Analysis of sensor impulse response effects on Cramèr–Rao lower bounds for signal parameter estimators

In this study, a generic analysis of sensor impulse response effects on linearly filtered channel noise is presented to illustrate the resulting variations to the Cramèr–Rao lower bounds (CRLBs) of signal parameter estimators in signal processing and communication applications. The authors start by deriving the density function of a filtered signal, which is shown to be a mixture density, and hence the exact expressions for the mean and variance. Simulation results are used to confirm the derivations, which are then used to investigate the effects of impulse response length and variance, as well as channel noise length and variance effects on the resulting CRLBs. Results indicate that for non-zero-mean channel noise and impulse responses, the resulting mean of filtered noise can be relatively large causing adverse deviations to parameter estimations. The filtered noise variance is shown to be proportional to the impulse response energy, where for long duration of signal capture the CRLB is significantly increased