Time Synchronization of Spread-Spectrum Systems 323 equation describing the dynamic behaviour of the tracking loop. The multi-user code track- ing in multipath channels was also introduced in Section 5.9.2 to derive the interference contribution due to the timing error. Problems 5.1 A BPSK direct sequence spread-spectrum system transmits data using a spreading code of length N = 31 and a clock of 1.8822 MHz. Assume the carrier frequency is a priori known and the acquisition system uses a single dwell serial search in step of 0.25 T c . Given the probability of detection of p d = 0.75, probability of false alarm P fa = 10 -3 and the average acquisition time not exceeding 60 chip durations. Calculate: i. false alarm penalty ii. variance of the acquisition time 5.2 Consider the acquisition system in Problem 5.1 when the system is subjected to code Doppler of 2.3 kHz. Calculate: i. mean acquisition time ii. variance of the acquisition time 5.3 A serial search scheme is used to acquire the code phase of a direct sequence