Mathematic and experimental evaluation of phase errors when receiving hydro-acoustic PSK-signals with sweep-spread carrier in reverberant underwater environments

When propagating in water, acoustic signals experience distortions and thus received signals can essentially distinct from those which were transmitted. Basic distortions originate from interference of multipath arrivals comprising random energies, phases and Doppler shifts. Assuming an underwater acoustic environment for middle and high telemetry frequencies as a channel with (in wide sense) stationary uncorrelated scattering, each multipath arrival of a received signal is characterized with a random propagation delay, random energy and (equally distributed) phase, as well as random Doppler shift. Based on such assumption, a receive signal with sweep-spread carrier was represented with a mathematical model, which was used for derivation of a analytical expression for estimation of maximum phase errors expected to be registered in underwater acoustic channels with given multipath. The use of the mathematical expressions allowed to quantify the upper limit of phase errors in different conditions of the multipath channel (different excess propagation delays and relative attenuations of delayed multipath arrivals). Expected phase errors obtained by means of this expression and values measured during physical experiments demonstrated a good agreement.