Viterbi Detection of PSK Signals in Markov Impulsive Noise

The ambient soundscape in warm shallow waters is dominated by snapping shrimp noise at frequencies greater than 2 kHz. The noise process is impulsive and exhibits memory. Within the human audible range, this manifests as a persistent background crackle, akin to the popping of corn. Unless catered for, underwater acoustic communication systems are vulnerable to large drops in error performance in such waters. With the advent of new effective statistical models, namely the $\alpha$-sub-Gaussian noise model with memory order $m(\alpha \mathbf{SGN}(m))$, it is now possible to mitigate snapping shrimp noise by exploiting the latter's temporal amplitude statistics. In our work, we accomplish this by deriving the passband Viterbi algorithm (VA) for a single-carrier scheme in $\alpha \mathbf{SGN}(m)$. The results are compared to the symbol-by-symbol maximum-likelihood (ML) detector and conventional L2-norm detection in scenarios representative of severe snapping shrimp noise. As the VA algorithm is optimal in $\alpha \mathbf{SGN}(m)$, it is of much interest to know how it fairs in snapping shrimp noise. This is investigated in our work.