The simplest way to acquire the signal (not necessarily the most effective or least computationally expensive) is to compute the dot product of a window of the digitalized signal with a set of locally generated replicas. The locally generated replicas vary in carrier frequency and code phase to cover all the already mentioned search space which is the Cartesian product of the frequency search space and the code phase search space. The carrier is a complex number where real and imaginary components are both sinusoids as described by Euler's formula. The replica that generates the highest magnitude of dot product is likely the one that best matches the code phase and frequency of the signal; therefore, if that magnitude is above a threshold, the receiver proceeds to track the signal or further refine the estimated parameters before tracking. The threshold is used to minimize false positives (apparently detecting a signal when there is in fact no signal), but some may still occur occasionally.