Error analysis of the Doppler correction factor in underwater communications

Abstract

One limitation to the attainment of high spectral resolution in underwater communications is the Doppler effect. In principle, this purely geometric, or kinematic, effect can be defined precisely and the attendant Doppler-generated frequency shift can be removed by suitable signal processing. In practice, however, uncertainties in knowledge of instantaneous position and velocity of transmitter and receiver always exist and constitute an instrinsic limitation to spectral resolution. An error analysis is presented here of the Doppler correction factor for underwater communication between the sonar systems of two mobile platforms whose instantaneous positions and velocities, including rotation and other accelerations, are known imprecisely. Doppler errors produced by inhomogeneities in flow structure and sound profile are ignored, but the uncertainty in knowledge of sound speed is recognized. Some simple expressions for rms and worst-case errors are derived for cases which are distinguished by the relative size of transmission time to a characteristic rotational period. An application to spectral resolution by mobile parametric receivers is mentioned.