Maximum-mean-square-soft-output (M²S²O): A method for carrier synchronization of low SNR short packet turbo coded signals

Turbo codes enable the operation of communication systems at very low SNR values, but the needed carrier frequency and phase synchronization at the receiver still remains a problem for short packets at these low SNR values. In this paper, a new efficient carrier synchronization method, the M ²S²O (Maximum-Mean-Square-Soft-Output) method, for turbo coded short packet communication at low SNR values is presented. This method is based on maximizing a newly invented cost function, the MSSO function. This function is the Mean Squared Soft Output of the turbo decoder and is found to be a convex function of the phase and frequency errors, with a global single maximum, thus enabling both acquisition and tracking of the carrier frequency and phase offsets. It is shown, via simulations, that this carrier synchronization algorithm enables un- degraded turbo decoding performance at these very low SNR values.