On the distribution of the acquisition time in spread-spectrum serial-search code acquisition

The probability density function of the acquisition time in spread-spectrum serial search initial code acquisition systems has been analyzed, and it was shown that very accurate results can be obtained if the distribution of the partial acquisition times is approximated by the binomial distribution. Furthermore, binomial approximation led to the introduction of the equivalent single-dwell system, i.e., showed that an arbitrary detection/verification scheme can be modeled very well by the simplest single-dwell detection scheme, whose parameters depend only on the mean decision times, and not on their distribution. Based on the exact results, a simple closed-form approximation for the cumulative density function in the case of the straight-line serial search with uniform a priori distribution is derived.