Frequency offset estimation of the linear mixture of two co-frequency 8 phase-shift keying modulated signals

A frequency offset estimation (FOE) algorithm based on the maximum-likelihood criterion is proposed for the linear mixture of two 8PSK modulated signals with fixed frame length and frame synchronisation code on the condition that the frame length is known when the signals are coded asynchronously. FOE is calculated by optimising the objective function, which is obtained from cross-correlation computation, given that timing error, amplitude attenuation and phase offset are unknown. The optimised process is accomplished by utilising hierarchical search. Cramer-Rao bound (CRB) of mixed-signal FOE is derived to evaluate the performance of the proposed algorithm. The estimation performance of the algorithm can come close to the CRB performance with low E_s/N₀. The proposed algorithm is also applied to the FOE of a mixed signal whose power is asymmetrical.