check (LDPC) codes and convolutional codes.

We consider in this paper the problem of phase offset and Carrier Frequency Offset (CFO) estimation for Low-Density Parity-Check (LDPC) coded systems. We propose new blind estimation techniques based on the calculation and minimization of functions of the Log-Likelihood Ratios (LLR) of the syndrome elements obtained according to the parity check matrix of the error-correcting code. In the first part of this paper, we consider phase offset estimation for a Binary Phase Shift Keying (BPSK) modulation and propose a novel estimation technique. Simulation results show that the proposed method is very effective and outperforms many existing algorithms. Then, we modify the estimation criterion so that it can work for higher-order modulations. One interesting feature of the proposed algorithm when applied to high-order modulations is that the phase offset of the channel can be blindly estimated without any ambiguity. In the second part of the paper, we consider the problem of CFO estimation and propose estimation techniques that are based on the same concept as the ones presented for the phase offset estimation. The Mean Squared Error (MSE) and Bit Error Rate (BER) curves show the efficiency of the proposed estimation techniques.