Consistent signal parameter estimation with 1-bit dithered sampling

We consider the problem of estimating a parameter θ of a signal s(x; θ) corrupted by noise when only 1-bit precision samples are allowed. We propose and analyze a new estimator based on dithered 1-bit samples. Our estimate is consistent and satisfies an asymptotic CLT for a wide class of dither distributions. In particular, uniformly distributed dither leads to only a logarithmic rate loss compared to the case of full precision samples.