Mellin-Frequency Division Multiplexing through the Underwater Acoustic Channels

The Orthogonal Frequency Division Multiplexing (OFDM) has been very successful in terrestrial communication, but it is challenged in underwater acoustic (UWA) channels. This is because OFDM was engineered for under-spread channels, while UWA channels are intrinsically over-spread. In this paper, we will represent the channel in the scale-delay (S-D) domain and propose the Mellin-Frequency Division Multiplexing (MFDM) modulation scheme. When represented in the S-D domain, the received signal is equal to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\omega$</tex>-convolution of the transmitted signal and the channel response. We can then convert the signals and channel response to the Mellin-Frequency (M-F) domain through the Mellin-Fourier transform. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\omega$</tex>-convolution thus becomes point-wise multiplication, leading to low-complexity detection. Based on this motivation, we model the system in a continuous form and then propose a discretized approach for practical system implementation. The symbol error rate (SER) performance of MFDM is compared with two existing modulation schemes: Orthogonal Delay Scale Space (ODSS) and Cyclic Prefix-OFDM (CP-OFDM). It is not surprising to see that CP-OFDM performs the worst. As for the other two modulation schemes, ODSS is based on scale-delay domain equalization, and the interference among symbols resulting from the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\omega$</tex>-convolution was ignored. In comparison, the equalization was conducted in the Mellin-Frequency domain for the proposed MFDM, leading to improved SER performance.