Estimation of bandlimited signals from the signs of noisy samples

The sampling, quantization, and estimation of a bounded dynamic-range bandlimited signal affected by additive independent Gaussian noise is studied in this work. Considering the desirability of cheap, low-precision sensors, the use of single-bit analog to digital convertors (ADCs) is considered. For bandlimited signals, the distortion due to additive independent Gaussian noise can be reduced by oversampling (statistical diversity). The pointwise expected mean-squared error is used as a distortion metric for signal estimate in this work. If N is the oversampling ratio with respect to the Nyquist rate, then we show that a distortion of O(1/N) can be achieved with single-bit ADCs that record the signs of the observed noisy signal. This improves the (best known) distortion result by Masry for quantizing bandlimited signals in noise, using signs of noisy signal samples, from O(1/N^2/3). This improvement comes by exploiting the structure of bandlimited signals in the estimation of original signal from noisy quantized bits.