improved Bayesian estimation of weak signals in non-Gaussian noise by optimal quantization

In this paper, we present a new improved method for signal shape estimation in non-Gaussian noise with low signal to noise ratio. We combine a nonlinear preprocessing with Wiener filtering. In the proposed method, the data received is first quantized by a symmetric 3-level quantizer before processing by the Wiener filter. A complete theoretical analysis of this quantizer-estimator is worked out under low signal to noise ratio conditions. In this framework, we show that if the noise is sufficiently non-Gaussian and the quantizer thresholds are optimally chosen, the quantization, although limited to 3-levels, leads to an enhancement of the estimation performed by the Wiener filter. Numerical results comparing the quantizer-estimator with the Wiener filter applied alone are presented to confirm the theory. Non-Gaussian noise distributions specifically relevant for an underwater acoustic environment are chosen for illustration.