Statistical performance of IF estimation of LFM signals with time-varying amplitude using the peak of WVD

The instantaneous frequency (IF) estimation of the linear frequency modulated (LFM) signals with time-varying amplitude using the peak of the Wigner-Ville distribution (WVD) is studied. Theoretical analysis shows that the estimation on LFM signals with time-varying amplitude is unbiased, only if WVD of time-varying amplitude reaches its maximum at frequency zero no matter in which time. The statistical performance in the case of additive white Guassian noise is evaluated and an analytical expression for the variance is provided. The simulations using LFM signals with Gaussian envelope testify that IF can be estimated accurately using the peak of WVD for four models of amplitude variation. Furthermore the statistical result of estimation on the signals with amplitude descending before rising is better than that of the signals with constant amplitude when the amplitude variation rate is moderate.