In order to determine the direction of origin of a signal, we have to add a time delay to the recorded signal from microphone that is equal and opposite of the delay caused by the extra travel time. That will result in signals that are perfectly in-phase with each other. Summing these in-phase signals will result in constructive interference that will amplify the result by the number of microphones in the array. The question is how to know what time delay to add that will produce the desired constructive interference. The only solution is to iteritively test time delays for all possible directions. If the guess is wrong, the signal will destructively interfere resulting in an diminished output signal, but the correct guess will result in the signal amplification described above.