Lag-optimized G4 function for the third order phase parameter estimation of polynomial phase signals

This paper looks into G4 function, which helps to estimate the third order phase coefficient parameter of a polynomial phase signal (PPS). However, the use of the lag parameter of G4 function has not yet been fully exploited. Therefore, in this paper, we theoretically derive the optimal lag with respect to the ratio of mean square error (MSE) to the Cramer-Rao low bound (CRB). When the signal-to-noise ratio (SNR) is high, the resulting ratio of the MSE to the CRB can be as low as 0.4dB. Simulation results show that the estimated lag is optimal and G4 function with the optimal lag achieves a much more accurate parameter estimation than its competitors.