Mobile underwater acoustic (UWA) channels always exhibit large delay spread and Doppler spread. Multicarrier modulation is an efficient technique for the communications over multipath channels. However, the orthogonality of the transmit signals, e.g., OFDM signals, will be destroyed by the Doppler spread and interference will be produced. Thus, an equalizer is required in the receiver. For this reason, we argue that multicarrier modulation with Gaussian pulse (symmetric in time and frequency domains) as the transmit filter is more suitable for the UWA communication systems than the OFDM. The key problem for the multicarrier modulation is to design/optimize the number of carriers and the parameter alpha in the Gaussian pulse which will greatly affect the system performance. In this paper, we investigate the optimization problem for four kinds of channels: AWGN channel, frequency-selective channel, time-selective channel and doubly selective channel. Channel information is assumed known in the transmitter by feedback. Analytical results are obtained and the numerical examples are given. To achieve the cost function, a 2D MMSE-DFE equalizer is used. Finally, we propose the balanced design for the practical engineering.
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