A Generalized Analysis for a Dual Threshold Sequential Detection PN Acquisition Receiver

Spread spectrum techniques have become very useful in modern communications. A common spread spectrum technique is to directly modulate a pseudorandom noise (PN) code onto the carrier. Systems employing this technique are called direct sequence (DS) systems. A primary concern with direct sequence systems involves PN code synchronization (acquisition) of the incoming and local signals to within at least one PN symbol followed by a fine alignment (tracking) which must be maintained throughout transmission. This paper is concerned with the PN acquisition aspect of code synchronization. Specifically, a dual threshold sequential detection receiver is analyzed and a general expression is derived which addresses the probability that the sequential detection procedure ceases after an arbitrary number of samples. This expression is needed in order to support a characteristic function approach in deriving acquisition Probability as a function of time which will be the topic of a subsequent paper.