On the distribution function of the spread-spectrum code acquisition time

By using the direct approach to the analysis of the serial-search spread-spectrum code acquisition, the author presents the approximate analysis of the cumulative probability density function (CDF) of the acquisition time. This approach is based on the binomial approximation to the distribution of the partial acquisition times, instead of the Gaussian one used previously. The binomial approximation gives very accurate results but, more importantly, it shows that the analysis of the arbitrary detection/verification scheme can be reduced to the much simpler analysis of the equivalent single-dwell system, whose parameters depend only on the mean test times and not on their distribution. Based on the exact results, simple closed-form approximations are derived for the CDF in the case of the straight-line serial search with uniform a priori distribution, which might be useful in practice.<
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