A BPSK direct sequence spread-spectrum system transmits data using a spreading code clock of 1.8822MHz and the spreading code is a maximum length sequence generated using a shift register of length 6. Assume the carrier frequency is a priori known and the acquisition system uses a single dwell serial search in step of 0.5Tc. Given the probability of detection of Pd =0.75, probability of false alarmPfa =10−3 and the false alarmpenalty 72Ti where Ti is the fixed integration time. Calculate the:

i. average acquisition time

ii. variance of the acquisition time

iii. variance of the acquisition time given by (5.16)

iv. variance of the acquisition time for the ideal case.