Efficient reconstruction of sampled 1-bit quantized Gaussian signals from sine wave crossings

We study the reconstruction of a Gaussian random signal, subject to extreme clipping. The reconstruction is achieved by adding a high frequency sinusoidal reference signal prior to the hard-limiter, and by low pass filtering the output. Such a scheme belongs to the area of signal reconstruction from Sine Wave Crossings (SWC). In the present paper we study in detail the effect of sampling in time domain on the reconstruction algorithm, and we carry out an analysis, valid for high sampling rates, leading to approximate analytical expressions of the cross-correlation coefficient between the signal and its reconstructed version. As a result of our analysis, the best achievable cross-correlation coefficient, together with the corresponding setting of the configuration parameters, i.e., the frequency and power of the reference signal, is obtained as a function of the sampling rate. Asymptotic closed form formulas are derived in the limit of very large sampling rates.