Abstract: Multiple level signals are constructed from more than one level of component sequences each having correlation properties. A receiver receives the multiple level signal. A signal detector in the receiver performs correlation or matched filtering to the received signal. When a signal is detected, the signal detector triggers a timing estimator, a phase estimator, and a frequency estimator. The timing estimator employs an output signal from the signal detector, performs interpolation and timing estimation. The timing estimate adjusts a sampling clock for time synchronization. The phase estimator employs output signals from the correlation devices to estimate phase. The phase estimate is employed to achieve phase synchronization. The received signal is converted to an equivalent continuous wave signal by the frequency estimator. The frequency estimator performs discrete Fourier transform to the continuous wave signal, and estimates frequency offset.