Statistical Analysis of Wide-Band Pseudorandom Matched Filter Sonars

A stochastic model of pseudorandom (PR) signals is adopted and a statistical analysis carried out of the velocity (i. e., Doppler) and acceleration tolerances of wide-band PR matched filter sonar systems. The reference functions for these correlation detection systems are considered to be time-compressed or time-expanded replicas of the transmitted signal. Results are derived for the case of a PR signal having a flat power spectral density over a finite bandwidth. It is shown that the velocity and acceleration tolerances are essentially independent of the signal bandwidth and that therefore the radar-derived expressions for the narrow-band tolerances can be extended to the wide-band sonar case. An interesting result is that the derived acceleration tolerance is approximately three times the widely used estimate that is based on the target remaining in the same Doppler channel over the integration time.