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

This paper looks into G
₄
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 G
₄
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 G
₄
function with the optimal lag achieves a much more accurate parameter estimation than its competitors.