This paper is based on Extended Symbol OFDM (ES-OFDM) where symbols are extended in time. This way ES-OFDM can operate at low SNR. Each doubling of the symbol length improves the SNR performance by 3 dB in case of a coherent receiver. One of the basic questions is how to synchronize to signals far below the noise floor. An algorithm is presented which is based on the transmission of pilot symbols. At the receiver, the received signal is cross correlated with the known pilot symbol and the maximum magnitude is determined. The position of the maximum value within the cross correlation function indicates the time difference between transmitter and receiver. The performance of the algorithm in case of an Additive White Gaussian Noise (AWGN) channel, is assessed based on a theoretical approximation of the probability of correct detection of the time difference. The theoretical approximation matches with simulation results and shows that synchronization can be achieved for low (negative) SNRs.
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