Coherent integration efficiency, diversity, and detectivity of temporally integrated random coherent LADAR signals

In this paper we develop spectral models for windowed speckle-modulated continuous coherent ladar signals with arbitrary coherence time as a function of the window duration and shape. This processing chain (compute the spectrum of the window random signal) is typical for many coherent ladar applications where the target is distributed in range, such as wind lidar. We link the peak of the spectrum to the signal's carrier-to-noise ratio (CNR) and the number of integrated signal photoelectrons. We also develop theoretical models for the SNR of the integrator output and the resultant coherent integration efficiency. In addition, we generalize Goodman's rectangular integrator diversity model to arbitrary window functions and show that the product of diversity and efficiency is close to one for arbitrary integration times and window functions. These general models are then applied to various signal autocorrelation functions and window functions. The analysis demonstrates that the shape of the window function has little impact on the output SNR, efficiency and speckle diversity. We show that if the coherence time is long compared to the integration time then the conventional CNR expression is valid, and the signal has unit diversity and the coherent integration efficiency is 100%. However, when the coherence time is short compared to the integration time, the CNR is reduced by roughly the ratio of these times and the diversity is increased by roughly the same factor. Finally, we also show how signal detectivity is related to SNR and diversity.