Underwater wireless communication remains a challenging topic, particularly for applications such as wreck penetration where multipath and Doppler effects are very intense. These effects are becoming even more difficult to mitigate for fast data transmission systems that utilize wideband signals. Due to the low propagation speed of acoustic wave in the water, there is a significant difference between the Doppler shift for lower and upper frequencies of the utilized spectrum. To address these challenges, this paper describes various methods for determining the Doppler frequency shift for MFSK signals, including crosscorrelation, double FFT, pilots, and additional Up-Down chirp signals. The reception quality of the transmitted data in a real environment was used as an evaluation criterion for each method. The tests were carried out in motion within the towing tank for different movement speeds of the transmitter relative to the receiver. The tank's limited dimensions created conditions for multipath signal propagation. Under very difficult multipath signal propagation conditions, the pilots method was found to be the most effective. It gave over two times lower BER than the well-known Up-Down chirp method.