On the definition of receiver output SNR and the probability of bit error

The performance of a communications receiver may be given in terms of the receiver output signal-to-noise ratio (SNR). Different research groups use different definitions of the output SNR, which hinders meaningful comparison of research results. The issue is relevant to communications research in general, but the present study focuses on underwater acoustic communications. The paper summarizes some of the definitions found in literature, and looks at their differences when they are applied to communication signals received in additive white Gaussian noise channels and acoustic channels. At high values of the output SNR all definitions converge to the same result, but significant departures occur at intermediate and low values. One definition is consistently in agreement with the measured bit error ratio and confirms the assumption of Gaussian symbol scatter at the output of an adaptive equalizer applied to a large and varied set of acoustic data.