Loopback signal, receiver and transmitter for synchronization

A method for synchronizing timing and frequency with a loopback signal relayed to a loopback receiver, the method comprising:

• receiving, at the loopback receiver, an Rx signal representing the loopback signal;
• and
• estimating with a common Fast Fourier Transform (FFT), during an acquisition mode and a tracking mode, an estimated timing offset and an estimated frequency offset of the Rx signal compared to the loopback signal,
• wherein the loopback signal comprises a burst comprising a GOLD Pseudo Noise (PN) sequence having a good circular correlation and the GOLD PN sequence has cross-correlations within a set.

A receiver to synchronize timing and frequency with a signal relayed to the receiver, the receiver comprising:

• an Rx signal representing the signal received at the receiver;
• a common Fast Fourier Transform (FFT) to estimate, during an acquisition mode and a tracking mode, an estimated timing offset and an estimated frequency offset of the Rx signal compared to the signal;
• a generalized complex interpolator, in the acquisition mode and the tracking mode of the Rx signal, to calculate the estimated timing offset and the estimated frequency offset;
• and
• a double linearizer, in the tracking mode, to correct a bias of the estimated timing offset and the estimated frequency offset.