A Study on the Wide-Sense Stationarity of the Underwater Acoustic Channel for Coherent Communication Systems

In this paper, we test the wide sense stationarity of the estimation error achieved by an exponentially weighted least squares algorithm, used to estimate the channel impulse response. We choose to study the stationarity of this process because it is closely tied to the bit error rate performance of adaptive equalizers used for symbol estimation. The predictability of this error process is therefore closely related to the predictability of the quality of the communications channel and will be important in the development of link quality predictors in underwater acoustic communications networks. Most adaptive estimators are based upon estimated channel statistics which assume that the process is wide sense stationary. We analyze the SPACE08 data set, which has been collected near Martha's Vineyard Island during October 2008. In this data set the environmental conditions such as the height of the waves and the wind direction vary significantly in time, causing non-stationarity to the channel impulsive response. We choose to use a stationarity test based on an analysis of the frequency-time properties, which uses surrogates and doesn't assume any model on how the data has been generated. Understanding the time interval of stationarity for the error process of the channel estimation algorithm is important to set the adaptation rate of the parameters of the channel quality estimator. In particular this study aims at investigating the possibility of developing some predictor of the communications performance in order to trigger adaptive algorithms in the upper layers. Moreover these results are useful to estimate the channel statistics for coherent communications systems and develop better channel model for shallow water, in particular we search for correlations between the environmental data and variabilities and the acoustic fluctuations.