Performance bounds of the phase gradient autofocus algorithm for synthetic aperture ladar

Abstract

An important issue in synthetic aperture ladar is phase noise mitigation, since phase noise corrupts image quality. There are many phase noise contributors including, residual platform motion, local oscillator phase/frequency instability, atmospheric turbulence, and additive receiver noise. The Phase Gradient Autofocus (PGA) algorithm is a common phase noise correction algorithm utilized in synthetic aperture radar. The Cramer-Rao Lower Bound for the phase-difference estimate variance of PGA can be found in the radar literature. This lower bound describes the precision of the phasedifference estimate between any two pulses as a function of the carrier-to-noise ratio (CNR). However, this lower bound does not account for speckle saturation limitations, present in both synthetic aperture ladar and radar. This paper extends the PGA performance theory to include a high CNR saturation term which accounts for speckle decorrelation. This term is shown to be proportional to the ratio of the image spot size to the laser pulse repetition frequency (PRF). This paper also describes impact of PGA estimate variance on image cross-range resolution. We show, given a fixed PRF and fixed PGA phase-difference estimate variance, that resolution initially improves with increasing dwell times but eventually saturates to a level proportional to the product of the PGA estimate variance and the laser PRF.