A modem for use with a subsea transmission line comprises a digital signal processor responsive to a succession of segments of a data signal to produce a respective set of orthogonal frequency division multiplexed signals and to transmit those signals as a burst on the transmission line, and to prepend the burst with a start signal comprising a cyclically time-varying signal envelope-modulated with a Gaussian waveform. The modem is also arranged to convert signals received from the transmission line into a succession of digital samples and to process those samples to obtain an indication of the peak of the Gaussian waveform whereby to provide a datum for decoding a received burst of OFDM signals.