Error patterns in correlators with four-level quantisation

Abstract

In the evaluation of the analogue correlation from the digital correlation of coarsely quantised Gaussian signals, it is necessary to know the threshold levels used in the quantisation. The formulas used in the evaluation normally assume that the levels are accurate and stable. In this paper, errors in digital correlation arising from threshold variations of ±2%, ±5% and ±10% are evaluated for four-level correlators with lower-order correlation products deleted. The classification of the threshold errors into patterns shows that at low correlation coefficients, the largest contribution to the correlation error originates from the threshold of the comparator which detects the sign of the signal. An error analysis for the case of unequal delays in the signal paths is also presented. In the analysis, the comparator outputs of the quantiser are treated as data streams to which individual path delays can be inserted and the effect of any delay differences on the correlation coefficient readily obtained.