Correlation Statistics of Quantized Noiselike Signals

I calculate the statistics of correlation of two digitized noiselike signals,which are drawn from complex Gaussian distributions, sampled, quantized,correlated, and averaged. Averaged over many such samples, the correlation rapproaches a Gaussian distribution. The mean and variance of r fullycharacterize the distribution of r. The mean corresponds to the reproduciblepart of the measurement, and the variance corresponds to the random part, ornoise. I investigate the case of nonnegligible covariance rho between thesignals. Noise in the correlation can increase or decrease, depending onquantizer parameters, when rho increases. This contrasts with the correlationof continuously valued or unquantized signals, for which the noise in phasewith rho increases with increasing rho, and noise out of phase decreases.Indeed, for some quantizer parameters, I find that the correlation of quantizedsignals provides a more accurate estimate of rho than would correlation withoutquantization. I present analytic results in exact form and as polynomialexpansions, and compare these mathematical results with results of computersimulations.Comment: 23 pages, 5 figure