Confidence Estimates for Acquisition Times and Hold-In Times for PN-SSMA Synchronizer Employing Envelope Correlation

In this paper, a bound on the acquisition time probability distribution is obtained by calculating the variance of the acquisition time and using Chebyshev´s inequality. Recursive computer calculations are used to show that the hold-in time distribution is approximately exponential. The means and variances of the acquisition and hold-in times, together with the distribution estimate and bound, are determined in terms of the number of users and power-to-Gaussian noise density ratio of the channel. These calculations pertain to a receiver used by Hopkins, which combines acquisition and tracking in a way which facilitates implementation. The utility of the distribution estimates in comparing the relating synchronization times, failure to achieve synchronization, message transmission times, and message error rates is illustrated for two data transmission protocols. The dependence of these quantities on the number of users, information bit rate, data block format, and power-to-noise ratio of the (Gaussian) transmission channel is also illustrated.