Null subcarriers based Doppler scale estimation for multicarrier communication over underwater acoustic non-uniform Doppler shift channels

The Doppler scale estimation based on Null subcarriers in underwater acoustic (UWA) orthogonal frequency division multiplexing (OFDM) communication is investigated, which is an optimization problem for finding extremum. The cost function constructed of the total energy of null subcarriers in ultra-wideband UWA channels is proposed. The frequencies of null subcarriers are calculated according to non-uniform Doppler shifts at each tentative scaling factor. Then it is shown that the cost function can be fitted as a quadratic polynomial near the global minimum. So an accurate Doppler scale estimation is achieved by location of the global minimum through polynomial interpolation with several samples around the global minimum, without the conflict between precision and computation complexity. In order to locate the global minimum roughly to take samples, a Doppler scale coarse estimating method is developed based on the delay change between two pilots. The data from a shallow water experiment is used to demonstrate the performance. Excellent performance results are obtained in ultra-wideband underwater acoustic channels with a relative bandwidth of 67%, when the transmitter and the receiver are moving at a relative speed of 5kn, which validates the method proposed.