Performance analysis of both hybrid and frequency-hopped phase-coherent spread-spectrum systems. I. A hybrid DS/FH system

The authors present and analyze a model for both hybrid and frequency-hopped spread-spectrum systems in which a fully digital coherent receiver is used to demodulate the data. A receiver for a hybrid DS/FH (direct-sequence/frequency-hopped) system using a digital delay-lock loop is considered. In the absence of frequency uncertainty, it is shown that the tracking error can be modeled as an ergodic Markov chain with a finite-state set, and the probability density function of the steady-state tracking error is evaluated. When there is a frequency uncertainty, the dynamics of the resulting nonstationary phase error can be obtained, and an expression to evaluate the probability distribution of the first time at which the phase error hits predetermined boundary values is derived. Bit error rate performance is determined in the presence of both additive white Gaussian noise and various types of interference, and the performance is compared to that of noncoherent FSK systems