Synchronization of Spread Spectrum Signals

For the reciever to be able to demodulate the recived signal, the reciever clock and the transmitter clock need to be in sync. So this is why the reciver clock and the transmitter clock are extremely stable and accurate. This would work well if the reciver was right next to the transmitter, but in most cases they are not very close at all. Therefore there is a time uncertainty.

This is the formual for the time delay, where N is the number of chips in the spreading code and Tc is the time taken for on chip.
So if we were to search over the time uncertainty inerval in time steps of 1/2Tc, then the time required to establish initial synchronization is: