Cramer–Rao lower bound on range error for LADARs with Geiger-mode avalanche photodiodes

The Cramer-Rao lower bound (CRLB) on range error is calculated for laser detection and ranging (LADAR) systems using Geiger-mode avalanche photodiodes (GMAPDs) to detect reflected laser pulses. For the cases considered, the GMAPD range error CRLB is greater than the CRLB for a photon-counting device. It is also shown that the GMAPD range error CRLB is minimized when the mean energy in the received laser pulse is finite. Given typical LADAR system parameters, a Gaussian-envelope received pulse, and a noise detection rate of less than 4 MHz, the GMAPD range error CRLB is minimized when the quantum efficiency times the mean number of received laser pulse photons is between 2.2 and 2.3.