Convolutionally Coded Hopping Pattern for MFSK Modulation in Underwater Acoustic Communication

A convolutionally coded <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-ary frequency shift keying (MFSK) modulation scheme for underwater acoustic communication is introduced. It uses a rate <inline-formula> <tex-math notation="LaTeX">$1/\log _{2}{M}$ </tex-math></inline-formula> inner convolutional code, whose coded symbols are used as transmission symbols. An interleaver in the frequency domain is applied to improve the average channel clearing time. It thereby achieves almost the same data rate as a comparable uncoded frequency hopped frequency shift keying (FH-FSK) modulation scheme, but obtains the error correcting properties of the convolutional code. Bit and packet error rates are evaluated on the additive white Gaussian noise (AWGN) channel and the so-called Watermark channel model, which is a benchmark for underwater acoustic modulation schemes based on sea trial measurements. The JANUS standard which uses convolutionally coded FH-FSK is used for comparison. On the AWGN channel, the proposed scheme achieves a gain of 4 dB with respect to the required <inline-formula> <tex-math notation="LaTeX">$E_{b}/N_{0}$ </tex-math></inline-formula> for a given packet error rate (PER) compared with JANUS. In the Watermark scenarios, the best proposed-scheme achieves a PER < <inline-formula> <tex-math notation="LaTeX">$10^{-3}$ </tex-math></inline-formula> at more than 10 dB lower <inline-formula> <tex-math notation="LaTeX">$E_{b}/N_{0}$ </tex-math></inline-formula> than the JANUS implementation.