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On the error analysis of correlation devices Chang, Ke-yen

Abstract

The use of uniformly distributed auxiliary random noise in the polarity-coincidence correlator has been described in the past. It has the advantage of constructional simplicity. It also gives an unbiased and consistent estimate of the correlation function. In this thesis, the method of using auxiliary random noise is extended to the multi-level digital correlator. It is found that any random noise of which the characteristic function has periodic zeros can be used as an auxiliary noise, that uniformly distributed noise is a special case, and that quantizing the auxiliary random noise has the same effect as directly quantizing the input signals. The mean-square error of this modified digital correlator is analyzed in detail. It differs from the mean-square error of the direct correlator only by a term which is inversely proportional to the total number of samples taken, provided that the power spectrum of the auxiliary noise is wide enough. This additional error is the combined effect of sampling, quantizing and adding auxiliary noise. It can be reduced to any desired value by taking a larger number of samples, by using a higher sampling rate, or by quantizing more finely. For completeness, the mean-square errors of the digital correlator, the Stieltjes correlator and the modified Stieltjes correlator are also derived. The mean-square error of the modified polarity-coincidence correlator, which is a special case of the modified digital correlator, is compared with the error of the multi-level modified digital correlator. Despite its constructional simplicity, the modified polarity-coincidence has a much larger error than the multi-level correlator. A small increase in the number of quantization levels reduces the error considerably. The implementation of a modified digital correlator with coarse quantization is also considered. A fast direct multiplier is designed to obtain high operation speed. Finally, the use of pseudo-random noise as an auxiliary noise is discussed.

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