Apparatus and method for despreading a received continuous phase modulated spread spectrum signal includes a power divider for dividing a received spread spectrum signal into a real signal and an imaginary signal. A real CPM correlator demodulates the real signal into I and Q components and separately correlates the real I component and the real Q component without generating a correlation sequence, thereby performing self-synchronizing correlation. Likewise, an imaginary CPM correlator demodulates the imaginary signal into I and Q components and separately correlates the imaginary I component and the imaginary Q component without generating a correlation sequence, thereby performing self-synchronizing correlation. The real I and imaginary I correlation signals are combined into a final I correlation signal, and the real Q and imaginary Q correlation signals are combined into a final Q correlation signal.