Cramer-Rao lower bounds for sonar broad-band modulation parameters

A role of passive sonar signal processing is the detection and estimation of the parameters associated with amplitude modulated broad-band signals. An example of such signals is propeller noise. Discrete frequency lines occur at the rotational frequency of the propulsion shaft and at the blade frequency. This correspondence provides expressions for the Cramer-Rao lower bounds for the estimates of broad-band signal power, modulation level, modulation frequency, and modulation phase. It is shown that for low broad-band-signal-to-broad-band-noise ratios, the estimates of power and modulation level are uncoupled from the estimates of modulation frequency and phase.