Modified Cramer-Rao Bounds for Parameter Estimation of Hybrid Modulated Signal Combining PRBC and LFM

This paper focuses on the modified Cramer-Rao bounds (MCRBs) related to estimating the parameters of a noisy hybrid modulated signal which combines the pseudo-random binary codes (PRBC) phase modulation and linear frequency modulation (LFM) and gives a theoretical performance for estimators. The parameters to be estimated of the PRBC-LFM signal include signal amplitude, carrier phase, carrier frequency, chirp rate and symbol width. The pseudo-random binary codes are interference which make the analytical calculation of the real CRBs difficult. The MCRB for estimating a single parameter while treating the others as unwanted parameters was derived. The explicit expressions of the MCRBs for every parameter are calculated. Then the results are compared with the CRBs of the estimated parameters of a common LFM signal, and an inequality relationship is given. In the end, the MCRBs of carrier frequency and chirp rate are evaluated by numerical simulations and the results show that the MCRBs of parameters are effective.