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Remote sensing with phased antenna arrays is based on measurement of thecross-correlations between the signals from each antenna pair. Digitalcorrelators have systematic errors due to the quantization losses. Thecorrelation errors allow substantial abatement based on the assumption that theanalog signals are stochastic processes sampled from a statistical distribution(usually the Gaussian). The correlation correction technique is named after VanVleck who was the first to apply it to two-level clipping quantizers. Thecorrection is especially important for high correlation levels, e.g. in studiesof solar radio emissions. We offer a generalized method that for every antennapair inputs the quantized signals' covariance and standard deviations, andoutputs high-precision estimates of the analog correlation. Althoughcorrelation correction methods have been extensively investigated in the past,there are several problems that, as far as we know, have not been publishedyet. We consider a very general quantization scheme with arbitrary set oftransition thresholds and output levels, and our correction method is designedfor correlations obtained from signals with generally unequal standarddeviations. We also provide a method for estimation of the analog standarddeviation from the quantized one for subsequent use in the correlationcorrection. We apply the correction to the the complex-valued analytic signals,overwhelmingly used in modern remote sensing systems with arrays of antennas.The approach is valid not only for analytic signals with the imaginary partbeing the Hilbert transform of the real one, but also for more general,circularly symmetric complex processes whose real and imaginary parts may havearbitrary relationships to each other. This work was motivated by the need forgreater precision in analysis of data from the Murchison Widefield Array (MWA).

Van Vleck correction generalization for complex correlators with multilevel quantization