Simulation of Coherent Doppler Lidar Performance in the Weak-Signal Regime

Abstract

The performance of coherent Doppler lidar in the weak-signal regime is investigated by computer simulations of velocity estimators that accumulate the signal from N pulses of zero-mean complex Gaussian stationary lidar data described by a Gaussian covariance function. The probability density function of the resulting estimates is modeled as a fraction b of uniformly distributed had estimates or random outliers and a localized distribution of good estimates with standard deviation g. Results are presented for various velocity estimators and for typical boundary layer measurements of 2-µm coherent lidars and also for proposed space-based measurements with 2- and 10-µm lidars. For weak signals and insufficient pulse accumulation, the fraction of bad estimates is high and g ≈ WV, the spectral width of the signal in velocity space. For a large number of accumulated pulses N, there are few bad estimates and g ? WvN?1/2. The threshold signal energy or average number of coherent photoelectrons per pulse with accumulation is defined by a given fraction of random outliers and is proportional to N?1/2 for large N and decreases faster than N?1/2 for small N. At the threshold level, the standard deviation g of the good estimates is approximately constant for large N. For space-based measurements and with the signal statistics determined by the wind fluctuations over the range gate the, 2- and 10-µm lidars have similar performance when referenced to the average number of photoelectrons detected per velocity estimate. The threshold signal level for large, N can be described by simple empirical functions.