Detection statistics for a packet-based CDMA system

We consider a wireless CDMA channel which operates in a true packet mode. Multiple users share the same spreading code, and may collide at the receiver. As each packet user is not strictly time synchronized, the receiver is essentially in a continuous acquisition mode testing a window of delays for the presence of a packet. We develop expressions for probability of detection and false alarm for Gaussian, flat Rayleigh fading, and multipath Rayleigh fading. Most of these expressions can be written in closed form